From 6cd38003a199f24be07c6a363599da720c7143c3 Mon Sep 17 00:00:00 2001
From: hujiaxi <hujiaxi@msh.team>
Date: Tue, 27 Jan 2026 07:51:14 +0000
Subject: [PATCH 1/5] upload gated_oja_operator

---
 fla/ops/gated_oja_rule/OJA.pdf            | Bin 0 -> 249404 bytes
 fla/ops/gated_oja_rule/__init__.py        |   7 +
 fla/ops/gated_oja_rule/chunk.py           | 318 +++++++++
 fla/ops/gated_oja_rule/chunk_h.py         | 821 ++++++++++++++++++++++
 fla/ops/gated_oja_rule/chunk_kkt.py       | 517 ++++++++++++++
 fla/ops/gated_oja_rule/chunk_o.py         | 691 ++++++++++++++++++
 fla/ops/gated_oja_rule/fused_recurrent.py | 265 +++++++
 fla/ops/gated_oja_rule/wy_fast.py         | 289 ++++++++
 8 files changed, 2908 insertions(+)
 create mode 100644 fla/ops/gated_oja_rule/OJA.pdf
 create mode 100644 fla/ops/gated_oja_rule/__init__.py
 create mode 100644 fla/ops/gated_oja_rule/chunk.py
 create mode 100644 fla/ops/gated_oja_rule/chunk_h.py
 create mode 100644 fla/ops/gated_oja_rule/chunk_kkt.py
 create mode 100644 fla/ops/gated_oja_rule/chunk_o.py
 create mode 100644 fla/ops/gated_oja_rule/fused_recurrent.py
 create mode 100644 fla/ops/gated_oja_rule/wy_fast.py

diff --git a/fla/ops/gated_oja_rule/OJA.pdf b/fla/ops/gated_oja_rule/OJA.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..0d7536717705bca2f74ff81d5543d6cfde7cbce2
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diff --git a/fla/ops/gated_oja_rule/__init__.py b/fla/ops/gated_oja_rule/__init__.py
new file mode 100644
index 0000000000..4bb7a799df
--- /dev/null
+++ b/fla/ops/gated_oja_rule/__init__.py
@@ -0,0 +1,7 @@
+from .chunk import chunk_gated_oja_rule
+from .fused_recurrent import fused_recurrent_gated_oja_rule
+
+__all__ = [
+    "chunk_gated_oja_rule",
+    "fused_recurrent_gated_oja_rule"
+]
diff --git a/fla/ops/gated_oja_rule/chunk.py b/fla/ops/gated_oja_rule/chunk.py
new file mode 100644
index 0000000000..32f3673f71
--- /dev/null
+++ b/fla/ops/gated_oja_rule/chunk.py
@@ -0,0 +1,318 @@
+# # -*- coding: utf-8 -*-
+# # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+import warnings
+from typing import Optional
+
+import torch
+
+from fla.modules.l2norm import l2norm_bwd, l2norm_fwd
+from fla.ops.utils import chunk_local_cumsum, solve_tril
+from fla.utils import autocast_custom_bwd, autocast_custom_fwd, input_guard
+
+from fla.ops.gated_oja_rule.wy_fast import prepare_wy_repr_bwd, recompute_w_u_fwd
+from fla.ops.gated_oja_rule.chunk_kkt import chunk_scaled_dot_kkt_fwd, chunk_scaled_dot_kkt_bwd_gk
+from fla.ops.gated_oja_rule.chunk_h import (
+    chunk_oja_fwd_h, 
+    chunk_oja_bwd_dhu, 
+    chunk_oja_bwd_dvwg_h)
+from fla.ops.gated_oja_rule.chunk_o import (
+    chunk_oja_fwd_o, 
+    chunk_oja_bwd_dA, 
+    chunk_oja_bwd_dqk, 
+    chunk_oja_bwd_dv_o, 
+    )
+
+def chunk_oja_fwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gv: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    output_final_state: bool,
+    g_cumsum: bool = True,
+    cu_seqlens: Optional[torch.LongTensor] = None
+):  
+    if g_cumsum:
+        gv = chunk_local_cumsum(gv, chunk_size=64, cu_seqlens=cu_seqlens)
+    A = chunk_scaled_dot_kkt_fwd(
+        k=v,
+        gk=gv,
+        beta=beta,
+        cu_seqlens=cu_seqlens,
+        output_dtype=torch.float32
+    )
+    A = solve_tril(
+        A=A,
+        cu_seqlens=cu_seqlens,
+        output_dtype=k.dtype
+    )
+    w, u, vg = recompute_w_u_fwd(
+        k=k,
+        v=v,
+        beta=beta,
+        A=A,
+        gv=gv,
+        cu_seqlens=cu_seqlens,
+    )
+    h, k_new, final_state = chunk_oja_fwd_h(
+        v=vg,
+        w=w,
+        u=u,
+        gv=gv,
+        initial_state=initial_state,
+        output_final_state=output_final_state,
+        cu_seqlens=cu_seqlens,
+    )
+    _, o = chunk_oja_fwd_o(
+        q=q,
+        k=k_new,
+        v=v,
+        h=h,
+        gv=gv,
+        scale=scale,
+        cu_seqlens=cu_seqlens,
+    )
+    return gv, o, A, final_state
+
+
+def chunk_oja_bwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gv: torch.Tensor,
+    beta: torch.Tensor,
+    A: torch.Tensor,
+    o: torch.Tensor,
+    scale: float,
+    initial_state: torch.Tensor,
+    do: torch.Tensor,
+    dht: torch.Tensor,
+    dgk: Optional[torch.Tensor] = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+):  
+    w, u, vg = recompute_w_u_fwd(
+        k=k,
+        v=v,
+        beta=beta,
+        A=A,
+        gv=gv,
+        cu_seqlens=cu_seqlens,
+    )
+
+    h, k_new, _ = chunk_oja_fwd_h(
+        v=vg,
+        w=w,
+        u=u,
+        gv=gv,
+        initial_state=initial_state,
+        output_final_state=False,
+        cu_seqlens=cu_seqlens,
+    )
+    
+    dAqk = chunk_oja_bwd_dA(
+        v=v,
+        gv=gv,
+        do=do,
+        scale=scale,
+        cu_seqlens=cu_seqlens,
+    )
+
+    Aqk, dq, dk_new = chunk_oja_bwd_dqk(
+        q=q,
+        k=k_new,
+        h=h,
+        gv=gv,
+        dA=dAqk,
+        do=do,
+        scale=scale,
+        cu_seqlens=cu_seqlens,
+    )
+
+    dh, dh0, dk_new = chunk_oja_bwd_dhu(
+        q=q,
+        vg=vg,
+        w=w,
+        gv=gv,
+        h0=initial_state,
+        dht=dht,
+        do=do,
+        dk=dk_new,
+        scale=scale,
+        cu_seqlens=cu_seqlens,
+        states_in_fp32=False,
+    )
+
+    # grid = (NV, NT, B * H)
+    dv, dw, dgv_last = chunk_oja_bwd_dvwg_h(
+        k=k_new,
+        v=v,
+        gv=gv,
+        h=h,
+        dh=dh,
+        dk=dk_new,
+        dgk=dgk,
+        cu_seqlens=cu_seqlens,
+    )
+
+    dv, dgv1 = chunk_oja_bwd_dv_o(
+        v=v,
+        gv=gv,
+        o=o,
+        A=Aqk,
+        dv=dv,
+        do=do,
+        cu_seqlens=cu_seqlens,
+    )
+
+    dk, dv1, db, dgv2, dAvv = prepare_wy_repr_bwd(
+        k=k,
+        v=v,
+        beta=beta,
+        gv=gv,
+        A=A,
+        dw=dw,
+        du=dk_new,
+        cu_seqlens=cu_seqlens,
+    )
+
+    dv2, dgv3, db2 = chunk_scaled_dot_kkt_bwd_gk(
+        k=v,
+        g=gv,
+        beta=beta,
+        dA=dAvv,
+        cu_seqlens=cu_seqlens,
+    )
+    
+    dv = dv.add_(dv1).add_(dv2)
+    db = db.add_(db2)
+    dgv = dgv_last.add_(chunk_local_cumsum(dgv1.add_(dgv2).add_(dgv3), chunk_size=64, reverse=True, cu_seqlens=cu_seqlens))
+    return dq, dk, dv, db, dgv, dh0
+
+
+class ChunkOJAFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    @autocast_custom_fwd
+    def forward(
+        ctx,
+        q: torch.Tensor,
+        k: torch.Tensor,
+        v: torch.Tensor,
+        gv: torch.Tensor,
+        beta: torch.Tensor,
+        scale: float,
+        initial_state: torch.Tensor,
+        output_final_state: bool,
+        cu_seqlens: Optional[torch.LongTensor] = None,
+        use_q_l2norm: bool = False,
+        use_k_l2norm: bool = False,
+    ):
+        q_rstd, k_rstd = None, None
+        if use_q_l2norm:
+            q, q_rstd = l2norm_fwd(q)
+        if use_k_l2norm:
+            k, k_rstd = l2norm_fwd(k)
+
+        gv, o, A, final_state = chunk_oja_fwd(
+            q=q,
+            k=k,
+            v=v,
+            gv=gv,
+            beta=beta,
+            scale=scale,
+            initial_state=initial_state,
+            output_final_state=output_final_state,
+            cu_seqlens=cu_seqlens,
+        )
+        ctx.save_for_backward(q, q_rstd, k, k_rstd, v, gv, beta, A, o, initial_state, cu_seqlens)
+        ctx.scale = scale
+        ctx.use_q_l2norm = use_q_l2norm
+        ctx.use_k_l2norm = use_k_l2norm
+        return o.to(q.dtype), final_state
+
+    @staticmethod
+    @input_guard
+    @autocast_custom_bwd
+    def backward(
+        ctx,
+        do: torch.Tensor,
+        dht: torch.Tensor
+    ):
+        q, q_rstd, k, k_rstd, v, gv, beta, A, o, initial_state, cu_seqlens = ctx.saved_tensors
+        dq, dk, dv, db, dg, dh0 = chunk_oja_bwd(
+            q=q,
+            k=k,
+            v=v,
+            gv=gv,
+            beta=beta,
+            A=A,
+            o=o,
+            scale=ctx.scale,
+            initial_state=initial_state,
+            do=do,
+            dht=dht,
+            cu_seqlens=cu_seqlens,
+        )
+
+        if ctx.use_q_l2norm:
+            dq = l2norm_bwd(q, q_rstd, dq)
+        if ctx.use_k_l2norm:
+            dk = l2norm_bwd(k, k_rstd, dk)
+        return dq.to(q), dk.to(k), dv.to(v), dg.to(gv), db.to(beta), None, dh0, None, None, None, None
+
+
+@torch.compiler.disable
+def chunk_gated_oja_rule(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gv: torch.Tensor,
+    beta: torch.Tensor,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+    use_q_l2norm: bool = False,
+    use_k_l2norm: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    **kwargs,
+):
+    if 'head_first' in kwargs:
+        warnings.warn(
+            "head_first is deprecated and will be removed in a future version. "
+            "Please use head_first=False for now instead."
+        )
+    if 'use_qk_l2norm_in_kernel' in kwargs and (not use_q_l2norm and not use_k_l2norm):
+        use_q_l2norm = True
+        use_k_l2norm = True
+
+    if cu_seqlens is not None:
+        if q.shape[0] != 1:
+            raise ValueError(
+                f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
+                f"Please flatten variable-length inputs before processing."
+            )
+        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
+            raise ValueError(
+                f"The number of initial states is expected to be equal to the number of input sequences, "
+                f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}."
+            )
+    if scale is None:
+        scale = k.shape[-1] ** -0.5
+    o, final_state = ChunkOJAFunction.apply(
+        q,
+        k,
+        v,
+        gv,
+        beta,
+        scale,
+        initial_state,
+        output_final_state,
+        cu_seqlens,
+        use_q_l2norm,
+        use_k_l2norm
+    )
+    return o, final_state
diff --git a/fla/ops/gated_oja_rule/chunk_h.py b/fla/ops/gated_oja_rule/chunk_h.py
new file mode 100644
index 0000000000..096a492a9b
--- /dev/null
+++ b/fla/ops/gated_oja_rule/chunk_h.py
@@ -0,0 +1,821 @@
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils import prepare_chunk_indices, prepare_chunk_offsets
+from fla.ops.utils.op import exp
+from fla.utils import is_nvidia_hopper, use_cuda_graph
+from fla.utils import check_shared_mem
+
+BKV_LIST = [64, 128] if check_shared_mem() else [32, 64]
+NUM_WARPS = [2, 4] if is_nvidia_hopper else [2, 4, 8, 16]
+
+
+@triton.heuristics({
+    'USE_GV': lambda args: args['gv'] is not None,
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'SAVE_NEW_KEY': lambda args: args['k_new'] is not None,
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4]
+        for num_stages in [2, 3, 4]
+        for BK in [32, 64]
+    ],
+    key=['H', 'K', 'V', 'BT'],
+    use_cuda_graph=use_cuda_graph,
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_fwd_kernel_h_blockdim64(
+    v,
+    u,
+    w,
+    k_new,
+    gv,
+    h,
+    h0,
+    ht,
+    cu_seqlens,
+    chunk_offsets,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    SAVE_NEW_KEY: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):  
+    # (triton.cdiv(K, meta['BK']), N*H)
+    i_k, i_nh = tl.program_id(0), tl.program_id(1)
+    i_n, i_h = i_nh // H, i_nh % H
+    if IS_VARLEN:
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+        boh = tl.load(chunk_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NT = tl.cdiv(T, BT)
+        boh = i_n * NT
+
+    # [BK, BV]
+    b_h1 = tl.zeros([BK, 64], dtype=tl.float32)
+    if V > 64:
+        b_h2 = tl.zeros([BK, 64], dtype=tl.float32)
+    if V > 128:
+        b_h3 = tl.zeros([BK, 64], dtype=tl.float32)
+    if V > 192:
+        b_h4 = tl.zeros([BK, 64], dtype=tl.float32)
+
+    # calculate offset
+    h += ((boh * H + i_h) * K*V).to(tl.int64)
+    v += ((bos * H + i_h) * V).to(tl.int64)
+    u += ((bos * H + i_h) * K).to(tl.int64)
+    w += ((bos * H + i_h) * V).to(tl.int64)
+    if SAVE_NEW_KEY:
+        k_new += ((bos * H + i_h) * K).to(tl.int64)
+    stride_v = H*V
+    stride_h = H*K*V
+    stride_k = H*K
+    if USE_INITIAL_STATE:
+        h0 = h0 + i_nh * K*V
+    if STORE_FINAL_STATE:
+        ht = ht + i_nh * K*V
+    BV=64
+
+    # load initial state
+    if USE_INITIAL_STATE:
+        p_h0_1 = tl.make_block_ptr(h0, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0))
+        b_h1 += tl.load(p_h0_1, boundary_check=(0, 1)).to(tl.float32)
+        if V > 64:
+            p_h0_2 = tl.make_block_ptr(h0, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
+            b_h2 += tl.load(p_h0_2, boundary_check=(0, 1)).to(tl.float32)
+        if V > 128:
+            p_h0_3 = tl.make_block_ptr(h0, (K, V), (V, 1), (i_k * BK, 128), (BK, 64), (1, 0))
+            b_h3 += tl.load(p_h0_3, boundary_check=(0, 1)).to(tl.float32)
+        if V > 192:
+            p_h0_4 = tl.make_block_ptr(h0, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
+            b_h4 += tl.load(p_h0_4, boundary_check=(0, 1)).to(tl.float32)
+
+    # main recurrence
+    for i_t in range(NT):
+        p_h1 = tl.make_block_ptr(h + i_t * stride_h, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0))
+        tl.store(p_h1, b_h1.to(p_h1.dtype.element_ty), boundary_check=(0, 1))
+        if V > 64:
+            p_h2 = tl.make_block_ptr(h + i_t * stride_h, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
+            tl.store(p_h2, b_h2.to(p_h2.dtype.element_ty), boundary_check=(0, 1))
+        if V > 128:
+            p_h3 = tl.make_block_ptr(h + i_t * stride_h, (K, V), (V, 1), (i_k * BK, 128), (BK, 64), (1, 0))
+            tl.store(p_h3, b_h3.to(p_h3.dtype.element_ty), boundary_check=(0, 1))
+        if V > 192:
+            p_h4 = tl.make_block_ptr(h + i_t * stride_h, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
+            tl.store(p_h4, b_h4.to(p_h4.dtype.element_ty), boundary_check=(0, 1))
+
+        p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))
+        b_w = tl.load(p_w, boundary_check=(0, 1))
+        b_k = tl.dot(b_w, tl.trans(b_h1).to(b_w.dtype)) # BT BK
+        if V > 64:
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            b_k += tl.dot(b_w, tl.trans(b_h2).to(b_w.dtype))
+        if V > 128:
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            b_k += tl.dot(b_w, tl.trans(b_h3).to(b_w.dtype))
+        if V > 192:
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            b_k += tl.dot(b_w, tl.trans(b_h4).to(b_w.dtype))
+
+        p_u = tl.make_block_ptr(u, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        b_k = tl.load(p_u, boundary_check=(0, 1)) - b_k
+
+        if SAVE_NEW_KEY:
+            p_k = tl.make_block_ptr(k_new, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+            tl.store(p_k, b_k.to(p_k.dtype.element_ty), boundary_check=(0, 1))
+
+        last_idx = min((i_t + 1) * BT, T) - 1
+
+        if USE_GV:
+            o_v1 = tl.arange(0, 64)
+            b_gk_last1 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v1, mask=(o_v1 < V), other=0.)
+            b_h1 *= exp(b_gk_last1)[None, :]
+            if K > 64:
+                o_v2 = 64 + o_v1
+                b_gk_last2 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v2, mask=(o_v2 < V), other=0.)
+                b_h2 *= exp(b_gk_last2)[None, :]
+            if K > 128:
+                o_v3 = 128 + o_v1
+                b_gk_last3 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v3, mask=(o_v3 < V), other=0.)
+                b_h3 *= exp(b_gk_last3)[None, :]
+            if K > 192:
+                o_v4 = 192 + o_v1
+                b_gk_last4 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v4, mask=(o_v4 < K), other=0.)
+                b_h4 *= exp(b_gk_last4)[None, :]
+
+        b_k = b_k.to(v.dtype.element_ty) # BT BK
+
+        p_v = tl.make_block_ptr(v, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))
+        b_v = tl.load(p_v, boundary_check=(0, 1)) # BT BV
+        b_h1 += tl.dot(tl.trans(b_k), b_v)
+        if V > 64:
+            p_v = tl.make_block_ptr(v, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            b_h2 += tl.dot(tl.trans(b_k), b_v)
+        if V > 128:
+            p_v = tl.make_block_ptr(v, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            b_h3 += tl.dot(tl.trans(b_k), b_v)
+        if V > 192:
+            p_v = tl.make_block_ptr(v, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            b_h4 += tl.dot(tl.trans(b_k), b_v)
+    # epilogue
+    if STORE_FINAL_STATE:
+        p_ht = tl.make_block_ptr(ht, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0))
+        tl.store(p_ht, b_h1.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+        if V > 64:
+            p_ht = tl.make_block_ptr(ht, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
+            tl.store(p_ht, b_h2.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+        if V > 128:
+            p_ht = tl.make_block_ptr(ht, (K, V), (V, 1), (i_k * BK, 128), (BK, 64), (1, 0))
+            tl.store(p_ht, b_h3.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+        if V > 192:
+            p_ht = tl.make_block_ptr(ht, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
+            tl.store(p_ht, b_h4.to(p_ht.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_oja_fwd_h(
+    v: torch.Tensor,
+    w: torch.Tensor,
+    u: torch.Tensor,
+    gv: Optional[torch.Tensor] = None,
+    initial_state: Optional[torch.Tensor] = None,
+    output_final_state: bool = False,
+    chunk_size: int = 64,  # SY: remove this argument and force chunk size 64?
+    save_new_key: bool = True,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    B, T, H, V, K = *v.shape, u.shape[-1]
+    BT = chunk_size
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, chunk_size) if cu_seqlens is not None else None
+    # N: the actual number of sequences in the batch with either equal or variable lengths
+    if cu_seqlens is None:
+        N, NT, chunk_offsets = B, triton.cdiv(T, BT), None
+    else:
+        N, NT, chunk_offsets = len(cu_seqlens) - 1, len(chunk_indices), prepare_chunk_offsets(cu_seqlens, BT)
+    assert V <= 256, "current kernel does not support head dimension larger than 256."
+
+    h = v.new_empty(B, NT, H, K, V)
+    final_state = v.new_empty(N, H, K, V, dtype=torch.float32) if output_final_state else None
+
+    k_new = torch.empty_like(u) if save_new_key else None
+    def grid(meta): return (triton.cdiv(K, meta['BK']), N*H)
+    chunk_oja_fwd_kernel_h_blockdim64[grid](
+        v=v,
+        u=u,
+        w=w,
+        k_new=k_new,
+        gv=gv,
+        h=h,
+        h0=initial_state,
+        ht=final_state,
+        cu_seqlens=cu_seqlens,
+        chunk_offsets=chunk_offsets,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT
+    )
+    return h, k_new, final_state
+
+
+
+
+
+@triton.heuristics({
+    'USE_GV': lambda args: args['gv'] is not None,
+    'USE_INITIAL_STATE': lambda args: args['dh0'] is not None,
+    'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not None,
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4]
+        for num_stages in [4, 3, 2]
+        for BK in [64, 32]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'USE_GV'],
+    use_cuda_graph=use_cuda_graph,
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_bwd_kernel_dhu_blockdim64(
+    q,
+    vg,
+    w,
+    gv,
+    dht,
+    dh0,
+    do,
+    dh,
+    dk,
+    dk2,
+    cu_seqlens,
+    chunk_offsets,
+    scale,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    USE_GV: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    USE_FINAL_STATE_GRADIENT: tl.constexpr,
+    IS_VARLEN: tl.constexpr
+):
+    i_k, i_nh = tl.program_id(0), tl.program_id(1)
+    i_n, i_h = i_nh // H, i_nh % H
+    if IS_VARLEN:
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+        boh = tl.load(chunk_offsets + i_n).to(tl.int32)
+    else:
+        bos, eos = i_n * T, i_n * T + T
+        NT = tl.cdiv(T, BT)
+        boh = i_n * NT
+
+    # [BK, BV]
+    b_dh1 = tl.zeros([BK, 64], dtype=tl.float32)
+    if V > 64:
+        b_dh2 = tl.zeros([BK, 64], dtype=tl.float32)
+    if V > 128:
+        b_dh3 = tl.zeros([BK, 64], dtype=tl.float32)
+    if V > 192:
+        b_dh4 = tl.zeros([BK, 64], dtype=tl.float32)
+
+    # calculate offset
+    q += ((bos * H + i_h) * K).to(tl.int64)
+    vg += ((bos * H + i_h) * V).to(tl.int64)
+    w += ((bos * H + i_h) * V).to(tl.int64)
+    do += ((bos * H + i_h) * V).to(tl.int64)
+    dk += ((bos * H + i_h) * K).to(tl.int64)
+    dk2 += ((bos * H + i_h) * K).to(tl.int64)
+    dh += ((boh * H + i_h) * K*V).to(tl.int64)
+    if USE_GV:
+        gv += ((bos * H + i_h) * V).to(tl.int64)
+
+    stride_v = H*V
+    stride_h = H*K*V
+    stride_k = H*K
+    if USE_INITIAL_STATE:
+        dh0 += i_nh * K*V
+    if USE_FINAL_STATE_GRADIENT:
+        dht += i_nh * K*V
+
+    if USE_FINAL_STATE_GRADIENT:
+        p_dht1 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0)) # [BK, BV]
+        b_dh1 += tl.load(p_dht1, boundary_check=(0, 1))
+        if V > 64:
+            p_dht2 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
+            b_dh2 += tl.load(p_dht2, boundary_check=(0, 1))
+        if V > 128:
+            p_dht3 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 128), (BK, 64), (1, 0))
+            b_dh3 += tl.load(p_dht3, boundary_check=(0, 1))
+        if V > 192:
+            p_dht4 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
+            b_dh4 += tl.load(p_dht4, boundary_check=(0, 1))
+
+    for i_t in range(NT - 1, -1, -1):
+        p_dh1 = tl.make_block_ptr(dh + i_t*stride_h, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0))
+        tl.store(p_dh1, b_dh1.to(p_dh1.dtype.element_ty), boundary_check=(0, 1))
+        if V > 64:
+            p_dh2 = tl.make_block_ptr(dh + i_t*stride_h, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
+            tl.store(p_dh2, b_dh2.to(p_dh2.dtype.element_ty), boundary_check=(0, 1))
+        if V > 128:
+            p_dh3 = tl.make_block_ptr(dh + i_t*stride_h, (K, V), (V, 1), (i_k * BK, 128), (BK, 64), (1, 0))
+            tl.store(p_dh3, b_dh3.to(p_dh3.dtype.element_ty), boundary_check=(0, 1))
+        if V > 192:
+            p_dh4 = tl.make_block_ptr(dh + i_t*stride_h, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
+            tl.store(p_dh4, b_dh4.to(p_dh4.dtype.element_ty), boundary_check=(0, 1))
+
+        last_idx = min((i_t + 1) * BT, T) - 1
+
+        # Update dk_new, 按K切分
+        p_dk = tl.make_block_ptr(dk, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) # [BT, BK]
+        p_dk2 = tl.make_block_ptr(dk2, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) # [BT, BK]
+
+        if V > 0:
+            p_v = tl.make_block_ptr(vg, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1)) # [BT, BV]
+            b_dk = tl.dot(b_v, tl.trans(b_dh1).to(b_v.dtype)) # [BT, BV] @ [BV, BK] -> [BT, BK]
+
+        if V > 64:
+            p_v = tl.make_block_ptr(vg, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1))   
+            b_dk += tl.dot(b_v, tl.trans(b_dh2).to(b_v.dtype))
+
+        if V > 128:
+            p_v = tl.make_block_ptr(vg, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            b_dk += tl.dot(b_v, tl.trans(b_dh3).to(b_v.dtype))
+
+        if V > 192:
+            p_v = tl.make_block_ptr(vg, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))
+            b_v = tl.load(p_v, boundary_check=(0, 1))
+            b_dk += tl.dot(b_v, tl.trans(b_dh4).to(b_v.dtype))
+
+        b_dk += tl.load(p_dk, boundary_check=(0, 1))
+
+        tl.store(p_dk2, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+        
+        
+        # Update dh, 按照K切分，收集所有V维度，q一次就好，wdo要收集所有
+        
+        p_q = tl.make_block_ptr(q, (K, T), (1, stride_k), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) # [BK, BT]
+        b_q = tl.load(p_q, boundary_check=(0, 1))   
+        
+        if V > 0:
+            p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0)) # [BT, BV]
+            b_do = tl.load(p_do, boundary_check=(0, 1))
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0)) # [BT, BV]
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0)) # [BT, BV]
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            if USE_GV:
+                o_v1 = tl.arange(0, 64)
+                b_gv_last1 = tl.load(gv + last_idx * H*V + o_v1, mask=(o_v1 < V), other=0.)
+                b_dh1 *= exp(b_gv_last1[None, :])
+                b_do *= exp(b_gv)
+            b_dh1 += tl.dot(b_q.to(b_q.dtype), b_do.to(b_q.dtype)) * scale - tl.dot(tl.trans(b_dk).to(b_w.dtype), b_w) # [BK, BT] @ [BT, BV] - [BK, BT] @ [BT, BV]
+
+        if V > 64:
+            p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
+            b_do = tl.load(p_do, boundary_check=(0, 1))
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0)) # [BT, BV]
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0)) # [BT, BV]
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            if USE_GV:
+                o_v2 = 64 + o_v1
+                b_gv_last2 = tl.load(gv + last_idx * H*V + o_v2, mask=(o_v2 < V), other=0.)
+                b_dh2 *= exp(b_gv_last2[None, :])
+                b_do *= exp(b_gv)
+            b_dh2 += tl.dot(b_q.to(b_q.dtype), b_do.to(b_q.dtype)) * scale - tl.dot(tl.trans(b_dk).to(b_w.dtype), b_w)
+
+        if V > 128:
+            p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))
+            b_do = tl.load(p_do, boundary_check=(0, 1))
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0)) # [BT, BV]
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0)) # [BT, BV]
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            if USE_GV:
+                o_v3 = 128 + o_v1
+                b_gv_last3 = tl.load(gv + last_idx * H*V + o_v3, mask=(o_v3 < V), other=0.)
+                b_dh3 *= exp(b_gv_last3[None, :])
+                b_do *= exp(b_gv)
+            b_dh3 += tl.dot(b_q.to(b_q.dtype), b_do.to(b_q.dtype)) * scale - tl.dot(tl.trans(b_dk).to(b_w.dtype), b_w)
+
+        if V > 192:
+            p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))
+            b_do = tl.load(p_do, boundary_check=(0, 1))
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0)) # [BT, BV]
+            b_w = tl.load(p_w, boundary_check=(0, 1))
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0)) # [BT, BV]
+            b_gv = tl.load(p_gv, boundary_check=(0, 1))
+            if USE_GV:
+                o_v4 = 192 + o_v1
+                b_gv_last4 = tl.load(gv + last_idx * H*V + o_v4, mask=(o_v4 < V), other=0.)
+                b_dh4 *= exp(b_gv_last4[None, :])
+                b_do *= exp(b_gv)
+            b_dh4 += tl.dot(b_q.to(b_q.dtype), b_do.to(b_q.dtype)) * scale - tl.dot(tl.trans(b_dk).to(b_w.dtype), b_w)
+
+    if USE_INITIAL_STATE:
+        p_dh0 = tl.make_block_ptr(dh0, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0))
+        tl.store(p_dh0, b_dh1.to(p_dh0.dtype.element_ty), boundary_check=(0, 1))
+        if V > 64:
+            p_dh1 = tl.make_block_ptr(dh0, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
+            tl.store(p_dh1, b_dh2.to(p_dh1.dtype.element_ty), boundary_check=(0, 1))
+        if V > 128:
+            p_dh2 = tl.make_block_ptr(dh0, (K, V), (V, 1), (i_k * BK, 128), (BK, 64), (1, 0))
+            tl.store(p_dh2, b_dh3.to(p_dh2.dtype.element_ty), boundary_check=(0, 1))
+        if V > 192:
+            p_dh3 = tl.make_block_ptr(dh0, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
+            tl.store(p_dh3, b_dh4.to(p_dh3.dtype.element_ty), boundary_check=(0, 1))
+        
+
+def chunk_oja_bwd_dhu(
+    q: torch.Tensor,
+    vg: torch.Tensor,
+    w: torch.Tensor,
+    do: torch.Tensor,
+    dk: torch.Tensor,
+    gv: Optional[torch.Tensor] = None,
+    h0: Optional[torch.Tensor] = None,
+    dht: Optional[torch.Tensor] = None,
+    scale: Optional[float] = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64,  # SY: remove this argument and force chunk size 64?
+    states_in_fp32: bool = False
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+    B, T, H, K, V = *q.shape, do.shape[-1]
+    # N: the actual number of sequences in the batch with either equal or variable lengths
+    BT = 64
+    assert K <= 256, "current kernel does not support head dimension being larger than 256."
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, chunk_size) if cu_seqlens is not None else None
+    if cu_seqlens is None:
+        N, NT, chunk_offsets = B, triton.cdiv(T, BT), None
+    else:
+        N, NT, chunk_offsets = len(cu_seqlens) - 1, len(chunk_indices), prepare_chunk_offsets(cu_seqlens, BT)
+
+    dh = q.new_empty(B, NT, H, K, V, dtype=q.dtype if not states_in_fp32 else torch.float)
+    dh0 = torch.empty_like(h0, dtype=torch.float32) if h0 is not None else None
+    dk2 = torch.empty_like(dk)
+
+    def grid(meta): return (triton.cdiv(K, meta['BK']), N*H)
+    chunk_oja_bwd_kernel_dhu_blockdim64[grid](
+        q=q,
+        vg=vg,
+        w=w,
+        gv=gv,
+        dht=dht,
+        dh0=dh0,
+        do=do,
+        dh=dh,
+        dk=dk,
+        dk2=dk2,
+        cu_seqlens=cu_seqlens,
+        chunk_offsets=chunk_offsets,
+        scale=scale,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+    )
+    return dh, dh0, dk2
+
+
+
+
+
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT']
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_gsa_bwd_k_kernel_dqkvg(
+    q,
+    k,
+    v,
+    h,
+    g,
+    A,
+    do,
+    dh,
+    dq,
+    dk,
+    dv,
+    dg,
+    dgv,
+    dA,
+    cu_seqlens,
+    chunk_indices,
+    scale,
+    T,
+    B: tl.constexpr,
+    HQ: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NG: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_hq = i_bh // HQ, i_bh % HQ
+    i_h = i_hq // NG
+    if IS_VARLEN:
+        i_tg = i_t
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        all = T
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+        all = B * T
+
+    o_i = tl.arange(0, BT)
+    o_t = min(i_t * BT + BT, T)
+    m_s = o_i[:, None] >= o_i[None, :]
+
+    p_q = tl.make_block_ptr(q + (bos*HQ+i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_k = tl.make_block_ptr(k + (bos*H+i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_A = tl.make_block_ptr(A + ((i_k*all+bos)*HQ+i_hq)*BT, (T, BT), (HQ*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+
+    # [BT, BK]
+    b_q = tl.load(p_q, boundary_check=(0, 1))
+    b_k = tl.load(p_k, boundary_check=(0, 1))
+    # [BT, BT]
+    b_A = tl.dot((b_q * scale).to(b_q.dtype), tl.trans(b_k))
+    b_A = tl.where(m_s, b_A, 0.)
+    tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
+
+    b_dq = tl.zeros([BT, BK], dtype=tl.float32)
+    b_dk = tl.zeros([BT, BK], dtype=tl.float32)
+    for i_v in range(tl.cdiv(V, BV)):
+        o_v = i_v * BV + tl.arange(0, BV)
+        p_v = tl.make_block_ptr(v + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_g = tl.make_block_ptr(g + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_gn = g + (bos + o_t - 1) * H*V + i_h * V + o_v
+        p_do = tl.make_block_ptr(do + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_dv = tl.make_block_ptr(dv + ((i_k*all+bos)*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_dg = tl.make_block_ptr(dg + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_dgv = tl.make_block_ptr(dgv+((i_k*all+bos)*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_h = tl.make_block_ptr(h + (i_tg * H + i_h) * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
+        p_dh = tl.make_block_ptr(dh + (i_tg * HQ + i_hq) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        m_v = o_v < V
+
+        # [BV,]
+        b_gn = tl.load(p_gn, mask=m_v, other=0)
+        # [BT, BV]
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        b_g = tl.load(p_g, boundary_check=(0, 1))
+        b_gv = exp(b_gn[None, :] - b_g)
+        # [BV, BK]
+        b_h = tl.load(p_h, boundary_check=(0, 1))
+        # [BT, BV]
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+        b_do = (b_do * exp(b_g) * scale).to(b_do.dtype)
+        # [BK, BV]
+        b_dh = tl.load(p_dh, boundary_check=(0, 1))
+        # [BV]
+        b_dg = tl.sum(tl.trans(b_h) * b_dh, 0) * exp(b_gn)
+
+        b_dh = b_dh.to(b_k.dtype)
+        # [BT, BK]
+        b_dq += tl.dot(b_do, b_h.to(b_k.dtype))
+        b_dk += tl.dot((b_v * b_gv).to(b_v.dtype), tl.trans(b_dh))
+        # [BT, BV]
+        b_dv = tl.dot(b_k, b_dh) * b_gv
+        # [BV]
+        b_dg += tl.sum(b_dv * b_v, 0)
+
+        if i_k == 0:
+            b_dgv = tl.load(p_dg, boundary_check=(0, 1)) + b_dg[None, :]
+        else:
+            b_dgv = tl.zeros([BT, BV], dtype=tl.float32) + b_dg[None, :]
+
+        tl.store(p_dgv, b_dgv.to(p_dgv.dtype.element_ty), boundary_check=(0, 1))
+        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+    p_dA = tl.make_block_ptr(dA + (bos*HQ + i_hq) * BT, (T, BT), (HQ*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    p_dq = tl.make_block_ptr(dq + (bos*HQ + i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_dk = tl.make_block_ptr(dk + (bos*HQ + i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    # [BT, BT]
+    b_dA = tl.load(p_dA, boundary_check=(0, 1))
+    # [BT, BK]
+    b_dq += tl.dot(b_dA, b_k)
+    b_dk += tl.dot(tl.trans(b_dA).to(b_k.dtype), b_q)
+
+    tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+    
+    
+
+    
+    
+    
+    
+@triton.heuristics({
+    'USE_GV': lambda args: args['gv'] is not None,
+    'HAVE_GK': lambda args: args['dgk'] is not None,
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in NUM_WARPS
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'USE_GV'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_bwd_kernel_dvwg_h(
+    k,
+    v,
+    gv,
+    h,
+    dh,
+    dk,
+    dw,
+    dv,
+    dgv_last,
+    dgk,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_GV: tl.constexpr,
+    HAVE_GK: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+
+    if IS_VARLEN:
+        i_tg = i_t
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+
+    # offset calculation
+    k += (bos * H + i_h) * K
+    v += (bos * H + i_h) * V
+    gv += (bos * H + i_h) * V
+    h += (i_tg * H + i_h).to(tl.int64) * K*V
+    dh += (i_tg * H + i_h).to(tl.int64) * K*V
+    dk += (bos * H + i_h) * K
+    dw += (bos * H + i_h) * V
+    dv += (bos * H + i_h) * V
+    dgv_last += (bos * H + i_h) * V
+
+    b_dvg = tl.zeros([BT, BV], dtype=tl.float32)
+    b_dw = tl.zeros([BT, BV], dtype=tl.float32)
+    b_dgv_last = tl.zeros([BV,], dtype=tl.float32)
+
+    if USE_GV:
+        o_v = i_v * BV + tl.arange(0, BV)
+        m_v = o_v < V
+        p_gn = gv + (min(T, i_t * BT + BT) - 1) * H*V + o_v
+        p_gv = tl.make_block_ptr(gv, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_gn = tl.load(p_gn, mask=m_v, other=0)
+        b_gv = tl.load(p_gv, boundary_check=(0, 1))
+        
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_dk = tl.make_block_ptr(dk, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_h = tl.make_block_ptr(h, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        p_dh = tl.make_block_ptr(dh, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+        b_k = tl.load(p_k, boundary_check=(0, 1)) # BT BK
+        b_dk = tl.load(p_dk, boundary_check=(0, 1)) # BT BK
+        b_h = tl.load(p_h, boundary_check=(0, 1)) # BK BV
+        b_dh = tl.load(p_dh, boundary_check=(0, 1)) # BK BV
+
+        b_dvg += tl.dot(b_k, b_dh.to(b_k.dtype)) # BT BK @ BK BV -> BT BV
+        b_dw += tl.dot(b_dk.to(b_k.dtype), b_h.to(b_k.dtype)) # BT BK @ BK BV -> BT BV
+        b_dgv_last += tl.sum((b_h * b_dh) * exp(b_gn), axis=0)
+
+    if USE_GV:
+        b_dv = b_dvg * exp(b_gn[None, :] - b_gv)
+    
+    p_v = tl.make_block_ptr(v, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_dv = tl.make_block_ptr(dv, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_dw = tl.make_block_ptr(dw, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_dgv_last = tl.make_block_ptr(dgv_last, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    b_v = tl.load(p_v, boundary_check=(0, 1))
+    
+    b_dgv_last += tl.sum(b_dv * b_v, axis=0)
+    
+    # 留给GSA2的接口
+    if HAVE_GK:
+        dgk += (bos * H + i_h) * V
+        p_dgk = tl.make_block_ptr(dgk, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_dgk = tl.load(p_dgk, boundary_check=(0, 1))
+        b_dgv_last = b_dgk + b_dgv_last[None, :]
+    else:   
+        b_dgv_last = tl.zeros([BT, BV], dtype=tl.float32) + b_dgv_last[None, :]
+    
+    tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_dw, -b_dw.to(p_dw.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_dgv_last, b_dgv_last.to(p_dgv_last.dtype.element_ty), boundary_check=(0, 1))
+    
+      
+
+
+def chunk_oja_bwd_dvwg_h(
+    k: torch.Tensor,
+    v: torch.Tensor,
+    h: torch.Tensor,
+    dh: torch.Tensor,
+    dk: torch.Tensor,
+    gv: Optional[torch.Tensor] = None,
+    dgk: Optional[torch.Tensor] = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64,
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+
+    B, T, H, K, V = *k.shape, v.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+
+    CONST_TILING = 64 if check_shared_mem() else 32
+    BK = min(max(triton.next_power_of_2(K), 16), CONST_TILING)
+    BV = min(max(triton.next_power_of_2(V), 16), CONST_TILING)
+    NV = triton.cdiv(V, BV)
+    dv = torch.empty_like(v, dtype=torch.float)
+    dw = torch.empty_like(v)
+    dgv_last = torch.empty_like(gv)
+
+    grid = (NV, NT, B * H)
+    chunk_oja_bwd_kernel_dvwg_h[grid](
+        k=k,
+        v=v,
+        gv=gv,
+        h=h,
+        dh=dh,
+        dw=dw,
+        dk=dk,
+        dv=dv,
+        dgv_last=dgv_last,
+        dgk=dgk,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+    )
+    return dv, dw, dgv_last
\ No newline at end of file
diff --git a/fla/ops/gated_oja_rule/chunk_kkt.py b/fla/ops/gated_oja_rule/chunk_kkt.py
new file mode 100644
index 0000000000..8ff0a21d96
--- /dev/null
+++ b/fla/ops/gated_oja_rule/chunk_kkt.py
@@ -0,0 +1,517 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils import prepare_chunk_indices
+from fla.ops.utils.op import exp
+
+
+@triton.heuristics({
+    'USE_G': lambda args: args['g'] is not None,
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64, 128]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'BT', 'IS_VARLEN'],
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_scaled_dot_kkt_fwd_kernel(
+    k,
+    g,
+    beta,
+    A,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+    USE_G: tl.constexpr,
+):
+    i_t, i_bh = tl.program_id(0), tl.program_id(1)
+    i_b, i_h = i_bh // H, i_bh % H
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+    o_t = i_t * BT + tl.arange(0, BT)
+    m_t = o_t < T
+
+    p_b = tl.make_block_ptr(beta + bos*H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
+    b_b = tl.load(p_b, boundary_check=(0,))
+
+    b_A = tl.zeros([BT, BT], dtype=tl.float32)
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        b_A += tl.dot(b_k, tl.trans(b_k))
+
+    if USE_G:
+        p_g = tl.make_block_ptr(g + bos*H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
+        b_g = tl.load(p_g, boundary_check=(0,))
+        b_g_diff = b_g[:, None] - b_g[None, :]
+        b_A *= exp(b_g_diff)
+    b_A *= b_b[:, None]
+
+    m_A = (o_t[:, None] > o_t[None, :]) & (m_t[:, None] & m_t)
+    b_A = tl.where(m_A, b_A, 0)
+    p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (BT*H, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64]
+        for num_warps in [1, 2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=["BC"]
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_scaled_dot_kkt_fwd_kernel_intra_sub_inter(
+    k,
+    g,
+    beta,
+    A,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BK: tl.constexpr,
+    NC: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_t, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    i_i, i_j = i_c // NC, i_c % NC
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    if i_t * BT + i_i * BC >= T:
+        return
+    if i_i <= i_j:
+        return
+
+    k += (bos * H + i_h) * K
+    g += (bos * H + i_h) * K
+    A += (bos * H + i_h) * BT
+
+    p_b = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT + i_i * BC,), (BC,), (0,))
+    b_b = tl.load(p_b, boundary_check=(0,))
+
+    b_A = tl.zeros([BC, BC], dtype=tl.float32)
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
+        p_g = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
+        b_kt = tl.make_block_ptr(k, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1))
+        p_gk = tl.make_block_ptr(g, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1))
+
+        o_k = i_k * BK + tl.arange(0, BK)
+        m_k = o_k < K
+        # [BK,]
+        b_gn = tl.load(g + (i_t * BT + i_i * BC) * H*K + o_k, mask=m_k, other=0)
+        # [BC, BK]
+        b_g = tl.load(p_g, boundary_check=(0, 1))
+        b_k = tl.load(p_k, boundary_check=(0, 1)) * exp(b_g - b_gn[None, :])
+        # [BK, BC]
+        b_gk = tl.load(p_gk, boundary_check=(0, 1))
+        b_kt = tl.load(b_kt, boundary_check=(0, 1)) * exp(b_gn[:, None] - b_gk)
+        # [BC, BC]
+        b_A += tl.dot(b_k, b_kt)
+    b_A *= b_b[:, None]
+
+    p_A = tl.make_block_ptr(A, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0))
+    tl.store(p_A, b_A.to(A.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=1),
+        triton.Config({}, num_warps=2),
+        triton.Config({}, num_warps=4),
+        triton.Config({}, num_warps=8),
+    ],
+    key=["BK", "BT"]
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_scaled_dot_kkt_fwd_kernel_intra_sub_intra(
+    k,
+    g,
+    beta,
+    A,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BK: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_t, i_i, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    if i_t * BT + i_i * BC >= T:
+        return
+
+    o_i = tl.arange(0, BC)
+    o_k = tl.arange(0, BK)
+    m_k = o_k < K
+    m_A = (i_t * BT + i_i * BC + o_i) < T
+    o_A = (bos + i_t * BT + i_i * BC + o_i) * H*BT + i_h * BT + i_i * BC
+
+    p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0))
+    p_g = tl.make_block_ptr(g + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0))
+    p_b = beta + (bos + i_t * BT + i_i * BC + o_i) * H + i_h
+
+    b_k = tl.load(p_k, boundary_check=(0, 1)) * tl.load(p_b, mask=m_A, other=0)[:, None]
+    b_g = tl.load(p_g, boundary_check=(0, 1))
+
+    p_kt = k + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k
+    p_gk = g + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k
+    for j in range(0, min(BC, T - i_t * BT - i_i * BC)):
+        b_kt = tl.load(p_kt, mask=m_k, other=0).to(tl.float32)
+        b_gk = tl.load(p_gk, mask=m_k, other=0).to(tl.float32)
+        b_A = tl.sum(b_k * b_kt[None, :] * exp(b_g - b_gk[None, :]), 1)
+        b_A = tl.where(o_i > j, b_A, 0.)
+
+        tl.store(A + o_A + j, b_A, mask=m_A)
+        p_kt += H*K
+        p_gk += H*K
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [1, 2, 4, 8]
+    ],
+    key=['BK', 'NC', 'BT'],
+)
+@triton.jit(do_not_specialize=['B', 'T'])
+def chunk_scaled_dot_kkt_bwd_kernel_gk(
+    k,
+    g,
+    beta,
+    dA,
+    dk,
+    dg,
+    db,
+    cu_seqlens,
+    chunk_indices,
+    B,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BK: tl.constexpr,
+    NC: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    i_t, i_i = i_c // NC, i_c % NC
+
+    all = B * T
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+    else:
+        bos, eos = i_b * T, i_b * T + T
+    T = eos - bos
+    if i_t * BT + i_i * BC >= T:
+        return
+
+    o_k = i_k * BK + tl.arange(0, BK)
+    m_k = o_k < K
+
+    k += (bos * H + i_h) * K
+    g += (bos * H + i_h) * K
+    beta += bos * H + i_h
+
+    dA += (bos * H + i_h) * BT
+    dk += (bos * H + i_h) * K
+    dg += (bos * H + i_h) * K
+    db += (i_k * all + bos) * H + i_h
+
+    p_g = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
+    p_b = tl.make_block_ptr(beta, (T,), (H,), (i_t * BT + i_i * BC,), (BC,), (0,))
+    # [BC, BK]
+    b_g = tl.load(p_g, boundary_check=(0, 1))
+    b_dk = tl.zeros([BC, BK], dtype=tl.float32)
+    # [BC]
+    b_b = tl.load(p_b, boundary_check=(0,))
+    if i_i > 0:
+        p_gn = g + (i_t * BT + i_i * BC) * H*K + o_k
+        # [BK,]
+        b_gn = tl.load(p_gn, mask=m_k, other=0)
+        for i_j in range(0, i_i):
+            p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0))
+            p_gk = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0))
+            p_dA = tl.make_block_ptr(dA, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0))
+            # [BC, BK]
+            b_k = tl.load(p_k, boundary_check=(0, 1))
+            b_gk = tl.load(p_gk, boundary_check=(0, 1))
+            b_kg = b_k * exp(b_gn[None, :] - b_gk)
+            # [BC, BC]
+            b_dA = tl.load(p_dA, boundary_check=(0, 1))
+            # [BC, BK]
+            b_dkb = tl.dot(b_dA, b_kg) * exp(b_g - b_gn[None, :])
+            b_dk += b_dkb
+
+    o_i = tl.arange(0, BC)
+    m_dA = (i_t * BT + i_i * BC + o_i) < T
+    o_dA = (i_t * BT + i_i * BC + o_i) * H*BT + i_i * BC
+    p_kj = k + (i_t * BT + i_i * BC) * H*K + o_k
+    p_gkj = g + (i_t * BT + i_i * BC) * H*K + o_k
+
+    p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
+    b_k = tl.load(p_k, boundary_check=(0, 1))
+    for j in range(0, min(BC, T - i_t * BT - i_i * BC)):
+        # [BC]
+        b_dA = tl.load(dA + o_dA + j, mask=m_dA, other=0)
+        # [BK]
+        b_kj = tl.load(p_kj, mask=m_k, other=0).to(tl.float32)
+        b_gkj = tl.load(p_gkj, mask=m_k, other=0).to(tl.float32)
+        # [BC, BK]
+        m_i = o_i[:, None] >= j
+        # [BC, BK]
+        b_dkb = tl.where(m_i, b_dA[:, None] * b_kj[None, :] * exp(b_g - b_gkj[None, :]), 0.)
+        b_dk += b_dkb
+
+        p_kj += H*K
+        p_gkj += H*K
+    b_db = tl.sum(b_dk * b_k, 1)
+    b_dk *= b_b[:, None]
+    p_db = tl.make_block_ptr(db, (T,), (H,), (i_t * BT + i_i * BC,), (BC,), (0,))
+    tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0,))
+
+    tl.debug_barrier()
+    # [BC, BK]
+    b_dkt = tl.zeros([BC, BK], dtype=tl.float32)
+
+    NC = min(NC, tl.cdiv(T - i_t * BT, BC))
+    if i_i < NC - 1:
+        p_gn = g + (min(i_t * BT + i_i * BC + BC, T) - 1) * H*K + o_k
+        # [BK,]
+        b_gn = tl.load(p_gn, mask=m_k, other=0)
+        for i_j in range(i_i + 1, NC):
+            p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0))
+            p_gk = tl.make_block_ptr(g, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k*BK), (BC, BK), (1, 0))
+            p_dA = tl.make_block_ptr(dA, (BT, T), (1, H*BT), (i_i * BC, i_t * BT + i_j * BC), (BC, BC), (0, 1))
+            p_b = tl.make_block_ptr(beta, (T,), (H,), (i_t * BT + i_j * BC,), (BC,), (0,))
+
+            o_j = i_t * BT + i_j * BC + o_i
+            m_j = o_j < T
+            # [BC]
+            b_b = tl.load(p_b, boundary_check=(0,))
+            # [BC, BK]
+            b_kb = tl.load(p_k, boundary_check=(0, 1)).to(tl.float32) * b_b[:, None]
+            b_gk = tl.load(p_gk, boundary_check=(0, 1))
+            b_kbg = b_kb * tl.where(m_j[:, None], exp(b_gk - b_gn[None, :]), 0)
+            # [BC, BC]
+            b_dA = tl.load(p_dA, boundary_check=(0, 1))
+            # [BC, BK]
+            # (SY 09/17) important to not use bf16 here to have a good precision.
+            b_dkt += tl.dot(b_dA, b_kbg)
+        b_dkt *= exp(b_gn[None, :] - b_g)
+    o_dA = (i_t * BT + i_i * BC) * H*BT + i_i * BC + o_i
+    p_kj = k + (i_t * BT + i_i * BC) * H*K + o_k
+    p_gkj = g + (i_t * BT + i_i * BC) * H*K + o_k
+    p_bj = beta + (i_t * BT + i_i * BC) * H
+
+    for j in range(0, min(BC, T - i_t * BT - i_i * BC)):
+        # [BC,]
+        b_dA = tl.load(dA + o_dA + j * H*BT)
+        # [BK,]
+        b_kbj = tl.load(p_kj, mask=m_k, other=0).to(tl.float32) * tl.load(p_bj)
+        b_gkj = tl.load(p_gkj, mask=m_k, other=0).to(tl.float32)
+        b_kbgj = b_kbj[None, :] * exp(b_gkj[None, :] - b_g)
+        # [BC, BK]
+        m_i = o_i[:, None] <= j
+        b_dkt += tl.where(m_i, b_dA[:, None] * b_kbgj, 0.)
+
+        p_kj += H*K
+        p_gkj += H*K
+        p_bj += H
+    b_dg = (b_dk - b_dkt) * b_k
+    b_dk += b_dkt
+
+    p_dk = tl.make_block_ptr(dk, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
+    p_dg = tl.make_block_ptr(dg, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
+    tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1))
+
+
+def chunk_scaled_dot_kkt_fwd(
+    k: torch.Tensor,
+    g: Optional[torch.Tensor] = None,
+    gk: Optional[torch.Tensor] = None,
+    beta: Optional[torch.Tensor] = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64,
+    output_dtype: torch.dtype = torch.float32
+) -> torch.Tensor:
+    r"""
+    Compute beta * K * K^T.
+
+    Args:
+        k (torch.Tensor):
+            The key tensor of shape `[B, T, H, K]`.
+        beta (torch.Tensor):
+            The beta tensor of shape `[B, T, H]`.
+        g (torch.Tensor):
+            The cumulative sum of the gate tensor of shape `[B, T, H]`. Default: `None`.
+        gk (torch.Tensor):
+            The cumulative sum of the gate tensor of shape `[B, T, H, K]` applied to the key tensor. Default: `None`.
+        cu_seqlens (torch.LongTensor):
+            The cumulative sequence lengths of the input tensor.
+            Default: None
+        chunk_size (int):
+            The chunk size. Default: 64.
+        output_dtype (torch.dtype):
+            The dtype of the output tensor. Default: `torch.float32`
+
+    Returns:
+        beta * K * K^T of shape `[B, T, H, BT]` where `BT` is the chunk size.
+    """
+    B, T, H, K = k.shape
+    BT = chunk_size
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    if gk is None:
+        A = torch.empty(B, T, H, BT, device=k.device, dtype=output_dtype)
+        chunk_scaled_dot_kkt_fwd_kernel[(NT, B * H)](
+            k=k,
+            g=g,
+            beta=beta,
+            A=A,
+            cu_seqlens=cu_seqlens,
+            chunk_indices=chunk_indices,
+            T=T,
+            H=H,
+            K=K,
+            BT=BT,
+        )
+        return A
+
+    BC = min(16, BT)
+    NC = triton.cdiv(BT, BC)
+    BK = max(triton.next_power_of_2(K), 16)
+    A = torch.zeros(B, T, H, BT, device=k.device, dtype=output_dtype)
+    grid = (NT, NC * NC, B * H)
+    chunk_scaled_dot_kkt_fwd_kernel_intra_sub_inter[grid](
+        k=k,
+        g=gk,
+        beta=beta,
+        A=A,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        H=H,
+        K=K,
+        BT=BT,
+        BC=BC,
+        NC=NC,
+    )
+
+    grid = (NT, NC, B * H)
+    chunk_scaled_dot_kkt_fwd_kernel_intra_sub_intra[grid](
+        k=k,
+        g=gk,
+        beta=beta,
+        A=A,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        H=H,
+        K=K,
+        BT=BT,
+        BC=BC,
+        BK=BK,
+    )
+    return A
+
+
+def chunk_scaled_dot_kkt_bwd_gk(
+    k: torch.Tensor,
+    g: torch.Tensor,
+    beta: torch.Tensor,
+    dA: torch.Tensor,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64
+):
+    B, T, H, K = k.shape
+    BT = chunk_size
+    BC = min(16, BT)
+    BK = min(64, triton.next_power_of_2(K))
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, chunk_size) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    NC = triton.cdiv(BT, BC)
+    NK = triton.cdiv(K, BK)
+
+    dk = torch.empty_like(k, dtype=torch.float)
+    dg = torch.empty_like(g, dtype=torch.float)
+    db = beta.new_empty(NK, *beta.shape, dtype=torch.float)
+    grid = (NK, NT * NC, B * H)
+    chunk_scaled_dot_kkt_bwd_kernel_gk[grid](
+        k=k,
+        g=g,
+        beta=beta,
+        dA=dA,
+        dk=dk,
+        dg=dg,
+        db=db,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        B=B,
+        T=T,
+        H=H,
+        K=K,
+        BT=BT,
+        BC=BC,
+        BK=BK,
+        NC=NC,
+    )
+    db = db.sum(0)
+
+    return dk, dg, db
diff --git a/fla/ops/gated_oja_rule/chunk_o.py b/fla/ops/gated_oja_rule/chunk_o.py
new file mode 100644
index 0000000000..791ec178ea
--- /dev/null
+++ b/fla/ops/gated_oja_rule/chunk_o.py
@@ -0,0 +1,691 @@
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils import prepare_chunk_indices
+from fla.ops.utils.op import exp
+from fla.utils import check_shared_mem, is_nvidia_hopper
+from fla.ops.utils.cumsum import chunk_local_cumsum
+
+BKV_LIST = [64, 128] if check_shared_mem() else [32, 64]
+NUM_WARPS = [2, 4] if is_nvidia_hopper else [2, 4, 8]
+
+exp = tl.exp
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({'BK': BK, 'BV': BV}, num_warps=num_warps, num_stages=num_stages)
+        for BK in [32, 64]
+        for BV in [32, 64]
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT']
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_fwd_inter(
+    q,
+    k,
+    h,
+    gv,
+    o,
+    A,
+    cu_seqlens,
+    chunk_indices,
+    scale,
+    T,
+    HQ: tl.constexpr,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    NG: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_hq = i_bh // HQ, i_bh % HQ
+    i_h = i_hq // NG
+    if IS_VARLEN:
+        i_tg = i_t
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+
+    o_i = tl.arange(0, BT)
+    m_s = o_i[:, None] >= o_i[None, :]
+
+    b_o = tl.zeros([BT, BV], dtype=tl.float32)
+    b_A = tl.zeros([BT, BT], dtype=tl.float32)
+    for i_k in range(tl.cdiv(K, BK)):
+        p_q = tl.make_block_ptr(q + (bos * HQ + i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
+        p_h = tl.make_block_ptr(h + (i_tg * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
+
+        # [BT, BK]
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+        b_q = (b_q * scale).to(b_q.dtype)
+        # [BK, BT]
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        # [BK, BV]
+        b_h = tl.load(p_h, boundary_check=(0, 1))
+        # [BT, BV]
+        b_o += tl.dot(b_q, b_h)
+        # [BT, BT]
+        b_A += tl.dot(b_q, b_k)
+    p_g = tl.make_block_ptr(gv + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_o = tl.make_block_ptr(o + (bos * HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+    p_A = tl.make_block_ptr(A + (bos * HQ + i_hq) * BT, (T, BT), (HQ*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    # [BT, BV]
+    b_g = tl.load(p_g, boundary_check=(0, 1))
+    b_o = b_o * exp(b_g)
+    tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
+
+    # [BT, BT]
+    b_A = tl.where(m_s, b_A, 0.)
+    if i_v == 0:
+        tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
+
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_fwd_intra(
+    v,
+    gv,
+    o,
+    A,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    HQ: tl.constexpr,
+    H: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BV: tl.constexpr,
+    NC: tl.constexpr,
+    NG: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_hq = i_bh // HQ, i_bh % HQ
+    i_h = i_hq // NG
+    i_t, i_i = i_c // NC, i_c % NC
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    o_v = i_v * BV + tl.arange(0, BV)
+    m_v = o_v < V
+
+    if i_t * BT + i_i * BC >= T:
+        return
+
+    p_g = tl.make_block_ptr(gv + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
+    p_gn = gv + (bos + min(i_t * BT + i_i * BC, T)) * H*V + i_h * V + o_v
+    # [BV,]
+    b_gn = tl.load(p_gn, mask=m_v, other=0)
+    # [BC, BV]
+    b_o = tl.zeros([BC, BV], dtype=tl.float32)
+    for i_j in range(0, i_i):
+        p_A = tl.make_block_ptr(A + (bos*HQ+i_hq) * BT, (T, BT), (HQ*BT, 1), (i_t*BT+i_i*BC, i_j * BC), (BC, BC), (1, 0))
+        p_v = tl.make_block_ptr(v + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0))
+        p_gv = tl.make_block_ptr(gv + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0))
+        # [BC, BV]
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        b_gv = tl.load(p_gv, boundary_check=(0, 1))
+        b_vg = (b_v * exp(b_gn[None, :] - b_gv)).to(b_v.dtype)
+        # [BC, BC]
+        b_A = tl.load(p_A, boundary_check=(0, 1))
+        b_o += tl.dot(b_A, b_vg)
+    # [BC, BV]
+    b_g = tl.load(p_g, boundary_check=(0, 1))
+    b_o *= exp(b_g - b_gn[None, :])
+
+    o_i = tl.arange(0, BC)
+    o_A = (bos + i_t * BT + i_i * BC + tl.arange(0, BC)) * HQ*BT + i_hq * BT + i_i * BC
+    m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T
+    for j in range(0, min(BC, T - i_t * BT - i_i * BC)):
+        p_v = v + (bos + i_t * BT + i_i * BC + j) * H*V + i_h * V + o_v
+        p_gv = gv + (bos + i_t * BT + i_i * BC + j) * H*V + i_h * V + o_v
+        # [BC,]
+        b_A = tl.load(A + o_A + j, mask=m_A, other=0)
+        # [BV,]
+        b_v = tl.load(p_v, mask=m_v, other=0).to(tl.float32)
+        b_gv = tl.load(p_gv, mask=m_v, other=0).to(tl.float32)
+        # [BC, BV]
+        b_vg = b_v[None, :] * exp(b_g - b_gv[None, :])
+        # avoid 0 * inf = inf
+        b_o += tl.where(o_i[:, None] >= j, b_A[:, None] * b_vg, 0.)
+    p_o = tl.make_block_ptr(o + (bos*HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
+    b_o += tl.load(p_o, boundary_check=(0, 1))
+    tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
+    
+    
+    
+    
+def chunk_oja_fwd_o(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gv: torch.Tensor,
+    h: torch.Tensor,
+    scale: float = 1.,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+    B, T, H, K, V = *k.shape, v.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    BC = min(16, BT)
+    BV = min(64, triton.next_power_of_2(V))
+    HQ = q.shape[2]
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    NC = triton.cdiv(BT, BC)
+    NG = HQ // H
+
+    o = v.new_empty(B, T, HQ, V)
+    A = q.new_empty(B, T, HQ, BT)
+    def grid(meta): return (triton.cdiv(V, meta['BV']), NT, B * HQ)
+    chunk_oja_fwd_inter[grid](
+        q,
+        k,
+        h,
+        gv,
+        o,
+        A,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        scale=scale,
+        T=T,
+        HQ=HQ,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        NG=NG,
+    )
+
+    def grid(meta): return (triton.cdiv(V, meta['BV']), NT * NC, B * HQ)
+    chunk_oja_fwd_intra[grid](
+        v,
+        gv,
+        o,
+        A,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        HQ=HQ,
+        H=H,
+        V=V,
+        BT=BT,
+        BC=BC,
+        BV=BV,
+        NC=NC,
+        NG=NG,
+        num_warps=4,
+        num_stages=2
+    )
+    return A, o
+
+
+
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps)
+        for num_warps in [2, 4, 8]
+    ],
+    key=["BT"]
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_bwd_kernel_dA(
+    v,
+    gv,
+    do,
+    dA,
+    chunk_indices,
+    cu_seqlens,
+    scale,
+    T,
+    B: tl.constexpr,
+    H: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BV: tl.constexpr,
+    NC: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    i_t, i_i, i_j = i_c // (NC * NC), (i_c % (NC * NC)) // NC, (i_c % (NC * NC)) % NC
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        all = T
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+        all = B * T
+
+    o_v = i_v * BV + tl.arange(0, BV)
+    m_v = o_v < V
+
+    if i_t * BT + i_i * BC >= T:
+        return
+
+    # [BC, BC]
+    b_dA = tl.zeros([BC, BC], dtype=tl.float32)
+    if i_i > i_j:
+        p_v = tl.make_block_ptr(v + (bos*H+i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t*BT + i_j*BC), (BV, BC), (0, 1))
+        p_gv = tl.make_block_ptr(gv + (bos*H+i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t*BT + i_j*BC), (BV, BC), (0, 1))
+        p_gn = gv + (bos + i_t*BT + i_i*BC) * H*V + i_h * V + o_v
+        p_g = tl.make_block_ptr(gv + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+        p_do = tl.make_block_ptr(do + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+        # [BV,]
+        b_gn = tl.load(p_gn, mask=m_v, other=0.)
+        # [BC, BV]
+        b_g = tl.load(p_g, boundary_check=(0, 1))
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+        b_do = (b_do * exp(b_g - b_gn[None, :]) * scale).to(b_do.dtype)
+        # [BV, BC]
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        b_gv = tl.load(p_gv, boundary_check=(0, 1))
+        b_vg = (b_v * exp(b_gn[:, None] - b_gv)).to(b_v.dtype)
+        # [BC, BC]
+        b_dA = tl.dot(b_do, b_vg)
+    elif i_i == i_j:
+        p_g = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+        p_do = tl.make_block_ptr(do + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+        p_v = v + (bos + i_t*BT + i_j*BC) * H*V + i_h * V + o_v
+        p_gv = gv + (bos + i_t*BT + i_j*BC) * H*V + i_h * V + o_v
+        # [BC, BV]
+        b_g = tl.load(p_g, boundary_check=(0, 1))
+        b_do = tl.load(p_do, boundary_check=(0, 1)) * scale
+        m_v = o_v < V
+
+        o_i = tl.arange(0, BC)
+        # [BC, BC]
+        m_dA = o_i[:, None] >= o_i[None, :]
+        for j in range(0, min(BC, T - i_t * BT - i_j * BC)):
+            # [BV,]
+            b_v = tl.load(p_v, mask=m_v, other=0).to(tl.float32)
+            b_gv = tl.load(p_gv, mask=m_v, other=0).to(tl.float32)
+            # [BC,]
+            b_dAj = tl.sum(b_do * b_v[None, :] * exp(b_g - b_gv[None, :]), 1)
+            b_dA = tl.where((o_i == j)[None, :], b_dAj[:, None], b_dA)
+
+            p_v += H*V
+            p_gv += H*V
+        b_dA = tl.where(m_dA, b_dA, 0.)
+        
+    p_dA = tl.make_block_ptr(dA+((i_v*all+bos)*H+i_h)*BT, (T, BT), (H*BT, 1), (i_t*BT+i_i*BC, i_j*BC), (BC, BC), (1, 0))
+    tl.store(p_dA, b_dA.to(dA.dtype.element_ty), boundary_check=(0, 1))
+    
+    
+
+
+
+def chunk_oja_bwd_dA(
+    v: torch.Tensor,
+    gv: torch.Tensor,
+    do: torch.Tensor,
+    scale: float = 1.,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64
+):
+    B, T, H, V = v.shape
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    BC = min(16, BT)
+    BV = min(64, triton.next_power_of_2(V))
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    NC = triton.cdiv(BT, BC)
+    NV = triton.cdiv(V, BV)
+
+    dA = v.new_empty(NV, B, T, H, BT)
+    # 计算dA
+    grid = (NV, NT * NC * NC, B * H)
+    chunk_oja_bwd_kernel_dA[grid](
+        v,
+        gv,
+        do,
+        dA,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        scale=scale,
+        T=T,
+        B=B,
+        H=H,
+        V=V,
+        BT=BT,
+        BC=BC,
+        BV=BV,
+        NC=NC,
+    )
+    dA = dA.sum(0, dtype=dA.dtype)
+
+    return dA
+
+
+
+
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['BT']
+)
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_bwd_kernel_dqk(
+    q,
+    k,
+    h,
+    gv,
+    A,
+    dq,
+    dk,
+    dA,
+    do,
+    scale,
+    cu_seqlens,
+    chunk_indices,
+    B,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    if IS_VARLEN:
+        i_tg = i_t
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        all = T
+        T = eos - bos
+        NT = tl.cdiv(T, BT)
+    else:
+        NT = tl.cdiv(T, BT)
+        i_tg = i_b * NT + i_t
+        bos, eos = i_b * T, i_b * T + T
+        all = B * T
+
+    o_i = tl.arange(0, BT)
+    m_s = o_i[:, None] >= o_i[None, :]
+    
+    # [B, T, H, BT]
+    p_q = tl.make_block_ptr(q + (bos*H+i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_k = tl.make_block_ptr(k + (bos*H+i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_A = tl.make_block_ptr(A + ((i_k*all+bos)*H+i_h)*BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    b_q = tl.load(p_q, boundary_check=(0, 1))
+    b_k = tl.load(p_k, boundary_check=(0, 1))
+    
+    b_A = tl.dot((b_q * scale).to(b_q.dtype), tl.trans(b_k))
+    b_A = tl.where(m_s, b_A, 0.)
+    tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
+
+    b_dq = tl.zeros([BT, BK], dtype=tl.float32)
+    
+    # 先计算do对应的dq
+    for i_v in range(tl.cdiv(V, BV)):
+        p_h = tl.make_block_ptr(h + (i_tg * H + i_h) * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
+        p_do = tl.make_block_ptr(do + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_gv = tl.make_block_ptr(gv + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_h = tl.load(p_h, boundary_check=(0, 1))
+        b_do = tl.load(p_do, boundary_check=(0, 1))
+        b_gv = tl.load(p_gv, boundary_check=(0, 1))
+        b_do = (b_do * exp(b_gv) * scale).to(b_do.dtype)
+        b_dq += tl.dot(b_do, b_h.to(b_do.dtype))
+        
+    # 接着计算dA对应的dq, dk
+    p_dA = tl.make_block_ptr(dA + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    p_dq = tl.make_block_ptr(dq + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    p_dk = tl.make_block_ptr(dk + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+    # [BT, BT]
+    b_dA = tl.load(p_dA, boundary_check=(0, 1))
+    # [BT, BK]
+    b_dq += tl.dot(b_dA.to(b_q.dtype), b_k)
+    b_dk = tl.dot(tl.trans(b_dA).to(b_q.dtype), b_q)
+
+    tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+    
+    
+    
+
+def chunk_oja_bwd_dqk(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    h: torch.Tensor,
+    gv: torch.Tensor,
+    dA: torch.Tensor,
+    do: torch.Tensor,
+    scale: float = 1.,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64
+):
+    B, T, H, K, V = *q.shape, gv.shape[-1]
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    BK = min(64, triton.next_power_of_2(K))
+    BV = min(64, triton.next_power_of_2(V))
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    NK = triton.cdiv(K, BK)
+
+    dq = torch.empty_like(q)
+    dk = torch.empty_like(k)
+    A = dA.new_empty(NK, B, T, H, BT)
+    # 计算dA
+    grid = (NK, NT, B * H)
+    chunk_oja_bwd_kernel_dqk[grid](
+        q,
+        k,
+        h,
+        gv,
+        A,
+        dq,
+        dk,
+        dA,
+        do,
+        scale,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        B=B,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV
+    )
+
+    A = A.sum(0, dtype=A.dtype)
+    
+    return A, dq, dk
+
+
+
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.jit(do_not_specialize=['T'])
+def chunk_oja_bwd_kernel_dv_o(
+    v,
+    g,
+    o,
+    A,
+    do,
+    dv,
+    dv2,
+    dg,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BC: tl.constexpr,
+    BV: tl.constexpr,
+    NC: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
+    i_b, i_h = i_bh // H, i_bh % H
+    i_t, i_i = i_c // NC, i_c % NC
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    o_v = i_v * BV + tl.arange(0, BV)
+    m_v = o_v < V
+
+    if i_t * BT + i_i * BC >= T:
+        return
+
+    p_gv = tl.make_block_ptr(g + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
+    p_gn = g + (bos + min(i_t * BT + i_i * BC + BC, T)-1)*H*V + i_h*V + o_v
+    # [BV,]
+    b_gn = tl.load(p_gn, mask=m_v, other=0)
+    # [BC, BV]
+    b_gv = tl.load(p_gv, boundary_check=(0, 1))
+    b_dvg = tl.zeros([BC, BV], dtype=tl.float32)
+    for i_j in range(i_i + 1, NC):
+        p_g = tl.make_block_ptr(g + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0))
+        p_A = tl.make_block_ptr(A + (bos*H+i_h) * BT, (BT, T), (1, H*BT), (i_i*BC, i_t*BT + i_j*BC), (BC, BC), (0, 1))
+        p_do = tl.make_block_ptr(do + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_j*BC, i_v*BV), (BC, BV), (1, 0))
+        # [BC, BV]
+        b_g = tl.load(p_g, boundary_check=(0, 1))
+        b_do = tl.load(p_do, boundary_check=(0, 1)) * exp(b_g - b_gn[None, :])
+        # [BC, BC]
+        b_A = tl.load(p_A, boundary_check=(0, 1))
+        # [BC, BV]
+        b_dvg += tl.dot(b_A, b_do.to(b_A.dtype))
+    b_dv = b_dvg * exp(b_gn[None, :] - b_gv)
+
+    o_i = tl.arange(0, BC)
+    o_c = i_i * BC + tl.arange(0, BC)
+
+    p_g = g + (bos + i_t * BT + i_i * BC) * H*V + i_h * V + o_v
+    p_A = A + (bos + i_t*BT + i_i*BC) * H*BT + i_h * BT + o_c
+    p_do = do + (bos + i_t*BT + i_i*BC) * H*V + i_h * V + o_v
+    for j in range(0, min(BC, T - i_t * BT - i_i * BC)):
+        # [BC,]
+        b_A = tl.load(p_A)
+        # [BV,]
+        b_g = tl.load(p_g, mask=m_v, other=0)
+        b_do = tl.load(p_do, mask=m_v, other=0)
+        # [BC, BV]
+        m_i = o_i[:, None] <= j
+        b_dv += tl.where(m_i, exp(b_g[None, :] - b_gv) * b_A[:, None] * b_do[None, :], 0.)
+
+        p_g += H * V
+        p_A += H * BT
+        p_do += H * V
+    p_o = tl.make_block_ptr(o + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+    p_v = tl.make_block_ptr(v + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+    p_do = tl.make_block_ptr(do + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+    p_dv = tl.make_block_ptr(dv + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+    p_dv2 = tl.make_block_ptr(dv2 + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+    p_dg = tl.make_block_ptr(dg + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0))
+
+    b_o = tl.load(p_o, boundary_check=(0, 1)).to(tl.float32)
+    b_v = tl.load(p_v, boundary_check=(0, 1)).to(tl.float32)
+    b_do = tl.load(p_do, boundary_check=(0, 1)).to(tl.float32)
+    b_dv = b_dv + tl.load(p_dv, boundary_check=(0, 1)).to(tl.float32)
+    b_dg = b_o * b_do - b_v * b_dv
+    tl.store(p_dv2, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1))
+
+
+
+
+def chunk_oja_bwd_dv_o(
+    v: torch.Tensor,
+    gv: torch.Tensor,
+    o: torch.Tensor,
+    A: torch.Tensor,
+    dv: torch.Tensor,
+    do: torch.Tensor,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    chunk_size: int = 64
+):
+    B, T, H, V = v.shape
+    BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
+    BC = min(16, BT)
+    BV = min(64, triton.next_power_of_2(V))
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    NC = triton.cdiv(BT, BC)
+
+    dv2 = torch.empty_like(v, dtype=torch.float)
+    dgv = torch.empty_like(gv)
+    # 计算dA
+    def grid(meta): return (triton.cdiv(V, meta['BV']), NT * NC, B * H)
+    chunk_oja_bwd_kernel_dv_o[grid](
+        v=v,
+        g=gv,
+        o=o,
+        A=A,
+        do=do,
+        dv=dv,
+        dv2=dv2,
+        dg=dgv,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        H=H,
+        V=V,
+        BT=BT,
+        BC=BC,
+        BV=BV,
+        NC=NC,
+        num_warps=4,
+        num_stages=2
+    )
+    return dv2, dgv
+
+
diff --git a/fla/ops/gated_oja_rule/fused_recurrent.py b/fla/ops/gated_oja_rule/fused_recurrent.py
new file mode 100644
index 0000000000..4da96020b4
--- /dev/null
+++ b/fla/ops/gated_oja_rule/fused_recurrent.py
@@ -0,0 +1,265 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+from fla.ops.utils.op import exp
+from fla.utils import input_guard
+
+
+@triton.heuristics({
+    'USE_GV': lambda args: args['gv'] is not None,
+    'USE_INITIAL_STATE': lambda args: args['h0'] is not None,
+    'STORE_FINAL_STATE': lambda args: args['ht'] is not None,
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.jit(do_not_specialize=['T'])
+def fused_recurrent_oja_fwd_kernel(
+    q,
+    k,
+    v,
+    gv,
+    beta,
+    o,
+    h0,
+    ht,
+    cu_seqlens,
+    scale,
+    T,
+    B: tl.constexpr,
+    H: tl.constexpr,
+    HV: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    USE_GV: tl.constexpr,
+    USE_Q_L2NORM: tl.constexpr,
+    USE_K_L2NORM: tl.constexpr,
+    IS_BETA_HEADWISE: tl.constexpr,
+    USE_INITIAL_STATE: tl.constexpr,
+    STORE_FINAL_STATE: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+):
+    i_v, i_nh = tl.program_id(0), tl.program_id(1)
+    i_n, i_hv = i_nh // HV, i_nh % HV
+    i_h = i_hv // (HV // H)
+    if IS_VARLEN:
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int64), tl.load(cu_seqlens + i_n + 1).to(tl.int64)
+        T = eos - bos
+    else:
+        bos, eos = i_n * T, i_n * T + T
+    o_k = tl.arange(0, BK)
+    o_v = i_v * BV + tl.arange(0, BV)
+
+    p_q = q + (bos * H + i_h) * K + o_k
+    p_k = k + (bos * H + i_h) * K + o_k
+    p_v = v + (bos * HV + i_hv) * V + o_v
+    if USE_GV:
+        p_gv = gv + (bos * HV + i_hv) * V + o_v
+    if IS_BETA_HEADWISE:
+        p_beta = beta + bos * HV + i_hv
+    else:
+        p_beta = beta + (bos * HV + i_hv) * V + o_v
+
+    p_o = o + (bos * HV + i_hv) * V + o_v
+
+    mask_k = o_k < K
+    mask_v = o_v < V
+    mask_h = mask_k[:, None] & mask_v[None, :]
+
+    b_h = tl.zeros([BK, BV], dtype=tl.float32)
+    if USE_INITIAL_STATE:
+        p_h0 = h0 + i_nh * K*V + o_k[:, None] * V + o_v[None, :]
+        b_h += tl.load(p_h0, mask=mask_h, other=0).to(tl.float32)
+
+    for _ in range(0, T):
+        b_q = tl.load(p_q, mask=mask_k, other=0).to(tl.float32)
+        b_k = tl.load(p_k, mask=mask_k, other=0).to(tl.float32)
+        b_v = tl.load(p_v, mask=mask_v, other=0).to(tl.float32)
+        if USE_Q_L2NORM:
+            b_q = b_q / tl.sqrt(tl.sum(b_q * b_q) + 1e-6)
+        if USE_K_L2NORM:
+            b_k = b_k / tl.sqrt(tl.sum(b_k * b_k) + 1e-6)
+        b_q = b_q * scale
+        if IS_BETA_HEADWISE:
+            b_beta = tl.load(p_beta).to(tl.float32)
+        else:
+            b_beta = tl.load(p_beta, mask=mask_v, other=0).to(tl.float32)
+
+        # [BK, BV]
+        if USE_GV:
+            b_gv = tl.load(p_gv).to(tl.float32)
+            b_h *= exp(b_gv[None, :])
+        
+        b_k = b_beta * (b_k - tl.sum(b_h * b_v[None, :], 1))
+        b_h += b_k[:, None] * b_v
+
+        # [BV]
+        b_o = tl.sum(b_h * b_q[:, None], 0)
+        tl.store(p_o, b_o.to(p_o.dtype.element_ty), mask=mask_v)
+
+        p_q += H*K
+        p_k += H*K
+        p_v += HV*V
+        if USE_GV:
+            p_gv += HV*V
+        p_beta += HV * (1 if IS_BETA_HEADWISE else V)
+        p_o += HV*V
+
+    if STORE_FINAL_STATE:
+        p_ht = ht + i_nh * K*V + o_k[:, None] * V + o_v[None, :]
+        tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), mask=mask_h)
+
+
+def fused_recurrent_oja_fwd(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gv: Optional[torch.Tensor] = None,
+    beta: Optional[torch.Tensor] = None,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+    use_q_l2norm: bool = False,
+    use_k_l2norm: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    B, T, H, K, V = *k.shape, v.shape[-1]
+    assert V <= 128
+    HV = v.shape[2]
+    N = B if cu_seqlens is None else len(cu_seqlens) - 1
+    BK, BV = triton.next_power_of_2(K), min(triton.next_power_of_2(V), 256)
+    NV = triton.cdiv(V, BV)
+    num_stages = 3
+    num_warps = 1
+
+    o = torch.empty_like(v)
+    final_state = q.new_empty(N, HV, K, V, dtype=torch.float32) if output_final_state else None
+
+    grid = (NV, N * HV)
+    fused_recurrent_oja_fwd_kernel[grid](
+        q=q,
+        k=k,
+        v=v,
+        gv=gv,
+        beta=beta,
+        o=o,
+        h0=initial_state,
+        ht=final_state,
+        cu_seqlens=cu_seqlens,
+        scale=scale,
+        T=T,
+        B=B,
+        H=H,
+        HV=HV,
+        K=K,
+        V=V,
+        BK=BK,
+        BV=BV,
+        IS_BETA_HEADWISE=beta.ndim != v.ndim,
+        USE_Q_L2NORM=use_q_l2norm,
+        USE_K_L2NORM=use_k_l2norm,
+        num_warps=num_warps,
+        num_stages=num_stages,
+    )
+    return o, final_state
+
+
+class FusedRecurrentFunction(torch.autograd.Function):
+
+    @staticmethod
+    @input_guard
+    def forward(
+        ctx,
+        q: torch.Tensor,
+        k: torch.Tensor,
+        v: torch.Tensor,
+        gv: Optional[torch.Tensor] = None,
+        beta: Optional[torch.Tensor] = None,
+        scale: float = None,
+        initial_state: torch.Tensor = None,
+        output_final_state: bool = False,
+        use_q_l2norm: bool = False,
+        use_k_l2norm: bool = False,
+        cu_seqlens: Optional[torch.LongTensor] = None,
+    ):
+        o, final_state = fused_recurrent_oja_fwd(
+            q=q,
+            k=k,
+            v=v,
+            gv=gv,
+            beta=beta,
+            scale=scale,
+            initial_state=initial_state,
+            output_final_state=output_final_state,
+            use_q_l2norm=use_q_l2norm,
+            use_k_l2norm=use_k_l2norm,
+            cu_seqlens=cu_seqlens,
+        )
+
+        return o, final_state
+
+    @staticmethod
+    @input_guard
+    def backward(ctx, do, dht):
+        raise NotImplementedError(
+            "Backward pass is not implemented yet and we do not have plans to implement it "
+            "because we haven't figured out how to compute dg without materializing the full "
+            "hidden states for all time steps."
+        )
+
+
+def fused_recurrent_gated_oja_rule(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    gv: Optional[torch.Tensor] = None,
+    beta: Optional[torch.Tensor] = None,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+    use_q_l2norm: bool = False,
+    use_k_l2norm: bool = False,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+    **kwargs,
+) -> Tuple[torch.Tensor, torch.Tensor]:
+
+    if 'use_qk_l2norm_in_kernel' in kwargs and (not use_q_l2norm and not use_k_l2norm):
+        use_q_l2norm = True
+        use_k_l2norm = True
+
+    if cu_seqlens is not None:
+        if q.shape[0] != 1:
+            raise ValueError(
+                f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
+                f"Please flatten variable-length inputs before processing."
+            )
+        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
+            raise ValueError(
+                f"The number of initial states is expected to be equal to the number of input sequences, "
+                f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}."
+            )
+    if scale is None:
+        scale = k.shape[-1] ** -0.5
+    if beta is None:
+        beta = torch.ones_like(q[..., 0])
+
+    o, final_state = FusedRecurrentFunction.apply(
+        q,
+        k,
+        v,
+        gv,
+        beta,
+        scale,
+        initial_state,
+        output_final_state,
+        use_q_l2norm,
+        use_k_l2norm,
+        cu_seqlens,
+    )
+    return o, final_state
diff --git a/fla/ops/gated_oja_rule/wy_fast.py b/fla/ops/gated_oja_rule/wy_fast.py
new file mode 100644
index 0000000000..7fdd5d994c
--- /dev/null
+++ b/fla/ops/gated_oja_rule/wy_fast.py
@@ -0,0 +1,289 @@
+# -*- coding: utf-8 -*-
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+
+from typing import Optional, Tuple
+
+import torch
+import triton
+import triton.language as tl
+
+
+from fla.ops.utils import chunk_local_cumsum, prepare_chunk_indices
+from fla.ops.utils.op import exp
+from fla.utils import check_shared_mem
+
+
+@triton.heuristics({
+    'STORE_VG': lambda args: args['vg'] is not None,
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4, 8]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'IS_VARLEN'],
+)
+@triton.jit(do_not_specialize=['T'])
+def recompute_w_u_fwd_kernel(
+    k,
+    v,
+    vg,
+    beta,
+    w,
+    u,
+    A,
+    gv,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    STORE_VG: tl.constexpr,
+    IS_VARLEN: tl.constexpr
+):
+    i_t, i_bh = tl.program_id(0), tl.program_id(1)
+    i_b, i_h = i_bh // H, i_bh % H
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+    p_b = tl.make_block_ptr(beta + bos*H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
+    b_b = tl.load(p_b, boundary_check=(0,))
+
+    p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    b_A = tl.load(p_A, boundary_check=(0, 1))
+    
+    for i_v in range(tl.cdiv(V, BV)):
+        p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_w = tl.make_block_ptr(w + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        b_vb = b_v * b_b[:, None]
+
+        p_gv = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_gv = tl.load(p_gv, boundary_check=(0, 1))
+        b_vb *= exp(b_gv)
+        if STORE_VG:
+            last_idx = min(i_t * BT + BT, T) - 1
+
+            o_v = i_v * BV + tl.arange(0, BV)
+            m_v = o_v < V
+            b_gn = tl.load(gv + ((bos + last_idx) * H + i_h) * V + o_v, mask=m_v, other=0.)
+            b_vg = b_v * exp(b_gn - b_gv)
+
+            p_vg = tl.make_block_ptr(vg + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+            tl.store(p_vg, b_vg.to(p_vg.dtype.element_ty), boundary_check=(0, 1))
+
+        b_w = tl.dot(b_A, b_vb.to(b_v.dtype))
+        tl.store(p_w, b_w.to(p_w.dtype.element_ty), boundary_check=(0, 1))
+
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_u = tl.make_block_ptr(u + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        b_kb = (b_k * b_b[:, None]).to(b_k.dtype)
+        b_u = tl.dot(b_A, b_kb, allow_tf32=False)
+        tl.store(p_u, b_u.to(p_u.dtype.element_ty), boundary_check=(0, 1))
+
+
+@triton.heuristics({
+    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
+})
+@triton.autotune(
+    configs=[
+        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
+        for num_warps in [2, 4]
+        for num_stages in [2, 3, 4]
+    ],
+    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'IS_VARLEN']
+)
+@triton.jit(do_not_specialize=['T'])
+def prepare_wy_repr_bwd_kernel(
+    k,
+    v,
+    beta,
+    gv,
+    A,
+    dA,
+    dw,
+    du,
+    dk,
+    dv,
+    db,
+    dgv,
+    cu_seqlens,
+    chunk_indices,
+    T,
+    H: tl.constexpr,
+    K: tl.constexpr,
+    V: tl.constexpr,
+    BT: tl.constexpr,
+    BK: tl.constexpr,
+    BV: tl.constexpr,
+    IS_VARLEN: tl.constexpr
+):
+    i_t, i_bh = tl.program_id(0), tl.program_id(1)
+    i_b, i_h = i_bh // H, i_bh % H
+    if IS_VARLEN:
+        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
+        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
+        T = eos - bos
+    else:
+        bos, eos = i_b * T, i_b * T + T
+
+    p_b = tl.make_block_ptr(beta + (bos*H + i_h), (T,), (H,), (i_t * BT,), (BT,), (0,))
+    p_db = tl.make_block_ptr(db + (bos*H + i_h), (T,), (H,), (i_t * BT,), (BT,), (0,))
+    p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))
+
+    b_b = tl.load(p_b, boundary_check=(0,))
+    b_db = tl.zeros([BT], dtype=tl.float32)
+    b_A = tl.load(p_A, boundary_check=(0, 1))
+    b_dA = tl.zeros([BT, BT], dtype=tl.float32)
+
+    for i_v in range(tl.cdiv(V, BV)):
+        p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_dv = tl.make_block_ptr(dv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        p_dw = tl.make_block_ptr(dw + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_v = tl.load(p_v, boundary_check=(0, 1))
+        p_gv = tl.make_block_ptr(gv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        b_gv_exp = exp(tl.load(p_gv, boundary_check=(0, 1)))
+        b_vbg = b_v * b_b[:, None] * b_gv_exp
+        b_dw = tl.load(p_dw, boundary_check=(0, 1))
+
+        b_dA += tl.dot(b_dw, tl.trans(b_vbg).to(b_dw.dtype))
+        b_dvbg = tl.dot(b_A, b_dw)
+        b_dv = b_dvbg * b_gv_exp * b_b[:, None]
+        b_db += tl.sum(b_dvbg * b_v * b_gv_exp, 1)
+        b_dgv = b_dvbg * b_vbg
+        
+        p_dgv = tl.make_block_ptr(dgv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
+        tl.store(p_dgv, b_dgv.to(p_dgv.dtype.element_ty), boundary_check=(0, 1))
+        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
+        
+    for i_k in range(tl.cdiv(K, BK)):
+        p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_dk = tl.make_block_ptr(dk + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        p_du = tl.make_block_ptr(du + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
+        # [BT, BK]
+        b_k = tl.load(p_k, boundary_check=(0, 1))
+        b_kb = (b_k * b_b[:, None]).to(b_k.dtype) # BT BK
+        b_du = tl.load(p_du, boundary_check=(0, 1)) # BT BK
+        b_dA += tl.dot(b_du, tl.trans(b_kb)) # BT BT
+        b_dkb = tl.dot(b_A, b_du) # BT BK
+        b_dk = b_dkb * b_b[:, None]
+        b_db += tl.sum(b_dkb * b_k, 1)
+        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
+
+    o_t = i_t * BT + tl.arange(0, BT)
+    m_t = o_t < T
+    m_A = (o_t[:, None] > o_t[None, :]) & (m_t[:, None] & m_t)
+    b_dA = tl.where(m_A, b_dA, 0)
+    b_dA = tl.dot(b_dA.to(b_A.dtype), b_A)
+    b_dA = tl.dot(b_A, b_dA.to(b_A.dtype))
+
+    b_dA = tl.where(m_A, -b_dA, 0)
+    
+    # if USE_GV:
+    p_dA = tl.make_block_ptr(dA + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
+    tl.store(p_dA, b_dA.to(p_dA.dtype.element_ty), boundary_check=(0, 1))
+    tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0,))
+
+
+def recompute_w_u_fwd(
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    A: torch.Tensor,
+    gv: Optional[torch.Tensor] = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+) -> Tuple[torch.Tensor, torch.Tensor]:
+    B, T, H, K, V = *k.shape, v.shape[-1]
+    BT = A.shape[-1]
+    BK = 64
+    BV = 64
+
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+
+    w = torch.empty_like(v)
+    u = torch.empty_like(k)
+    vg = torch.empty_like(v) if gv is not None else None
+    recompute_w_u_fwd_kernel[(NT, B*H)](
+        k=k,
+        v=v,
+        vg=vg,
+        beta=beta,
+        w=w,
+        u=u,
+        A=A,
+        gv=gv,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+    )
+    return w, u, vg
+
+
+def prepare_wy_repr_bwd(
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    A: torch.Tensor,
+    dw: torch.Tensor,
+    du: torch.Tensor,
+    gv: torch.Tensor = None,
+    cu_seqlens: Optional[torch.LongTensor] = None,
+) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+    B, T, H, K, V = *k.shape, v.shape[-1]
+    BT = 64
+    chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
+    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
+    CONST_TILING = 64 if check_shared_mem() else 32
+    BK = min(max(triton.next_power_of_2(K), 16), CONST_TILING)
+    BV = min(max(triton.next_power_of_2(V), 16), CONST_TILING)
+
+    dk = torch.empty_like(k)
+    dv = torch.empty_like(v, dtype=torch.float)
+
+    dgv = torch.empty_like(gv, dtype=torch.float)
+    dA = torch.empty_like(A, dtype=torch.float)
+    db = torch.empty_like(beta, dtype=torch.float)
+        
+    prepare_wy_repr_bwd_kernel[(NT, B * H)](
+        k=k,
+        v=v,
+        beta=beta,
+        gv=gv,
+        A=A,
+        dA=dA,
+        dw=dw,
+        du=du,
+        dk=dk,
+        dv=dv,
+        db=db,
+        dgv=dgv,
+        cu_seqlens=cu_seqlens,
+        chunk_indices=chunk_indices,
+        T=T,
+        H=H,
+        K=K,
+        V=V,
+        BT=BT,
+        BK=BK,
+        BV=BV,
+    )
+    
+    return dk, dv, db, dgv, dA

From a9830af4e3ddad9b9ab26f2d63e277d662882f07 Mon Sep 17 00:00:00 2001
From: hujiaxi <hujiaxi@msh.team>
Date: Tue, 27 Jan 2026 08:03:44 +0000
Subject: [PATCH 2/5] upload gated_oja_operator test

---
 tests/ops/test_oja.py | 472 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 472 insertions(+)
 create mode 100644 tests/ops/test_oja.py

diff --git a/tests/ops/test_oja.py b/tests/ops/test_oja.py
new file mode 100644
index 0000000000..65808e9f12
--- /dev/null
+++ b/tests/ops/test_oja.py
@@ -0,0 +1,472 @@
+# -*- coding: utf-8 -*-
+
+import os
+from typing import List, Optional
+
+import pytest
+import torch
+import torch.nn.functional as F
+from einops import rearrange, repeat
+
+from fla.ops.gated_oja_rule import fused_recurrent_gated_oja_rule
+from fla.ops.gated_oja_rule import chunk_gated_oja_rule
+from fla.utils import assert_close, device, is_intel_alchemist
+
+
+
+def recurrent_oja_ref(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    beta: torch.Tensor,
+    g: torch.Tensor,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+):
+    q, k, v, beta, g = map(lambda x: x.transpose(1, 2).contiguous().to(torch.float32), [q, k, v, beta, g])
+    B, H, T, K, V = *k.shape, v.shape[-1]
+    o = torch.zeros(B, H, T, V).to(v)
+    h = torch.zeros(B, H, K, V).to(v)
+    if initial_state is not None:
+        h = initial_state
+    if scale is None:
+        scale = 1 / (q.shape[-1] ** 0.5)
+    q = q * scale
+    for i in range(T):
+        b_q = q[:, :, i]
+        b_k = k[:, :, i]
+        b_v = v[:, :, i] # B H D
+        g_i = g[:, :, i]
+        # breakpoint()
+        h = h * g_i.exp()[:, :, None, :]
+        b_beta = beta[:, :, i]
+        b_k = b_k - (h * b_v[:, :, None, :]).sum(-1)
+        b_v = b_v * b_beta[..., None]
+        h = h + b_k.unsqueeze(-1) * b_v.unsqueeze(-2)
+        o[:, :, i] = torch.einsum('bhd,bhdm->bhm', b_q, h)
+    if not output_final_state:
+        h = None
+    o = o.transpose(1, 2).contiguous()
+    return o, h
+
+
+def chunk_oja_ref(
+    q: torch.Tensor,
+    k: torch.Tensor,
+    v: torch.Tensor,
+    g: torch.Tensor,
+    beta: torch.Tensor,
+    chunk_size: int = 64,
+    scale: float = None,
+    initial_state: torch.Tensor = None,
+    output_final_state: bool = False,
+):
+    BT = chunk_size
+    if scale is None:
+        scale = 1 / (q.shape[-1] ** 0.5)
+    # Calculate padding needed to make T a multiple of BT
+    q, k, v, beta, g = map(lambda x: x.transpose(1, 2).contiguous().to(torch.float32), [q, k, v, beta, g])
+
+    T = q.shape[-2]
+    pad_len = (BT - (T % BT)) % BT
+    if pad_len > 0:
+        # Pad all tensors
+        q = F.pad(q, (0, 0, 0, pad_len))
+        k = F.pad(k, (0, 0, 0, pad_len))
+        v = F.pad(v, (0, 0, 0, pad_len))
+        beta = F.pad(beta, (0, pad_len))
+        g = F.pad(g, (0, 0, 0, pad_len))
+    q, k, v, beta, g = map(lambda x: x.to(torch.float32), [q, k, v, beta, g])
+    chunk_size = BT
+    b, h, l, d_k = q.shape
+    d_v = v.shape[-1]
+    q = q * scale # B H T D
+    assert l % chunk_size == 0
+    # note that diagonal is masked.
+    mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=q.device), diagonal=0)
+    q, k, v, beta, g = map(
+        lambda x: rearrange(x, 'b h (n c) ... -> b h n c ...', c=chunk_size),
+        [q, k, v, beta, g]
+    )
+    g = g.cumsum(-2) # b h n c d
+
+    """
+    vector decay for attention
+    qkvg (B H N C D)
+    """
+    attn = torch.zeros(*q.shape[:-1], chunk_size, dtype=torch.float, device=q.device) # B H N C C
+    # attn = -((v_beta @ v.transpose(-1, -2))* L_mask).masked_fill(mask, 0) # B H N C C
+    for i in range(BT):
+        v_i = v[..., i, :] # B H N D
+        g_i = g[..., i:i+1, :] # B H N 1 Dv
+        attn[..., i] = torch.einsum('... c d, ... d -> ... c', v * (g - g_i).exp(), v_i) # B H N C
+    attn = attn * beta[..., None] # B H N C C
+
+    attn = -attn.masked_fill(mask, 0)
+
+    for i in range(1, chunk_size):
+        attn[..., i, :i] = attn[..., i, :i].clone() + (attn[..., i, :i, None].clone() * attn[..., :i, :i].clone()).sum(-2)
+    attn = (attn + torch.eye(chunk_size, dtype=torch.float, device=q.device)) * beta[..., None, :]
+
+    W = attn @ (v * g.exp()) # B H N C Dv
+    U = attn @ k # B H N C Dk
+
+    S = k.new_zeros(b, h, d_k, d_v)
+
+    if initial_state is not None:
+        S = initial_state
+    o = torch.zeros_like(v)
+    mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=q.device), diagonal=1)
+    for i in range(0, l // chunk_size):
+        q_i, u_i, v_i, g_i = q[:, :, i], U[:, :, i], v[:, :, i], g[:, :, i] # B H C Dv
+        k_new = u_i - W[:, :, i] @ S.transpose(-1, -2) # b h c dk - b h c dv @ b h dv dk
+        attn = q_i @ k_new.transpose(-1, -2) # b h c d @ b h d c -> b h c c
+        attn = attn.masked_fill(mask, 0) # b h c c
+        g_last = g_i[:, :, -1, :] # b h dv
+        o_inter = (q_i @ S) # b h c dv
+        vg_i = v_i / g_i.exp()
+        o[:, :, i] = (o_inter + (attn @ vg_i)) * g_i.exp()    # b h c dv + b h c c @ b h c dv
+        S = S * g_last[:, :, None, :].exp() # B H Dk Dv @ B H 1 D
+        S += k_new.transpose(-1, -2) @ (v_i * (g_last[:, :, None, :] - g_i).exp())
+    if not output_final_state:
+        S = None
+    # unpad
+    o = rearrange(o, 'b h n c d -> b h (n c) d')
+    o = o[:, :, :T]
+    o = o.transpose(1, 2)
+    return o, S
+
+@pytest.mark.parametrize(
+    ('B', 'T', 'H', 'D', 'scale', 'gate_logit_normalizer', 'dtype'),
+    [
+        pytest.param(*test, id="B{}-T{}-H{}-D{}-scale{}-gate_logit_normalizer{}-{}".format(*test))
+        for test in [
+            (4, 2048, 8, 128, 1, 10, torch.float),
+            (4, 1024, 4, 64, 0.1, 10, torch.float),
+            (2, 1536, 4, 128, 1, 100, torch.float16),
+            (4, 2048, 4, 256, 1, 100, torch.float16),
+        ]
+    ]
+)
+def test_naive_chunk_oja(
+    B: int,
+    T: int,
+    H: int,
+    D: int,
+    scale: float,
+    gate_logit_normalizer: float,
+    dtype: torch.dtype,
+):
+    torch.manual_seed(42)
+    q = torch.randn(B, T, H, D, dtype=torch.float32)
+    k = torch.randn(B, T, H, D, dtype=torch.float32)
+    v = torch.randn(B, T, H, D, dtype=dtype)
+    beta = torch.rand(B, T, H, dtype=dtype).sigmoid()
+    g = F.logsigmoid(torch.rand(B, T, H, D, dtype=torch.float32)) / gate_logit_normalizer
+    h0 = torch.randn(B, H, D, D, dtype=torch.float32)
+    q, k, v, beta, g, h0 = map(lambda x: x.to(device).requires_grad_(), (q, k, v, beta, g, h0))
+    ref, ref_ht = recurrent_oja_ref(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1),
+        beta=beta.clone(),
+        g=g.clone(),
+        scale=scale,
+        initial_state=h0.clone(),
+        output_final_state=True,
+    )
+    tri, tri_ht = chunk_oja_ref(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1),
+        beta=beta.clone(),
+        g=g.clone(),
+        scale=scale,
+        initial_state=h0.clone(),
+        output_final_state=True,
+    )
+    assert_close('ht', ref_ht, tri_ht, 0.002)
+    assert_close('o', ref, tri, 0.002)
+    
+
+
+@pytest.mark.parametrize(
+    ('B', 'T', 'H', 'D', 'scale', 'gate_logit_normalizer', 'dtype'),
+    [
+        pytest.param(*test, id="B{}-T{}-H{}-D{}-scale{}-gate_logit_normalizer{}-{}".format(*test))
+        for test in [
+            (1, 63, 1, 64, 1, 1, torch.float),
+            (2, 500, 4, 60, 1, 1, torch.float),
+            (2, 1000, 8, 128, 1, 0.1, torch.float),
+            (3, 1024, 4, 128, 0.1, 1, torch.float),
+            (4, 1024, 8, 128, 1, 10, torch.float),
+            (4, 2048, 8, 64, 0.1, 1, torch.float)
+        ]
+    ]
+)
+def test_fused_recurrent(
+    B: int,
+    T: int,
+    H: int,
+    D: int,
+    scale: float,
+    gate_logit_normalizer: float,
+    dtype: torch.dtype,
+):
+    torch.manual_seed(42)
+    q = torch.randn(B, T, H, D, dtype=dtype)
+    k = torch.randn(B, T, H, D, dtype=dtype)
+    v = torch.randn(B, T, H, D, dtype=torch.float32)
+    beta = torch.rand(B, T, H, dtype=dtype).sigmoid()
+    g = F.logsigmoid(torch.rand(B, T, H, D, dtype=torch.float32)) / gate_logit_normalizer
+    h0 = torch.randn(B, H, D, D, dtype=torch.float32)
+    q, k, v, beta, g, h0 = map(lambda x: x.to(device).requires_grad_(), (q, k, v, beta, g, h0))
+    ref, ref_ht = recurrent_oja_ref(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1).to(dtype),
+        beta=beta.clone(),
+        g=g.clone(),
+        scale=scale,
+        initial_state=h0.clone(),
+        output_final_state=True,
+    )
+    tri, tri_ht = fused_recurrent_gated_oja_rule(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1).to(dtype),
+        beta=beta.clone(),
+        gv=g.clone(),
+        scale=scale,
+        initial_state=h0.clone(),
+        output_final_state=True,
+    )
+    assert_close('o', ref, tri, 0.002)
+    assert_close('ht', ref_ht, tri_ht, 0.002)
+
+
+@pytest.mark.parametrize(
+    ('B', 'T', 'H', 'D', 'scale', 'gate_logit_normalizer', 'mask_p', 'dtype'),
+    [
+        pytest.param(*test, id="B{}-T{}-H{}-D{}-scale{}-gate_logit_normalizer{}-mask_p{}-{}".format(*test))
+        for test in [
+            (1, 63, 1, 64, 1, 0.01, 0, torch.float16),
+            (2, 500, 3, 60, 1, 1, 0, torch.float16),
+            (2, 1000, 3, 64, 0.1, 1, 0.5, torch.float16),
+            (3, 1024, 4, 100, 1, 0.1, 0, torch.float16), 
+            (4, 1024, 4, 128, 0.1, 1, 0, torch.float16),
+        ]
+    ]
+)
+def test_chunk_forward(
+    B: int,
+    T: int,
+    H: int,
+    D: int,
+    scale: float,
+    gate_logit_normalizer: float,
+    mask_p: float,
+    dtype: torch.dtype,
+):
+    torch.manual_seed(42)
+    q = torch.randn(B, T, H, D, dtype=dtype)
+    k = torch.randn(B, T, H, D, dtype=dtype)
+    v = torch.randn(B, T, H, D, dtype=torch.float32)
+    beta = torch.rand(B, T, H, dtype=dtype).sigmoid()
+    g = F.logsigmoid(torch.rand(B, T, H, D, dtype=torch.float32)) / gate_logit_normalizer
+    g = g * (torch.rand_like(g) > mask_p)
+    h0 = torch.randn(B, H, D, D, dtype=torch.float32)
+    q, k, v, beta, g, h0 = map(lambda x: x.to(device).requires_grad_(), (q, k, v, beta, g, h0))
+    ref, ref_ht = recurrent_oja_ref(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1).to(dtype),
+        beta=beta.clone(),
+        g=g.clone(),
+        scale=scale,
+        initial_state=h0.clone(),
+        output_final_state=True,
+    )
+    tri, tri_ht = chunk_gated_oja_rule(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1).to(dtype),
+        beta=beta.clone(),
+        gv=g.clone(),
+        scale=scale,
+        initial_state=h0.clone(),
+        output_final_state=True,
+    )
+    assert_close('o', ref, tri, 0.005)
+    assert_close('ht', ref_ht, tri_ht, 0.005)
+
+
+@pytest.mark.parametrize(
+    ('B', 'T', 'H', 'D', 'scale', 'gate_logit_normalizer', 'mask_p', 'dtype'),
+    [
+        pytest.param(
+            *test,
+            id="B{}-T{}-H{}-D{}-scale{}-gate_logit_normalizer{}-mask_p{}-{}".format(*test)
+        )
+        for test in [
+            (4, 4096, 4, 128, 1, 1, 0, torch.float16),
+            (1, 4096, 1, 64, 1, 1, 0, torch.float16),
+            (2, 4096, 3, 60, 1, 1, 0, torch.float16),
+        ]
+    ]
+)
+def test_chunk(
+    B: int,
+    T: int,
+    H: int,
+    D: int,
+    scale: float,
+    gate_logit_normalizer: float,
+    mask_p: float,
+    dtype: torch.dtype,
+):
+    torch.manual_seed(42)
+
+    q = torch.rand(B, T, H, D, dtype=dtype)
+    k = torch.rand(B, T, H, D, dtype=dtype)
+    v = torch.rand(B, T, H, D, dtype=torch.float)
+    beta = torch.rand(B, T, H, dtype=torch.float).sigmoid()
+    g = F.logsigmoid(torch.rand(B, T, H, D, dtype=torch.float)) / gate_logit_normalizer
+    g = g * (torch.rand_like(g) > mask_p)
+    h0 = torch.zeros(B, H, D, D, dtype=torch.float32)
+    q, k, v, beta, g, h0 = map(lambda x: x.to(device).requires_grad_(True), (q, k, v, beta, g, h0))
+    do = torch.randn_like(v)
+    dht = torch.randn_like(h0)
+    print('================== Running forward and backward ==================')
+
+    ref, ref_ht = recurrent_oja_ref(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1),
+        beta=beta.clone(),
+        g=g.clone(),
+        scale=scale,
+        output_final_state=True,
+        initial_state=h0.clone(),
+    )
+    
+    ((ref * do).sum() + (ref_ht * dht).sum()).backward(retain_graph=True)
+    ref_dq, ref_dk, ref_dv, ref_dbeta, ref_dg, ref_dh0 = q.grad, k.grad, v.grad, beta.grad, g.grad, h0.grad
+    q.grad = k.grad = v.grad = beta.grad = g.grad = h0.grad = None
+    
+    tri, tri_ht = chunk_gated_oja_rule(
+        q=q.clone(),
+        k=k.clone(),
+        v=F.normalize(v.clone(), p=2, dim=-1).to(dtype),
+        beta=beta.clone(),
+        gv=g.clone(),
+        scale=scale,
+        output_final_state=True,
+        initial_state=h0.clone(),
+    )
+    
+    ((tri * do).sum() + (tri_ht * dht).sum()).backward(retain_graph=True)
+    tri_dq, tri_dk, tri_dv, tri_dbeta, tri_dg, tri_dh0 = q.grad, k.grad, v.grad, beta.grad, g.grad, h0.grad
+    q.grad = k.grad = v.grad = g.grad = beta.grad = h0.grad = None
+    
+    # breakpoint()
+
+    assert_close('o', ref, tri, 0.005)
+    assert_close('ht', ref_ht, tri_ht, 0.005)
+    assert_close('dh0', ref_dh0, tri_dh0, 0.008)
+    assert_close('dq', ref_dq, tri_dq, 0.008)
+    assert_close('dk', ref_dk, tri_dk, 0.008)
+    assert_close('dv', ref_dv, tri_dv, 0.008)
+    assert_close('db', ref_dbeta, tri_dbeta, 0.02)
+    assert_close('dg', ref_dg, tri_dg, 0.005)
+    
+
+
+@pytest.mark.parametrize(
+    ('H', 'D', 'mask_p', 'cu_seqlens', 'dtype'),
+    [
+        pytest.param(*test, id="H{}-D{}-mask_p{}-cu_seqlens{}-{}".format(*test))
+        for test in [
+            (4, 60, 0, [0, 96, 177], torch.float16),
+            (16, 128, 0, [0, 256, 500, 1000], torch.float16),
+            (4, 64, 0.5, [0, 256, 500, 1000], torch.float16),
+            (4, 100, 0, [0, 15, 100, 300, 1200, 2000], torch.float16),
+        ]
+    ]
+)
+@pytest.mark.skipif(
+    os.getenv('SKIP_TEST_CHUNK_VARLEN') == '1',
+    reason='Skipping test_chunk_varlen because SKIP_TEST_CHUNK_VARLEN is set'
+)
+def test_chunk_varlen(
+    H: int,
+    D: int,
+    mask_p: float,
+    cu_seqlens: List[int],
+    dtype: torch.dtype,
+):
+    if is_intel_alchemist and D > 128:
+        pytest.skip(reason='chunk_gated_delta_rule is not supported on alchemist for D>128')
+    torch.manual_seed(42)
+    os.environ['TRITON_F32_DEFAULT'] = 'ieee'
+    # randomly split the sequence into N segments
+    cu_seqlens = torch.LongTensor(cu_seqlens).to(device)
+    T = cu_seqlens[-1]
+    N = len(cu_seqlens) - 1
+
+    # seq-first required for inputs with variable lengths
+    q = torch.randn((1, T, H, D), dtype=dtype)
+    k = torch.randn((1, T, H, D), dtype=dtype)
+    v = F.normalize(torch.randn(1, T, H, D, dtype=torch.float32), p=2, dim=-1).to(dtype)
+    g = F.logsigmoid(torch.rand(1, T, H, D, dtype=torch.float))
+    g = g * (torch.rand_like(g) > mask_p)
+    beta = torch.rand(1, T, H, dtype=torch.float32).sigmoid()
+    h0 = torch.randn((N, H, D, D), dtype=torch.float32)
+
+    q, k, v, beta, g, h0 = map(lambda x: x.to(device).requires_grad_(), (q, k, v, beta, g, h0))
+    do = torch.randn_like(v)
+    dht = torch.rand_like(h0)
+
+    tri, tri_ht = chunk_gated_oja_rule(
+        q=q.clone(),
+        k=k.clone(),
+        v=v.clone(),
+        beta=beta.clone(),
+        gv=g.clone(),
+        initial_state=h0.clone(),
+        output_final_state=True,
+        cu_seqlens=cu_seqlens,
+    )
+    ((tri * do).sum() + (tri_ht * dht).sum()).backward(retain_graph=True)
+    tri_dq, tri_dk, tri_dv, tri_dbeta, tri_dg, tri_dh0 = q.grad, k.grad, v.grad, beta.grad, g.grad, h0.grad
+    q.grad = k.grad = v.grad = beta.grad = g.grad = h0.grad = None
+
+    ref = []
+    ref_ht = []
+    for i in range(N):
+        ref_i, ref_ht_i = recurrent_oja_ref(
+            q=q[:, cu_seqlens[i]:cu_seqlens[i+1]],
+            k=k[:, cu_seqlens[i]:cu_seqlens[i+1]],
+            v=v[:, cu_seqlens[i]:cu_seqlens[i+1]],
+            beta=beta[:, cu_seqlens[i]:cu_seqlens[i+1]],
+            g=g[:, cu_seqlens[i]:cu_seqlens[i+1]],
+            initial_state=h0[i],
+            output_final_state=True,
+        )
+        ref.append(ref_i)
+        ref_ht.append(ref_ht_i)
+    ref = torch.cat(ref, 1)
+    ref_ht = torch.cat(ref_ht, 0)
+
+    ((ref * do).sum() + (ref_ht * dht).sum()).backward(retain_graph=True)
+    ref_dq, ref_dk, ref_dv, ref_dbeta, ref_dg, ref_dh0 = q.grad, k.grad, v.grad, beta.grad, g.grad, h0.grad
+
+    assert_close('o', ref, tri, 0.005)
+    assert_close('ht', ref_ht, tri_ht, 0.005)
+    assert_close('dq', ref_dq, tri_dq, 0.007)
+    assert_close('dk', ref_dk, tri_dk, 0.008)
+    assert_close('dv', ref_dv, tri_dv, 0.007)
+    assert_close('db', ref_dbeta, tri_dbeta, 0.015)
+    assert_close('dg', ref_dg, tri_dg, 0.015)
+    assert_close('dh0', ref_dh0, tri_dh0, 0.007)

From b569935b3e819e13f6358731caa9ac5c96e3167e Mon Sep 17 00:00:00 2001
From: lizhiyuan <lizhiyuan@moonshot.cn>
Date: Tue, 10 Feb 2026 03:25:55 +0000
Subject: [PATCH 3/5] fix lint

---
 fla/ops/gated_oja_rule/chunk.py           |  41 +++----
 fla/ops/gated_oja_rule/chunk_h.py         | 130 ++++++++++------------
 fla/ops/gated_oja_rule/chunk_kkt.py       |  12 +-
 fla/ops/gated_oja_rule/chunk_o.py         |  53 +++------
 fla/ops/gated_oja_rule/fused_recurrent.py |  26 ++---
 fla/ops/gated_oja_rule/wy_fast.py         |  35 +++---
 tests/ops/test_oja.py                     |  57 +++++-----
 7 files changed, 147 insertions(+), 207 deletions(-)

diff --git a/fla/ops/gated_oja_rule/chunk.py b/fla/ops/gated_oja_rule/chunk.py
index 32f3673f71..32de3251e0 100644
--- a/fla/ops/gated_oja_rule/chunk.py
+++ b/fla/ops/gated_oja_rule/chunk.py
@@ -1,27 +1,22 @@
-# # -*- coding: utf-8 -*-
 # # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
 
 import warnings
-from typing import Optional
 
 import torch
 
 from fla.modules.l2norm import l2norm_bwd, l2norm_fwd
+from fla.ops.gated_oja_rule.chunk_h import chunk_oja_bwd_dhu, chunk_oja_bwd_dvwg_h, chunk_oja_fwd_h
+from fla.ops.gated_oja_rule.chunk_kkt import chunk_scaled_dot_kkt_bwd_gk, chunk_scaled_dot_kkt_fwd
+from fla.ops.gated_oja_rule.chunk_o import (
+    chunk_oja_bwd_dA,
+    chunk_oja_bwd_dqk,
+    chunk_oja_bwd_dv_o,
+    chunk_oja_fwd_o,
+)
+from fla.ops.gated_oja_rule.wy_fast import prepare_wy_repr_bwd, recompute_w_u_fwd
 from fla.ops.utils import chunk_local_cumsum, solve_tril
 from fla.utils import autocast_custom_bwd, autocast_custom_fwd, input_guard
 
-from fla.ops.gated_oja_rule.wy_fast import prepare_wy_repr_bwd, recompute_w_u_fwd
-from fla.ops.gated_oja_rule.chunk_kkt import chunk_scaled_dot_kkt_fwd, chunk_scaled_dot_kkt_bwd_gk
-from fla.ops.gated_oja_rule.chunk_h import (
-    chunk_oja_fwd_h, 
-    chunk_oja_bwd_dhu, 
-    chunk_oja_bwd_dvwg_h)
-from fla.ops.gated_oja_rule.chunk_o import (
-    chunk_oja_fwd_o, 
-    chunk_oja_bwd_dA, 
-    chunk_oja_bwd_dqk, 
-    chunk_oja_bwd_dv_o, 
-    )
 
 def chunk_oja_fwd(
     q: torch.Tensor,
@@ -33,8 +28,8 @@ def chunk_oja_fwd(
     initial_state: torch.Tensor,
     output_final_state: bool,
     g_cumsum: bool = True,
-    cu_seqlens: Optional[torch.LongTensor] = None
-):  
+    cu_seqlens: torch.LongTensor | None = None
+):
     if g_cumsum:
         gv = chunk_local_cumsum(gv, chunk_size=64, cu_seqlens=cu_seqlens)
     A = chunk_scaled_dot_kkt_fwd(
@@ -90,9 +85,9 @@ def chunk_oja_bwd(
     initial_state: torch.Tensor,
     do: torch.Tensor,
     dht: torch.Tensor,
-    dgk: Optional[torch.Tensor] = None,
-    cu_seqlens: Optional[torch.LongTensor] = None,
-):  
+    dgk: torch.Tensor | None = None,
+    cu_seqlens: torch.LongTensor | None = None,
+):
     w, u, vg = recompute_w_u_fwd(
         k=k,
         v=v,
@@ -111,7 +106,7 @@ def chunk_oja_bwd(
         output_final_state=False,
         cu_seqlens=cu_seqlens,
     )
-    
+
     dAqk = chunk_oja_bwd_dA(
         v=v,
         gv=gv,
@@ -185,7 +180,7 @@ def chunk_oja_bwd(
         dA=dAvv,
         cu_seqlens=cu_seqlens,
     )
-    
+
     dv = dv.add_(dv1).add_(dv2)
     db = db.add_(db2)
     dgv = dgv_last.add_(chunk_local_cumsum(dgv1.add_(dgv2).add_(dgv3), chunk_size=64, reverse=True, cu_seqlens=cu_seqlens))
@@ -207,7 +202,7 @@ def forward(
         scale: float,
         initial_state: torch.Tensor,
         output_final_state: bool,
-        cu_seqlens: Optional[torch.LongTensor] = None,
+        cu_seqlens: torch.LongTensor | None = None,
         use_q_l2norm: bool = False,
         use_k_l2norm: bool = False,
     ):
@@ -277,7 +272,7 @@ def chunk_gated_oja_rule(
     output_final_state: bool = False,
     use_q_l2norm: bool = False,
     use_k_l2norm: bool = False,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     **kwargs,
 ):
     if 'head_first' in kwargs:
diff --git a/fla/ops/gated_oja_rule/chunk_h.py b/fla/ops/gated_oja_rule/chunk_h.py
index 096a492a9b..d65dbf56b6 100644
--- a/fla/ops/gated_oja_rule/chunk_h.py
+++ b/fla/ops/gated_oja_rule/chunk_h.py
@@ -1,4 +1,3 @@
-from typing import Optional, Tuple
 
 import torch
 import triton
@@ -6,8 +5,7 @@
 
 from fla.ops.utils import prepare_chunk_indices, prepare_chunk_offsets
 from fla.ops.utils.op import exp
-from fla.utils import is_nvidia_hopper, use_cuda_graph
-from fla.utils import check_shared_mem
+from fla.utils import check_shared_mem, is_nvidia_hopper, use_cuda_graph
 
 BKV_LIST = [64, 128] if check_shared_mem() else [32, 64]
 NUM_WARPS = [2, 4] if is_nvidia_hopper else [2, 4, 8, 16]
@@ -53,7 +51,7 @@ def chunk_oja_fwd_kernel_h_blockdim64(
     STORE_FINAL_STATE: tl.constexpr,
     SAVE_NEW_KEY: tl.constexpr,
     IS_VARLEN: tl.constexpr,
-):  
+):
     # (triton.cdiv(K, meta['BK']), N*H)
     i_k, i_nh = tl.program_id(0), tl.program_id(1)
     i_n, i_h = i_nh // H, i_nh % H
@@ -90,7 +88,6 @@ def chunk_oja_fwd_kernel_h_blockdim64(
         h0 = h0 + i_nh * K*V
     if STORE_FINAL_STATE:
         ht = ht + i_nh * K*V
-    BV=64
 
     # load initial state
     if USE_INITIAL_STATE:
@@ -122,7 +119,7 @@ def chunk_oja_fwd_kernel_h_blockdim64(
 
         p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))
         b_w = tl.load(p_w, boundary_check=(0, 1))
-        b_k = tl.dot(b_w, tl.trans(b_h1).to(b_w.dtype)) # BT BK
+        b_k = tl.dot(b_w, tl.trans(b_h1).to(b_w.dtype))  # BT BK
         if V > 64:
             p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
             b_w = tl.load(p_w, boundary_check=(0, 1))
@@ -162,10 +159,10 @@ def chunk_oja_fwd_kernel_h_blockdim64(
                 b_gk_last4 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v4, mask=(o_v4 < K), other=0.)
                 b_h4 *= exp(b_gk_last4)[None, :]
 
-        b_k = b_k.to(v.dtype.element_ty) # BT BK
+        b_k = b_k.to(v.dtype.element_ty)  # BT BK
 
         p_v = tl.make_block_ptr(v, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))
-        b_v = tl.load(p_v, boundary_check=(0, 1)) # BT BV
+        b_v = tl.load(p_v, boundary_check=(0, 1))  # BT BV
         b_h1 += tl.dot(tl.trans(b_k), b_v)
         if V > 64:
             p_v = tl.make_block_ptr(v, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
@@ -198,13 +195,13 @@ def chunk_oja_fwd_h(
     v: torch.Tensor,
     w: torch.Tensor,
     u: torch.Tensor,
-    gv: Optional[torch.Tensor] = None,
-    initial_state: Optional[torch.Tensor] = None,
+    gv: torch.Tensor | None = None,
+    initial_state: torch.Tensor | None = None,
     output_final_state: bool = False,
     chunk_size: int = 64,  # SY: remove this argument and force chunk size 64?
     save_new_key: bool = True,
-    cu_seqlens: Optional[torch.LongTensor] = None,
-) -> Tuple[torch.Tensor, torch.Tensor]:
+    cu_seqlens: torch.LongTensor | None = None,
+) -> tuple[torch.Tensor, torch.Tensor]:
     B, T, H, V, K = *v.shape, u.shape[-1]
     BT = chunk_size
 
@@ -241,9 +238,6 @@ def grid(meta): return (triton.cdiv(K, meta['BK']), N*H)
     return h, k_new, final_state
 
 
-
-
-
 @triton.heuristics({
     'USE_GV': lambda args: args['gv'] is not None,
     'USE_INITIAL_STATE': lambda args: args['dh0'] is not None,
@@ -327,7 +321,7 @@ def chunk_oja_bwd_kernel_dhu_blockdim64(
         dht += i_nh * K*V
 
     if USE_FINAL_STATE_GRADIENT:
-        p_dht1 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0)) # [BK, BV]
+        p_dht1 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 0), (BK, 64), (1, 0))  # [BK, BV]
         b_dh1 += tl.load(p_dht1, boundary_check=(0, 1))
         if V > 64:
             p_dht2 = tl.make_block_ptr(dht, (K, V), (V, 1), (i_k * BK, 64), (BK, 64), (1, 0))
@@ -355,17 +349,17 @@ def chunk_oja_bwd_kernel_dhu_blockdim64(
         last_idx = min((i_t + 1) * BT, T) - 1
 
         # Update dk_new, 按K切分
-        p_dk = tl.make_block_ptr(dk, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) # [BT, BK]
-        p_dk2 = tl.make_block_ptr(dk2, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) # [BT, BK]
+        p_dk = tl.make_block_ptr(dk, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))  # [BT, BK]
+        p_dk2 = tl.make_block_ptr(dk2, (T, K), (stride_k, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))  # [BT, BK]
 
         if V > 0:
             p_v = tl.make_block_ptr(vg, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))
-            b_v = tl.load(p_v, boundary_check=(0, 1)) # [BT, BV]
-            b_dk = tl.dot(b_v, tl.trans(b_dh1).to(b_v.dtype)) # [BT, BV] @ [BV, BK] -> [BT, BK]
+            b_v = tl.load(p_v, boundary_check=(0, 1))  # [BT, BV]
+            b_dk = tl.dot(b_v, tl.trans(b_dh1).to(b_v.dtype))  # [BT, BV] @ [BV, BK] -> [BT, BK]
 
         if V > 64:
             p_v = tl.make_block_ptr(vg, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
-            b_v = tl.load(p_v, boundary_check=(0, 1))   
+            b_v = tl.load(p_v, boundary_check=(0, 1))
             b_dk += tl.dot(b_v, tl.trans(b_dh2).to(b_v.dtype))
 
         if V > 128:
@@ -381,33 +375,33 @@ def chunk_oja_bwd_kernel_dhu_blockdim64(
         b_dk += tl.load(p_dk, boundary_check=(0, 1))
 
         tl.store(p_dk2, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
-        
-        
+
         # Update dh, 按照K切分，收集所有V维度，q一次就好，wdo要收集所有
-        
-        p_q = tl.make_block_ptr(q, (K, T), (1, stride_k), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) # [BK, BT]
-        b_q = tl.load(p_q, boundary_check=(0, 1))   
-        
+
+        p_q = tl.make_block_ptr(q, (K, T), (1, stride_k), (i_k * BK, i_t * BT), (BK, BT), (0, 1))  # [BK, BT]
+        b_q = tl.load(p_q, boundary_check=(0, 1))
+
         if V > 0:
-            p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0)) # [BT, BV]
+            p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))  # [BT, BV]
             b_do = tl.load(p_do, boundary_check=(0, 1))
-            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0)) # [BT, BV]
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))  # [BT, BV]
             b_w = tl.load(p_w, boundary_check=(0, 1))
-            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0)) # [BT, BV]
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 0), (BT, 64), (1, 0))  # [BT, BV]
             b_gv = tl.load(p_gv, boundary_check=(0, 1))
             if USE_GV:
                 o_v1 = tl.arange(0, 64)
                 b_gv_last1 = tl.load(gv + last_idx * H*V + o_v1, mask=(o_v1 < V), other=0.)
                 b_dh1 *= exp(b_gv_last1[None, :])
                 b_do *= exp(b_gv)
-            b_dh1 += tl.dot(b_q.to(b_q.dtype), b_do.to(b_q.dtype)) * scale - tl.dot(tl.trans(b_dk).to(b_w.dtype), b_w) # [BK, BT] @ [BT, BV] - [BK, BT] @ [BT, BV]
+            b_dh1 += tl.dot(b_q.to(b_q.dtype), b_do.to(b_q.dtype)) * scale - \
+                tl.dot(tl.trans(b_dk).to(b_w.dtype), b_w)  # [BK, BT] @ [BT, BV] - [BK, BT] @ [BT, BV]
 
         if V > 64:
             p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))
             b_do = tl.load(p_do, boundary_check=(0, 1))
-            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0)) # [BT, BV]
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))  # [BT, BV]
             b_w = tl.load(p_w, boundary_check=(0, 1))
-            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0)) # [BT, BV]
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 64), (BT, 64), (1, 0))  # [BT, BV]
             b_gv = tl.load(p_gv, boundary_check=(0, 1))
             if USE_GV:
                 o_v2 = 64 + o_v1
@@ -419,9 +413,9 @@ def chunk_oja_bwd_kernel_dhu_blockdim64(
         if V > 128:
             p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))
             b_do = tl.load(p_do, boundary_check=(0, 1))
-            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0)) # [BT, BV]
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))  # [BT, BV]
             b_w = tl.load(p_w, boundary_check=(0, 1))
-            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0)) # [BT, BV]
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 128), (BT, 64), (1, 0))  # [BT, BV]
             b_gv = tl.load(p_gv, boundary_check=(0, 1))
             if USE_GV:
                 o_v3 = 128 + o_v1
@@ -433,9 +427,9 @@ def chunk_oja_bwd_kernel_dhu_blockdim64(
         if V > 192:
             p_do = tl.make_block_ptr(do, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))
             b_do = tl.load(p_do, boundary_check=(0, 1))
-            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0)) # [BT, BV]
+            p_w = tl.make_block_ptr(w, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))  # [BT, BV]
             b_w = tl.load(p_w, boundary_check=(0, 1))
-            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0)) # [BT, BV]
+            p_gv = tl.make_block_ptr(gv, (T, V), (stride_v, 1), (i_t * BT, 192), (BT, 64), (1, 0))  # [BT, BV]
             b_gv = tl.load(p_gv, boundary_check=(0, 1))
             if USE_GV:
                 o_v4 = 192 + o_v1
@@ -456,7 +450,7 @@ def chunk_oja_bwd_kernel_dhu_blockdim64(
         if V > 192:
             p_dh3 = tl.make_block_ptr(dh0, (K, V), (V, 1), (i_k * BK, 192), (BK, 64), (1, 0))
             tl.store(p_dh3, b_dh4.to(p_dh3.dtype.element_ty), boundary_check=(0, 1))
-        
+
 
 def chunk_oja_bwd_dhu(
     q: torch.Tensor,
@@ -464,14 +458,14 @@ def chunk_oja_bwd_dhu(
     w: torch.Tensor,
     do: torch.Tensor,
     dk: torch.Tensor,
-    gv: Optional[torch.Tensor] = None,
-    h0: Optional[torch.Tensor] = None,
-    dht: Optional[torch.Tensor] = None,
-    scale: Optional[float] = None,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    gv: torch.Tensor | None = None,
+    h0: torch.Tensor | None = None,
+    dht: torch.Tensor | None = None,
+    scale: float | None = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64,  # SY: remove this argument and force chunk size 64?
     states_in_fp32: bool = False
-) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
     B, T, H, K, V = *q.shape, do.shape[-1]
     # N: the actual number of sequences in the batch with either equal or variable lengths
     BT = 64
@@ -511,11 +505,6 @@ def grid(meta): return (triton.cdiv(K, meta['BK']), N*H)
     return dh, dh0, dk2
 
 
-
-
-
-
-
 @triton.heuristics({
     'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
 })
@@ -648,13 +637,8 @@ def chunk_gsa_bwd_k_kernel_dqkvg(
 
     tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
     tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
-    
-    
 
-    
-    
-    
-    
+
 @triton.heuristics({
     'USE_GV': lambda args: args['gv'] is not None,
     'HAVE_GK': lambda args: args['dgk'] is not None,
@@ -729,46 +713,44 @@ def chunk_oja_bwd_kernel_dvwg_h(
         p_gv = tl.make_block_ptr(gv, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
         b_gn = tl.load(p_gn, mask=m_v, other=0)
         b_gv = tl.load(p_gv, boundary_check=(0, 1))
-        
+
     for i_k in range(tl.cdiv(K, BK)):
         p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
         p_dk = tl.make_block_ptr(dk, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
         p_h = tl.make_block_ptr(h, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
         p_dh = tl.make_block_ptr(dh, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
-        b_k = tl.load(p_k, boundary_check=(0, 1)) # BT BK
-        b_dk = tl.load(p_dk, boundary_check=(0, 1)) # BT BK
-        b_h = tl.load(p_h, boundary_check=(0, 1)) # BK BV
-        b_dh = tl.load(p_dh, boundary_check=(0, 1)) # BK BV
+        b_k = tl.load(p_k, boundary_check=(0, 1))  # BT BK
+        b_dk = tl.load(p_dk, boundary_check=(0, 1))  # BT BK
+        b_h = tl.load(p_h, boundary_check=(0, 1))  # BK BV
+        b_dh = tl.load(p_dh, boundary_check=(0, 1))  # BK BV
 
-        b_dvg += tl.dot(b_k, b_dh.to(b_k.dtype)) # BT BK @ BK BV -> BT BV
-        b_dw += tl.dot(b_dk.to(b_k.dtype), b_h.to(b_k.dtype)) # BT BK @ BK BV -> BT BV
+        b_dvg += tl.dot(b_k, b_dh.to(b_k.dtype))  # BT BK @ BK BV -> BT BV
+        b_dw += tl.dot(b_dk.to(b_k.dtype), b_h.to(b_k.dtype))  # BT BK @ BK BV -> BT BV
         b_dgv_last += tl.sum((b_h * b_dh) * exp(b_gn), axis=0)
 
     if USE_GV:
         b_dv = b_dvg * exp(b_gn[None, :] - b_gv)
-    
+
     p_v = tl.make_block_ptr(v, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
     p_dv = tl.make_block_ptr(dv, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
     p_dw = tl.make_block_ptr(dw, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
     p_dgv_last = tl.make_block_ptr(dgv_last, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
     b_v = tl.load(p_v, boundary_check=(0, 1))
-    
+
     b_dgv_last += tl.sum(b_dv * b_v, axis=0)
-    
+
     # 留给GSA2的接口
     if HAVE_GK:
         dgk += (bos * H + i_h) * V
         p_dgk = tl.make_block_ptr(dgk, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
         b_dgk = tl.load(p_dgk, boundary_check=(0, 1))
         b_dgv_last = b_dgk + b_dgv_last[None, :]
-    else:   
+    else:
         b_dgv_last = tl.zeros([BT, BV], dtype=tl.float32) + b_dgv_last[None, :]
-    
+
     tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
     tl.store(p_dw, -b_dw.to(p_dw.dtype.element_ty), boundary_check=(0, 1))
     tl.store(p_dgv_last, b_dgv_last.to(p_dgv_last.dtype.element_ty), boundary_check=(0, 1))
-    
-      
 
 
 def chunk_oja_bwd_dvwg_h(
@@ -777,11 +759,11 @@ def chunk_oja_bwd_dvwg_h(
     h: torch.Tensor,
     dh: torch.Tensor,
     dk: torch.Tensor,
-    gv: Optional[torch.Tensor] = None,
-    dgk: Optional[torch.Tensor] = None,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    gv: torch.Tensor | None = None,
+    dgk: torch.Tensor | None = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64,
-) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
 
     B, T, H, K, V = *k.shape, v.shape[-1]
     BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
@@ -818,4 +800,4 @@ def chunk_oja_bwd_dvwg_h(
         BK=BK,
         BV=BV,
     )
-    return dv, dw, dgv_last
\ No newline at end of file
+    return dv, dw, dgv_last
diff --git a/fla/ops/gated_oja_rule/chunk_kkt.py b/fla/ops/gated_oja_rule/chunk_kkt.py
index 8ff0a21d96..d9f1f14deb 100644
--- a/fla/ops/gated_oja_rule/chunk_kkt.py
+++ b/fla/ops/gated_oja_rule/chunk_kkt.py
@@ -1,7 +1,5 @@
-# -*- coding: utf-8 -*-
 # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
 
-from typing import Optional
 
 import torch
 import triton
@@ -383,10 +381,10 @@ def chunk_scaled_dot_kkt_bwd_kernel_gk(
 
 def chunk_scaled_dot_kkt_fwd(
     k: torch.Tensor,
-    g: Optional[torch.Tensor] = None,
-    gk: Optional[torch.Tensor] = None,
-    beta: Optional[torch.Tensor] = None,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    g: torch.Tensor | None = None,
+    gk: torch.Tensor | None = None,
+    beta: torch.Tensor | None = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64,
     output_dtype: torch.dtype = torch.float32
 ) -> torch.Tensor:
@@ -476,7 +474,7 @@ def chunk_scaled_dot_kkt_bwd_gk(
     g: torch.Tensor,
     beta: torch.Tensor,
     dA: torch.Tensor,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64
 ):
     B, T, H, K = k.shape
diff --git a/fla/ops/gated_oja_rule/chunk_o.py b/fla/ops/gated_oja_rule/chunk_o.py
index 791ec178ea..2c6ff015d0 100644
--- a/fla/ops/gated_oja_rule/chunk_o.py
+++ b/fla/ops/gated_oja_rule/chunk_o.py
@@ -1,4 +1,3 @@
-from typing import Optional, Tuple
 
 import torch
 import triton
@@ -7,12 +6,10 @@
 from fla.ops.utils import prepare_chunk_indices
 from fla.ops.utils.op import exp
 from fla.utils import check_shared_mem, is_nvidia_hopper
-from fla.ops.utils.cumsum import chunk_local_cumsum
 
 BKV_LIST = [64, 128] if check_shared_mem() else [32, 64]
 NUM_WARPS = [2, 4] if is_nvidia_hopper else [2, 4, 8]
 
-exp = tl.exp
 
 @triton.heuristics({
     'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
@@ -98,7 +95,6 @@ def chunk_oja_fwd_inter(
         tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
 
 
-
 @triton.heuristics({
     'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
 })
@@ -177,10 +173,8 @@ def chunk_oja_fwd_intra(
     p_o = tl.make_block_ptr(o + (bos*HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
     b_o += tl.load(p_o, boundary_check=(0, 1))
     tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
-    
-    
-    
-    
+
+
 def chunk_oja_fwd_o(
     q: torch.Tensor,
     k: torch.Tensor,
@@ -188,9 +182,9 @@ def chunk_oja_fwd_o(
     gv: torch.Tensor,
     h: torch.Tensor,
     scale: float = 1.,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64
-) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
     B, T, H, K, V = *k.shape, v.shape[-1]
     BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
     BC = min(16, BT)
@@ -247,9 +241,6 @@ def grid(meta): return (triton.cdiv(V, meta['BV']), NT * NC, B * HQ)
     return A, o
 
 
-
-
-
 @triton.heuristics({
     'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
 })
@@ -341,12 +332,9 @@ def chunk_oja_bwd_kernel_dA(
             p_v += H*V
             p_gv += H*V
         b_dA = tl.where(m_dA, b_dA, 0.)
-        
+
     p_dA = tl.make_block_ptr(dA+((i_v*all+bos)*H+i_h)*BT, (T, BT), (H*BT, 1), (i_t*BT+i_i*BC, i_j*BC), (BC, BC), (1, 0))
     tl.store(p_dA, b_dA.to(dA.dtype.element_ty), boundary_check=(0, 1))
-    
-    
-
 
 
 def chunk_oja_bwd_dA(
@@ -354,7 +342,7 @@ def chunk_oja_bwd_dA(
     gv: torch.Tensor,
     do: torch.Tensor,
     scale: float = 1.,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64
 ):
     B, T, H, V = v.shape
@@ -392,10 +380,6 @@ def chunk_oja_bwd_dA(
     return dA
 
 
-
-
-
-
 @triton.heuristics({
     'IS_VARLEN': lambda args: args['cu_seqlens'] is not None
 })
@@ -448,20 +432,20 @@ def chunk_oja_bwd_kernel_dqk(
 
     o_i = tl.arange(0, BT)
     m_s = o_i[:, None] >= o_i[None, :]
-    
+
     # [B, T, H, BT]
     p_q = tl.make_block_ptr(q + (bos*H+i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
     p_k = tl.make_block_ptr(k + (bos*H+i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
     p_A = tl.make_block_ptr(A + ((i_k*all+bos)*H+i_h)*BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
     b_q = tl.load(p_q, boundary_check=(0, 1))
     b_k = tl.load(p_k, boundary_check=(0, 1))
-    
+
     b_A = tl.dot((b_q * scale).to(b_q.dtype), tl.trans(b_k))
     b_A = tl.where(m_s, b_A, 0.)
     tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
 
     b_dq = tl.zeros([BT, BK], dtype=tl.float32)
-    
+
     # 先计算do对应的dq
     for i_v in range(tl.cdiv(V, BV)):
         p_h = tl.make_block_ptr(h + (i_tg * H + i_h) * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
@@ -472,7 +456,7 @@ def chunk_oja_bwd_kernel_dqk(
         b_gv = tl.load(p_gv, boundary_check=(0, 1))
         b_do = (b_do * exp(b_gv) * scale).to(b_do.dtype)
         b_dq += tl.dot(b_do, b_h.to(b_do.dtype))
-        
+
     # 接着计算dA对应的dq, dk
     p_dA = tl.make_block_ptr(dA + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
     p_dq = tl.make_block_ptr(dq + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
@@ -485,9 +469,7 @@ def chunk_oja_bwd_kernel_dqk(
 
     tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
     tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
-    
-    
-    
+
 
 def chunk_oja_bwd_dqk(
     q: torch.Tensor,
@@ -497,7 +479,7 @@ def chunk_oja_bwd_dqk(
     dA: torch.Tensor,
     do: torch.Tensor,
     scale: float = 1.,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64
 ):
     B, T, H, K, V = *q.shape, gv.shape[-1]
@@ -538,11 +520,8 @@ def chunk_oja_bwd_dqk(
     )
 
     A = A.sum(0, dtype=A.dtype)
-    
-    return A, dq, dk
-
-
 
+    return A, dq, dk
 
 
 @triton.heuristics({
@@ -640,8 +619,6 @@ def chunk_oja_bwd_kernel_dv_o(
     tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1))
 
 
-
-
 def chunk_oja_bwd_dv_o(
     v: torch.Tensor,
     gv: torch.Tensor,
@@ -649,7 +626,7 @@ def chunk_oja_bwd_dv_o(
     A: torch.Tensor,
     dv: torch.Tensor,
     do: torch.Tensor,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64
 ):
     B, T, H, V = v.shape
@@ -687,5 +664,3 @@ def grid(meta): return (triton.cdiv(V, meta['BV']), NT * NC, B * H)
         num_stages=2
     )
     return dv2, dgv
-
-
diff --git a/fla/ops/gated_oja_rule/fused_recurrent.py b/fla/ops/gated_oja_rule/fused_recurrent.py
index 4da96020b4..13d24f26d9 100644
--- a/fla/ops/gated_oja_rule/fused_recurrent.py
+++ b/fla/ops/gated_oja_rule/fused_recurrent.py
@@ -1,7 +1,5 @@
-# -*- coding: utf-8 -*-
 # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
 
-from typing import Optional, Tuple
 
 import torch
 import triton
@@ -95,7 +93,7 @@ def fused_recurrent_oja_fwd_kernel(
         if USE_GV:
             b_gv = tl.load(p_gv).to(tl.float32)
             b_h *= exp(b_gv[None, :])
-        
+
         b_k = b_beta * (b_k - tl.sum(b_h * b_v[None, :], 1))
         b_h += b_k[:, None] * b_v
 
@@ -120,15 +118,15 @@ def fused_recurrent_oja_fwd(
     q: torch.Tensor,
     k: torch.Tensor,
     v: torch.Tensor,
-    gv: Optional[torch.Tensor] = None,
-    beta: Optional[torch.Tensor] = None,
+    gv: torch.Tensor | None = None,
+    beta: torch.Tensor | None = None,
     scale: float = None,
     initial_state: torch.Tensor = None,
     output_final_state: bool = False,
     use_q_l2norm: bool = False,
     use_k_l2norm: bool = False,
-    cu_seqlens: Optional[torch.LongTensor] = None,
-) -> Tuple[torch.Tensor, torch.Tensor]:
+    cu_seqlens: torch.LongTensor | None = None,
+) -> tuple[torch.Tensor, torch.Tensor]:
     B, T, H, K, V = *k.shape, v.shape[-1]
     assert V <= 128
     HV = v.shape[2]
@@ -179,14 +177,14 @@ def forward(
         q: torch.Tensor,
         k: torch.Tensor,
         v: torch.Tensor,
-        gv: Optional[torch.Tensor] = None,
-        beta: Optional[torch.Tensor] = None,
+        gv: torch.Tensor | None = None,
+        beta: torch.Tensor | None = None,
         scale: float = None,
         initial_state: torch.Tensor = None,
         output_final_state: bool = False,
         use_q_l2norm: bool = False,
         use_k_l2norm: bool = False,
-        cu_seqlens: Optional[torch.LongTensor] = None,
+        cu_seqlens: torch.LongTensor | None = None,
     ):
         o, final_state = fused_recurrent_oja_fwd(
             q=q,
@@ -218,16 +216,16 @@ def fused_recurrent_gated_oja_rule(
     q: torch.Tensor,
     k: torch.Tensor,
     v: torch.Tensor,
-    gv: Optional[torch.Tensor] = None,
-    beta: Optional[torch.Tensor] = None,
+    gv: torch.Tensor | None = None,
+    beta: torch.Tensor | None = None,
     scale: float = None,
     initial_state: torch.Tensor = None,
     output_final_state: bool = False,
     use_q_l2norm: bool = False,
     use_k_l2norm: bool = False,
-    cu_seqlens: Optional[torch.LongTensor] = None,
+    cu_seqlens: torch.LongTensor | None = None,
     **kwargs,
-) -> Tuple[torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor]:
 
     if 'use_qk_l2norm_in_kernel' in kwargs and (not use_q_l2norm and not use_k_l2norm):
         use_q_l2norm = True
diff --git a/fla/ops/gated_oja_rule/wy_fast.py b/fla/ops/gated_oja_rule/wy_fast.py
index 7fdd5d994c..0067e97a5e 100644
--- a/fla/ops/gated_oja_rule/wy_fast.py
+++ b/fla/ops/gated_oja_rule/wy_fast.py
@@ -1,14 +1,11 @@
-# -*- coding: utf-8 -*-
 # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
 
-from typing import Optional, Tuple
 
 import torch
 import triton
 import triton.language as tl
 
-
-from fla.ops.utils import chunk_local_cumsum, prepare_chunk_indices
+from fla.ops.utils import prepare_chunk_indices
 from fla.ops.utils.op import exp
 from fla.utils import check_shared_mem
 
@@ -60,7 +57,7 @@ def recompute_w_u_fwd_kernel(
 
     p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
     b_A = tl.load(p_A, boundary_check=(0, 1))
-    
+
     for i_v in range(tl.cdiv(V, BV)):
         p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
         p_w = tl.make_block_ptr(w + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
@@ -162,21 +159,21 @@ def prepare_wy_repr_bwd_kernel(
         b_dv = b_dvbg * b_gv_exp * b_b[:, None]
         b_db += tl.sum(b_dvbg * b_v * b_gv_exp, 1)
         b_dgv = b_dvbg * b_vbg
-        
+
         p_dgv = tl.make_block_ptr(dgv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
         tl.store(p_dgv, b_dgv.to(p_dgv.dtype.element_ty), boundary_check=(0, 1))
         tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
-        
+
     for i_k in range(tl.cdiv(K, BK)):
         p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
         p_dk = tl.make_block_ptr(dk + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
         p_du = tl.make_block_ptr(du + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
         # [BT, BK]
         b_k = tl.load(p_k, boundary_check=(0, 1))
-        b_kb = (b_k * b_b[:, None]).to(b_k.dtype) # BT BK
-        b_du = tl.load(p_du, boundary_check=(0, 1)) # BT BK
-        b_dA += tl.dot(b_du, tl.trans(b_kb)) # BT BT
-        b_dkb = tl.dot(b_A, b_du) # BT BK
+        b_kb = (b_k * b_b[:, None]).to(b_k.dtype)  # BT BK
+        b_du = tl.load(p_du, boundary_check=(0, 1))  # BT BK
+        b_dA += tl.dot(b_du, tl.trans(b_kb))  # BT BT
+        b_dkb = tl.dot(b_A, b_du)  # BT BK
         b_dk = b_dkb * b_b[:, None]
         b_db += tl.sum(b_dkb * b_k, 1)
         tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
@@ -189,7 +186,7 @@ def prepare_wy_repr_bwd_kernel(
     b_dA = tl.dot(b_A, b_dA.to(b_A.dtype))
 
     b_dA = tl.where(m_A, -b_dA, 0)
-    
+
     # if USE_GV:
     p_dA = tl.make_block_ptr(dA + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
     tl.store(p_dA, b_dA.to(p_dA.dtype.element_ty), boundary_check=(0, 1))
@@ -201,9 +198,9 @@ def recompute_w_u_fwd(
     v: torch.Tensor,
     beta: torch.Tensor,
     A: torch.Tensor,
-    gv: Optional[torch.Tensor] = None,
-    cu_seqlens: Optional[torch.LongTensor] = None,
-) -> Tuple[torch.Tensor, torch.Tensor]:
+    gv: torch.Tensor | None = None,
+    cu_seqlens: torch.LongTensor | None = None,
+) -> tuple[torch.Tensor, torch.Tensor]:
     B, T, H, K, V = *k.shape, v.shape[-1]
     BT = A.shape[-1]
     BK = 64
@@ -245,8 +242,8 @@ def prepare_wy_repr_bwd(
     dw: torch.Tensor,
     du: torch.Tensor,
     gv: torch.Tensor = None,
-    cu_seqlens: Optional[torch.LongTensor] = None,
-) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+    cu_seqlens: torch.LongTensor | None = None,
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
     B, T, H, K, V = *k.shape, v.shape[-1]
     BT = 64
     chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
@@ -261,7 +258,7 @@ def prepare_wy_repr_bwd(
     dgv = torch.empty_like(gv, dtype=torch.float)
     dA = torch.empty_like(A, dtype=torch.float)
     db = torch.empty_like(beta, dtype=torch.float)
-        
+
     prepare_wy_repr_bwd_kernel[(NT, B * H)](
         k=k,
         v=v,
@@ -285,5 +282,5 @@ def prepare_wy_repr_bwd(
         BK=BK,
         BV=BV,
     )
-    
+
     return dk, dv, db, dgv, dA
diff --git a/tests/ops/test_oja.py b/tests/ops/test_oja.py
index 65808e9f12..8ae564d265 100644
--- a/tests/ops/test_oja.py
+++ b/tests/ops/test_oja.py
@@ -1,19 +1,15 @@
-# -*- coding: utf-8 -*-
 
 import os
-from typing import List, Optional
 
 import pytest
 import torch
 import torch.nn.functional as F
-from einops import rearrange, repeat
+from einops import rearrange
 
-from fla.ops.gated_oja_rule import fused_recurrent_gated_oja_rule
-from fla.ops.gated_oja_rule import chunk_gated_oja_rule
+from fla.ops.gated_oja_rule import chunk_gated_oja_rule, fused_recurrent_gated_oja_rule
 from fla.utils import assert_close, device, is_intel_alchemist
 
 
-
 def recurrent_oja_ref(
     q: torch.Tensor,
     k: torch.Tensor,
@@ -36,7 +32,7 @@ def recurrent_oja_ref(
     for i in range(T):
         b_q = q[:, :, i]
         b_k = k[:, :, i]
-        b_v = v[:, :, i] # B H D
+        b_v = v[:, :, i]  # B H D
         g_i = g[:, :, i]
         # breakpoint()
         h = h * g_i.exp()[:, :, None, :]
@@ -81,7 +77,7 @@ def chunk_oja_ref(
     chunk_size = BT
     b, h, l, d_k = q.shape
     d_v = v.shape[-1]
-    q = q * scale # B H T D
+    q = q * scale  # B H T D
     assert l % chunk_size == 0
     # note that diagonal is masked.
     mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=q.device), diagonal=0)
@@ -89,19 +85,19 @@ def chunk_oja_ref(
         lambda x: rearrange(x, 'b h (n c) ... -> b h n c ...', c=chunk_size),
         [q, k, v, beta, g]
     )
-    g = g.cumsum(-2) # b h n c d
+    g = g.cumsum(-2)  # b h n c d
 
     """
     vector decay for attention
     qkvg (B H N C D)
     """
-    attn = torch.zeros(*q.shape[:-1], chunk_size, dtype=torch.float, device=q.device) # B H N C C
+    attn = torch.zeros(*q.shape[:-1], chunk_size, dtype=torch.float, device=q.device)  # B H N C C
     # attn = -((v_beta @ v.transpose(-1, -2))* L_mask).masked_fill(mask, 0) # B H N C C
     for i in range(BT):
-        v_i = v[..., i, :] # B H N D
-        g_i = g[..., i:i+1, :] # B H N 1 Dv
-        attn[..., i] = torch.einsum('... c d, ... d -> ... c', v * (g - g_i).exp(), v_i) # B H N C
-    attn = attn * beta[..., None] # B H N C C
+        v_i = v[..., i, :]  # B H N D
+        g_i = g[..., i:i+1, :]  # B H N 1 Dv
+        attn[..., i] = torch.einsum('... c d, ... d -> ... c', v * (g - g_i).exp(), v_i)  # B H N C
+    attn = attn * beta[..., None]  # B H N C C
 
     attn = -attn.masked_fill(mask, 0)
 
@@ -109,8 +105,8 @@ def chunk_oja_ref(
         attn[..., i, :i] = attn[..., i, :i].clone() + (attn[..., i, :i, None].clone() * attn[..., :i, :i].clone()).sum(-2)
     attn = (attn + torch.eye(chunk_size, dtype=torch.float, device=q.device)) * beta[..., None, :]
 
-    W = attn @ (v * g.exp()) # B H N C Dv
-    U = attn @ k # B H N C Dk
+    W = attn @ (v * g.exp())  # B H N C Dv
+    U = attn @ k  # B H N C Dk
 
     S = k.new_zeros(b, h, d_k, d_v)
 
@@ -119,15 +115,15 @@ def chunk_oja_ref(
     o = torch.zeros_like(v)
     mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=q.device), diagonal=1)
     for i in range(0, l // chunk_size):
-        q_i, u_i, v_i, g_i = q[:, :, i], U[:, :, i], v[:, :, i], g[:, :, i] # B H C Dv
-        k_new = u_i - W[:, :, i] @ S.transpose(-1, -2) # b h c dk - b h c dv @ b h dv dk
-        attn = q_i @ k_new.transpose(-1, -2) # b h c d @ b h d c -> b h c c
-        attn = attn.masked_fill(mask, 0) # b h c c
-        g_last = g_i[:, :, -1, :] # b h dv
-        o_inter = (q_i @ S) # b h c dv
+        q_i, u_i, v_i, g_i = q[:, :, i], U[:, :, i], v[:, :, i], g[:, :, i]  # B H C Dv
+        k_new = u_i - W[:, :, i] @ S.transpose(-1, -2)  # b h c dk - b h c dv @ b h dv dk
+        attn = q_i @ k_new.transpose(-1, -2)  # b h c d @ b h d c -> b h c c
+        attn = attn.masked_fill(mask, 0)  # b h c c
+        g_last = g_i[:, :, -1, :]  # b h dv
+        o_inter = (q_i @ S)  # b h c dv
         vg_i = v_i / g_i.exp()
         o[:, :, i] = (o_inter + (attn @ vg_i)) * g_i.exp()    # b h c dv + b h c c @ b h c dv
-        S = S * g_last[:, :, None, :].exp() # B H Dk Dv @ B H 1 D
+        S = S * g_last[:, :, None, :].exp()  # B H Dk Dv @ B H 1 D
         S += k_new.transpose(-1, -2) @ (v_i * (g_last[:, :, None, :] - g_i).exp())
     if not output_final_state:
         S = None
@@ -137,6 +133,7 @@ def chunk_oja_ref(
     o = o.transpose(1, 2)
     return o, S
 
+
 @pytest.mark.parametrize(
     ('B', 'T', 'H', 'D', 'scale', 'gate_logit_normalizer', 'dtype'),
     [
@@ -188,7 +185,6 @@ def test_naive_chunk_oja(
     )
     assert_close('ht', ref_ht, tri_ht, 0.002)
     assert_close('o', ref, tri, 0.002)
-    
 
 
 @pytest.mark.parametrize(
@@ -254,7 +250,7 @@ def test_fused_recurrent(
             (1, 63, 1, 64, 1, 0.01, 0, torch.float16),
             (2, 500, 3, 60, 1, 1, 0, torch.float16),
             (2, 1000, 3, 64, 0.1, 1, 0.5, torch.float16),
-            (3, 1024, 4, 100, 1, 0.1, 0, torch.float16), 
+            (3, 1024, 4, 100, 1, 0.1, 0, torch.float16),
             (4, 1024, 4, 128, 0.1, 1, 0, torch.float16),
         ]
     ]
@@ -350,11 +346,11 @@ def test_chunk(
         output_final_state=True,
         initial_state=h0.clone(),
     )
-    
+
     ((ref * do).sum() + (ref_ht * dht).sum()).backward(retain_graph=True)
     ref_dq, ref_dk, ref_dv, ref_dbeta, ref_dg, ref_dh0 = q.grad, k.grad, v.grad, beta.grad, g.grad, h0.grad
     q.grad = k.grad = v.grad = beta.grad = g.grad = h0.grad = None
-    
+
     tri, tri_ht = chunk_gated_oja_rule(
         q=q.clone(),
         k=k.clone(),
@@ -365,11 +361,11 @@ def test_chunk(
         output_final_state=True,
         initial_state=h0.clone(),
     )
-    
+
     ((tri * do).sum() + (tri_ht * dht).sum()).backward(retain_graph=True)
     tri_dq, tri_dk, tri_dv, tri_dbeta, tri_dg, tri_dh0 = q.grad, k.grad, v.grad, beta.grad, g.grad, h0.grad
     q.grad = k.grad = v.grad = g.grad = beta.grad = h0.grad = None
-    
+
     # breakpoint()
 
     assert_close('o', ref, tri, 0.005)
@@ -380,7 +376,6 @@ def test_chunk(
     assert_close('dv', ref_dv, tri_dv, 0.008)
     assert_close('db', ref_dbeta, tri_dbeta, 0.02)
     assert_close('dg', ref_dg, tri_dg, 0.005)
-    
 
 
 @pytest.mark.parametrize(
@@ -403,7 +398,7 @@ def test_chunk_varlen(
     H: int,
     D: int,
     mask_p: float,
-    cu_seqlens: List[int],
+    cu_seqlens: list[int],
     dtype: torch.dtype,
 ):
     if is_intel_alchemist and D > 128:

From c996dc24854734f24fbfbb2396fe2885b21b4fa8 Mon Sep 17 00:00:00 2001
From: lizhiyuan <lizhiyuan@moonshot.cn>
Date: Wed, 18 Feb 2026 08:07:36 +0000
Subject: [PATCH 4/5] fix

---
 fla/ops/gated_oja_rule/chunk_h.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/fla/ops/gated_oja_rule/chunk_h.py b/fla/ops/gated_oja_rule/chunk_h.py
index d65dbf56b6..1f4e121060 100644
--- a/fla/ops/gated_oja_rule/chunk_h.py
+++ b/fla/ops/gated_oja_rule/chunk_h.py
@@ -146,17 +146,17 @@ def chunk_oja_fwd_kernel_h_blockdim64(
             o_v1 = tl.arange(0, 64)
             b_gk_last1 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v1, mask=(o_v1 < V), other=0.)
             b_h1 *= exp(b_gk_last1)[None, :]
-            if K > 64:
+            if V > 64:
                 o_v2 = 64 + o_v1
                 b_gk_last2 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v2, mask=(o_v2 < V), other=0.)
                 b_h2 *= exp(b_gk_last2)[None, :]
-            if K > 128:
+            if V > 128:
                 o_v3 = 128 + o_v1
                 b_gk_last3 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v3, mask=(o_v3 < V), other=0.)
                 b_h3 *= exp(b_gk_last3)[None, :]
-            if K > 192:
+            if V > 192:
                 o_v4 = 192 + o_v1
-                b_gk_last4 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v4, mask=(o_v4 < K), other=0.)
+                b_gk_last4 = tl.load(gv + (bos + last_idx) * H*V + i_h * V + o_v4, mask=(o_v4 < V), other=0.)
                 b_h4 *= exp(b_gk_last4)[None, :]
 
         b_k = b_k.to(v.dtype.element_ty)  # BT BK

From 9ab4771007a1be9dd9f710ae2d7b65ca0cfdb400 Mon Sep 17 00:00:00 2001
From: lizhiyuan <lizhiyuan@moonshot.cn>
Date: Wed, 18 Feb 2026 08:12:27 +0000
Subject: [PATCH 5/5] fix

---
 fla/ops/gated_oja_rule/chunk.py           | 2 +-
 fla/ops/gated_oja_rule/chunk_h.py         | 2 +-
 fla/ops/gated_oja_rule/chunk_o.py         | 2 +-
 fla/ops/gated_oja_rule/fused_recurrent.py | 2 +-
 fla/ops/gated_oja_rule/wy_fast.py         | 2 +-
 tests/ops/test_oja.py                     | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/fla/ops/gated_oja_rule/chunk.py b/fla/ops/gated_oja_rule/chunk.py
index 32de3251e0..e2e71255d2 100644
--- a/fla/ops/gated_oja_rule/chunk.py
+++ b/fla/ops/gated_oja_rule/chunk.py
@@ -1,4 +1,4 @@
-# # Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
+# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
 
 import warnings
 
diff --git a/fla/ops/gated_oja_rule/chunk_h.py b/fla/ops/gated_oja_rule/chunk_h.py
index 1f4e121060..66ea7031f3 100644
--- a/fla/ops/gated_oja_rule/chunk_h.py
+++ b/fla/ops/gated_oja_rule/chunk_h.py
@@ -201,7 +201,7 @@ def chunk_oja_fwd_h(
     chunk_size: int = 64,  # SY: remove this argument and force chunk size 64?
     save_new_key: bool = True,
     cu_seqlens: torch.LongTensor | None = None,
-) -> tuple[torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor | None, torch.Tensor | None]:
     B, T, H, V, K = *v.shape, u.shape[-1]
     BT = chunk_size
 
diff --git a/fla/ops/gated_oja_rule/chunk_o.py b/fla/ops/gated_oja_rule/chunk_o.py
index 2c6ff015d0..086714d3e8 100644
--- a/fla/ops/gated_oja_rule/chunk_o.py
+++ b/fla/ops/gated_oja_rule/chunk_o.py
@@ -184,7 +184,7 @@ def chunk_oja_fwd_o(
     scale: float = 1.,
     cu_seqlens: torch.LongTensor | None = None,
     chunk_size: int = 64
-) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor]:
     B, T, H, K, V = *k.shape, v.shape[-1]
     BT = min(chunk_size, max(16, triton.next_power_of_2(T)))
     BC = min(16, BT)
diff --git a/fla/ops/gated_oja_rule/fused_recurrent.py b/fla/ops/gated_oja_rule/fused_recurrent.py
index 13d24f26d9..b40aced3ac 100644
--- a/fla/ops/gated_oja_rule/fused_recurrent.py
+++ b/fla/ops/gated_oja_rule/fused_recurrent.py
@@ -91,7 +91,7 @@ def fused_recurrent_oja_fwd_kernel(
 
         # [BK, BV]
         if USE_GV:
-            b_gv = tl.load(p_gv).to(tl.float32)
+            b_gv = tl.load(p_gv, mask=mask_v, other=0).to(tl.float32)
             b_h *= exp(b_gv[None, :])
 
         b_k = b_beta * (b_k - tl.sum(b_h * b_v[None, :], 1))
diff --git a/fla/ops/gated_oja_rule/wy_fast.py b/fla/ops/gated_oja_rule/wy_fast.py
index 0067e97a5e..8077dd4f77 100644
--- a/fla/ops/gated_oja_rule/wy_fast.py
+++ b/fla/ops/gated_oja_rule/wy_fast.py
@@ -200,7 +200,7 @@ def recompute_w_u_fwd(
     A: torch.Tensor,
     gv: torch.Tensor | None = None,
     cu_seqlens: torch.LongTensor | None = None,
-) -> tuple[torch.Tensor, torch.Tensor]:
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor | None]:
     B, T, H, K, V = *k.shape, v.shape[-1]
     BT = A.shape[-1]
     BK = 64
diff --git a/tests/ops/test_oja.py b/tests/ops/test_oja.py
index 8ae564d265..3c1a75b73e 100644
--- a/tests/ops/test_oja.py
+++ b/tests/ops/test_oja.py
@@ -402,7 +402,7 @@ def test_chunk_varlen(
     dtype: torch.dtype,
 ):
     if is_intel_alchemist and D > 128:
-        pytest.skip(reason='chunk_gated_delta_rule is not supported on alchemist for D>128')
+        pytest.skip(reason='chunk_gated_oja_rule is not supported on alchemist for D>128')
     torch.manual_seed(42)
     os.environ['TRITON_F32_DEFAULT'] = 'ieee'
     # randomly split the sequence into N segments