[Kernel] ReplaySSM: cache SSM inputs for faster Gated DeltaNet standard decode

[Johnny-Liou]

Background

This is the second sub-PR split from the large draft PR #47576, which presents the full ReplaySSM design across Mamba2 and Gated DeltaNet for both standard and speculative decode. The first sub-PR, Mamba2 standard decode (#48018), landed as 866fea2b9, so this is a plain diff against main. It lands the next stage: Gated DeltaNet (GDN) standard decode. ReplaySSM caches recent SSM inputs instead of writing the recurrent state back to HBM on every step. It is a collaboration between Dao AI Lab and NVIDIA, and the full derivation and figures are in the blog post. AI assistance was used for parts of this work, and the authors have reviewed every changed line.

Core concept

GDN decode is memory-bound. Each step loads and stores the delta-rule recurrent state (a head_v x head_k matrix per value head), and that per-step state store dominates HBM traffic. ReplaySSM keeps a small ring buffer of recent per-step inputs (the key k, the corrected value d, and the scalar gate g) together with a periodic checkpoint state. On most steps it reconstructs the state and reads the output from the checkpoint plus the buffer, and it writes the full state back only on periodic flushes, once every L steps, where L is the buffer length. On the non-flush steps the per-step state store becomes a small input append, which removes the dominant traffic.

The baseline only becomes bandwidth-bound at large batch. The table below reports the DRAM bandwidth the baseline fused_recurrent_gated_delta_rule_packed_decode reaches, as a percentage of peak, measured in isolation with cold L2 at L=16.

bs	H100 fp32	H100 fp16	B300 fp32	B300 fp16
1	9.0%	5.9%	6.5%	3.9%
8	35.2%	27.5%	24.2%	18.0%
32	71.3%	54.8%	56.7%	39.1%
128	84.5%	79.6%	78.3%	68.6%
256	86.3%	83.4%	82.4%	74.5%
512	87.5%	85.3%	84.5%	77.4%

At small batch the per-request state footprint is tiny and the launch grid is small, so too few memory transactions are in flight to cover HBM latency, and the kernel is latency-bound rather than bandwidth-bound. In a hybrid model the small-batch step is also dominated by the MLP layers, not the SSM layers. Small batch is therefore not the target regime. ReplaySSM targets serving batch, where the GDN kernel saturates HBM and the per-step state store is the bottleneck.

What this PR adds

Everything here is opt-in. With the feature off, the decode path is byte-for-byte the baseline.

• The GDN cached decode kernel fused_recurrent_gated_delta_rule_replayssm (state-reconstruction route), plus its hardware-keyed launch-config helper (_gdn_decode in replayssm_config.py).
• No new config flags. It reuses the two flags added in [Kernel] ReplaySSM: cache SSM inputs for faster Mamba2 standard decode #48018: --use-replayssm turns on cached decode, and --replayssm-buffer-len sets the history buffer length L (default 16).
• Integration. The Qwen3.5 GDN mixer dispatches to the kernel under the flag, the GDN attention metadata builder carries the per-row ring cursor, and the state-shape and state-dtype calculators size the extra d/k/g caches on the paged state. Single-token prefill rows route to the prefill path rather than the cached decode kernel. The conv path reuses vLLM's causal_conv1d_update unchanged.
• Prefix caching. Align mode (--mamba-cache-mode align) is supported: the builder re-anchors the ring at each mamba block start and forces a flush on the block-completing step, so the checkpoint carries the exact block-boundary state for reuse and cached prefixes match the baseline.

This covers standard (non-speculative) decode only.

Design notes

Paged cache layout

The input ring caches (d, k, g) and the checkpoint state live inside the paged KV block, appended as extra tensors on the baseline (conv, ssm) state, for five tensors total. They stay live across decode steps, the checkpoint until the next flush and the ring across many steps, so they must sit in HBM between kernel launches. Appending them onto the paged state reuses vLLM's per-request block allocation and block-table indexing directly. g_cache is fp32; the d and k caches use fp16 when activations are bf16 for better numerical precision.

CUDA graphs and continuous batching

Whether a row flushes is per-row runtime data. Under continuous batching the rows in one captured batch sit at different buffer positions, so the flush status varies across the batch and cannot be a compile-time constant, even for standard decode. The write position is decode_step mod L, computed on the host each step from scheduler token counts and copied to the device asynchronously, so no device-to-host sync is needed. The metadata builder computes the per-row flush flag on the host (a row flushes at its last buffer slot, write_pos == replayssm_buffer_len - 1, and, in align prefix-caching mode, on the step that completes a mamba block) and passes it to the kernel as a per-row input, so one captured graph per batch size covers both the non-flush and the flush rows. Deriving the cursor from decode_step mod L each step also means recycled paged blocks need no zero-init.

Results

Unlike the Mamba2 sub-PR, GDN has no tuned/default baseline split. The shipped launch config is the swept per-hardware optimum, and the baseline is vLLM's fused_recurrent_gated_delta_rule_packed_decode at its own config, so every speedup below is a single honest number.

Two models are evaluated: Qwen3.5-4B (BF16) on one H100 and Qwen3.5-122B-A10B-NVFP4 on one B300, at buffer length 16 with fp32 and fp16 SSM state, greedy, and CUDA graphs on. End-to-end numbers are produced with benchmarks/replayssm/e2e_decode_speedup.py.

Blackwell (B300) support: this sub-PR ships a Triton kernel only, and on B300 that Triton kernel is bandwidth-capped for fp16 state (44% DRAM utilization). fp16 state on B300 is therefore not enabled in this sub-PR. fp32 state is not capped this way and reaches 1.49x at bs512, but is still suboptimal.
A CuTe-DSL kernel targeting Blackwell removes the cap, and is planned as a subsequent separate PR. At bs512 it lifts the B300 kernel-level speedup from 1.49x to 1.66x for fp32 state, and from 1.05x to 1.61x for fp16 state.

End-to-end speedup

Whole-model per-step speedup, standard ms/step / ReplaySSM ms/step, greedy, CUDA graphs on.

bs	Qwen3.5-4B H100 fp32	Qwen3.5-4B H100 fp16	Qwen3.5-122B B300 fp32
1	0.99x	0.99x	0.96x
8	1.03x	1.01x	1.03x
32	1.08x	1.03x	1.09x
64	1.14x	1.05x	1.11x
128	1.21x	1.06x	1.16x
256	1.27x	1.07x	1.20x
512	1.30x	1.08x	1.22x

ReplaySSM wins most at serving batch, where the GDN layers take a growing share of the step, and stays roughly break-even at bs 1 to 8. fp16-state end-to-end on the dense 4B is lower than fp32-state because the fp16 GDN kernel is a smaller share of the MLP-dominated step.

Kernel-level speedup

Isolated per-kernel CUDA-time speedup.

bs	H100 fp32	H100 fp16	B300 fp32	B300 fp16
1	0.88x	0.58x	0.51x	0.39x
8	1.34x	1.07x	1.16x	0.85x
32	1.54x	1.27x	1.37x	0.94x
128	1.66x	1.37x	1.44x	1.04x
256	1.68x	1.39x	1.46x	1.05x
512	1.67x	1.41x	1.49x	1.05x

Kernel speedup rises with batch and saturates by about bs 128 to 256. fp16 state on blackwell is not supported in this sub-PR.

Buffer length

Isolated per-kernel speedup vs the baseline. Each cell lists buffer length L = 8 / 16 / 32, with the best of the three in bold.

model	bs 8	bs 32	bs 256
Qwen3.5-4B (H100) fp32	1.27x / 1.33x / 1.21x	1.46x / 1.54x / 1.43x	1.58x / 1.68x / 1.59x
Qwen3.5-4B (H100) fp16	1.04x / 1.05x / 0.94x	1.24x / 1.27x / 1.10x	1.34x / 1.39x / 1.20x
Qwen3.5-122B (B300) fp32	1.13x / 1.17x / 1.11x	1.28x / 1.37x / 1.31x	1.36x / 1.46x / 1.40x

Speedup is bell-shaped in buffer length, trading flush frequency against per-step traffic. L=16 is best in every entry and is the shipped default.

Tests

Correctness is checked at four levels, all on GDN.

Per-step kernel correctness lives in tests/kernels/test_replayssm_standard_decode_gdn.py. Every decode step is checked against the baseline packed-decode kernel over multi-flush sequences, across six state and activation precision combinations, the production model geometries (small, Qwen3.5-4B, Qwen3.5-122B), buffer lengths 4 and 16, strided and contiguous layouts, and continuous batching with per-row buffer positions and null-padded slots. A separate case sweeps per-row write positions across a batch. Tolerances are near-exact at fp32 (output rtol 1e-4, atol 1e-4; state rtol 1e-3, atol 2e-3), tight enough to catch a TF32 matmul-precision regression, and looser at bf16 and fp16 where rounding dominates.

Prefill and decode equivalence lives in tests/kernels/test_replayssm_teacher_decode_equivalence_gdn.py. Because the delta-rule recurrence is path-independent, the chunked prefill kernel (chunk_gated_delta_rule, the path the model runs at prefill) and step-by-step decode must give the same per-position outputs and final state. Both the baseline and the ReplaySSM step decoders are anchored on the chunked-prefill teacher, whose inputs are built with the same shared fused_post_conv_prep the model uses.

Metadata-builder unit tests live in tests/v1/attention/test_gdn_metadata_builder.py. The per-row write position and flush flag are the riskiest new logic, so they are covered on CPU with no model: fresh decode, flush boundary, buffer wrap, resume re-anchor after preemption, and per-row independence across a batch. Align mode adds the block re-anchor, the forced boundary flush, and a buffer length that does not divide the mamba block size. Two cases pin the batch split: a final single-token prefill chunk stays in the decode group so a full cudagraph replays with a refreshed cursor, and a first-token prefill stays a prefill. One case asserts the builder rejects stochastic rounding.

Engine-level parity lives in tests/v1/e2e/test_replayssm_decode.py. It compares the baseline (feature off) against ReplaySSM (feature on) with greedy decode and check_logprobs_close on Qwen3.5-4B, at TP1 and, under @multi_gpu_test, at TP2.

The two kernel files are 90 passed (126s, one H100), and the builder file is 23 passed on CPU. TP1 and TP2 engine parity both pass; the TP2 run confirms the per-rank sharded caches and checkpoint stay correct.

pytest tests/kernels/test_replayssm_standard_decode_gdn.py \
       tests/kernels/test_replayssm_teacher_decode_equivalence_gdn.py \
       tests/v1/attention/test_gdn_metadata_builder.py \
       tests/v1/e2e/test_replayssm_decode.py -q

Model evaluation (GSM8K)

Evaluated on Qwen3.5-4B (1x H100), greedy, fp32 SSM state, CUDA graphs on, with the <think> block disabled in the chat template (chat_template_kwargs={"enable_thinking": False}). Accuracy is reported under CoT prompting. Baseline and ReplaySSM use the identical prompt and seed, so the parity comparison is unaffected by the prompt choice.

CoT prompt (verbatim; {question} is the GSM8K problem):

{question}

Solve step by step, then give the final answer as 'The answer is <number>.'

Answer extraction: the number following an answer is, answer:, ####, or \boxed{} marker (last match), falling back to the last number in the output.

config	accuracy (CoT, N=1319)
baseline (no ReplaySSM)	0.917 +/- 0.008
ReplaySSM (L=16)	0.920 +/- 0.008

The 0.003 difference is within one binomial standard error, so ReplaySSM matches the baseline.

Prefix caching (align): on a 20-shot CoT run (N=200) with --enable-prefix-caching --mamba-cache-mode align, get_metrics() reports a prefix-cache hit rate of 0.90 for the baseline and 0.86 for ReplaySSM, and accuracy is 0.925 for both. The align cached path is also covered by the e2e test test_replayssm_prefix_caching_matches_baseline, which asserts cache hits.

Duplicate check

No open PR addresses ReplaySSM GDN standard decode. This PR is split from the large draft PR #47576, which stays open as the full design, and builds on the Mamba2 standard-decode sub-PR #48018. The related prior ReplaySSM PRs we are aware of are Mamba2-focused and do not cover GDN:

• #43102 and #43439, earlier PRs from our collaborator on the same ReplaySSM effort. This is the newer, more complete version.
• #46239, opened by another contributor based on our original fork. We have since made substantial changes, intend to land the feature ourselves, and have notified the author.

Out of scope

• Stochastic rounding for low precision state.
• Speculative decode for GDN, which will land in a later sub-PR.

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[mergify]

This pull request has merge conflicts that must be resolved before it can be
merged. Please rebase the PR, @Johnny-Liou.

https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/syncing-a-fork

[mergify]

This pull request has merge conflicts that must be resolved before it can be
merged. Please rebase the PR, @Johnny-Liou.

https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/syncing-a-fork

[vadiklyutiy]

@Johnny-Liou just interested in how this PR is going?

[Johnny-Liou]

Hi @vadiklyutiy, this PR is ready for the review. Thanks.

[vadiklyutiy]

@Johnny-Liou
GDN reads the state at both q and k, but the same expansion applies to both reads:

S_{t-1} @ q_t = T * (S_ckpt @ q_t) + sum_j r_j * (k_j . q_t) * d_j
S_{t-1} @ k_t = T * (S_ckpt @ k_t) + sum_j r_j * (k_j . k_t) * d_j

so an output-only route looks possible for GDN as well: two sets of precomputed scalars instead of
one, with reconstruction kept for the flush step, i.e. the same two-route structure as the Mamba2
kernel #48018.

Is there some specific reason why we use different approach for GDN?