docs(audit): FORGE assessment + residency-aware epilogue-fusion track

[gstoner]

Assessment of FORGE (arXiv:2606.22932v2, dk4248/FORGE) — fusing the optimizer step into the weight-gradient GEMM epilogue at tile granularity, so grad_W never reaches HBM — and the generalization it opens for Tessera:

Fuse a consumer into its producer's tiled epilogue when the consumer's read-locality is no coarser than the producer's tile partition, and prove statically that the intermediate never materializes.

FORGE is one instance (optimizer ← weight-gradient GEMM). Eight workstreams W1–W8 generalize it to N consumers × M producers with declared legality, arbiter admission, and a compiler that reports when the win isn't there.

Files

File
docs/audit/compiler/FORGE_ASSESSMENT.md	audit_role: plan, plan_state: open, 371 lines
tests/unit/test_fused_wgrad_optimizer_contract.py	14 tests, pure numpy, 0.5 s — declared oracle (Decision #31b) for the not-yet-landed pass
docs/audit/compiler/README.md	routed twice: question table + scoped-plan catalog

Math verified, not asserted

Nine propositions are stated in the plan and shipped as an executable contract, so W3/W4 inherit a gate rather than an argument. Identifiers match §2 of the doc.

• P1 — per-tile exactness is bitwise and partition-independent. The single-use ∧ consumer-is-optimizer guard subsumes FORGE Rem. 2 (tied weights) structurally: a tied weight's %g1 is consumed by an add, so the match cannot fire. Because our optimizer ops are value-semantic and Pure, FORGE's in-place ΔX-before-update hazard — which its repo guards with a comment and a correctness script — cannot occur at Graph IR.
• P2 — exact global-norm clipping provably cannot be fused (m_t(c) − c·m_t(1) = (1−c)β₁m_{t−1} needs an O(P) tensor). Both candidate approximations fail: clip-the-update and delayed-norm each leave √v̄ inflated 3.18× ten steps after a spike — identical to no clipping at all. grad_clip_scope must fail closed (Decision #21a). FORGE ships with clipping switched off and says so only in two appendix protocol lines.
• P3 — the affine reduce-into-state trick composes with Decision Phase 8.5 — apple_gpu story doc + CLAUDE.md update #16 (ZeRO-2); owner is unambiguous under reduce-scatter.
• P5 — folding state decay into the GEMM's β breaks conditionally-routed weights: 2.24× error at 50% routing. A verifier condition, given tessera.moe_swiglu_block.
• P6 — the fp32-accumulator precision benefit is worth ~900× with fp32 state and ~1× with bf16 state. The paper measures it inside a BF16-everywhere recipe that masks it and reports 4.4%; its own int8/fp8 rows are 4× and 44× worse than baseline. Whether the benefit is realizable is a numeric_policy question — the measured motivation for the Decision docs: scope GPU-resident activations / persistent device-handle model #32 carrier work.

What's already in tree and easy to miss

• The weight-gradient GEMM reaches Graph IR via LinearTransposeInterface, not AdjointInterface — MatmulOp doesn't implement the latter, so grepping only for adjoints yields a false "no compiled matmul VJP" conclusion. MatmulOp::buildLinearTranspose emits dRhs = matmul(lhs, dy, transposeA=true); fixture autodiff_paired_matmul.mlir.
• TrainingStepFusionPass already implements the identical pattern one level down (loss_backward → adamw), with a negative fixture and a LOWER-COUNT-1: linalg.generic check that proves non-materialization in the IR rather than by peak-memory measurement. That makes this track gateable on any host — no 8B model or 141 GB card needed.
• MatmulOp::getLoopIteratorTypes() → {parallel, parallel} with K kept whole, stamped tessera.full_k — that is FORGE Prop. 1's legality condition, currently with no consumer (a live Decision Apple GPU MLA: native f16/bf16 for the absorbed decode kernel #29 gap this closes).
• MatmulLowering already does "bf16 accumulate in f32 then truncf" — that truncf is exactly the rounding FORGE deletes, testable on CPU.

Claim hygiene on the source

The public repo ships AdamW and SGD only — no torch.distributed, no all_reduce, no bucket coordinator, and none of Muon/LAMB/Lion/Adafactor/SM3. §4 and Appendices I, K–N are not reproducible from the release. Recorded in §0; the single-GPU mechanism is an evidence row, the distributed and multi-optimizer results are not.

Scope

Direction only (Decision #26). INTEGRATED_COMPILER_PLAN.md keeps global order. MASTER_AUDIT.md / COMPILER_AUDIT.md deliberately untouched — nothing is built yet, so the all-up picture hasn't shifted.

Verification

• test_audit_docs.py — caught two real routing obligations on first run; both fixed. 11 pass.
• check_generated_docs.sh — 25 generated docs in sync (also passed the pre-push hook).
• ruff clean.
• Suite delta measured against a stashed tree: 37 failed, 1212 passed → 37 failed, 1226 passed — exactly the +14 new tests, same pre-existing failures (they need a built tessera-opt / fresh Apple dylib, absent on this Mac).

🤖 Generated with Claude Code