Round 33 Track C Audit Report: Decode GDN Recurrence (gdn.metal) & glue.metal #

• Agent: argon-r33-gdn-and-glue-opt (gemini-4-argon)
• Target Device: Apple M5 (10-core GPU, 24 GB unified memory)
• Patch Path: /tmp/argon_r33_gdn/argon_r33_gdn.patch (git -C vendor/strata apply --check clean)
• Scratch Repo: /tmp/argon_r33_gdn/strata
• Baseline Kernels: /tmp/argon_r33_gdn/base_kernels

1. Optimizations Implemented & Tested #

Target 1: gdn_step_t (metal/kernels/gdn.metal, lines 99–162) #

1. Critical-Path kl Split Across Barrier 1 and Barrier 2:
   • Immediately after Barrier 1 (line 125), only tot_k, rsk, and kl = (rsk * ks[qk_idx]) * scale are computed before launching the 32-iteration kv FMA loop (for (int r = 0; r < RPT; ++r) kv = fma(st[r], simd_broadcast(kl, ushort(r)), kv);) and storing red[ib][j] = kv.
   • tot_q, rsq, ql = (rsq * qs[qk_idx]) * scale, g = gb[0], be = gb[1], and vj = vs[j] are issued after red[ib][j] = kv right before Barrier 2 (line 140), shortening the live range of ql, g, be, and vj across the 32-step kv loop and overlapping their latency with the red[ib][j] store and Barrier 2.
2. Early Conv-History Commit (hist_out) & Pre-Barrier-3 State Commit (state):
   • Conv History (hist_out): hst[0..2] is fully updated at the end of the conv + SiLU block (line 101, before Barrier 1). Emitting the hist_out[ch * 3 + k] = hst[k] stores immediately inside if (ch >= 0) when t + 1 == commit_at && (tid >= 256 || h < int(a.h_k)) makes hst[0..2] dead before Barrier 1 on single-token decode (GDN_NTOK == 1) and on the final token of any multi-token window.
   • Recurrent State (state): st[0..31] is finalized at the end of the st/o update loop (line 150, before Barrier 3). Previously, the 32 global state stores per thread were deferred until after Barrier 3, the ib == 0 readout reduction, Barrier 4, and the ib == 0 y/plane stores — leaving simdgroups ib = 1..3 (75% of the threadgroup) idle across two barriers before issuing 64 KB of global stores per head. Issuing st_base[r * st_stride] = st[r] immediately before Barrier 3 overlaps the global state writeback with ib == 0's readout norm and output plane stores across Barriers 3 and 4.
   • Rejected Variant (1b — deferring tot_q/rsq/ql/g/be until after Barrier 2): Tested and rejected (+1.5% to +3.7% regression) because issuing 7 threadgroup loads (part[0..3], gb[0..1], qs[qk_idx]) and rsqrt after Barrier 2 delays the red[0..3][j] loads and the st/o loop.
   • Rejected Variant (zz load moved after st/o loop): Tested and rejected (+1% to +5% regression) because prefetching zz at the top of the token loop hides its global memory latency behind the 4 barriers of token t.

Target 2: swiglu_prep & moe_combine_sh (metal/kernels/glue.metal, lines 18–56) #

• In moe_combine_sh: hoisted const int row_base = int(t * a.topk);, device const int* te = plan + P_TOKENT + row_base;, and device const float* yep = ye + k; outside the 10-way unrolled expert accumulation loop so yep[te[j] * int(a.n_embd)] eliminates the + k address addition across all 10 loads.
• In swiglu_prep: hoisted const uint idx = t * a.n + d; across g[idx], u[idx], and xp + idx while preserving the uniform t * (a.n / 16) + tg.x address for the j == 0 plane-4 sum write.

Test Harness (metal/tests/gdn_parity.cpp) #

• Extended gdn_parity --ab <ref.metal|ref_dir> to accept a directory (/tmp/argon_r33_gdn/base_kernels) or file path, run all 88/88 GDN bitwise checks (ntok = 1..8, plane = 0 / 49152, commit = 0 / 1 / 0x101..0x107), run paired A/B timings across all 32 (plane, ntok, commit) configurations (36 layers rotated, 113 MB state), and when glue.metal is present in ref_dir, run 24/24 bitwise checks (swiglu_prep and moe_combine_sh for ntok = 1..8, topk = 10, 8) plus paired A/B timings.

2. Verification & Bitwise Parity Results #

• gdn_parity --ab /tmp/argon_r33_gdn/base_kernels (gdn_step, IB = 4, 512 threads):
  • Pipeline occupancy: max 512 threads per threadgroup (the kernel needs 512) for all GDN_NTOK = 1..8.
  • GDN A/B bitwise checks: 88/88 PASS (0 fail(s)) across y, state, and hist_out.
  • Glue A/B bitwise checks: 24/24 PASS (0 fail(s)) across swiglu_prep (xp planes 0..4) and moe_combine_sh (bo, topk = 10, 8).
• GDN_IB8=1 gdn_parity --ab /tmp/argon_r33_gdn/base_kernels --no-bench (gdn_step8, IB = 8, 1024 threads):
  • Pipeline occupancy: max 1024 threads per threadgroup (the kernel needs 1024) for all GDN_NTOK = 1..8.
  • GDN A/B bitwise checks: 88/88 PASS (0 fail(s)).
• gdn_parity (double-precision CPU reference + window invariants + plane = 49152 verification): ALL PASS.
• fuse_parity (gemv_cat, router_route, moe_combine_sh + gr_norm == gr_norm_comb / gr_norm_comb_4s across ntok = 1..8): ALL PASS.

3. Paired A/B Benchmark Results on Apple M5 #

3.1 gdn_step Paired A/B (36 layers rotated, 7 interleaved pairs x 72 dispatches) #

3.2 glue.metal Paired A/B (swiglu_prep & moe_combine_sh, 256 dispatches/cb with buffer barrier) #