N7 · model/forward-parity

Regime N (Numerical / linear-algebra). The internal/model package implements a from-scratch, pure-Go transformer forward pass — embedding lookup, the decoder stack (RMSNorm/LayerNorm, RoPE, causal multi-head/GQA/MLA attention, SwiGLU/MoE FFN, residuals, topology-selected norm placement), final norm, and the tied LM head — producing per-layer hidden states and per-position vocab logits. internal/modelengine wraps a loaded Model for decode/generation. “Correct” here means oracle parity: the Go forward pass must reproduce the independently-computed PyTorch/HF reference (exported by export_oracle.py to .cache/oracle-* / .cache/<model>). Per witness-kind §3.1 of 00-METHOD.md, a float forward pass is correct when hidden-state cosine ≈ 1.0, the per-position argmax matches the oracle at every position (a single ULP of drift cannot flip an argmax the oracle pins), and the greedy continuation ids match token-for-token. This doc discharges (1) end-to-end forward parity against the HF oracle, and (2) whether that parity holds across the supported arch families.

Witness command (this node, native go1.26 darwin/arm64): go test -run 'Oracle|Parity|Greedy|Argmax|Forward' ./internal/model/ -count=1 -timeout 240s -v Package result: ok github.com/anthony-chaudhary/fak/internal/model 4.816s. The only oracle fixture present on this node is internal/model/.cache/smollm2-135m (model_type=llama, 30 layers); every .cache/oracle-* family export is absent, so those rungs SKIP.

THEOREM 1 — end-to-end forward pass matches the HF oracle (loaded llama family)

THEOREM. For the loaded HF oracle (smollm2-135m, model_type=llama), the pure-Go Forward pass reproduces HF’s per-layer hidden states (cosine ≈ 1.0 at the embedding, an early/mid/last decoder layer, and the final-norm slot), matches HF’s per-position argmax at EVERY position (go == hf == oracle), reproduces final logits to < 0.05 max abs diff, and the cached NewSession().Prefill last-position logits agree with cacheless Forward within 1e-4.

REGIME. N — oracle parity (cosine + argmax-pin + greedy-id), the gold witness of §3.1.

PROOF. Forward (internal/model/forward.go:45) does the embedding lookup, runs the decoder stack appending one hidden slot per layer (forward.go:58, forward.go:67), then finalNorm (internal/model/weights.go:1478) + the tied-head matmul (forward.go:72-78) to logits. The witness assertForwardMatchesHFOracleMode (internal/model/oracle_test.go:1016) reads HF’s exported .hidden.f32 / .logits.f32, computes cosine (oracle_test.go:139) and Errorfs when cs < 0.9999 (oracle_test.go:1059-1061), asserts gotAM == refAM == p.ArgmaxPos[pos] at every position (oracle_test.go:1066-1074), checks last-position logit max|Δ| ≤ 0.05 (oracle_test.go:1079-1081), and checks cached Prefill within 1e-4 (oracle_test.go:1082-1087). With the smollm2 fixture present, no Errorf fired.

WITNESS. go test -run 'Oracle|Parity|Greedy|Argmax|Forward' ./internal/model/ -count=1 -timeout 240s -v → TestForwardMatchesHFOracle / …/smollm2-135m. Greedy-id parity is additionally pinned by TestForwardOnGoDecodedWeights (internal/model/safetensors_test.go:77), which runs Generate on Go-decoded (no-torch) weights and asserts each id equals HF’s: logged go-decoded greedy=[7042 30 7042 314 …] ≡ hf greedy=[7042 30 7042 314 …].

VERDICT. PROVEN (2026-06-20). --- PASS: TestForwardMatchesHFOracle (1.79s) and …/smollm2-135m (1.79s); log shows cos=1.000000 at embedding/layer1/layer15/layer29/final-norm for all 3 prompts and logits[last] max|Δ|=6.008e-05 argmax=7042 ✓ (and 4.768e-05/4.339e-05 for prompts 1/2). --- PASS: TestForwardOnGoDecodedWeights (0.63s).

DOS. bound at ship (audit the proof-shipping commit with dos commit-audit from the fleet repo root; mechanism last shipped under 66ccb27 (forward.go) and witness tier 4c3e150 (oracle_test.go)).

THEOREM 2 — parity holds across the supported arch families

THEOREM. The same forward-pass HF-oracle parity (hidden cosine ≈ 1, per-position argmax, greedy ids) holds not only for llama but across the supported arch families: qwen3 (QK-norm), qwen3moe (hybrid dense/sparse), gpt_oss (MXFP4 MoE), gemma3 (local/global attention, sandwich norm), glm_moe_dsa (MLA + Dynamic Sparse Attention + MoE), mistral (sliding-window), llama3 (rope scaling + EOS list), phi3 (longrope), deepseek-v2 (MLA).

REGIME. N — oracle parity per family.

PROOF. The witnesses exist and each routes through the same assertForwardMatchesHFOracle assertion (internal/model/oracle_test.go:1011): TestOptionalQwen3OracleCoversQKNorm (oracle_test.go:304), TestOptionalQwen3MoEOracleCoversHybridDenseSparseLayers (:330), TestOptionalGPTOSSMXFP4ForwardMatchesHFOracle (internal/model/safetensors_stream_test.go:488), TestOptionalGemma3OracleCoversLocalGlobalAttention (:374), TestOptionalGLMMoeDsaOracleForwardMatchesHFCacheless (:814) and …SessionCacheMatchesHF (:824), TestOptionalMistralSWAOracleNonVacuous (:260), TestOptionalLlama3OracleCoversScalingAndEOSList (:286), TestOptionalPhi3LongropeOracleCoversLongFactor (:976), TestOptionalDeepSeekV2OracleDocumentsMLABoundary (:435). Forward really dispatches glm_moe_dsa to layerGLMDsa (forward.go:62, body at forward.go:130) and all other families to layer (forward.go:65), so the per-family code paths are genuine, and each Optional rung additionally asserts the family-distinguishing config axes (QK-norm tensors, MoE dense/sparse split, MLA q_a/q_b geometry, DSA indexer shapes, sliding-window non-vacuity, longrope factor) before the numeric compare. But the numeric parity is not witnessed here: on this node only internal/model/.cache/smollm2-135m (a llama export) is present; every .cache/oracle-<family> export is absent, so every Optional rung SKIPPED with no exported weights in .cache/oracle-<family>. No deterministic witness for a non-llama family ran green, so cross-family parity is honestly un-witnessed.

WITNESS. Same command as Theorem 1; the family rungs are the TestOptional* set. The helper tests TestOracleMatrixDirsFromEnv and TestMissingOracleFamilies PASS but assert env/string family-matrix derivation, not numeric parity, so they do not close this theorem.

VERDICT. OPEN (2026-06-20). All non-llama family rungs SKIP for want of fixtures (e.g. --- SKIP: TestOptionalQwen3OracleCoversQKNorm … no exported weights in .cache/oracle-qwen3; likewise qwen3moe, gpt_oss, gemma3, glm (6 GLM rungs), mistral, llama3, phi3, deepseek-v2). Only the llama family (smollm2-135m) is actually witnessed green here. To close: export the per-family tiny oracles — python internal/model/export_oracle.py --out .cache/oracle-qwen3 … for each, and the GLM rung via the documented --online --trust-remote-code --model yujiepan/glm-5-tiny-random --out .cache/oracle-glm --prompt-ids-json '…' hint — then re-run the command so the Optional rungs execute and corroborate cosine/argmax/greedy parity per family. This is an honest OPEN, not a false PROVEN: the llama rung being green is necessary but not sufficient for the family-coverage claim.

DOS. bound at ship (no PROVEN to bind; the OPEN is recorded as the residual dos review should surface — closing it requires the fixture exports above, which are gitignored and absent on this node).

THEOREM 3 — Qwen3.6 (hybrid Gated-DeltaNet) multi-token greedy parity — REFUTED

THEOREM (under test). fak’s in-kernel greedy decode of Qwen3.6-27B (qwen35, hybrid GDN: 48 linear-attn + 16 full-attn layers) reproduces the llama.cpp reference greedy continuation token-for-token on the same q4_k_m GGUF — i.e. multi-token greedy parity, the decode-side analogue of Theorem 1’s llama greedy-id parity.

REGIME. N — oracle parity (greedy-id match against an independent engine).

PROOF / counterexample. The theorem is false as stated. On the exact 22-token ChatML oracle prompt (You are a helpful assistant. / Say OK., ids [248045,8678,198,…,74455,198]) at temperature=0, top_k=1, fak and the oracle agree on tokens 0–1 (248068 <think>, 198 \n) and diverge at token index 2 (the third token): fak emits 8160 (Here, logit 23.18, with 90700 second at 21.43), the oracle emits 90700 (Thinking, logprob −0.547, with 8160 second at −0.945). Both engines surface the same top-2 set {8160, 90700} ranked oppositely — a near-tie argmax flip at the decision boundary, the signature of accumulated f32 drift (token 0’s argmax matches — fak logit 28.30, the oracle pins it at logprob −0.0008/near-certain; the first token is at parity, the third is not). The drift’s root cause (the f32 Gated-DeltaNet recurrent scan, the int8 SDOT decode reduction rounding, or attention/softmax accumulation order vs llama.cpp’s Metal kernels) is not yet isolated — this row refutes the parity claim, it does not diagnose it. Note this is a strictly harder claim than Theorem 1 (a 27B hybrid-GDN multi-token continuation, vs a 135M llama single-step + short greedy) and does not contradict Theorem 1’s PROVEN.

WITNESS (counter-witness, deterministic, weight-backed / “Optional”). The captured artifact pair is the recorded counterexample: fak/experiments/qwen36/native-gguf-q8-multitoken-parity-20260619.json (expect_match:false, generated_ids:[248068,198,8160] vs expected_ids:[248068,198,90700]) and the oracle …/llamacpp-qwen36-multitoken-oracle-20260619.json (llama-server -m Qwen3.6-27B.q4_k_m.gguf -ngl 99, tokens:[248068,198,90700]). Re-run on a node where the gated 27B GGUF is present — -expect self-checks and exits non-zero on the mismatch:

go -C fak run ./cmd/qwen35check -gguf ~/.cache/fak-models/gguf/Qwen3.6-27B.q4_k_m.gguf -n 3 -topk 5 \
  -ids 248045,8678,198,2523,513,264,10631,17313,13,248046,198,248045,846,198,44240,10092,13,248046,198,248045,74455,198 \
  -expect 248068,198,90700

VERDICT. REFUTED (2026-06-20, this M3 Pro node, q4_k_m GGUF). fak’s shipped decode is forward-parity-PROVEN on llama (Theorem 1) and first-token-parity on Qwen3.6, but its greedy continuation on the hybrid-GDN model fails at token 3 — so fak is not at correctness parity yet on this arch. Recorded as a finding, not deleted (00-METHOD §4). Full status + the MLX-bar / swap-contamination measurement caveats: ../../experiments/qwen36/QWEN36-PARITY-AND-MEASUREMENT-STATUS-2026-06-20.md.

DOS. bound at ship (the REFUTED row binds to the commit that records it; the counter-witness artifacts are committed under fak/experiments/qwen36/).

Honest scope notes