Limits table — the delivered form vs the registered baselines

Every registered opponent in bench/limits/ crossed with the named-optimization corpus (bench/discovery/cases/). ratio is baseline ÷ mlopt — the results-doc convention: >1× means the delivered form is ahead, ~1× is parity (a rediscovery of the known impl), <1× is an honest loss. caveat carries what the number hides: measured-only arms, scratch-dep skips, verify failures.

• lane: fast (symbolic dag_cost)
• date: 2026-10-20T00:10:29+00:00 · git: e7dc703 (dirty) · torch 2.14.0+cu130 on cpu

case	category	baseline	kind	mlopt	baseline	ratio	verdict	caveat
blelloch_scan	speed	eager	eager	752	759	1.01×	parity	no compilation — the unoptimized floor
blelloch_scan	speed	hand_carrier	carrier	752	759	1.01×	parity	same extracted term — executor routing is the delta
blelloch_scan	speed	paper_impl	impl	752	1,494	1.99×	WIN	from bench.discovery.refs — the hand-built floor
blelloch_scan	speed	torch_compile	compile	752	—	—	—	measured-only — no symbolic form
conv_bn_fold	speed	eager	eager	27,649	29,186	1.06×	WIN	no compilation — the unoptimized floor
conv_bn_fold	speed	hand_carrier	carrier	27,649	—	—	—	no carrier executor claims the extraction — generic lowering would duplicate the mlopt arm
conv_bn_fold	speed	paper_impl	impl	27,649	27,649	1.00×	parity	from bench.discovery.refs — the hand-built floor
conv_bn_fold	speed	torch_compile	compile	27,649	—	—	—	measured-only — no symbolic form
flash_attention	memory	eager	eager	32,772	33,544	1.02×	WIN	no compilation — the unoptimized floor
flash_attention	memory	hand_carrier	carrier	32,772	—	—	—	no carrier executor claims the extraction — generic lowering would duplicate the mlopt arm
flash_attention	memory	paper_impl	impl	32,772	32,772	1.00×	parity	from bench.discovery.refs — the hand-built floor
flash_attention	memory	torch_compile	compile	32,772	—	—	—	measured-only — no symbolic form
mul_unsq_nat	speed	eager	eager	50	75	1.50×	WIN	no compilation — the unoptimized floor
mul_unsq_nat	speed	hand_carrier	carrier	50	—	—	—	no carrier executor claims the extraction — generic lowering would duplicate the mlopt arm
mul_unsq_nat	speed	paper_impl	impl	50	50	1.00×	parity	from bench.discovery.refs — the hand-built floor
mul_unsq_nat	speed	torch_compile	compile	50	—	—	—	measured-only — no symbolic form
retnet_chunkwise	memory	eager	eager	761,862	761,863	1.00×	parity	no compilation — the unoptimized floor
retnet_chunkwise	memory	fla	kernel	761,862	—	—	—	fla not installed (scratch dep)
retnet_chunkwise	memory	hand_carrier	carrier	761,862	—	—	—	no carrier executor claims the extraction — generic lowering would duplicate the mlopt arm
retnet_chunkwise	memory	paper_impl	impl	761,862	491,656	0.65×	loss	from bench.discovery.refs — the hand-built floor
retnet_chunkwise	memory	torch_compile	compile	761,862	—	—	—	measured-only — no symbolic form
swiglu_mlp	speed	eager	eager	4,355	4,356	1.00×	parity	no compilation — the unoptimized floor
swiglu_mlp	speed	hand_carrier	carrier	4,355	—	—	—	no carrier executor claims the extraction — generic lowering would duplicate the mlopt arm
swiglu_mlp	speed	paper_impl	impl	4,355	4,485	1.03×	WIN	from bench.discovery.refs — the hand-built floor
swiglu_mlp	speed	torch_compile	compile	4,355	—	—	—	measured-only — no symbolic form
weight_chain_fold	speed	eager	eager	2,049	4,098	2.00×	WIN	no compilation — the unoptimized floor
weight_chain_fold	speed	hand_carrier	carrier	2,049	—	—	—	no carrier executor claims the extraction — generic lowering would duplicate the mlopt arm
weight_chain_fold	speed	opt_einsum	order	2,049	—	—	—	ordering, not a graph — measured-only
weight_chain_fold	speed	paper_impl	impl	2,049	2,049	1.00×	parity	from bench.discovery.refs — the hand-built floor
weight_chain_fold	speed	torch_compile	compile	2,049	—	—	—	measured-only — no symbolic form

The registered roster

• eager (eager) — PyTorch eager — the spelled module, as written · all cases · record: launch-bound crossover: carriers lose to eager below ~T=512 (0.51×, docs/results.md)
• fla (kernel) — FLA chunk_retention — the Triton-kernel floor · cases: retnet_chunkwise · record: ~7–11× ahead of the fused carrier — kernel-level: fp64 GEMMs + a materialized score tensor on our side (bench/drivers/probes/retnet_baseline_probe.py)
• hand_carrier (carrier) — carrier term, generic lowering (no batched schedule) · all cases · record: 0.51× vs eager below the T=512 crossover — the carrier without its level-batched schedule (docs/results.md)
• opt_einsum (order) — opt_einsum greedy — the contraction-ordering baseline · cases: weight_chain_fold · record: oe-greedy is the contraction board's floor — the engine's ordering players tie its cost under the shared pair model (bench/players leaderboard)
• paper_impl (impl) — known-good impl — the case's registered ref · all cases · record: paper chunkwise ties the fused carrier (2.08 vs 2.12 ms T=2048; faster under graph replay) — bench/drivers/probes/retnet_baseline_probe.py
• torch_compile (compile) — torch.compile — the Inductor pipeline · all cases · record: pointwise fusion 0.82–0.88× loss (Inductor wins); weight chain 3.96× mlopt (no fold without freezing) — docs/results.md