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scaling study , why

the case for stopping point-experiments and measuring the scaling curve instead.

the evidence that forced this

thirty-five point-experiments (D1–D35), none beat the supervised ~1320 baseline, every one run on a single fixed ~32M model. the failure is not any single trick , it is the method: guessing one lever at a time on one model size, graded by a noisy expensive signal.

D35 made the confound explicit:

  • offline value metrics do not predict play. joint-from-scratch won the held-out decisive-sign metric by +6.67pp (65.95% → 72.62%) and came out level-to-behind at the board (0.175 vs 0.225 score vs stockfish-1320, within the ±0.09 noise of a 20-game match). the whole D30–D35 value-repair campaign was optimizing a proxy that doesn't track the goal.
  • match play is a terrible optimization signal. 20 games ⇒ score SE ≈ 0.09, so two configs 0.05 apart are indistinguishable. every gate we ran was under-powered.
  • the only lever that moved strength was search depth. value_final went 0.100 → 0.225 from 64 → 256 sims, then plateaus. search is an inference-time crutch, not a better model.

full numbers: reports/search_depth/results.json, figures in reports/joint_scratch/ and reports/search_depth/.

what a scaling law buys us

instead of anecdotes, a prediction. fit policy cross-entropy L(N, D) over model size N and positions seen D, then extrapolate to the one question that actually matters:

what N and D reach a target move-match (an elo proxy), and is that reachable on the 8gb 4060 , or is this fundamentally a cloud-scale problem?

policy cross-entropy is the right anchor because it is cheap, smooth, and low-variance , the opposite of match play. this is the chinchilla / kaplan method (arXiv:2001.08361, 2203.15556). the scale reference is deepmind's searchless-chess (arXiv:2402.04494): 2895 lichess elo with 270M params on ~15b positions, no search. locating ourselves against that curve tells us honestly whether the laptop can ever get there.

the hard constraint

the backbone must be attention. the current model is mostly SSM (attention_every=3, blocks 0/3/6/9 attention, the rest selective-SSM). the study sets attention_every=1 so every trunk block is causal attention, and scales width and depth from there. design and ladder: design.md.