README.md

metadata

license: mit
tags:
  - ml-intern
  - replication
  - chess
  - scaling-laws
  - reinforcement-learning

Replication: "Understanding Reasoning from Pretraining to Post-Training"

Reduced-scale replication of core claims from "Understanding Reasoning from Pretraining to Post-Training" (Shen et al., arXiv:2607.16097), using the authors' released checkpoints, benchmark and code (pavelslab-nyu, Pre2Post-Chess-RL, GitHub).

Scope (agreed with the task owner): T0 = rebuild + calibrate the eval harness against the authors' protocol; T2 = replicate the joint pretraining–RL scaling law (their Fig. 3); T4 = replicate the move-level mechanism analysis (their Sec. 4.1 / App. H). Faithful but reduced-scale; no training of our own.

T0 — Eval harness (calibrated)

We reconstructed the authors' exact evaluation protocol from their released code (verl fork rollout worker, reward_function_multiturn.py, sft/evaluation/multiturn_puzzle_evaluator.py):

• SFT protocol (code/eval_chess.py --protocol sft): natural-CoT generation up to 1024 tokens from {pgn}<T>, stopping at </T>; then a move loop (≤32 tokens per move, stop at <call_env>), env replies injected after <call_env>, ≤5 solver moves, temp 1.0. Episode success = every solver move matches the ground-truth UCI line (= paper's pass@1).
• verl protocol (--protocol verl, for RL checkpoints): fixed 1024-token thinking budget where a premature </T> is replaced by <sep> and thinking continues; forced </T> at budget exhaustion; answer phase (≤1536 tokens, ≤6 env calls); extraction = first LAN move after </T>, else last LAN move in the segment (the authors' fallback).
• Batched generation uses left padding (verified exactly equal to unbatched greedy generation); right padding was verified incorrect.

Calibration on released checkpoints (B1+B2, 25/bin, k=8, temp 1.0):

checkpoint	protocol	pass@1	pass@8	first-move acc
SFT model_20m_5.3B	sft	1.5%	8%	5.3%
SFT model_680m_16B	sft	2.5%	12%	15.3%
RL model_20m_5.3B @ step 5000	verl	3.3%	12%	—

This already reproduces three qualitative claims: RL improves pass@1 without improving pass@k; larger pretraining improves move quality; absolute pass@1 is percent-level, consistent with the paper's own R₀(L) = 14.62·10^(−4.30·L) fit. Dominant failure mode at 20M: illegal committed moves (~78%), matching the authors' own illegal_move failure category.

T2 — Joint pretraining–RL scaling law

Data. 48 RL evals across the full 20M family (10 pretraining budgets × up to 5 RL steps; steps 100–5000) on the paper's fitting bins B3+B4 (results/t2/), plus a focused high-power sweep on B1+B2 (6 pretraining levels × 3 RL steps, 640 draws/point; results/t2b_*.json). Pretraining validation loss L(N,T) computed on 3000 held-out Lichess 2023-01 games (460k tokens per checkpoint; results/loss/) — a proxy for the authors' unreleased val split.

Finding 1 (B3+B4 floors out). On the paper's fitting bins, the entire 20M family measures 0–1% pass@1 (B4 = 0.000 in all 48 evals; only 40B@step4900 reaches 1%). At our measurement scale (400 draws/point vs the paper's ~8900) these bins cannot resolve the correlation. The paper used B3–B4 to avoid saturation of larger models; at 20M with our draw budget nothing saturates, so we moved the high-power sweep to B1+B2.

Finding 2 (claim 4a — pretraining loss predicts post-RL pass@1: reproduced directionally). On B1+B2, measured pass@1 at fixed RL compute (step 5000) vs our L: Spearman ρ = −0.54, Pearson r = −0.63 (n = 6; lower pretraining loss → higher post-RL pass@1). The paper reports ρ = −0.93…−0.99 via R_ref extrapolated to C_ref = 10²⁰ FLOPs; our extrapolated R_ref is noise-dominated (ρ = +0.60, wrong sign) because each per-run slope is fit from 3 points with ±0.7% per-point noise and then extrapolated ~3.5 decades. We therefore treat the non-extrapolated correlation as our replication of 4a and report the extrapolation failure as a scale limitation.

Measured points (B1+B2, step 5000):

pretrain tokens	L (ours)	pass@1
0.53B	0.704	2.0%
1.6B	0.588	3.3%
5.3B	0.531	2.5%
11B	0.513	3.6%
32B	0.488	4.4%
53B	0.480	2.8%

Finding 3 (claim 4b — RL slope grows with log pretraining tokens: not resolvable). Per-run slopes B from 3-point curves at our noise level are unidentified (Pearson r(B, log T) = −0.66, wrong sign, driven by one noisy point). The paper's r = +0.84 over 36 runs with ~8900 draws/point is outside what this budget can resolve.

T4 — Mechanism analysis (RL policy evolution)

Induced root-conditioned move policies π̂(a|s) via K=10–12 verl-protocol trace rollouts per puzzle and teacher-forced move scoring (paper: K=128), 12 puzzles each from B1 (easy), B4, B5 (hard); SFT vs RL steps 100/300/500; Table-13 categorization (top-k=3, ε_tail=0.05). Counts per bin (results/t4_mechanism.json):

category	B1 (rl100/300/500)	B4	B5
gt_amplification	1/2/2	4/3/4	2/3/3
tail_discovery	3/1/4	0/2/0	2/2/0
gt_regression	1/2/1	0/1/1	0/1/3
topk_correction	1/1/1	0/0/1	0/0/1
wrong_mode_amplification	0/1/0	2/1/3	2/1/1
other	6/5/4	6/5/3	6/5/5

Partially reproduced / not resolved. All five categories of the authors' taxonomy occur, including tail discovery on hard bins at intermediate RL steps (2/12 on B4 at step 300; 2/12 on B5 at steps 100–300). But the paper's headline contrast (amplification concentrated on easy puzzles, discovery on hard ones) is not resolved at K≈12 rollouts and 12 puzzles/bin: our dominant consistent signal is amplification on B4/B5, and single-count swings dominate. K=128 and larger puzzle samples would be needed for a decisive test.

Deviations from the paper

1. Validation loss is a proxy (held-out Lichess 2023-01 games, our tokenization/windows) — absolute L values are not comparable to the authors'; correlations use our internally consistent L.
2. Measurement scale: 400–640 draws/point vs the paper's ~8900; K≈12 rollouts vs 128 for T4. This is the dominant limitation and is the explanation we propose for the un-resolved claims, since the harness itself is calibrated against the authors' code paths.
3. Bin substitution for the high-power sweep (B1+B2 instead of B3+B4), justified above.
4. 20m_21B/40B RL runs excluded from loss correlations (no released pretrain checkpoint for those budgets).
5. RL-compute C per step estimated as 10·N·2048·(L_prompt+L_resp) with measured prompt length and assumed response length (paper App. D); slopes are unaffected by the constant.

Artifacts

• code/ — eval harness, val-loss computation, scaling-law fit, mechanism analysis
• results/t2/ — 48 B3+B4 RL evals + B1+B2 evals (t2b_* tags)
• results/loss/ — held-out pretraining loss for 32 checkpoints
• results/fit_results.json — all fit statistics
• results/t4_mechanism.json — induced policies + category counts
• Calibration JSONs: results/t2/… (see T0 table; B1+B2 25/bin runs)

Citation

Paper: https://arxiv.org/abs/2607.16097 — Shen, Li, Rahman, Sun, Goldblum, Telgarsky, Izmailov, "Understanding Reasoning from Pretraining to Post-Training", 2026. All checkpoints/data evaluated here are the authors' release.