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From Correctness to Recoverability

Rethinking what hidden-state probes measure in chain-of-thought reasoning

Paper in progress
Role
AI/ML Researcher, Algoverse
When
Jun 2026 – now
Model
DeepSeek-R1-Distill-Qwen-1.5B
Data
MATH-500, levels 3–5

Hidden-state probes look like they can tell whether a reasoning trace will end correctly. Within a single problem they sit at chance, and at the last token they do no better than the trace's length. Re-rolling the same prefix does far better, and shows that many traces that end wrong were still recoverable mid-reasoning.

Can you tell, mid-trace, whether the answer will be right?

Within-problem AUROC (0.5 is a coin flip). The shaded band is the 95% interval for re-rolling. DeepSeek-R1-Distill-Qwen-1.5B on MATH-500, levels 3–5.

.50.60.70.80.90chance1282565121,0242,0484,096last tokentokens into the reasoning traceProbe, strict sweep, 128 tokens: 0.549Probe, strict sweep, 256 tokens: 0.519Probe, strict sweep, 512 tokens: 0.487Probe, strict sweep, 1024 tokens: 0.547Probe, strict sweep, 2048 tokens: 0.495Probe, strict sweep, 4096 tokens: 0.498Probe, same prefixes, 512 tokens: 0.50Probe, same prefixes, 2048 tokens: 0.53Probe, same prefixes, 4096 tokens: 0.55Recoverability, 512 tokens: 0.626 [0.56, 0.69]Recoverability, 2048 tokens: 0.655 [0.58, 0.72]Recoverability, 4096 tokens: 0.811 [0.76, 0.86]re-rolling the prefixprobeprobe, strict sweep+.26Probe at the last token: 0.809Length baseline at the last token: 0.787probe .81length .79
  • Recoverability: 448 traces, 88 problems, 8 re-rolls per prefix, scored by 1 − r̂. It's a lower bound, since 8 re-rolls leave 10–20% of pairs tied.
  • Strict sweep: 2,202 traces, 106 mixed-outcome problems, nested cross-validation, within-problem.
  • Last token: the probe beats length by +.02 [-0.004, +.05], which is not significant.

What we found

  • Within a problem, probes can't tell a trace that will end right from one that will end wrong. Across 2,202 traces from 106 mixed-outcome problems, every 95% interval from 128 to 4,096 tokens contains 0.5.
  • Re-rolling 8 continuations from the same prefix predicts the outcome far better: 0.63 AUROC at 512 tokens, rising to 0.81 at 4,096. That's a gap of +0.26 over the probe on the same prefixes.
  • At the last token the probe scores 0.809, but trace length alone scores 0.787, and the difference isn't significant. The probe mostly reads out difficulty.

What I did

  • Designed the experiments
  • Ran training and ablations
  • Built the evaluation pipeline

Methods

  • Recoverability metrics
  • Logistic-regression and gradient-boosted probes
  • Text baselines (length, TF-IDF)
  • Error injection

Status

Co-authoring a technical paper we're aiming to submit to AAAI and ICLR conferences and workshops. These are working numbers and may change before the paper is out. Nothing has been accepted yet; this page will link the paper once it's public.