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arxiv: 2511.06209 · v5 · submitted 2025-11-09 · 💻 cs.AI · cs.CL

ReProbe: Efficient Test-Time Scaling of Multi-Step Reasoning by Probing Internal States of Large Language Models

Jingwei Ni , Ekaterina Fadeeva , Tianyi Wu , Mubashara Akhtar , Jiaheng Zhang , Elliott Ash , Markus Leippold , Timothy Baldwin
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See-kiong Ng Artem Shelmanov Mrinmaya Sachan
This is my paper

Pith reviewed 2026-05-18 00:15 UTC · model grok-4.3

classification 💻 cs.AI cs.CL
keywords test-time scalingreasoning verificationinternal state probingprocess reward modelslightweight probesmulti-step reasoningLLM self-assessment
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The pith

Small probes on the internal states of frozen LLMs match or exceed the performance of process reward models up to 810 times larger for verifying reasoning steps.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a lightweight transformer probe can read the hidden activations inside a frozen large language model to score how credible each step in a generated reasoning chain is. This provides a cheap way to verify and select among multiple candidate steps during test-time scaling, replacing the need for much larger and more expensive process reward models. The probes train on annotations from a bigger model or from the original model itself and work across mathematics, planning, and general knowledge tasks. If the approach holds, verification becomes far more accessible and can be applied to longer reasoning chains without exploding compute costs. The work treats the internal states as carrying usable self-assessment signals that a small added component can extract.

Core claim

A transformer-based probe with fewer than 10 million parameters can be trained to estimate the credibility of individual reasoning steps by reading the internal states of a frozen LLM during generation. Training uses either labels from a larger model such as DeepSeek-R1 or self-supervised signals from the base model. When used for step verification in test-time scaling, these probes match or exceed the accuracy of process reward models up to 810 times larger across mathematics, planning, and question-answering domains.

What carries the argument

Transformer-based probe that processes internal activations from a frozen LLM to produce credibility scores for each reasoning step.

If this is right

  • Test-time scaling for multi-step tasks becomes feasible with far lower verification cost than current PRM approaches.
  • Annotation requirements for training verifiers drop because self-supervised signals from the base model can suffice.
  • Longer reasoning chains can be scaled at test time without proportional growth in compute for verification.
  • LLMs gain a practical route to introspective step selection that does not require retraining the base model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same probe architecture could be applied during generation to steer away from low-credibility steps in real time rather than only selecting among completed paths.
  • If internal-state patterns prove consistent across model families, probes trained on one LLM might transfer to others with minimal retraining.
  • Combining the probe scores with surface-level heuristics could create hybrid verifiers that improve accuracy in high-stakes domains such as planning or safety-critical reasoning.

Load-bearing premise

The internal states of a frozen LLM contain reliable signals about the credibility of its own reasoning steps that a small probe can extract and use across domains and annotation sources.

What would settle it

If the probes underperform large process reward models on a new domain when measured against independent human step-level annotations, the claim that internal states provide sufficient generalizable signals would be challenged.

Figures

Figures reproduced from arXiv: 2511.06209 by Artem Shelmanov, Ekaterina Fadeeva, Elliott Ash, Jiaheng Zhang, Jingwei Ni, Markus Leippold, Mrinmaya Sachan, Mubashara Akhtar, See-kiong Ng, Tianyi Wu, Timothy Baldwin.

Figure 1
Figure 1. Figure 1: Left: Given a problem set, target LLM generates CoTs and an annotator LLM labels step-level correctness. Middle: Training ReProbe with target LLM providing internal states while frozen. Right: at inference, ReProbe and PRM monitors internal states and output text correspondingly. ReProbe has significantly fewer parameters. increases GPU memory usage and computational cost. Third, PRMs are typically fine-tu… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the two prevalent test-time scal [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: PR-AUC of ReProbes with increas￾ing training set size (x-axis). Right: scaling training data either by adding new unique questions or by sam￾pling additional trajectories. Average PR-AUC across all datasets is reported. The results for each individual dataset are in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Best-of-N accuracy on GSM8k and Sci￾enceQA for different N values (Qwen3-8B). Impact of reasoning length on the performance of ReProbes and PRMs is investigated in §A.4. We show that the performance of both PRMs and ReProbes degrades with increasing reasoning length, but only slightly. Scaling the number of samples N [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Top 2 rows: PR-AUC of ReProbes with increasing training set size (x-axis). Bottom 2 rows: scaling [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: ROC-AUC on the step-level MATH benchmark using Qwen3-8B, evaluated across bins of reasoning chain [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Prompt template for Phi-4 and Qwen3-8B in non-thinking mode. The prompt is designed to elicit [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Prompt template for Qwen3-1.7B in native thinking mode. [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Two-step prompting procedure for step-level correctness annotation. The first stage evaluates the solution [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The prompt used for annotating chain-level correctness by evaluating the full reasoning trace. [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Prompt template for annotating correctness of reasoning steps in native thinking mode. [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
read the original abstract

LLMs can solve complex tasks by generating long, multi-step reasoning chains. Test-time scaling (TTS) can further improve performance by sampling multiple variants of intermediate reasoning steps, verifying their correctness, and selecting the best steps for continuation. However, existing verification approaches, such as Process Reward Models (PRMs), are computationally expensive and require large-scale human or model-generated annotations. We propose a lightweight alternative for step-level reasoning verification based on probing the internal states of LLMs. We train a transformer-based probe that uses the internal states of a frozen LLM to estimate the credibility of its reasoning steps during generation. Annotation can be provided either by a larger LLM (e.g., DeepSeek-R1) or in a self-supervised manner by the original model itself. The probes are lightweight, containing fewer than 10M parameters. Across multiple domains, including mathematics, planning, and general knowledge question answering, our probes match or exceed the performance of PRMs that are up to 810x larger. These results suggest that LLM internal states encode confidence in their reasoning processes and can serve as reliable signals for step verification, offering a promising path toward scalable, generalizable TTS and more introspective LLMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces ReProbe, a lightweight transformer-based probe (<10M parameters) trained on the internal hidden states of a frozen LLM to estimate the credibility of individual reasoning steps. Annotations are obtained either from a larger model (e.g., DeepSeek-R1) or via self-supervision by the base model. Experiments across mathematics, planning, and general-knowledge QA show that these probes match or exceed the performance of process reward models (PRMs) up to 810x larger when used for test-time scaling of multi-step reasoning.

Significance. If the central empirical claims hold after addressing controls, the work would provide a scalable, low-cost alternative to large PRMs for step-level verification in test-time scaling. It would also supply evidence that frozen-LLM internal states encode extractable signals about reasoning quality, supporting more efficient and introspective verification methods. The direct performance comparisons to existing PRMs constitute a clear strength.

major comments (2)
  1. [§4] §4 (Experimental Setup): No ablation is reported in which the probe is retrained on the raw token sequence of the reasoning steps or on final-layer embeddings instead of the selected internal hidden states. This control is load-bearing for the claim that performance derives from internal-state signals rather than probe architecture or annotation quality, especially since labels are supplied by larger models or self-supervision.
  2. [§5] §5 (Results): Performance tables report point estimates of matching or exceeding larger PRMs without error bars, number of independent runs, or statistical tests. Given the stochasticity of sampling in TTS, this omission prevents assessment of whether the reported gains are robust.
minor comments (2)
  1. [Abstract] The abstract states 'up to 810x larger' without listing exact parameter counts for the compared PRMs; these numbers should appear in a table or §5 for precise verification.
  2. [§3] Notation for the probe architecture (e.g., layer selection and aggregation of hidden states) is introduced in §3 but could be clarified with a diagram or explicit equation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important controls and reporting practices that will strengthen the manuscript. We address each major comment below and will incorporate the suggested changes in the revision.

read point-by-point responses

  1. Referee: [§4] §4 (Experimental Setup): No ablation is reported in which the probe is retrained on the raw token sequence of the reasoning steps or on final-layer embeddings instead of the selected internal hidden states. This control is load-bearing for the claim that performance derives from internal-state signals rather than probe architecture or annotation quality, especially since labels are supplied by larger models or self-supervision.

    Authors: We agree that this ablation is necessary to isolate the value of the selected internal hidden states. In the revised manuscript we will retrain identical probe architectures on (i) raw token sequences of the reasoning steps and (ii) final-layer embeddings only, using the same annotation sources and evaluation protocol. The results will be reported alongside the original internal-state results to directly address whether performance gains are attributable to the probed states rather than architecture or label quality. revision: yes

  2. Referee: [§5] §5 (Results): Performance tables report point estimates of matching or exceeding larger PRMs without error bars, number of independent runs, or statistical tests. Given the stochasticity of sampling in TTS, this omission prevents assessment of whether the reported gains are robust.

    Authors: We acknowledge that the stochastic nature of test-time sampling makes variability reporting essential. In the revision we will repeat all main experiments across at least five independent random seeds, add standard-error bars to the tables, and include paired statistical tests (e.g., t-tests or Wilcoxon tests) between ReProbe and the compared PRMs. These additions will allow readers to assess the robustness of the reported performance matches and improvements. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical validation is self-contained

full rationale

The paper presents an empirical method for training a lightweight probe on frozen-LLM hidden states to estimate reasoning-step credibility, with annotations sourced externally (larger LLM or self-supervised) and results shown via direct performance comparisons to larger PRMs across domains. No equations, derivations, or claims reduce the central performance results to inputs by construction, self-definition, or load-bearing self-citation. The reported gains are framed as experimental outcomes rather than forced by the fitting process itself, making the derivation chain independent and falsifiable through the described benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unproven domain assumption that LLM hidden states contain extractable credibility information about reasoning steps; this is tested empirically rather than derived from first principles.

axioms (1)
  • domain assumption Internal states of LLMs encode information about the credibility of reasoning steps
    This assumption underpins the entire probing approach and is invoked to justify training the probe on frozen LLM activations.

pith-pipeline@v0.9.0 · 5556 in / 1170 out tokens · 36132 ms · 2026-05-18T00:15:47.547563+00:00 · methodology

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Forward citations

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  2. Hypothesis generation and updating in large language models

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    LLMs exhibit Bayesian-like hypothesis updating with strong-sampling bias and an evaluation-generation gap but generalize poorly outside observed data.

  3. Hidden Failures in Robustness: Why Supervised Uncertainty Quantification Needs Better Evaluation

    cs.CL 2026-04 conditional novelty 6.0

    Supervised uncertainty probes for LLMs show poor robustness under distribution shift, with middle-layer representations and multi-token aggregation proving more reliable than final-layer or single-token features.

Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages · cited by 3 Pith papers · 3 internal anchors

  1. [1]

    Training Verifiers to Solve Math Word Problems

    Training verifiers to solve math word prob- lems.Preprint, arXiv:2110.14168. DeepSeek-AI. 2025. Deepseek-r1: Incentivizing rea- soning capability in llms via reinforcement learning. Preprint, arXiv:2501.12948. Ekaterina Fadeeva, Aleksandr Rubashevskii, Artem Shelmanov, Sergey Petrakov, Haonan Li, Hamdy Mubarak, Evgenii Tsymbalov, Gleb Kuzmin, Alexan- der ...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    Improve Mathematical Reasoning in Language Models by Automated Process Supervision

    Let’s verify step by step. InThe Twelfth Inter- national Conference on Learning Representations. Zhen Lin, Shubhendu Trivedi, and Jimeng Sun. 2024. Generating with confidence: Uncertainty quantifica- tion for black-box large language models. Chengwu Liu, Ye Yuan, Yichun Yin, Yan Xu, Xin Xu, Zaoyu Chen, Yasheng Wang, Lifeng Shang, Qun Liu, and Ming Zhang. ...

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  3. [3]

    InProceed- ings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pa- pers), pages 9426–9439, Bangkok, Thailand

    Math-shepherd: Verify and reinforce LLMs step-by-step without human annotations. InProceed- ings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pa- pers), pages 9426–9439, Bangkok, Thailand. Associ- ation for Computational Linguistics. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quo...

    work page 2022

  4. [4]

    Stepwiser: Stepwise generative judges for wiser reasoning, 2025 c

    An implementation of generative prm. Wei Xiong, Wenting Zhao, Weizhe Yuan, Olga Golovneva, Tong Zhang, Jason Weston, and Sain- bayar Sukhbaatar. 2025. Stepwiser: Stepwise generative judges for wiser reasoning.Preprint, arXiv:2508.19229. Hang Yan, Fangzhi Xu, Rongman Xu, Yifei Li, Jian Zhang, Haoran Luo, Xiaobao Wu, Luu Anh Tuan, Haiteng Zhao, Qika Lin, et...

    work page arXiv 2025

  5. [5]

    Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models

    Tree of thoughts: Deliberate problem solving with large language models.Advances in neural information processing systems, 36:11809–11822. Zhangyue Yin, Qiushi Sun, Qipeng Guo, Zhiyuan Zeng, Xiaonan Li, Junqi Dai, Qinyuan Cheng, Xuanjing Huang, and Xipeng Qiu. 2024. Reasoning in flux: Enhancing large language models reasoning through uncertainty-aware ada...

    work page internal anchor Pith review Pith/arXiv arXiv 2024