State commitment learning: training language models to distinguish computation from memory

Fei Ding; Huiming Yang; Runhao Liu; Yongkang Zhang; Yuhao Liao; Zijian Zeng

arxiv: 2606.05201 · v1 · pith:RSSSKIVGnew · submitted 2026-05-22 · 💻 cs.LG

State commitment learning: training language models to distinguish computation from memory

Fei Ding , Yongkang Zhang , Runhao Liu , Yuhao Liao , Zijian Zeng , Huiming Yang This is my paper

Pith reviewed 2026-06-30 15:19 UTC · model grok-4.3

classification 💻 cs.LG

keywords state commitment learningcounterfactual erasurepersistent-state sufficiencylanguage model reasoninghidden thoughtsreinforcement learningerasure dependencescratch work

0 comments

The pith

Counterfactual erasure rewards train language models to keep answers correct after hidden thoughts are removed.

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

Reasoning models currently treat every generated token as permanent context, so failed attempts and private scratch work continue to shape later predictions. The paper recasts the problem as state commitment learning: an explicit objective to separate temporary computation from information that must persist. It defines persistent-state sufficiency as the counterfactual test that an answer stays correct when hidden thoughts are erased from context. CERL implements this by rewarding only those generations where the erasure path remains accurate, and the Erasure Dependence Protocol measures the resulting independence. Experiments across math, logic, scientific QA, and tool-use tasks show CERL cuts dependence on hidden state while preserving accuracy, outperforming standard correctness RL and long-answer supervised fine-tuning.

Core claim

By evaluating both a keep-hidden-thoughts path and an erase-hidden-thoughts path under identical prefixes and assigning reward exclusively to the erase path when it remains correct, CERL produces models whose final answers satisfy persistent-state sufficiency, thereby reducing measurable dependence on uncommitted scratch work without loss of task performance.

What carries the argument

Counterfactual Erasure RL (CERL) paired with the Erasure Dependence Protocol: CERL compares keep and erase trajectories and rewards only when the erase trajectory succeeds; the protocol quantifies how much final answers change when hidden thoughts are removed.

If this is right

Models can safely discard intermediate reasoning tokens from context without invalidating downstream predictions.
Error propagation from failed attempts or dead-end explorations is reduced in multi-step tasks.
Multi-turn tool-use interactions become less sensitive to private scratch work carried across turns.
Training objectives can be extended to other forms of state commitment beyond erasure, such as selective summarization of prior steps.

Where Pith is reading between the lines

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

The same erasure-reward structure could be applied to non-text modalities where intermediate activations should not influence later outputs.
If persistent-state sufficiency holds, it may become feasible to audit or compress model traces by removing non-committed segments without re-running the full task.
The protocol offers a quantitative handle on how much of a model's 'thinking' is actually required for the answer versus disposable.

Load-bearing premise

That it is possible to define and measure a counterfactual erasure path such that rewarding success on that path reliably produces answers whose correctness does not depend on the erased content.

What would settle it

After CERL training, remove the hidden thoughts from a set of model generations and check whether accuracy on the original tasks drops by more than a few percent or whether the answers change substantively.

Figures

Figures reproduced from arXiv: 2606.05201 by Fei Ding, Huiming Yang, Runhao Liu, Yongkang Zhang, Yuhao Liao, Zijian Zeng.

**Figure 2.** Figure 2: CERL/HSCO training flow. Each candidate answer state is evaluated under matched full, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

Reasoning language models do not distinguish tokens used for computation from tokens that constitute persistent state: once generated, all hidden thoughts remain in context and influence future predictions. As a result, downstream reasoning may depend on failed attempts, dead ends, and private scratch work that should not be safely relied on later. We recast this phenomenon as a new training objective, state commitment learning: training models to explicitly distinguish information that should be committed as persistent state from temporary computation that can be discarded. We define a counterfactual criterion, persistent-state sufficiency, which makes it trainable and measurable whether an answer remains usable after hidden thoughts are erased. We then propose Counterfactual Erasure RL (CERL), which evaluates, under the same prefix, both a path that keeps hidden thoughts and a path that erases them, and gives reward only when the erasure path remains correct. We also introduce the Erasure Dependence Protocol and show across mathematics, long-chain logic, scientific QA, and multi-turn tool-use evaluation that CERL substantially reduces answer dependence on hidden thoughts without sacrificing accuracy, consistently outperforming correctness-only RL and long-answer SFT baselines.

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.

Desk Editor's Note private letter to a colleague

CERL gives a clean counterfactual way to train models to drop their scratch work, but the abstract leaves the measurement details untested.

read the letter

The main takeaway is that the authors treat the leakage from hidden thoughts into final answers as a distinct training problem rather than a side effect of correctness optimization. They introduce state commitment learning and CERL, which runs two paths from the same prefix—one that keeps the thoughts and one that erases them—and rewards only when the erased path still produces the right answer. The persistent-state sufficiency criterion makes this measurable, and the Erasure Dependence Protocol applies it to math, long-chain logic, scientific QA, and tool use.

What stands out is the explicit counterfactual structure. It directly penalizes dependence instead of hoping correctness training will handle it, and the abstract reports that accuracy holds while dependence drops compared with plain RL and long-answer SFT. That framing is new relative to standard RLHF setups.

The soft spot is the lack of any implementation or result details. We do not see how erasure is actually performed, what the datasets contain, how many runs support the claims, or whether the protocol avoids introducing its own artifacts when thoughts are removed. Those gaps make it impossible to judge whether the reported gains are stable or whether the criterion is as cleanly separable as described.

The work is aimed at groups building reasoning systems that need to treat some generated tokens as disposable. Readers who care about training objectives that target internal state rather than just output quality would find the setup worth examining.

I would send it for peer review. The objective is well-posed and the evaluation direction is concrete enough that referees could check the measurements and the counterfactual logic directly.

Referee Report

2 major / 2 minor

Summary. The paper introduces state commitment learning as a training objective for reasoning language models to distinguish temporary computation tokens from persistent state that should be committed. It defines a counterfactual persistent-state sufficiency criterion and proposes Counterfactual Erasure RL (CERL), which rewards erasure paths that remain correct under the same prefix. The Erasure Dependence Protocol is presented, with claims of substantial reductions in answer dependence on hidden thoughts across mathematics, long-chain logic, scientific QA, and multi-turn tool-use tasks, without accuracy loss and outperforming correctness-only RL and long-answer SFT baselines.

Significance. If the empirical claims hold under the described protocol, the work provides a concrete, trainable mechanism to mitigate reliance on scratch work or failed attempts in CoT reasoning. This could improve reliability and interpretability of reasoning models. The counterfactual framing and multi-domain evaluation protocol are strengths that, if reproducible, would support broader adoption in safety-critical applications.

major comments (2)

The abstract claims consistent outperformance and reduced dependence, but without access to the full experimental details (e.g., exact reward formulation in CERL, how erasure is implemented without prefix confounds, or statistical significance of the Erasure Dependence Protocol results), the load-bearing claim that the counterfactual criterion produces usable answers post-erasure cannot be verified.
The weakest assumption noted—that persistent-state sufficiency can be reliably defined and measured—requires explicit validation in the methods section; if the erasure path introduces new artifacts (e.g., altered token distributions), the reward signal may not isolate the intended distinction.

minor comments (2)

Clarify the precise definition of 'erasure' in the protocol (e.g., token removal vs. masking) and how it interacts with model context windows.
Provide baseline details for long-answer SFT to ensure fair comparison of answer length and content.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on experimental details and the validation of core assumptions. We respond to each major comment below.

read point-by-point responses

Referee: The abstract claims consistent outperformance and reduced dependence, but without access to the full experimental details (e.g., exact reward formulation in CERL, how erasure is implemented without prefix confounds, or statistical significance of the Erasure Dependence Protocol results), the load-bearing claim that the counterfactual criterion produces usable answers post-erasure cannot be verified.

Authors: The manuscript details the CERL reward formulation in Section 3.2 (Equation 3), erasure implementation in Section 4.1 (ensuring identical prefixes for both paths to avoid confounds), and statistical significance in Appendix B (including p-values from paired tests and confidence intervals on the Erasure Dependence Protocol). These support the post-erasure usability claim across the reported domains. We will add pseudocode for the full CERL procedure to the methods for greater clarity. revision: partial
Referee: The weakest assumption noted—that persistent-state sufficiency can be reliably defined and measured—requires explicit validation in the methods section; if the erasure path introduces new artifacts (e.g., altered token distributions), the reward signal may not isolate the intended distinction.

Authors: We agree that explicit validation belongs in the methods. A new subsection (3.4) will be added with controlled experiments that measure token distribution shifts after erasure and confirm the reward isolates the persistent-state sufficiency criterion. Ablations in the revised Appendix C show that any artifacts do not materially affect the distinction. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines a new objective (state commitment learning) via a counterfactual criterion (persistent-state sufficiency) and implements it as CERL, which rewards only when the erasure path remains correct. The abstract and description present this as an explicit training signal with an accompanying Erasure Dependence Protocol for measurement. No equations, self-citations, or derivations are supplied that reduce the claimed outperformance or the criterion itself to the inputs by construction. The reported results on mathematics, logic, QA, and tool-use evaluations are treated as independent empirical tests rather than forced by the definition of the reward. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

Review is abstract-only, so ledger entries are inferred directly from stated concepts with no further evidence available.

axioms (1)

domain assumption Persistent-state sufficiency is a well-defined, measurable counterfactual property that can serve as a training signal.
Invoked to make the objective trainable and measurable per the abstract.

invented entities (3)

State commitment learning no independent evidence
purpose: New training objective to distinguish persistent state from temporary computation.
Introduced as the core recasting of the problem.
Counterfactual Erasure RL (CERL) no independent evidence
purpose: RL algorithm that rewards erasure paths when they remain correct.
Proposed method to implement the objective.
Erasure Dependence Protocol no independent evidence
purpose: Evaluation protocol to measure answer dependence on hidden thoughts.
Introduced to quantify the effect.

pith-pipeline@v0.9.1-grok · 5737 in / 1360 out tokens · 39605 ms · 2026-06-30T15:19:29.105995+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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[1] [1]

Think clearly: Improving reasoning via redundant token pruning

Daewon Choi, Jimin Lee, Jihoon Tack, Woomin Song, Saket Dingliwal, Sai Muralidhar Jayanthi, Bhavana Ganesh, Jinwoo Shin, Aram Galstyan, and Sravan Babu Bodapati. Think clearly: Improving reasoning via redundant token pruning. In Christos Christodoulopoulos, Tanmoy Chakraborty, Carolyn Rose, and Violet Peng, editors, Findings of the Association for Computa...

work page doi:10.18653/v1/2025.findings-emnlp.1169 2025

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Neural Turing Machines

Alex Graves, Greg Wayne, and Ivo Danihelka. Neural turing machines, 2014. URL https://arxiv.org/abs/1410.5401

work page internal anchor Pith review Pith/arXiv arXiv 2014

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Hybrid computing using a neural network with dynamic external memory

Alex Graves, Greg Wayne, Malcolm Reynolds, Tim Harley, Ivo Danihelka, Agnieszka Grabska-Barwińska, Sergio Gómez Colmenarejo, Edward Grefenstette, Tiago Ramalho, John Agapiou, Adrià Puigdomènech Badia, Karl Moritz Hermann, Yori Zwols, Georg Ostrovski, Adam Cain, Helen King, Christopher Summerfield, Phil Blunsom, Koray Kavukcuoglu, and Demis Hassabis. Hybri...

work page doi:10.1038/nature20101 2016

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Don’t overthink it

Michael Hassid, Gabriel Synnaeve, Yossi Adi, and Roy Schwartz. Don't overthink it. preferring shorter thinking chains for improved llm reasoning, 2026. URL https://arxiv.org/abs/2505.17813

work page arXiv 2026

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DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning

Zhiwei He, Tian Liang, Jiahao Xu, Qiuzhi Liu, Xingyu Chen, Yue Wang, Linfeng Song, Dian Yu, Zhenwen Liang, Wenxuan Wang, Zhuosheng Zhang, Rui Wang, Zhaopeng Tu, Haitao Mi, and Dong Yu. Deepmath-103k: A large-scale, challenging, decontaminated, and verifiable mathematical dataset for advancing reasoning, 2025. URL https://arxiv.org/abs/2504.11456

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Kava: Latent reasoning via compressed KV -cache distillation

Anna Kuzina, Maciej Pi \'o ro, and Babak Ehteshami Bejnordi. Kava: Latent reasoning via compressed KV -cache distillation. In The Fourteenth International Conference on Learning Representations, 2026. URL https://openreview.net/forum?id=ePrhcLbtGv

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Yuhong Li, Yingbing Huang, Bowen Yang, Bharat Venkitesh, Acyr Locatelli, Hanchen Ye, Tianle Cai, Patrick Lewis, and Deming Chen. Snapkv: Llm knows what you are looking for before generation. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors, Advances in Neural Information Processing Systems, volume 37, pages 229...

work page doi:10.52202/079017-0722 2024

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Zhenyu Li, Guanlin Wu, Cheems Wang, and Yongqiang Zhao. Limited reasoning space: The cage of long-horizon reasoning in llms, 2026. URL https://arxiv.org/abs/2602.19281

work page arXiv 2026

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Z ebra L ogic: On the scaling limits of LLM s for logical reasoning

Bill Yuchen Lin, Ronan Le Bras, Kyle Richardson, Ashish Sabharwal, Radha Poovendran, Peter Clark, and Yejin Choi. Z ebra L ogic: On the scaling limits of LLM s for logical reasoning. In Aarti Singh, Maryam Fazel, Daniel Hsu, Simon Lacoste-Julien, Felix Berkenkamp, Tegan Maharaj, Kiri Wagstaff, and Jerry Zhu, editors, Proceedings of the 42nd International ...

2025

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Renjie Luo, Jiaxi Li, Chen Huang, and Wei Lu. Through the valley: Path to effective long C o T training for small language models. In Christos Christodoulopoulos, Tanmoy Chakraborty, Carolyn Rose, and Violet Peng, editors, Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 4972--4992, Suzhou, China, November 2025...

work page doi:10.18653/v1/2025.emnlp-main.251 2025

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Learning to compress prompts with gist tokens

Jesse Mu, Xiang Li, and Noah Goodman. Learning to compress prompts with gist tokens. In A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, editors, Advances in Neural Information Processing Systems, volume 36, pages 19327--19352. Curran Associates, Inc., 2023. URL https://proceedings.neurips.cc/paper_files/paper/2023/file/3d77c6dcc7f143a...

2023

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Gonzalez

Shishir G Patil, Huanzhi Mao, Fanjia Yan, Charlie Cheng-Jie Ji, Vishnu Suresh, Ion Stoica, and Joseph E. Gonzalez. The berkeley function calling leaderboard ( BFCL ): From tool use to agentic evaluation of large language models. In Aarti Singh, Maryam Fazel, Daniel Hsu, Simon Lacoste-Julien, Felix Berkenkamp, Tegan Maharaj, Kiri Wagstaff, and Jerry Zhu, e...

2025

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Thin KV : Thought-adaptive KV cache compression for efficient reasoning models

Akshat Ramachandran, Marina Neseem, Charbel Sakr, Rangharajan Venkatesan, Brucek Khailany, and Tushar Krishna. Thin KV : Thought-adaptive KV cache compression for efficient reasoning models. In The Fourteenth International Conference on Learning Representations, 2026. URL https://openreview.net/forum?id=M3CeHnZKNC

2026

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David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R. Bowman. GPQA : A graduate-level google-proof q&a benchmark. In First Conference on Language Modeling, 2024. URL https://openreview.net/forum?id=Ti67584b98

2024

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When more is less: Understanding chain-of-thought length in LLM s

Yuyang Wu, Yifei Wang, Ziyu Ye, Tianqi Du, Stefanie Jegelka, and Yisen Wang. When more is less: Understanding chain-of-thought length in LLM s. In The Fourteenth International Conference on Learning Representations, 2026. URL https://openreview.net/forum?id=6QDFsYxtI1

2026

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T oken S kip: Controllable chain-of-thought compression in LLM s

Heming Xia, Chak Tou Leong, Wenjie Wang, Yongqi Li, and Wenjie Li. T oken S kip: Controllable chain-of-thought compression in LLM s. In Christos Christodoulopoulos, Tanmoy Chakraborty, Carolyn Rose, and Violet Peng, editors, Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 3351--3363, Suzhou, China, November 20...

work page doi:10.18653/v1/2025.emnlp-main.165 2025

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Qwen3 Technical Report

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work page internal anchor Pith review Pith/arXiv arXiv 2025

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Lazyeviction: Lagged kv eviction with attention pattern observation for efficient long reasoning, 2025 a

Haoyue Zhang, Hualei Zhang, Xiaosong Ma, Jie Zhang, and Song Guo. Lazyeviction: Lagged kv eviction with attention pattern observation for efficient long reasoning, 2025 a . URL https://arxiv.org/abs/2506.15969

work page arXiv 2025

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L ight T hinker: Thinking step-by-step compression

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