Pith. sign in

REVIEW 3 major objections 6 minor 42 references

FlowEdit trains language models to enumerate every valid resolution of a conflicting problem in a single pass by regulating internal reasoning flows with two dual mutual-information objectives.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 10:33 UTC pith:LAH3JARC

load-bearing objection The method is worth a serious look, but the MI-bound theory as written doesn't do what it claims: the estimators and the conditioning assumptions don't line up. the 3 major comments →

arxiv 2607.20500 v1 pith:LAH3JARC submitted 2026-06-20 cs.AI

FlowEdit: Information-Theoretic Control of LLM Reasoning Flows for Ill-posed Problems Involving Conflicts

Sizhe Tang , Guangyu Jiang , Yu Li , Rongqian Chen , Ioannis G. Kevrekidis , Tian Lan This is my paper
classification cs.AI
keywords ill-posed problemsconflicting conditionsconditional mutual informationreasoning flowsbranch-aware reasoningLLM reasoningflow regulationmulti-hypothesis reasoning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that ill-posed problems with conflicting conditions should not be treated as detect-and-reject cases but as multiply solvable ones, where each self-consistent subset of conditions yields a distinct valid answer. It proposes FlowEdit, a training framework that enforces this behaviour by regulating the model's internal reasoning flows: each flow is anchored to its own hypothesis and outcome (flow sufficiency), while sibling flows are pushed to carry minimal overlapping information beyond the shared analysis (flow separation). These two goals are expressed as conditional mutual information objectives on hidden-state summaries at designated tokens, optimised through tractable variational bounds under an epsilon-sufficiency assumption. Trained on a 5,000-problem dataset spanning three domains and one to four valid branches, a 4B model improves exact-set-match accuracy by 68% and information recovery by 24% over the strongest closed-source baseline, with gains growing with branch count. If correct, the framework gives a representation-level account of why parallel hypothesis maintenance succeeds where sequential next-token elaboration collapses.

Core claim

The central claim is that a single autoregressive pass can carry several mutually exclusive reasoning flows if the model is trained to keep their boundary representations simultaneously sufficient and separated. Concretely, FlowEdit maximizes the conditional mutual information I(ek; eyk | ea) between each hypothesis embedding and its answer embedding given the analysis embedding, and minimizes I(ei; ej | wij) between sibling hypothesis embeddings given a conditioning vector that absorbs the shared analysis and the preceding-flow autoregressive baseline. The paper shows these objectives can be optimised through an InfoNCE lower bound for sufficiency and a CLUB upper bound for separation, and

What carries the argument

The machinery is a set of boundary embeddings: hidden states of a causal language model at designated structural tokens ([ANA], [/ANA], [B], [SEP], [/B]) that summarise each reasoning flow at its boundaries. FlowEdit imposes two conditional-mutual-information objectives on these embeddings—maximising I(ek; eyk | ea) per flow for sufficiency, and minimising I(ei; ej | wij) across sibling flows for separation—and makes the optimisation tractable with an InfoNCE lower bound and a CLUB upper bound, conditioned on the analysis embedding ea and an autoregressive baseline summary. The epsilon-sufficiency condition on the embeddings is what makes the conditioning choice principled rather than heuris

Load-bearing premise

The objectives assume the boundary embeddings are near-sufficient summaries of their contexts and that the analysis segment contributes only positive partition information beyond the problem statement; at inference the model writes its own analysis, and if these conditions fail, conditioning on the analysis embedding no longer isolates the residual redundancy the separation term is meant to penalise.

What would settle it

On a held-out set where the model's self-generated analysis demonstrably differs from the oracle-constructed training analyses, compute the empirical gap I(ei; ej | ea_self) - I(ei; ej | ex). If conditioning on the self-generated analysis does not reduce cross-flow dependence below conditioning on the prompt alone (or the reduction is negative), the epsilon-sufficiency and positive-partition assumptions fail and the claimed provable optimisation of the conditional mutual information collapses.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A trained FlowEdit model returns the complete set of valid resolutions for a conflicting problem in a single structured pass, rather than silently committing to one hypothesis or rejecting the input.
  • The framework strictly generalises standard well-posed reasoning: with K*=1 the objectives reduce to conventional single-trace generation, so ordinary math performance is not sacrificed.
  • Gains scale with the number of valid branches: the largest improvements over baselines appear on K*=2 inputs, where parallel maintenance matters most against the 1/K* ceiling of single-hypothesis prompting.
  • Token-level entropy signatures (concentration inside answer spans, amplification at branch-opening tokens) provide a diagnostic that flow regulation acts at the predicted boundary positions, not diffusely.

Where Pith is reading between the lines

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

  • The same dual-objective scheme could be applied to any generation task where multiple mutually exclusive interpretations are valid—multi-document QA with contradictory sources, requirement analysis in systems engineering, or code generation from ambiguous specifications—since the paper's formulation does not depend on mathematics.
  • Because the model generates its own analysis at inference, the epsilon-sufficiency assumption is most fragile there; a testable extension is to train the analysis generator itself to be partition-informative, or to regularise the analysis to satisfy the sufficient-statistic property.
  • The reported entropy signature suggests a lightweight, training-free probe for multi-hypothesis maintenance: sharp next-token entropy spikes at branch openings in teacher-forced traces could be used to audit whether an LLM is genuinely keeping competing hypotheses separate.
  • The paper leaves the upstream branching decision implicit in the policy; an information-theoretic extension could make the choice of whether and how many branches to open an explicit random variable optimised by the same flow-regulation objective.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes FlowEdit, a training framework intended to make LLMs solve ill-posed problems with conflicting conditions by enumerating all valid resolutions in a single pass. The method interleaves an analysis segment with branch blocks, reads off boundary hidden states as 'reasoning flow' representations, and trains the model with two conditional mutual information objectives: maximizing I(e_k; e_yk | e_a) for flow sufficiency and minimizing I(e_i; e_j | w_ij) for flow separation. The authors claim these objectives provably optimize the underlying conditional MIs via InfoNCE and CLUB estimators under an epsilon-sufficiency condition, and they report substantial gains over closed-source baselines on a new synthetic dataset spanning K* = 1-4 branches. The paper also presents ablations and token-level entropy diagnostics attributed to the flow-regulation loss.

Significance. If the theoretical claims were sound, FlowEdit would be a notable contribution to multi-hypothesis reasoning, moving beyond detection-and-rejection to constructive enumeration of valid resolutions. The empirical results are genuinely promising: exact-set-match improves from 0.28 to 0.47 over the strongest closed-source baseline, information recovery from 0.41 to 0.51, and the ablations show that both loss terms contribute, with the conditioning choice (ea vs ex) mattering. The dataset construction pipeline with independent arithmetic verification and the held-out stratified split are strengths, as is the clear reporting of training dynamics and hyperparameter sensitivity. However, the central theoretical mechanism as stated is not supported by the estimators in Eqs. (4)-(5), so the 'provable optimization' claim requires substantial correction.

major comments (3)
  1. [Section 3.2, Eq. (4)] The InfoNCE estimator is claimed to be a lower bound on I(e_k; e_yk | e_a). A valid conditional InfoNCE lower bound requires the negatives {e_yk^(n)} to be sampled from p(e_yk | e_a) for the same conditioning ea. The text states that negatives are 'drawn from other branches in the minibatch,' which mixes branches with different analyses (and often different problems). The denominator then approximates an average over a marginal or mixture distribution, not p(e_yk | e_a), so the expression is not a lower bound on the conditional MI. Consequently, maximizing L_suf does not provably increase the intended quantity, and the central 'provable optimization' claim collapses at this step. Please implement negatives from p(e_yk | e_a) (e.g., same-problem branches with a shared ea), use a corrected conditional bound, or explicitly revise the theoretical claim.
  2. [Section 3.2, Eq. (5)] The conditional CLUB upper bound requires the second term E_{p(e_i,w_ij) p(e_j|w_ij)} log q(e_j|e_i,w_ij). The implementation described as 'shuffled (e_j, w_ij) pairs' samples from the product of marginals p(e_j)p(w_ij) (or its empirical approximation), not from p(e_j|w_ij) jointly with p(e_i,w_ij). The expression bICLUB is therefore not guaranteed to be an upper bound on I(e_i;e_j|w_ij), and minimizing it may not reduce the intended conditional dependence. Since the bounding direction is load-bearing for the separation objective, this is not a minor technicality. Please implement the conditional resampling required by CLUB or provide a different estimator with the claimed direction.
  3. [Section 3.2 / Appendix A, Proposition 1] The proof of Proposition 1 relies on the epsilon-sufficiency assumptions in Eq. (15) and on Delta_ij >= 0. These are asserted rather than measured. In particular, at inference the model generates its own analysis a, which need not match the oracle-constructed analyses used in training; the claim that A contributes positive partition information (Appendix A, 'On the sign of Delta_ij') is a property of the data construction, not of the learned representations. Without empirical checks of Delta_ij or of the epsilon-sufficiency bounds on the trained models, the conclusion that conditioning on ea 'provably isolates residual cross-flow redundancy' is not established. Please add measurements or significantly weaken the claim.
minor comments (6)
  1. [Figure 4] The claim that the D1 entropy gap 'grows monotonically from K*=2 to K*=4' appears to be based on visual inspection. Please report the relevant statistics or a trend test rather than an informal reading of the curves.
  2. [Table 1] The table is extremely dense, with both EM and IR in a single wide layout. Consider splitting into separate tables or highlighting the FlowEdit rows more clearly to improve readability.
  3. [Section 4.1] The blind-prompt and ill-posed-prompt conditions differ in more than the disclosure of ill-posedness (the requested output format is also different). This is acceptable for an ablation, but the paper should acknowledge that prompt format and information disclosure are confounded in the baseline comparisons.
  4. [Section D.1] The dataset is generated by a frontier LLM with a self-check and human spot-check. The statement that contamination with public benchmarks is 'not expected by construction' is reasonable but unverified; a simple n-gram overlap check with public math benchmarks would strengthen the claim.
  5. [Conclusion] The sentence 'the upstream decision of whether to branch remains implicit in the policy and are not the objects of the loss' contains a subject-verb agreement error ('decision ... are').
  6. [Section 3.2, Eq. (5) notation] The description of the shuffled pairs is ambiguous: it should state explicitly whether the shuffle is across the batch (destroying the conditioning) or within the same condition group. The current text reads as the former, which is inconsistent with the CLUB bound.

Circularity Check

1 steps flagged

Central FlowEdit derivation is not circular: EM/IR gains and ablations stand independently. One supporting token-entropy regularity (K*=1 D1 gap) is entailed by the loss definition, and the synthetic benchmark is self-referential though not definitionally circular.

specific steps
  1. self definitional [Section 4.3 (Token-Level Entropy Signatures), Figure 4 discussion]
    "(i) On K ⋆ = 1, trained and base D1 coincide: Lsep admits no active pair, so the absence of a boundary spike reflects the objective by design."

    Eq. (11) defines Lsep as an average over pairs (i,j) in P; when K*=1, P is empty, so Lsep=0 by definition and no gradient acts on [B] boundaries. The observed 'absence of a boundary spike' is therefore entailed by the loss construction, not an independent confirmation of the separation mechanism. The second regularity (D1 gap growing with K*) is also aligned with |P|=K(K-1)/2 growing with K*, though its monotonicity is not strictly forced. Presenting these as regularities that 'sharpen the reading' uses the definition of Lsep as evidence for the mechanism it defines.

full rationale

The paper's main claims — that FlowEdit improves exact-set-match and information recovery on held-out validation, and that ablations show both loss terms and the ea conditioning matter — are grounded in independent measurements (Table 1, Table 2, Fig. 2), not derived from the definitions of the objectives. Eq. (3)-(12) define the objectives; Prop. 1 is a conditional-MI identity under the stated epsilon-sufficiency assumptions; no fitted constant is relabeled as a prediction. Self-citations [1,27,30] appear only in related work and are not load-bearing. The closest thing to a circular step is in Sec. 4.3: the K*=1 regularity ('absence of boundary spike') is explicitly admitted to be by design because Lsep has no active pair when K=1 (Eq. 11 with P empty); presenting it as a regularity that 'sharpens the reading' of the mechanism is a self-definitional sanity check rather than independent evidence. The D1 growth with K* is also aligned with |P|=K(K-1)/2, though not strictly forced. The synthetic dataset fixes K* by construction (Appendix D.1), making the benchmark self-referential, but this is a data-validity concern, not a circular derivation; held-out evaluation against that same generator still measures generalization within the constructed distribution. The reviewer's concern about InfoNCE/CLUB bound directions is a correctness risk in the claimed 'provable' optimization, not a circularity, and is not scored here. Overall the central result has independent empirical content; the score reflects the one by-construction diagnostic, not a collapsed derivation.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 2 invented entities

The central method rests on a stated but unverified epsilon-sufficiency assumption, a positivity assumption on analysis-contributed dependence, and the validity of InfoNCE/CLUB as conditional MI bounds, which the implementation does not fully satisfy. The main free parameters are training/evaluation hyperparameters chosen by hand; none are fitted to external data.

free parameters (6)
  • lambda (flow-regulation weight) = 0.10
    Chosen by validation EM sweep over {0.05,0.10,0.15,0.20}; all main results use this value.
  • InfoNCE temperature tau = 0.07
    Fixed in Eq. (4); standard contrastive value, not swept in the paper.
  • CLUB per-pair clip bound = [-1, +1]
    Eq. (11); chosen to bound each pair's nats budget; arbitrary but load-bearing for training stability.
  • CLUB inner update schedule = 3 updates per outer step
    Appendix C.3; chosen to keep the upper-bound property tight, but accuracy of q_psi is not verified.
  • LoRA rank/alpha = r=16, alpha=32
    Appendix C.2; adopted from the LoRA fine-tuning recipe, not central to the theory.
  • Decoding temperature/top-p = T=0.7, p=0.9
    Appendix C.4; affects all evaluation numbers.
axioms (5)
  • domain assumption Boundary embeddings are epsilon-sufficient: I((X,A);(Ei,Ej)|ea) <= eps_a and I(X;(Ei,Ej)|ex) <= eps_x (Eq. 15).
    Assumed without measurement; required for Proposition 1 and for the claim that conditioning on ea isolates residual cross-flow redundancy.
  • domain assumption Delta_ij = I(Ei;Ej|X) - I(Ei;Ej|X,A) >= 0: the analysis A contributes partition information beyond X.
    Appendix A explicitly states this is treated as a property of the synthetic data construction rather than derived; not guaranteed for model-generated analyses at inference.
  • domain assumption The InfoNCE estimator is a lower bound on conditional MI and the CLUB estimator is an upper bound on conditional MI in the implementation used.
    Standard theorems do not cover the conditional setting as implemented; negatives are drawn from other branches and pairs are shuffled, so the required conditional distributions are not sampled.
  • domain assumption The structured output format (2) makes hidden states at [ANA], [/ANA], [B], [SEP], [/B] valid per-flow summaries.
    The entire method presupposes that these token positions address individual flows; no independent evidence establishes that hidden states at these tokens correspond to flow-level objects.
  • domain assumption For each ill-posed problem, the maximal self-consistent subsets of conditions induce well-posed subproblems with unique solutions.
    This defines Y*(x) in Eq. (1) and excludes cases where a maximal subset still has multiple solutions or where no such subset exists.
invented entities (2)
  • Structural boundary tokens ([ANA], [/ANA], [B], [SEP], [/B], [END]) no independent evidence
    purpose: Mark analysis and branch boundaries in the output so hidden states at these tokens can be read off as flow summaries; six new trainable vocabulary rows.
    Their semantics are defined purely by the training format and dataset; no external falsifiable handle exists.
  • Reasoning-flow boundary representations (ea, ek, eyk) no independent evidence
    purpose: Objects of the MI objectives: each flow is summarized by designated hidden states so that sufficiency and separation can be optimized.
    Internal representational construct; the paper provides no independent measurement of 'flows' outside its own loss design.

pith-pipeline@v1.3.0-alltime-deepseek · 22731 in / 14821 out tokens · 141042 ms · 2026-08-02T10:33:45.412896+00:00 · methodology

0 comments
read the original abstract

Large Language Models (LLMs) perform strongly on well-specified reasoning tasks with a feasible answer. However, problems encountered in the open world can become ill-posed due to inconsistent conditions, conflicting statements, or mutually incompatible requirements, admitting no valid responses. We argue that reasoning of such ill-posed problems involving conflicts require novel LLM capabilities to make hidden conflicts explicit, maintain competing hypotheses via multiple reasoning branches, and generate alternative responses in a single pass, all of which are challenging due to the limitation of the next-token prediction mechanism in LLMs. To this end, we propose FlowEdit, a novel framework that leverages information-theoretic principles to quantify and regulate internal reasoning flows of LLMs, for generating a full set of alternative responses under valid hypotheses. FlowEdit can be viewed as enforcing a branch-aware reasoning process using two dual information-theoretic objectives on the model's internal reasoning representations: maximizing the information flow from each selected hypothesis to the branch outcome, while minimizing the overlap and conditional dependence across sibling branches, to provide a diverse, informative set of responses with broad coverage. We show that this is achieved through tractable variational bounds under boundary embeddings being {\epsilon}-sufficient, optimizing the underlying conditional mutual information in LLM reasoning process. Extensive experiments demonstrate that FlowEdit outperforms leading proprietary models, improving exact-set-match accuracy by 68%, while boosting overall response informativeness by 24%. We further show that flow regulation surfaces in the token stream as a redistribution of next-token entropy that concentrates inside each branch, amplifies at flow boundaries, and scales with the number of flows the problem requires.

Figures

Figures reproduced from arXiv: 2607.20500 by Guangyu Jiang, Ioannis G. Kevrekidis, Rongqian Chen, Sizhe Tang, Tian Lan, Yu Li.

Figure 1
Figure 1. Figure 1: Overview of FLOWEDIT. On ill-posed problems involving conflicts, next-token prediction silently commits to one self-consistent hypothesis and collapses the answer set onto a single trajectory (left). FLOWEDIT regulates the model’s internal reasoning flows via two dual information-theoretic objectives on boundary representations (right). One example involving conflicts is demonstrated. 1 Introduction Large … view at source ↗
Figure 2
Figure 2. Figure 2: Training dynamics of FLOWEDIT based on Qwen-3-4B Base and Qwen-2.5-3B-Instruct with metrics of EM and IR. It is illustrated that the training of FLOWEDIT can converge stably with high performance. Shaded regions indicate standard deviation across three seeds. Exact-set-match (EM) credits a response only when Yˆ(x) = Y ⋆ (x), treating every deviation as a uniform failure and remaining silent on the share of… view at source ↗
Figure 3
Figure 3. Figure 3: Per-sample teacher-forced next-token entropy, one example per [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Window-aggregated entropy (mean ± 95% CI) at [B] (D1) and [SEP] (D2). The D1 gap vanishes at K⋆ = 1 and grows with K⋆ . We probe whether Lflow leaves observable signatures in token-level entropy through two diagnostic windows. D1 spans the 10 tokens after each [B] (hypothesis opening); D2 spans the 10 tokens after each [SEP] (answer span). The two windows isolate the two loss terms: Lsuf predicts trained D… view at source ↗
Figure 5
Figure 5. Figure 5: Training dynamics under varying flow-regulation weight [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: End-of-training EM and IR as a function of the flow-regulation weight [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ill-posed–aware prompt. The model is told the input is ill-posed and asked to enumerate all [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Blind prompt. The model is not told that problems may be ill-posed. [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 2 canonical work pages

  1. [1]

    Agent alpha: Tree search unifying generation, exploration and evaluation for computer-use agents.arXiv preprint arXiv:2602.02995, 2026

    Sizhe Tang, Rongqian Chen, and Tian Lan. Agent alpha: Tree search unifying generation, exploration and evaluation for computer-use agents.arXiv preprint arXiv:2602.02995, 2026

    arXiv 2026

  2. [2]

    Mint: Minimal information neuro-symbolic tree for objective-driven knowledge-gap reasoning and active elicitation.arXiv preprint arXiv:2602.05048, 2026

    Zeyu Fang, Mahdi Imani, and Tian Lan. Mint: Minimal information neuro-symbolic tree for objective-driven knowledge-gap reasoning and active elicitation.arXiv preprint arXiv:2602.05048, 2026

    Pith/arXiv arXiv 2026

  3. [3]

    Agentic ai for cyber defense: Llm-guided hierarchical multi-agent reinforcement learning

    Guangyu Jiang, Mahdi Imani, Nathaniel D Bastian, and Tian Lan. Agentic ai for cyber defense: Llm-guided hierarchical multi-agent reinforcement learning. InMILCOM 2025-2025 IEEE Military Communications Conference (MILCOM), pages 1518–1523. IEEE, 2025

    2025

  4. [4]

    Metric-gradient projection for stable multi-agent policy learning.arXiv preprint arXiv:2605.18809, 2026

    Zuyuan Zhang, Sizhe Tang, Mahdi Imani, and Tian Lan. Metric-gradient projection for stable multi-agent policy learning.arXiv preprint arXiv:2605.18809, 2026

    Pith/arXiv arXiv 2026

  5. [5]

    Training verifiers to solve math word problems.arXiv preprint arXiv:2110.14168, 2021

    Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. Training verifiers to solve math word problems.arXiv preprint arXiv:2110.14168, 2021

    Pith/arXiv arXiv 2021

  6. [6]

    Chain-of-thought prompting elicits reasoning in large language models

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824–24837, 2022

    2022

  7. [7]

    Metamath: Bootstrap your own mathematical questions for large language models.arXiv preprint arXiv:2309.12284, 2023

    Longhui Yu, Weisen Jiang, Han Shi, Jincheng Yu, Zhengying Liu, Yu Zhang, James T Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. Metamath: Bootstrap your own mathematical questions for large language models.arXiv preprint arXiv:2309.12284, 2023

    Pith/arXiv arXiv 2023

  8. [8]

    Deepseekmath: Pushing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024

    Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024

    Pith/arXiv arXiv 2024

  9. [9]

    Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning.arXiv preprint arXiv:2501.12948, 2025

    Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Peiyi Wang, Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning.arXiv preprint arXiv:2501.12948, 2025

    Pith/arXiv arXiv 2025

  10. [10]

    Exploring the compositional deficiency of large language models in mathematical reasoning through trap problems

    Jun Zhao, Jingqi Tong, Yurong Mou, Ming Zhang, Qi Zhang, and Xuan-Jing Huang. Exploring the compositional deficiency of large language models in mathematical reasoning through trap problems. InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 16361–16376, 2024

    2024

  11. [11]

    Large language models struggle with unreasonability in math problems

    Jingyuan Ma, Damai Dai, Zihang Yuan, Rui Li, Weilin Luo, Bin Wang, Qun Liu, Lei Sha, and Zhifang Sui. Large language models struggle with unreasonability in math problems. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 40, pages 32428–32436, 2026

    2026

  12. [12]

    Vcsearch: Bridging the gap between well-defined and ill-defined problems in mathematical reasoning

    Shi-Yu Tian, Zhi Zhou, Kun-Yang Yu, Ming Yang, Lin-Han Jia, Lan-Zhe Guo, and Yu-Feng Li. Vcsearch: Bridging the gap between well-defined and ill-defined problems in mathematical reasoning. InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 12721–12742, 2025. 10

    2025

  13. [13]

    Questbench: Can llms ask the right question to acquire information in reasoning tasks?arXiv preprint arXiv:2503.22674, 2025

    Belinda Z Li, Been Kim, and Zi Wang. Questbench: Can llms ask the right question to acquire information in reasoning tasks?arXiv preprint arXiv:2503.22674, 2025

    arXiv 2025

  14. [14]

    Reliablemath: Benchmark of reliable mathematical reasoning on large language models.arXiv preprint arXiv:2507.03133, 2025

    Boyang Xue, Qi Zhu, Rui Wang, Sheng Wang, Hongru Wang, Minda Hu, Fei Mi, Yasheng Wang, Lifeng Shang, Qun Liu, et al. Reliablemath: Benchmark of reliable mathematical reasoning on large language models.arXiv preprint arXiv:2507.03133, 2025

    arXiv 2025

  15. [15]

    Lingzhong Zhou, Abdul Sattar, and Scott D. Goodwin. Handling over-constrained problems in distributed multi-agent systems. In Balázs Kégl and Guy Lapalme, editors,Advances in Artificial Intelligence, 18th Conference of the Canadian Society for Computational Studies of Intelligence, Canadian AI 2005, Victoria, Canada, May 9-11, 2005, Proceedings, Lecture N...

    work page doi:10.1007/11424918 2005

  16. [16]

    Defining tools to address over- constrained geometric problems in computer aided design.Comput

    Mireille Moinet, Guillaume Mandil, and Philippe Serré. Defining tools to address over- constrained geometric problems in computer aided design.Comput. Aided Des., 48:42–52, 2014. doi: 10.1016/J.CAD.2013.11.002. URL https://doi.org/10.1016/j.cad.2013.11.002

    work page doi:10.1016/j.cad.2013.11.002 2014

  17. [17]

    Matthew Beaumont, John Thornton, Abdul Sattar, and Michael J. Maher. Solving over- constrained temporal reasoning problems using local search. In Chengqi Zhang, Hans W. Guesgen, and Wai-Kiang Yeap, editors,PRICAI 2004: Trends in Artificial Intelligence, 8th Pacific Rim International Conference on Artificial Intelligence, Auckland, New Zealand, August 9-13...

    doi:10.1007/978-3-540-28633-2 2004

  18. [18]

    Know what you don’t know: Unanswerable ques- tions for squad

    Pranav Rajpurkar, Robin Jia, and Percy Liang. Know what you don’t know: Unanswerable ques- tions for squad. InProceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 784–789, 2018

    2018

  19. [19]

    Language models (mostly) know what they know.arXiv preprint arXiv:2207.05221, 2022

    Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, et al. Language models (mostly) know what they know.arXiv preprint arXiv:2207.05221, 2022

    Pith/arXiv arXiv 2022

  20. [20]

    Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation.arXiv preprint arXiv:2302.09664, 2023

    Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation.arXiv preprint arXiv:2302.09664, 2023

    Pith/arXiv arXiv 2023

  21. [21]

    Teaching models to express their uncertainty in words.arXiv preprint arXiv:2205.14334, 2022

    Stephanie Lin, Jacob Hilton, and Owain Evans. Teaching models to express their uncertainty in words.arXiv preprint arXiv:2205.14334, 2022

    Pith/arXiv arXiv 2022

  22. [22]

    The pitfalls of next-token prediction.arXiv preprint arXiv:2403.06963, 2024

    Gregor Bachmann and Vaishnavh Nagarajan. The pitfalls of next-token prediction.arXiv preprint arXiv:2403.06963, 2024

    Pith/arXiv arXiv 2024

  23. [23]

    Self-consistency improves chain of thought reasoning in language models.arXiv preprint arXiv:2203.11171, 2022

    Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models.arXiv preprint arXiv:2203.11171, 2022

    Pith/arXiv arXiv 2022

  24. [24]

    Tree of thoughts: Deliberate problem solving with large language models.Ad- vances in neural information processing systems, 36:11809–11822, 2023

    Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models.Ad- vances in neural information processing systems, 36:11809–11822, 2023

    2023

  25. [25]

    Pal: Program-aided language models

    Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. Pal: Program-aided language models. InInternational conference on machine learning, pages 10764–10799. PMLR, 2023

    2023

  26. [26]

    Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks.arXiv preprint arXiv:2211.12588, 2022

    Wenhu Chen, Xueguang Ma, Xinyi Wang, and William W Cohen. Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks.arXiv preprint arXiv:2211.12588, 2022

    Pith/arXiv arXiv 2022

  27. [27]

    Reason in chains, learn in trees: Self-rectification and grafting for multi-turn agent policy optimization.arXiv preprint arXiv:2604.07165, 2026

    Yu Li, Sizhe Tang, and Tian Lan. Reason in chains, learn in trees: Self-rectification and grafting for multi-turn agent policy optimization.arXiv preprint arXiv:2604.07165, 2026. 11

    Pith/arXiv arXiv 2026

  28. [28]

    Wizardmath: Empowering mathematical rea- soning for large language models via reinforced evol-instruct.arXiv preprint arXiv:2308.09583, 2023

    Haipeng Luo, Qingfeng Sun, Can Xu, Pu Zhao, Jianguang Lou, Chongyang Tao, Xiubo Geng, Qingwei Lin, Shifeng Chen, and Dongmei Zhang. Wizardmath: Empowering mathematical rea- soning for large language models via reinforced evol-instruct.arXiv preprint arXiv:2308.09583, 2023

    Pith/arXiv arXiv 2023

  29. [29]

    Rstar-math: Small llms can master math reasoning with self-evolved deep thinking.arXiv preprint arXiv:2501.04519, 2025

    Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang. Rstar-math: Small llms can master math reasoning with self-evolved deep thinking.arXiv preprint arXiv:2501.04519, 2025

    Pith/arXiv arXiv 2025

  30. [30]

    Interactive critique- revision training for reliable structured llm generation.arXiv preprint arXiv:2605.08327, 2026

    Fei Xu Yu, Zuyuan Zhang, Mahdi Imani, Nathaniel D Bastian, and Tian Lan. Interactive critique- revision training for reliable structured llm generation.arXiv preprint arXiv:2605.08327, 2026

    Pith/arXiv arXiv 2026

  31. [31]

    R-tuning: Instructing large language models to say ‘i don’t know’

    Hanning Zhang, Shizhe Diao, Yong Lin, Yi Fung, Qing Lian, Xingyao Wang, Yangyi Chen, Heng Ji, and Tong Zhang. R-tuning: Instructing large language models to say ‘i don’t know’. InProceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), pages 7113...

    2024

  32. [32]

    On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems.Theoretical Computer Science, 209(1-2):237–260, 1998

    Edoardo Amaldi and Viggo Kann. On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems.Theoretical Computer Science, 209(1-2):237–260, 1998

    1998

  33. [33]

    Fast heuristics for the maximum feasible subsystem problem.INFORMS Journal on Computing, 13(3):210–223, 2001

    John W Chinneck. Fast heuristics for the maximum feasible subsystem problem.INFORMS Journal on Computing, 13(3):210–223, 2001

    2001

  34. [34]

    Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography.Communications of the ACM, 24(6):381–395, 1981

    Martin A Fischler and Robert C Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography.Communications of the ACM, 24(6):381–395, 1981

    1981

  35. [35]

    A randomized kaczmarz algorithm with exponential convergence.Journal of Fourier Analysis and Applications, 15(2):262–278, 2009

    Thomas Strohmer and Roman Vershynin. A randomized kaczmarz algorithm with exponential convergence.Journal of Fourier Analysis and Applications, 15(2):262–278, 2009

    2009

  36. [36]

    A subspace constrained randomized kaczmarz method for structure or external knowledge exploitation.Linear Algebra and its Applications, 698:220–260, 2024

    Jackie Lok and Elizaveta Rebrova. A subspace constrained randomized kaczmarz method for structure or external knowledge exploitation.Linear Algebra and its Applications, 698:220–260, 2024

    2024

  37. [37]

    Bert rediscovers the classical nlp pipeline

    Ian Tenney, Dipanjan Das, and Ellie Pavlick. Bert rediscovers the classical nlp pipeline. In Proceedings of the 57th annual meeting of the association for computational linguistics, pages 4593–4601, 2019

    2019

  38. [38]

    John Hewitt and Christopher D. Manning. A structural probe for finding syntax in word representations. InNAACL-HLT, 2019

    2019

  39. [39]

    Representation learning with contrastive predictive coding.arXiv preprint arXiv:1807.03748, 2018

    Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding.arXiv preprint arXiv:1807.03748, 2018

    Pith/arXiv arXiv 2018

  40. [40]

    Club: A contrastive log-ratio upper bound of mutual information

    Pengyu Cheng, Weituo Hao, Shuyang Dai, Jiachang Liu, Zhe Gan, and Lawrence Carin. Club: A contrastive log-ratio upper bound of mutual information. InInternational conference on machine learning, pages 1779–1788. PMLR, 2020

    2020

  41. [41]

    Qwen3 technical report.arXiv preprint arXiv:2505.09388, 2025

    An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report.arXiv preprint arXiv:2505.09388, 2025

    Pith/arXiv arXiv 2025

  42. [42]

    id": "sample_2368

    Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Liang Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models.Iclr, 1(2):3, 2022. 12 A Proof of Proposition 1 We restate the setting before the proof for self-containedness. Let X denote the random problem statement and A the analysis text generated fr...

    2022