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

arXiv: https://arxiv.org/abs/2607.20500 · HTML: https://mlsanity.com/paper/2607.20500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 20 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 30)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [QuestBench: Can LLMs ask the right question to acquire information in reasoning tasks?](https://mlsanity.com/paper/2503.22674/) (2025)
- [Large Language Models Struggle with Unreasonability in Math Problems](https://mlsanity.com/paper/2403.19346/) (2024)
- [Exploring the Compositional Deficiency of Large Language Models in Mathematical Reasoning](https://mlsanity.com/paper/2405.06680/) (2024)
- [Agent Alpha: Tree Search Unifying Generation, Exploration and Evaluation for Computer-Use Agents](https://mlsanity.com/paper/2602.02995/) (2026)
- [ReliableMath: Benchmark of Reliable Mathematical Reasoning on Large Language Models](https://mlsanity.com/paper/2507.03133/) (2025)
- [Reason in Chains, Learn in Trees: Self-Rectification and Grafting for Multi-turn Agent Policy Optimization](https://mlsanity.com/paper/2604.07165/) (2026)
- [VCSearch: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning](https://mlsanity.com/paper/2406.05055/) (2024)
- [MINT: Minimal Information Neuro-Symbolic Tree for Objective-Driven Knowledge-Gap Reasoning and Active Elicitation](https://mlsanity.com/paper/2602.05048/) (2026)
- [Metric-Gradient Projection for Stable Multi-Agent Policy Learning](https://mlsanity.com/paper/2605.18809/) (2026)
- [Interactive Critique-Revision Training for Reliable Structured LLM Generation](https://mlsanity.com/paper/2605.08327/) (2026)

## Abstract (arXiv)

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 ε-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.