# Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertainty

arXiv: https://arxiv.org/abs/2603.15500 · HTML: https://mlsanity.com/paper/2603.15500/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 37 of its 48 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 37)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [RLVMR: Reinforcement Learning with Verifiable Meta-Reasoning Rewards for Robust Long-Horizon Agents](https://mlsanity.com/paper/2507.22844/) (2025)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [Evaluating LLMs at Detecting Errors in LLM Responses](https://mlsanity.com/paper/2404.03602/) (2024)
- [Understanding Aha Moments: from External Observations to Internal Mechanisms](https://mlsanity.com/paper/2504.02956/) (2025)
- [Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs](https://mlsanity.com/paper/2505.12929/) (2025)
- [Understanding Chain-of-Thought in LLMs through Information Theory](https://mlsanity.com/paper/2411.11984/) (2024)
- [Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens](https://mlsanity.com/paper/2505.18237/) (2025)
- [ReflAct: World-Grounded Decision Making in LLM Agents via Goal-State Reflection](https://mlsanity.com/paper/2505.15182/) (2025)
- [Step-by-Step Reasoning for Math Problems via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2410.01920/) (2024)
- [Exploratory Memory-Augmented LLM Agent via Hybrid On- and Off-Policy Optimization](https://mlsanity.com/paper/2602.23008/) (2026)
- [AgentMath: Empowering Mathematical Reasoning for Large Language Models via Tool-Augmented Agent](https://mlsanity.com/paper/2512.20745/) (2025)

## Built on by (most cited first, 9 of 9)

- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation](https://mlsanity.com/paper/2606.23104/) (2026)
- [Agent Explorative Policy Optimization for Multimodal Agentic Reasoning](https://mlsanity.com/paper/2605.28774/) (2026)
- [Process Supervision of Confidence Margin for Calibrated LLM Reasoning](https://mlsanity.com/paper/2604.23333/) (2026)
- [Distilling LLM Feedback for Lean Theorem Proving](https://mlsanity.com/paper/2605.30861/) (2026)
- [Exploring Extrinsic and Intrinsic Properties for Effective Reasoning with Code Interpreter](https://mlsanity.com/paper/2606.16934/) (2026)
- [Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoning](https://mlsanity.com/paper/2609.33781/) (2026)
- [Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge](https://mlsanity.com/paper/2609.34327/) (2026)
- [Learning What to Distill: Bilevel Top-K Token Selection for Self-Distillation in Large Language Models](https://mlsanity.com/paper/2610.07247/) (2026)

## Abstract (arXiv)

LLMs often exhibit Aha moments such as self-correction after tokens like "Wait," yet the underlying mechanism remains unclear. Standard LLMs collapse mainly through silent divergence, where trajectories drift from the correct answer yet remain locally coherent, so no explicit error triggers reactive self-correction. We introduce an information-theoretic framework that separates reasoning into procedural advancement and epistemic verbalization, the token-level externalization of uncertainty, and prove that sporadic verbalization restores convergence toward the correct answer even without explicit error triggers. Empirically, a minimal doubt cue recovers failed trajectories, and small-scale SFT suffices to instill or suppress this capability, suggesting that strong reasoning hinges less on an extraordinary inner mechanism than on the linguistic habit of externalizing uncertainty. Our framework recasts reasoning as strategic information allocation under uncertainty, offering a new lens for understanding and advancing LLM reasoning.