# Reasoning as State Transition: A Representational Analysis of Reasoning Evolution in Large Language Models

arXiv: https://arxiv.org/abs/2602.00770 · HTML: https://mlsanity.com/paper/2602.00770/

## 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 32 of its 72 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [On the Interplay of Pre-Training, Mid-Training, and RL on Reasoning Language Models](https://mlsanity.com/paper/2512.07783/) (2025)
- [No Answer Needed: Predicting LLM Answer Accuracy from Question-Only Linear Probes](https://mlsanity.com/paper/2509.10625/) (2025)
- [RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs](https://mlsanity.com/paper/2509.21128/) (2025)
- [Physics of Language Models: Part 4.1, Architecture Design and the Magic of Canon Layers](https://mlsanity.com/paper/2512.17351/) (2025)
- [DeepDistill: Enhancing LLM Reasoning Capabilities via Large-Scale Difficulty-Graded Data Training](https://mlsanity.com/paper/2504.17565/) (2025)
- [CTRLS: Chain-of-Thought Reasoning via Latent State-Transition](https://mlsanity.com/paper/2507.08182/) (2025)
- [CLUE: Non-parametric Verification from Experience via Hidden-State Clustering](https://mlsanity.com/paper/2510.01591/) (2025)
- [Boosting Deductive Reasoning with Step Signals In RLHF](https://mlsanity.com/paper/2410.09528/) (2024)
- [Geometric Metrics and LLMs: What They Measure and When They Work](https://mlsanity.com/paper/2509.25359/) (2025)

## Abstract (arXiv)

Large Language Models have achieved remarkable performance on reasoning tasks, motivating research into how this ability evolves during training. Prior work has primarily analyzed this evolution via explicit generation outcomes, treating the reasoning process as a black box and obscuring internal changes. To address this opacity, we introduce a representational perspective to investigate the dynamics of the model's internal states. Through comprehensive experiments across models at various training stages, we discover that post-training yields only limited improvement in static initial representation quality. Furthermore, we reveal that, distinct from non-reasoning tasks, reasoning involves a significant continuous distributional shift in representations during generation. Comparative analysis indicates that post-training empowers models to drive this transition toward a better distribution for task solving. To clarify the relationship between internal states and external outputs, statistical analysis confirms a high correlation between generation correctness and the final representations; while counterfactual experiments identify the semantics of the generated tokens, rather than additional computation during inference or intrinsic parameter differences, as the dominant driver of the transition. Collectively, we offer a novel understanding of the reasoning process and the effect of training on reasoning enhancement, providing valuable insights for future model analysis and optimization.