# Towards Interpretable and Inference-Optimal COT Reasoning with Sparse Autoencoder-Guided Generation

arXiv: https://arxiv.org/abs/2510.01528 · HTML: https://mlsanity.com/paper/2510.01528/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [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)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [Forest-of-Thought: Scaling Test-Time Compute for Enhancing LLM Reasoning](https://mlsanity.com/paper/2412.09078/) (2024)
- [Let's reward step by step: Step-Level reward model as the Navigators for Reasoning](https://mlsanity.com/paper/2310.10080/) (2023)
- [KnowledGPT: Enhancing Large Language Models with Retrieval and Storage Access on Knowledge Bases](https://mlsanity.com/paper/2308.11761/) (2023)
- [Enhancing Neural Network Interpretability with Feature-Aligned Sparse Autoencoders](https://mlsanity.com/paper/2411.01220/) (2024)
- [Constrain Alignment with Sparse Autoencoders](https://mlsanity.com/paper/2411.07618/) (2024)
- [LF-Steering: Latent Feature Activation Steering for Enhancing Semantic Consistency in Large Language Models](https://mlsanity.com/paper/2501.11036/) (2025)
- [Prioritized Trajectory Replay: A Replay Memory for Data-driven Reinforcement Learning](https://mlsanity.com/paper/2306.15503/) (2023)

## Abstract (arXiv)

We propose a novel method that leverages sparse autoencoders (SAEs) and clustering techniques to analyze the internal token representations of large language models (LLMs) and guide generations in mathematical reasoning tasks. Our approach first trains an SAE to generate sparse vector representations for training tokens, then applies k-means clustering to construct a graph where vertices represent token clusters and weighted edges capture sequential token transitions. Using this graph, we define an edge-weight based reward function to quantify adherence to established reasoning traces, thereby identifying exploitative reasoning trajectories. Additionally, we measure generation diversity from clustering to assess the extent of exploration. Our findings indicate that balancing both exploitation and exploration is crucial for achieving high accuracy in mathematical reasoning tasks. During generation, the SAE can serve as a scalable reward model to guide generations, ensuring a balanced trade-off between exploitation and exploration. This prevents extreme behaviors in either direction, ultimately fostering a higher-quality reasoning process in LLMs.