# Controllable Mathematical Reasoning via Self-Optimizing Thought Vectors

arXiv: https://arxiv.org/abs/2510.22132 · HTML: https://mlsanity.com/paper/2510.22132/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 11 of its 11 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## 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, 11 of 11)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)

## Abstract (arXiv)

We present a novel approach for controllable mathematical reasoning that leverages self-optimizing thought vectors with entropy minimization. Our method introduces learnable thought vectors that dynamically modulate the internal reasoning process of large language models. Using Gemma-2-9B on GSM8K, we achieve 90.1% accuracy with a controllability score of 0.42, demonstrating that entropy-based rewards effectively guide focused reasoning patterns without requiring external reward annotations. Our analysis reveals distinct thought vector clusters and consistent low-entropy distributions across control conditions, validating our framework for controllable AI reasoning.