# Directional Attractors in LLM Reasoning: How Similarity Retrieval Steers Iterative Summarization Based Reasoning

arXiv: https://arxiv.org/abs/2601.08846 · HTML: https://mlsanity.com/paper/2601.08846/

## 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 7 of its 8 references that are in the map.
- First posted on arXiv 22 Dec 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, 7 of 7)

- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Large Language Models as Analogical Reasoners](https://mlsanity.com/paper/2310.01714/) (2023)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)

## Abstract (arXiv)

Iterative summarization based reasoning frameworks such as InftyThink enable long-horizon reasoning in large language models (LLMs) by controlling context growth, but they repeatedly regenerate similar reasoning strategies across tasks. We introduce InftyThink with Cross-Chain Memory, an extension that augments iterative reasoning with an embedding-based semantic cache of previously successful reasoning patterns. At each reasoning step, the model retrieves and conditions on the most semantically similar stored lemmas, guiding inference without expanding the context window indiscriminately. Experiments on MATH500, AIME2024, and GPQA-Diamond demonstrate that semantic lemma retrieval improves accuracy in structured domains while exposing failure modes in tests that include heterogeneous domains. Geometric analyses of reasoning trajectories reveal that cache retrieval induces directional biases in embedding space, leading to consistent fix (improve baseline accuracy) and break (degradation in baseline accuracy) attractors. Our results highlight both the benefits and limits of similarity-based memory for self-improving LLM reasoning.