Directional Attractors in LLM Reasoning: How Similarity Retrieval Steers Iterative Summarization Based Reasoning
Cagatay Tekin, Charbel Barakat, Luis Joseph Luna Limgenco
TL;DR
The paper addresses the context-window bottleneck in long-horizon LLM reasoning by augmenting InftyThink with an embedding-based semantic cache of past lemmas. Lemmas are retrieved via cosine similarity to the mean-pooled current query and injected into the context to bias reasoning without indiscriminately expanding the window. Empirical results show domain-specific gains on MATH500 and AIME2024, but degradation on GPQA Diamond, revealing that domain heterogeneity can induce noise through retrieval. A geometric analysis identifies directional attractors in embedding space that separate successful and unsuccessful reasoning trajectories, suggesting that effectiveness hinges on controlling these biases rather than solely maximizing semantic relevance. Overall, the work provides both a practical memory-augmented reasoning approach and a framework for analyzing its qualitative effects on LLM reasoning dynamics.
Abstract
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.