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[2602.20338] Emergent Manifold Separability during Reasoning in Large Language Models
Summary
This paper explores the dynamics of reasoning in Large Language Models (LLMs) through Manifold Capacity Theory, revealing how latent representations become linearly separable during computation.
Why It Matters
Understanding the geometric dynamics of reasoning in LLMs is crucial for improving their performance and interpretability. This research sheds light on how models manage representational capacity, which can inform future advancements in AI and machine learning.
Key Takeaways
- Chain-of-Thought prompting enhances reasoning in LLMs.
- Manifold Capacity Theory reveals transient geometric changes during reasoning.
- Dynamic Manifold Management optimizes representational capacity in LLMs.
Computer Science > Machine Learning arXiv:2602.20338 (cs) [Submitted on 23 Feb 2026] Title:Emergent Manifold Separability during Reasoning in Large Language Models Authors:Alexandre Polo, Chanwoo Chun, SueYeon Chung View a PDF of the paper titled Emergent Manifold Separability during Reasoning in Large Language Models, by Alexandre Polo and 2 other authors View PDF HTML (experimental) Abstract:Chain-of-Thought (CoT) prompting significantly improves reasoning in Large Language Models, yet the temporal dynamics of the underlying representation geometry remain poorly understood. We investigate these dynamics by applying Manifold Capacity Theory (MCT) to a compositional Boolean logic task, allowing us to quantify the linear separability of latent representations without the confounding factors of probe training. Our analysis reveals that reasoning manifests as a transient geometric pulse, where concept manifolds are untangled into linearly separable subspaces immediately prior to computation and rapidly compressed thereafter. This behavior diverges from standard linear probe accuracy, which remains high long after computation, suggesting a fundamental distinction between information that is merely retrievable and information that is geometrically prepared for processing. We interpret this phenomenon as \emph{Dynamic Manifold Management}, a mechanism where the model dynamically modulates representational capacity to optimize the bandwidth of the residual stream throughout the r...