Emergent Manifold Separability during Reasoning in Large Language Models
This work addresses the problem of understanding how reasoning emerges in LLMs for researchers, providing insights into representational dynamics, though it is incremental in nature.
The study investigated the temporal dynamics of representation geometry in Large Language Models during reasoning, revealing that reasoning manifests as a transient geometric pulse where concept manifolds become linearly separable just before computation and compress quickly after, diverging from standard linear probe accuracy.
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 reasoning chain.