Title: The Theoretical Benefits and Limitations of Latent Chain-of-Thought Reasoning
Primary area: interpretability and explainable AI
Keywords: latent reasoning, chain of thoughts, continuous chain of thoughts, information bottleneck, interpretability

Abstract: Recent advances in Latent Chain-of-Thought (Latent CoT) have gained significant attention, yet these models exhibit inconsistent performance across tasks and lack a rigorous theoretical understanding. Our contributions are threefold: (1) We theoretically characterize the fundamental exploration-execution trade-off. We prove that CoT's discrete, symbolic nature forces it into a high-certainty regime, guaranteeing computational fidelity but causing premature commitment that cripples exploration. Conversely, we show that Latent CoT's continuous representation enables robust exploration but is also the direct cause of its failure on computational tasks by amplifying noise. (2) We introduce the Symbolic Index—a measure of a model's decisional certainty—as the core mechanism governing this trade-off. Our unified framework proves that this single, quantifiable metric causally explains the contrasting behaviors of both paradigms, offering a principled way to analyze and design reasoning systems. (3) We prove that curriculum learning is a theoretically grounded and necessary method for training Latent CoT models. We show that without it, training is guaranteed to fail due to a fundamental distributional mismatch, confirming that the staged approach is essential for convergence. This work provides concrete design principles for next-generation reasoning architectures, suggesting a shift from a binary choice between architectures to designing adaptive systems that can dynamically regulate their decisional certainty.