Reproduce “Capabilities and Fundamental Limits of Latent Chain-of-Thought” on OpenResearch

About this paper

Jiaxuan Zou, Yaozhong Xiong, Yong Liu

This research introduces the Symbolic Index, a quantifiable metric of decisional certainty, to theoretically characterize the fundamental capabilities and limits of Latent Chain-of-Thought (Latent CoT) models. It establishes an exploration-execution trade-off where high certainty enables precise execution but limits exploration, while low certainty facilitates exploration but leads to compounding errors, further proving curriculum learning as a theoretical necessity for Latent CoT's training stability.

Key insights

• A fundamental exploration-execution trade-off is governed by decisional certainty: high $I_S$ ensures execution stability via an error-correcting discretization process but limits exploration, while low $I_S$ enables exploration but causes noise accumulation.
• Explicit CoT maintains symbolic integrity and robustness to sub-decisional perturbations due to its discrete token selection, whereas Latent CoT's continuous states are inherently vulnerable to compounding errors.
• Curriculum learning is a theoretical necessity for Latent CoT training, provably bridging a distributional mismatch between self-generated latent states and optimal reasoning trajectories to ensure convergence.

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