Capabilities and Fundamental Limits of Latent Chain-of-Thought

TL;DR

This paper analyzes the fundamental trade-off in Latent Chain-of-Thought models between exploration and execution, introducing a symbolic index to quantify decisional certainty and emphasizing the importance of curriculum learning for effective reasoning.

Contribution

It provides a theoretical characterization of the exploration-execution trade-off, introduces the symbolic index as a core mechanism, and proves the necessity of curriculum learning for Latent CoT models.

Findings

High certainty enables precise execution but limits exploration.

Low certainty promotes exploration but risks error accumulation.

Curriculum learning is theoretically necessary for effective training.

Abstract

Latent Chain-of-Thought (Latent CoT) models promise efficient reasoning via continuous representations, yet exhibit puzzling performance inconsistencies: excelling at exploration (ProsQA: 97.0%) but failing at computation (GSM8K: 34.1%). We reveal that this trade-off is governed by decisional certainty. Our contributions are threefold: (1) We theoretically characterize the fundamental Exploration-Execution Trade-off, proving that high certainty enables precise execution but inhibits exploration, while low certainty facilitates search but causes error accumulation. (2) We introduce the Symbolic Index--quantifying decisional commitment--as the core mechanism governing this trade-off and establish its causal relationship with both execution stability and exploration capability. (3) We prove that curriculum learning is theoretically necessary, as direct training provably fails due to distributional mismatch. Our framework shifts the design paradigm from binary architectural choices toward adaptive systems that dynamically regulate decisional certainty based on task demands.