Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks

TL;DR

This paper investigates whether latent-CoT models implement genuine step-by-step computation or rely on shortcuts. Using CODI on controlled polynomial-iteration tasks, it combines logit-lens decoding, linear probes, attention analysis, and activation patching to localize intermediate states and trace information flow. The main findings reveal a two-stream mechanism where a latent bridge-state is formed and a final input is routed directly to the answer, with longer horizons shifting to a late-bottleneck partial rollout; a sharp prime–composite modulus split explains when latent rollouts are feasible. Theoretical analysis shows that composite moduli induce contractions that favor compression, whereas prime moduli preserve full history dependence, accounting for observed behaviors. These results illuminate when latent-CoT can sustain iterative computation and motivate robust objective designs for sequential reasoning across different task structures.

Abstract

Latent Chain-of-Thought (Latent-CoT) aims to enable step-by-step computation without emitting long rationales, yet its mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential polynomial-iteration tasks. Using logit-lens decoding, linear probes, attention analysis, and activation patching, we localize intermediate-state representations and trace their routing to the final readout. On two- and three-hop tasks, CODI forms the full set of bridge states that become decodable across latent-thought positions, while the final input follows a separate near-direct route; predictions arise via late fusion at the end-of-thought boundary. For longer hop lengths, CODI does not reliably execute a full latent rollout, instead exhibiting a partial latent reasoning path that concentrates on late intermediates and fuses them with the last input at the answer readout position. Ablations show that this partial pathway can collapse under regime shifts, including harder optimization. Overall, we delineate when CODI-style latent-CoT yields faithful iterative computation versus compressed or shortcut strategies, and highlight challenges in designing robust latent-CoT objectives for sequential reasoning.

Figures (14)

• Figure 1: Mechanistic study of CODI on sequential reasoning tasks.Top: the CODI training setup used for our polynomial iteration task. Bottom: the four mechanistic interpretability methods we use to analyze the student model’s internal computations.
• Figure 2: Polynomial tasks for training CODI. The teacher is trained to generate an explicit CoT trace, while the student answers after generating a fixed-length latent-thought trajectory. A feature-space self-distillation loss aligns the teacher and student representations at the answer readout position [Ans].
• Figure 3: Logit Lens on intermediate states $s_1, s_2, s_3$ in the two-hop polynomial task. The bridge state $s_2$ becomes decodable during the latent computation, indicating that it is formed and maintained in the model's latent channel. Each cell show average decoding probability across all layers and all test inputs.
• Figure 4: Activation patching for input-token corruptions (two-hop). Cells show mean accuracy recovery (%) over corrupted samples. Patching at latent-thought positions rescues $x_2$ corruptions, implicating the latent channel in storing $s_2$. For $x_3$ corruptions, recovery concentrates at [Ans], consistent with direct routing of $x_3$ to the output.
• Figure 5: Logit Lens analysis of the $n$-hop polynomial task with modulus $50$. Only the final bridge state $s_n$ appears in the computation pathway, while earlier intermediate bridge states are collapsed.

Theorems & Definitions (4)

• Lemma 5.1: Bijection criterion
• Lemma 5.2: Exact contraction factor
• proof
• proof