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Latent Chain-of-Thought? Decoding the Depth-Recurrent Transformer

Wenquan Lu, Yuechuan Yang, Kyle Lee, Yanshu Li, Enqi Liu

arXiv:2507.02199v2cs.CLcs.AIcs.LG

TL;DR

Natural-language chain-of-thought can improve reasoning but may make inference verbose and slow, while it remains unclear whether current architectures perform reasoning in latent space. This paper probes Huginn’s arithmetic-task hidden states using logit and coda lenses and token-rank trajectories. The analyses find little evidence of structured latent reasoning, and greater recurrence depth yields only modest gains compared with explicit chain-of-thought prompting.

  • Problem

    Natural-language chain-of-thought may add verbosity and slow inference, while it remains unclear whether current architectures can reason in latent space.

    Source: §1 · p. 1

  • Method

    The paper probes Huginn’s hidden states on arithmetic tasks using logit and coda lenses and tracks token-rank trajectories.

    Source: §2.2 · p. 3, §3.3 · p. 5

  • Results

    Token-rank analysis finds no clear evidence of latent chain-of-thought, and increasing recurrence steps on GSM8K yields only modest gains that fall short of explicit chain-of-thought prompting.

    Source: §3.3 · p. 5, §3.4 · p. 5

  • Takeaways & Limitations

    The findings provide limited evidence for interpretable latent chain-of-thought in Huginn, while not definitively ruling out subtler or more distributed patterns.

    Source: §4 · p. 6

    The probing tools may miss latent chain-of-thought that is more subtle or distributed than the patterns they detect.

    Source: §4 · p. 6

Abstract

from arXiv · show

Chain-of-thought (CoT) reasoning has enabled transformer-based language models to excel at complex mathematics and multi-step planning. However, in standard decoder-only architectures, these reasoning steps are externalized in natural language, improving interpretability at the cost of efficiency. To capture reasoning that is not easily represented in words, many works have explored recurrent architectures that aim to internalize reasoning in latent space, potentially supporting latent CoT. In this paper, we investigate whether such reasoning structures emerge in Huginn-3.5B, a depth-recurrent Transformer that reuses layers at inference time without increasing parameter count. We examine the model's internal behavior on arithmetic tasks using a suite of probing techniques including the Logit Lens and Coda Lens. Our findings reveal limited evidence of interpretable latent CoT by tracking rank trajectories of final and intermediate result tokens. Furthermore, we uncover significant probing inconsistencies across recurrent blocks, where the interpretability of hidden states depends heavily on both the layer index and the decoding method. Finally, we empirically show that increasing recurrence depth yields only marginal gains and falls well short of models that explicitly externalize reasoning steps. The code is available at https://github.com/wenquanlu/huginn-latent-cot.

1 Introduction

The paper asks whether recurrent depth can support latent chain-of-thought reasoning, which could avoid the verbosity and slower inference associated with verbalized reasoning. It probes Huginn and reports limited evidence of latent reasoning, alongside inconsistent hidden-state interpretations and weak gains from greater recurrence depth.

1 Introduction

  • The study asks whether Huginn exhibits latent chain-of-thought reasoning during inference, a possibility left unclear for current architectures.The motivation contrasts natural-language intermediate steps, which may add verbosity and slow inference, with reasoning in latent space.Source: §1 · p. 1
  • The analysis suppresses explicit reasoning on arithmetic tasks and decodes an unrolled view of Huginn with logit lens, coda lens, and token-rank tracking.Figure 1 depicts applying both lenses to each block’s output to obtain logits.Source: §1 · p. 1, Figure 1 · p. 2
  • Huginn’s hidden-state semantics change sharply across recurrent blocks, and their interpretability depends on both block and decoding lens.R1 and R4 encode distinct information, unlike the smoothly evolving representations described for feedforward Transformers.Source: §1 · pp. 1–2
  • Token-rank trajectories provide little evidence of a structured latent reasoning pathway or temporal separation between intermediate and final answers.The authors report that both token ranks descend quickly, with the final token consistently at a lower rank than the intermediate token.Source: §1 · p. 2
  • On GSM8K, increasing recurrence steps yields only marginal gains and falls far short of explicit chain-of-thought prompting.The supplied contribution passage reports this comparison without giving its accuracy values.Source: §1 · p. 2

2 Method

The method unrolls Huginn’s recurrent computation into a sequence of block states, then decodes those states with logit and coda lenses. This enables inspection of model predictions across intermediate layers and recurrent steps.

2.1 Unrolled View of Huginn Architecture

  • The unrolled view represents a forward pass as 2 + 4r + 2 blocks: two Prelude blocks, four recurrent blocks repeated for r steps, and two Coda blocks.Each block is a standard causal self-attention block; the resulting hidden states can be tracked across intermediate computations.Source: §2.1 · p. 2

2.2 Decoding Hidden States by Logit Lens and Coda Lens

  • The logit lens RMS-normalizes each hidden state and projects it through the unembedding matrix to produce vocabulary logits.The analysis focuses on logits at the last token position to track the model’s current prediction across layers or recurrent steps.Source: §2.2 · p. 3
  • The coda lens decodes hidden states with Huginn’s learned two-block Coda module, a more expressive decoder than the logit lens.The method applies normalization both before and after the Coda module and also focuses on the last-token position.Source: §2.2 · p. 3

3 Experiment

The experiments suppress explicit CoT and examine Huginn on arithmetic using unrolled-block probes and token-rank trajectories. The probes vary by block and decoding lens, provide little evidence of latent CoT, and show only modest gains from greater recurrence depth compared with explicit CoT.

3.1 Experimental Setup for Mathematical Reasoning Without Explicit CoT

  • The setup uses 2k synthetic one-digit composite questions, where Huginn’s accuracy is 0.19, and also evaluates on GSM8K.Explicit CoT is suppressed with a system message and four in-context examples; unless otherwise noted, experiments use 16 recurrent steps, or 68 total blocks.Source: §3.1 · p. 3

3.2 Discontinuities in Hidden State Interpretability of Depth-Recurrent Transformer

  • Final-token ranks oscillate across unrolled blocks, with R4 spikes reversing between lenses; signed-prefix decoding and manual examples likewise show block- and lens-dependent interpretability.R4 produces uninterpretable logit-lens outputs but numerical coda-lens tokens, while R1 shows the reverse pattern.Source: Figure 2 · p. 4, Figure 3 · p. 4, §3.2 · p. 4

3.3 Tracing Final and Intermediate Tokens Provides Little Evidence for Latent CoT

  • Across 67 correctly answered single-digit problems, final and intermediate token ranks fall quickly without the expected phase separation, providing no clear evidence of latent CoT.A rank reversal around step 6 occurs in most examples and could indicate reevaluation of the final outcome using intermediate results; the authors leave it for future investigation.Source: Figure 4 · p. 5, §3.3 · p. 5

3.4 Scaling Recurrent Steps Cannot Beat Explicit Chain-of-Thought

  • GSM8K accuracy rose from 3.11 to 4.93 as recurrent steps increased from 4 to 32, then plateaued, versus 24.87/38.13 with explicit CoT.The table reports strict/flexible accuracy across models and recurrence steps.Source: Table 1 · p. 5, §3.4 · p. 5

4 Conclusion

On arithmetic tasks with explicit reasoning suppressed, the paper finds little evidence of structured latent chain-of-thought in Huginn, while noting that its analyses cannot rule latent CoT out.

4 Conclusion

  • Logit Lens and Coda Lens analyses find little evidence of structured latent CoT on arithmetic tasks with explicit reasoning suppressed.The conclusion cautions that latent CoT, if present, may be subtler or more distributed than these tools detect.Source: §4 · p. 6
  • The findings do not definitively rule out latent CoT, which may require more advanced probing to detect.The authors suggest activation patching as a possible future approach.Source: §4 · p. 6

A.1 Rank Trajectories of the Intermediate, Final and Random Tokens from Other Recurrent Blocks

The appendix figures track intermediate, final, and random-token rank trajectories under two decoding lenses across recurrent blocks.

A.1 Rank Trajectories of the Intermediate, Final and Random Tokens from Other Recurrent Blocks

  • Figure 5 tracks Logit Lens rank trajectories for intermediate, final, and random tokens at recurrent blocks 1, 2, and 4.Shading denotes ±1 relative standard deviation.Source: Figure 5 · p. 7
  • Figure 6 tracks Coda Lens rank trajectories for intermediate, final, and random tokens at recurrent blocks 1, 2, and 3.Shading denotes ±1 relative standard deviation.Source: Figure 6 · p. 7

A.2 Prompting with Suppressed CoT

The appendix documents prompts that instruct Huginn to return final answers directly, without explicit chain-of-thought reasoning, across arithmetic and word-problem tasks.

A.2 Prompting with Suppressed CoT

  • The section 3.4 prompt gives eight word-problem examples, while sections 3.2 and 3.3 show four arithmetic examples each.The examples cover arithmetic expressions and word problems involving quantities such as trees, cars, and money.Source: §A.2 · p. 8
  • The prompts for sections 3.2–3.4 instruct Huginn to give only the final answer, without explicit CoT reasoning.They include arithmetic questions and, in section 3.4, word problems.Source: §A.2 · p. 8
  • The section 3.3 in-context examples are additionally constrained to have single-digit answers.This matches that section’s experimental setup.Source: §A.2 · p. 9

A.3 Further Examples of the Decoded Top-5 Tokens

The appendix supplies top-five decoded-token tables across recurrent steps and reports that the numeric-token proportion shifts oppositely under the two lenses around R4.

A.3 Further Examples of the Decoded Top-5 Tokens

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