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Dynamics Within Latent Chain-of-Thought: An Empirical Study of Causal Structure

Zirui Li, Xuefeng Bai, Kehai Chen, Yizhi Li, Jian Yang, Chenghua Lin, Min Zhang

arXiv:2602.08783v3cs.AIcs.CL

TL;DR

Latent chain-of-thought lacks transparent, editable intermediate reasoning, limiting causal evaluation beyond correlation-based probes. This paper models latent steps as variables in a structural causal model and studies Coconut and CODI with step-wise interventions, finding staged functionality, non-local routing, and a persistent gap between early output bias and late representational commitment.

  • Problem

    Latent CoT replaces explicit rationales with hidden representations whose intermediate computations are difficult to evaluate causally and interpret mechanistically.

  • Method

    The paper models latent steps as structural-causal variables and applies step-wise do-interventions with controlled readouts to measure their effects.

  • Results

    Across Coconut and CODI on mathematical and general reasoning tasks, latent-step influence is heterogeneous, propagation is often non-local, and output preference precedes representational commitment.

  • Takeaways & Limitations

    The findings motivate mode-conditional and stability-aware analyses and suggest shaping routing and commitment rather than treating additional latent steps as homogeneous depth.

  • Takeaways & Limitations

    The study is limited to single-step edits, a fixed latent budget of T=6, and a controlled set of paradigms, backbones, and CoT-supervised benchmarks.

Abstract

from arXiv · show

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view latent chain-of-thought as a manipulable causal process in representation space by modeling latent steps as variables in a structural causal model (SCM) and analyzing their effects through step-wise do-interventions. We study two representative paradigms (i.e., Coconut and CODI) on both mathematical and general reasoning tasks to investigate three key questions: (1) which steps are causally necessary for correctness and when answers become decodable early; (2) how influence propagates across steps and how this structure compares to explicit CoT; and (3) whether intermediate trajectories retain competing answer modes and how output-level commitment differs from representational commitment across steps. We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing, and we identify a persistent gap between early output bias and late representational commitment. These results motivate mode-conditional and stability-aware analyses, together with corresponding training/decoding objectives, as more reliable tools for interpreting and improving latent reasoning systems. Code is available at https://github.com/J1mL1/causal-latent-cot.

1. Introduction

The paper frames latent chain-of-thought as a causal process whose intermediate steps can be manipulated and evaluated through step-wise interventions. Across three questions, it finds heterogeneous causal leverage, non-local influence propagation, and a gap between early output preference and later representational commitment.

  • Latent CoT moves reasoning from explicit tokens to continuous representations, reducing decoding overhead but making intermediate computations difficult to expose or edit.Traditional step editing and ablation do not directly apply when reasoning information is distributed across latent dimensions and iterative steps.
  • Step-wise do-interventions modify an intermediate latent state while preserving downstream computation, enabling causal sensitivity estimates and intervention-derived influence graphs.The graph is constructed from shifts in teacher-forced output distributions and represents information propagation through the latent process.
  • The evaluation asks which steps are necessary and when answers become decodable, how influence propagates, and whether trajectories retain competing hypotheses as commitment evolves.These correspond to necessity and early decodability, propagation and routing, and superposition and commitment.
  • Causal leverage is highly heterogeneous across latent steps, with a small subset exerting outsized influence.
  • Step-to-step effects are often non-local, while output preference can arise before representational consolidation.The latter indicates a persistent gap between early bias and later commitment.
  • The study distinguishes when a solution becomes available from which steps remain causally necessary, motivating routing- and commitment-oriented improvements rather than simply adding steps.The contribution also uses operator- and readout-conditioned analysis to recover dominant propagation routes without sparsity overclaims.

2. Related Work

Related work moves reasoning into continuous representations to improve efficiency and reduce unfaithful textual explanations, while this paper focuses on the internal causal organization of latent reasoning. It connects latent CoT to causal faithfulness analysis and contrasts it with broader reasoning-training directions.

  • Latent and continuous chain-of-thought reasoning: Latent CoT methods replace long textual rationales with continuous hidden-state computation, including recurrent depth-iterative approaches such as Coconut and CODI.Other approaches add supervision, mix latent and textual steps, or scale test-time computation through recurrent or parallel continuous updates.
  • Latent and continuous chain-of-thought reasoning: Most latent-reasoning literature emphasizes accuracy and efficiency, whereas this work examines internal causal organization and its relation to explicit CoT.
  • Large reasoning models and reinforcement learning for reasoning: Reasoning research also includes reinforcement learning, selective supervision, uncertainty estimation, and long-horizon inference for improving large reasoning models.
  • Chain-of-thought faithfulness and causal tests: Faithfulness studies show that model explanations can be convincing yet unfaithful and use interventions such as deleting, shuffling, or editing rationales to test their effect on answers.

V. Influence Estimation:

The paper situates influence estimation within causal and mechanistic analyses of internal representations. Its focus is on using interventions to distinguish behaviorally relevant internal components from representations that are merely correlated.

  • Parameter-level interventions provide another causal probe of whether a reasoning step is internally represented and used.
  • Causal and mechanistic analyses intervene on hidden activations to test whether internal components functionally contribute to model behavior.

3. Evaluation Framework: Latent CoT as a Causal System

The evaluation framework models latent reasoning steps as variables in a structural causal model and applies controlled interventions to hidden-state trajectories. It instantiates this protocol across Coconut and CODI, multiple backbones, and mathematical and commonsense reasoning datasets.

  • 3. Evaluation Framework: Latent CoT as a Causal System: Latent CoT is represented as a manipulable causal process whose intermediate reasoning steps are variables in a structural causal model.This formulation supports intervention-based causal queries and reproducible effect estimates under a fixed protocol.
  • 3. Evaluation Framework: Latent CoT as a Causal System: The framework asks whether individual steps are behaviorally necessary, how many steps make the correct answer decodable, and how perturbations propagate downstream.It summarizes propagation with a step-to-step influence matrix and empirical influence graph, while also examining superposition and commitment.
  • 3.2. Causal Variables, Minimal SCM, and Latent-step Interface: Each latent step H_t is a continuous hidden state, and the task output Y is generated by a decoder conditioned on the latent trajectory.The latent dynamics use fixed transition and decoding mechanisms with stochasticity represented in the SCM.
  • 3.2. Causal Variables, Minimal SCM, and Latent-step Interface: Interventions overwrite a realized intermediate state and recompute all downstream states using the same transition mechanism, producing a counterfactual trajectory and output.
  • 3.2. Causal Variables, Minimal SCM, and Latent-step Interface: Teacher-forced readouts and controlled randomness reduce sampling noise when estimating propagation effects.
  • Experimental instantiation: The experiments compare Coconut's recurrent continuous thought token with CODI's self-distilled continuous trajectory across GPT-2, Llama3-1B, and Qwen3-4B-Instruct.Evaluation uses GSM8K for mathematics and CommonsenseQA for general reasoning.

4. RQ1: Step-wise Necessity and Sufficiency

The paper separates step-wise necessity from answer availability: interventions identify which latent states affect decisions, while early stopping measures when correct answers become decodable. Across tasks and models, latent steps show differentiated sensitivity and task- and backbone-dependent decoding profiles.

  • Step-wise necessity: Zeroing one latent state and decoding the final answer measures decision-level dependence through the flip rate Flip(t).The baseline and intervention keep the input, parameters, downstream transition, and readout mechanisms unchanged.
  • Step-wise necessity: Flip(t) varies across intervened steps, with several settings showing mid-step peaks rather than flat or monotone sensitivity.This indicates that single-step removal selectively disrupts decisions more at some positions than others.
  • Step-wise necessity: GSM8K shows markedly higher flip rates than CommonsenseQA, with several settings around 0.1–0.2 or higher versus mostly below ∼0.1.The task gap appears across both Coconut and CODI variants.
  • Step-wise necessity: Coconut generally has larger flips than CODI under matched backbones, while stronger backbones suppress absolute flips without eliminating step dependence.Thus, both paradigm and backbone affect the magnitude of intervention sensitivity.
  • Latent-budget sufficiency: Early-stop decoding defines ki as the earliest step yielding a correct truncated decode and S(k) as the cumulative fraction solved by step k.Examples with no correct early-stop decode through T receive ki = ∞.
  • Latent-budget sufficiency: CommonsenseQA’s S(k) usually rises rapidly and saturates early, whereas GSM8K often continues gaining toward later steps, sometimes through k=6.Additional latent computation can make the correct answer decodable for more GSM8K instances.
  • Influence structure: Influence graphs contrast explicit CoT’s local structure with latent graphs’ skip-dominated propagation and greater non-locality.The supplied graph captions define nodes as six steps and edges as intervention-induced propagation strengths, with sparsification for readability.
  • Latent-budget sufficiency: Stronger backbones achieve higher S(1) and earlier saturation, while Coconut and CODI do not show consistently shared curve shapes within paradigms.When correctness becomes decodable therefore depends more on backbone capacity and task than on a stable paradigm signature.

5. RQ2: Information Flow and Stepwise Influence Structure

RQ2 compares step-to-step influence in explicit and latent reasoning using intervention-based readouts and influence matrices. Explicit CoT remains locally sequential, whereas latent models show skip-heavy, longer-range routing with functional differences between COCONUT and CODI.

  • Method: Single-step interventions are paired with downstream teacher-forced readouts to estimate how perturbations propagate through the reasoning trajectory.The resulting example-level shifts are aggregated into an influence matrix W under a fixed intervention and readout protocol.
  • Explicit CoT: Explicit CoT-SFT retains a near-chain topology, with adjacent dominant edges, locality at least 0.6, and low span across GSM8K backbones.These summaries indicate predominantly local dependencies between textual reasoning steps.
  • Latent CoT: Latent models contain more skip connections, lower locality, larger spans, and more influence terminating at late-step targets than explicit CoT.These patterns indicate that latent influence often bypasses intermediate steps rather than accumulating strictly along a local chain.
  • Latent CoT: COCONUT more often routes early steps directly toward late or final steps, whereas CODI shows less extreme early-to-final shortcuts and greater backbone variation.Both paradigms nevertheless depart from the near-chain topology observed in explicit CoT.
  • Implications: Influence structure shows that latentization changes internal routing, so computational adjacency in latent space need not mirror textual adjacency in natural-language rationales.The graph is protocol-conditioned and should be interpreted as an empirical influence structure rather than a uniquely identified true causal graph.

6. RQ3: Superposition and Commitment in Latent Dynamics

RQ3 examines whether latent trajectories retain competing Yes/No modes and distinguishes output-level bias from representational commitment. Teacher-forced readouts become skewed early, while probe readouts show that alternative modes can remain available until late in the trajectory.

  • Experiment Setting: RQ3 uses stochastic rollouts with both Yes and No outcomes on StrategyQA to track two answer modes across latent steps.The analysis retains prompts whose sampled rollouts contain both answers and partitions trajectories by final mode.
  • Teacher-Forced Readout: Teacher-forced scoring shows uniformly low superposition that varies modestly across steps, indicating early skew toward one answer mode.This pattern is compatible with early mode selection followed by propagation through non-local routes.
  • Probe Readout: Probe readouts show substantially higher superposition throughout the trajectory, followed by a clear drop at the final step.Intermediate states can therefore retain decodable support for an alternative mode even when teacher forcing appears committed.
  • Paradigm Comparison: CODI variants maintain higher probe-based superposition scores than COCONUT variants across latent steps.This separation aligns with CODI’s less extreme long-range routing and COCONUT’s more dominant early-to-late edges.
  • Commitment: Output preference may emerge before latent representations eliminate competing modes, so commitment is not a single collapse event.The two readouts expose a persistent gap between default answer bias and representational commitment.

7. Discussion

The discussion interprets latent reasoning as a structured, causally differentiated process rather than homogeneous extra depth. Unequal leverage, long-range routes, and delayed representational commitment motivate stability-aware and mode-conditional design choices.

  • Discussion: Latent-step budgets behave like structured interfaces: causal leverage is uneven, influence follows dominant long-range routes, and output bias can precede representational commitment.This combines the paper’s findings across necessity, propagation, and trajectory-level analyses.
  • Latent-Step Function: Single-step interventions reveal an implicit division of labor, with some latent steps acting as high-leverage sites and others contributing conditionally.The leverage profiles of COCONUT and CODI suggest that training paradigm influences where decision-relevant dependence concentrates.
  • Influence Routes: Principal influence graphs reconcile modest direct necessity with high-influence routes by showing how steps can shape downstream states that become consequential after later consolidation.This highlights functional routes that step-wise necessity profiles alone cannot identify.
  • Superposition and Commitment: Probe and teacher-forced readouts separate shared intermediate computation from externally visible collapse, because alternatives can remain representationally available after output distributions tilt.The discussion links this distinction to early decodability and later stabilization.
  • Design Implications: The paper proposes allocating computation, supervision, and regularization selectively to high-leverage steps or routes rather than treating every latent step as equivalent depth.Suggested constraints include readout consistency, perturbation robustness, downstream-state stability, and targets at causally important positions.

8. Conclusion

The conclusion frames latent chain-of-thought as an allocatable interface whose information is written and consolidated across causally differentiated steps. It emphasizes routing and stability, not merely increasing the number of latent steps.

  • Conclusion: Latent-step budgets should be treated as allocatable interfaces because causal leverage concentrates unevenly and propagates along dominant long-range routes.The conclusion also identifies a gap between early output bias and late representational commitment.
  • Conclusion: Future training and decoding should explicitly shape where information is written and how it is consolidated across latent steps.The paper gives stable bottlenecks and controllable routing as examples rather than recommending only larger latent budgets.

Limitations

The study’s conclusions are bounded by its intervention protocol, fixed six-step latent budget, and restricted evaluation scope. Broader testing is needed to assess generalizability.

  • The analysis is limited to single-step edits, a fixed latent budget of T=6, and a controlled set of paradigms, backbones, and CoT-supervised benchmarks.
  • Generalizability remains untested across more paradigms, longer horizons, adaptive latent budgets, and varied intervention types.

Impact Statement

The paper provides methodological tools for diagnosing latent computation while emphasizing responsible interpretation and safety testing. Its experiments use multiple intervention operators, teacher-forced readouts, and robustness analyses to characterize influence structures.

  • The work’s primary impact is methodological: intervention-based measurements help diagnose, compare, and potentially improve latent computation.
  • The paper cautions that improved latent reasoning may also lower the cost of persuasive or overconfident outputs, motivating standard safety testing and restrained causal interpretation.
  • The study reproduces COCONUT across three backbones and three datasets, while CODI uses official and reproduced checkpoints across dataset–backbone combinations.
  • Flip rate measures the fraction of examples whose final decoded prediction changes after intervention, aggregating both wrong→right and right→wrong changes.
  • Zero overwrite is the default intervention because it is deterministic, parameter-free, architecture-agnostic, and suitable for reproducible cross-model comparisons.
  • Teacher forcing reduces sampling variability by comparing predictive distributions along a fixed gold-answer path, yielding a more stable influence proxy.
  • Robustness analyses find non-uniform, non-local influence under alternative operators and readouts, while Sim-CoT shows relatively more local connectivity.

E. Additional Model Size Analysis

Additional-backbone analyses qualitatively reproduce heterogeneous step importance and non-uniform, long-range routing, while GSM8K mode analysis remains supporting evidence because its open-ended answer space requires stricter filtering.

  • Additional model-size analysis: The additional-backbone experiments are qualitative model-size and backbone checks, not a full scaling-law study, because training and reproduction conditions differ.
  • Additional model-size analysis: Step-wise flip rates remain heterogeneous across additional COCONUT backbones, supporting unequal causal leverage despite substantial variation in absolute rates.
  • Additional model-size analysis: Additional models show non-uniform propagation with long-range edges and model-specific routing, although matched-family scaling remains future work.
  • Trajectory and mode analysis: RQ3 samples multiple trajectories per input and tracks their latent states and final decoded answers to study multi-mode latent dynamics.
  • Trajectory and mode analysis: The two dominant modes are the two most frequent normalized terminal answers; residual modes are excluded from the binary analysis.
  • Trajectory and mode analysis: Lightweight probes map frozen latent states to step-wise distributions over the two answer modes, using regularized linear classifiers with balancing when needed.
  • Trajectory and mode analysis: Teacher-forced readouts deterministically score candidate answers as a complementary signal to probe outputs, using method-dependent answer templates.
  • Trajectory and mode analysis: GSM8K is supporting rather than central for RQ3 because its open-ended answer space yields stricter two-mode filtering and a smaller retained set.
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