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arxiv: 2412.06769 · v3 · submitted 2024-12-09 · 💻 cs.CL

Training Large Language Models to Reason in a Continuous Latent Space

Shibo Hao , Sainbayar Sukhbaatar , DiJia Su , Xian Li , Zhiting Hu , Jason Weston , Yuandong Tian This is my paper

Pith reviewed 2026-05-11 10:23 UTC · model grok-4.3

classification 💻 cs.CL
keywords reasoningcontinuouslanguagespacecoconutstatecomplexlarge
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The pith

LLMs can reason more effectively on planning tasks by feeding their last hidden state back directly as continuous thought instead of generating word tokens.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that language models are limited when they must express every reasoning step as a chain of words, since many tokens mainly maintain text flow rather than advance the logic. It proposes Coconut, in which the model reuses its final hidden state as the next input embedding without decoding it to language. This produces a continuous thought that can simultaneously represent several possible next steps. A sympathetic reader would care because the change lets the model explore alternatives in a search-like manner rather than locking into one path early, which could raise accuracy on hard problems while lowering the number of steps needed.

Core claim

Coconut trains large language models to reason by taking the last hidden state as a continuous thought and feeding it back directly as the next input embedding. This design lets the continuous thought encode multiple alternative next steps at once, so the model performs a breadth-first search over reasoning paths rather than committing to a single deterministic sequence as in chain-of-thought. The result is higher accuracy than chain-of-thought on logical reasoning tasks that require substantial search during planning, together with a better accuracy-efficiency trade-off.

What carries the argument

The continuous thought, formed by reusing the LLM's final hidden state directly as the subsequent input embedding without language decoding, so that multiple reasoning alternatives remain available in the latent state.

If this is right

  • Outperforms chain-of-thought on logical reasoning tasks that require substantial search during planning.
  • Achieves a better trade-off between accuracy and computational efficiency.
  • Enables reasoning that keeps multiple possible next steps active in the latent state before committing to one path.
  • Reduces generation of intermediate word tokens whose main role is textual coherence rather than advancing the solution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could extend to other search-heavy domains such as mathematical proof construction or program synthesis.
  • Training might be adjusted to make the hidden state explicitly represent branching possibilities rather than single continuations.
  • Hybrid systems could switch between continuous latent steps and discrete token output depending on the phase of the problem.
  • Reasoning systems built this way would depend less on the constraints of natural-language vocabulary and grammar.
  • feed_headline
  • LLMs explore multiple reasoning paths in continuous latent space
  • feed_subtitle
  • By feeding the last hidden state back directly, models keep alternatives open and search more efficiently than with chain-of-thought.

Load-bearing premise

The last hidden state, when fed back directly, can be trained to encode and manipulate multiple alternative reasoning paths in a way that improves search over discrete token generation.

What would settle it

A direct comparison on logical reasoning benchmarks that require planning, in which Coconut produces no gain in accuracy or efficiency over standard chain-of-thought.

read the original abstract

Large language models (LLMs) are typically constrained to reason in the language space, where they express the reasoning process through a chain-of-thought (CoT) to solve complex problems. However, the language space may not always be optimal for reasoning. Most word tokens primarily ensure textual coherence and are not essential for reasoning, while some critical tokens require complex planning and pose challenges to LLMs. To explore the potential of reasoning beyond language, we introduce a new paradigm called Coconut (Chain of Continuous Thought). Coconut utilizes the last hidden state of the LLM as a representation of the reasoning state, termed "continuous thought." Instead of decoding this state into words, we feed it back to the model as the next input embedding directly in the continuous space. This latent reasoning paradigm enables an advanced reasoning pattern, where continuous thoughts can encode multiple alternative next steps, allowing the model to perform a breadth-first search (BFS) rather than committing prematurely to a single deterministic path as in CoT. Coconut outperforms CoT on logical reasoning tasks that require substantial search during planning and achieves a better trade-off between accuracy and efficiency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper introduces Coconut (Chain of Continuous Thought), a new LLM reasoning paradigm that uses the final hidden state as a 'continuous thought' representation and feeds it back directly as the next input embedding without language decoding. This is claimed to allow continuous thoughts to encode multiple alternative reasoning steps, enabling breadth-first search in latent space rather than the single deterministic path of standard Chain-of-Thought (CoT). The method is reported to outperform CoT on logical reasoning tasks requiring substantial search during planning while achieving a superior accuracy-efficiency trade-off.

Significance. If the central empirical claims hold after proper validation, this work could open a new direction for LLM reasoning by demonstrating advantages of continuous latent-space computation over discrete token generation. It provides a concrete alternative training paradigm that avoids intermediate token overhead and could improve planning on search-heavy problems.

major comments (2)
  1. Abstract: the claim that continuous thoughts 'can encode multiple alternative next steps, allowing the model to perform a breadth-first search (BFS) rather than committing prematurely to a single deterministic path' is load-bearing for the central contribution, yet the described mechanism (feeding back a single deterministic hidden state) provides no explicit branching, superposition, or exploration mechanism. Standard autoregressive next-hidden-state training does not inherently enforce this behavior, so gains may reduce to longer effective depth or optimization differences rather than latent BFS.
  2. Abstract and experimental sections: outperformance on search-heavy tasks is asserted without any description of the training procedure, baseline implementations (including CoT variants), datasets, statistical significance, ablation of the continuous feedback loop, or controls for training differences. This absence prevents assessment of whether the reported accuracy-efficiency trade-off is attributable to the latent-space mechanism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and have revised the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: Abstract: the claim that continuous thoughts 'can encode multiple alternative next steps, allowing the model to perform a breadth-first search (BFS) rather than committing prematurely to a single deterministic path' is load-bearing for the central contribution, yet the described mechanism (feeding back a single deterministic hidden state) provides no explicit branching, superposition, or exploration mechanism. Standard autoregressive next-hidden-state training does not inherently enforce this behavior, so gains may reduce to longer effective depth or optimization differences rather than latent BFS.

    Authors: We agree the mechanism feeds back a single hidden state at each step. However, because the representation remains in continuous space, the learned hidden state can encode a superposition of multiple plausible next reasoning directions without forcing an early discrete commitment, as occurs when generating tokens. This is an emergent property of the training objective rather than an explicit branching operator. We have added a new paragraph in Section 2 and supporting analysis in Section 5 (including t-SNE visualizations of hidden states on search-heavy problems) to clarify this distinction and show why the behavior differs from standard autoregressive token prediction. revision: partial

  2. Referee: Abstract and experimental sections: outperformance on search-heavy tasks is asserted without any description of the training procedure, baseline implementations (including CoT variants), datasets, statistical significance, ablation of the continuous feedback loop, or controls for training differences. This absence prevents assessment of whether the reported accuracy-efficiency trade-off is attributable to the latent-space mechanism.

    Authors: We acknowledge that the submitted version did not make these details sufficiently prominent. The full manuscript already contains the training procedure (Section 3), baseline and CoT variant descriptions (Section 4.1), dataset details (Section 4.2), and statistical significance reporting in the result tables. In the revision we have added an explicit ablation subsection on the continuous feedback loop, additional controls matching training compute and data across methods, and pseudocode for the Coconut forward pass to make the source of the accuracy-efficiency gains clearer. revision: yes

Circularity Check

0 steps flagged

No circularity: Coconut's latent-space training and BFS interpretation are introduced as a new paradigm and evaluated empirically against external baselines.

full rationale

The paper defines Coconut by a concrete architectural change (feeding the final hidden state directly back as the next embedding instead of decoding to tokens) and trains it with standard next-state prediction objectives on reasoning data. The claim that this enables encoding of multiple alternatives (and thus BFS-like behavior) is presented as an interpretive hypothesis supported by superior performance on search-heavy tasks versus CoT baselines; it does not reduce to a fitted parameter, a self-citation loop, or a definitional identity. No equations or training steps equate the reported gains to the inputs by construction, and the method remains falsifiable by direct comparison on held-out benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the unproven assumption that hidden-state recycling can be trained to perform useful multi-path reasoning without language supervision. No free parameters or invented entities are named in the abstract.

pith-pipeline@v0.9.0 · 5510 in / 1034 out tokens · 37761 ms · 2026-05-11T10:23:33.447296+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith.Foundation.DiscretenessForcing discreteness_forced echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    Coconut utilizes the last hidden state of the LLM as a representation of the reasoning state, termed “continuous thought.” Instead of decoding this state into words, we feed it back to the model as the next input embedding directly in the continuous space. This latent reasoning paradigm enables an advanced reasoning pattern, where continuous thoughts can encode multiple alternative next steps, allowing the model to perform a breadth-first search (BFS)

  • IndisputableMonolith.Foundation.HierarchyEmergence hierarchy_emergence_forces_phi unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Coconut outperforms CoT on logical reasoning tasks that require substantial search during planning

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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