arxiv: 2604.17892 · v3 · submitted 2026-04-20 · 💻 cs.LG · cs.AI

Recognition: 2 theorem links

· Lean Theorem

LEPO: Latent Reasoning Policy Optimization for Large Language Models

Yuyan Zhou , Jiarui Yu , Hande Dong , Zhezheng Hao , Hong Wang , Jianqing Zhang , Qiang Lin

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:54 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords latent reasoningpolicy optimizationreinforcement learningGumbel-Softmaxlarge language modelscontinuous representationsstochastic sampling

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The pith

LEPO applies reinforcement learning directly to continuous latent representations in large language models by restoring stochasticity with Gumbel-Softmax

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

Latent reasoning supplies language models with rich continuous internal states yet without added noise these states collapse to one fixed inference path and lose the exploration required for reinforcement learning. The paper demonstrates that controllable stochasticity introduced by Gumbel-Softmax sampling restores the capacity to generate diverse reasoning trajectories while retaining the advantages of the continuous space. LEPO then builds a policy optimization method on this stochastic latent process that estimates gradients jointly for the latent variables and the discrete tokens produced from them. This unified treatment lets reinforcement learning operate inside the latent space rather than only on token sequences. Experiments indicate that the resulting policies outperform earlier reinforcement learning approaches applied to either discrete token reasoning or other latent techniques.

Core claim

LEPO is a framework that applies RL directly to continuous latent representations. In the rollout stage it maintains stochasticity via Gumbel-Softmax to enable diverse trajectory sampling. In the optimization stage it constructs a unified gradient estimation for both latent representations and discrete tokens. Extensive experiments show that LEPO significantly outperforms existing RL methods for discrete and latent reasoning.

What carries the argument

Gumbel-Softmax reparameterization applied to latent reasoning steps, which injects controllable stochasticity and supports unified gradient estimation across continuous latent representations and discrete tokens

If this is right

LEPO maintains stochasticity during rollout to sample diverse reasoning trajectories from continuous latent states
LEPO uses a single gradient estimator that jointly updates latent representations and the discrete tokens that follow them
LEPO significantly outperforms existing RL methods applied to either discrete token reasoning or other latent techniques
Latent reasoning becomes directly compatible with standard reinforcement learning frameworks

Where Pith is reading between the lines

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

Continuous latent states may encode intermediate reasoning steps more densely than discrete token sequences, which could improve search efficiency on multi-hop tasks
The unified treatment of latents and tokens suggests that internal activations can be optimized as policy actions without first forcing them into discrete categories
The same Gumbel-Softmax injection might stabilize training in other settings where continuous variables must be optimized alongside discrete outputs

Load-bearing premise

That adding Gumbel-Softmax stochasticity to latent reasoning restores exploratory capacity without introducing instability or bias, and that the unified gradient estimation for latents and tokens remains stable and effective

What would settle it

A controlled experiment in which removing the Gumbel-Softmax component causes LEPO performance to fall to the level of deterministic latent baselines or in which the combined gradient estimates produce training divergence on standard reasoning benchmarks

Figures

Figures reproduced from arXiv: 2604.17892 by Hande Dong, Hong Wang, Jianqing Zhang, Jiarui Yu, Qiang Lin, Yuyan Zhou, Zhezheng Hao.

**Figure 2.** Figure 2: Illustration of the LEPO framework. (a) Rollout Stage: We employ Gumbel-Softmax for stochastic [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Evolution of entropy. Comparison of entropy changes between LEPO and GRPO during the training process. 0 20 40 60 80 100 Training Steps 800 900 1000 1100 Tokens Training Tokens LEPO (Ours) GRPO [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Comparison of token consumption during the training. The plot shows the change in token counts over training steps. marks, indicating its robust generalization capabilities after training. 4.3 Training Dynamics and Analysis Entropy. We track the evolution of entropy during the training process based on Qwen2.5-7B shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Analysis of Hyperparameters and Training Dynamics using Qwen2.5-7B. (a) Performance com [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Qualitative comparison of GRPO, LEPO and latent COT on an arithmetic task from GSM8k. We [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: Example Prompt for Mathematical Reasoning in LEPO. [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: Example Prompt for GPQA-Diamond, ARC-C and MMLU-STEM in LEPO. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

**Figure 9.** Figure 9: Training analysis of LEPO versus GRPO on Qwen2.5-3B. (a) Evolution of training rewards, where [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: Training analysis of LEPO versus GRPO on Llama-3.2-3B-Instruct. (a) Evolution of training [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

read the original abstract

Recently, latent reasoning has been introduced into large language models (LLMs) to leverage rich information within a continuous space. However, without stochastic sampling, these methods inevitably collapse to deterministic inference, failing to discover diverse reasoning paths. To bridge the gap, we inject controllable stochasticity into latent reasoning via Gumbel-Softmax, restoring LLMs' exploratory capacity and enhancing their compatibility with Reinforcement Learning (RL). Building on this, we propose \textbf{\underline{L}}atent R\textbf{\underline{e}}asoning \textbf{\underline{P}}olicy \textbf{\underline{O}}ptimization~(\textbf{LEPO}), a novel framework that applies RL directly to continuous latent representations. Specifically, in rollout stage, LEPO maintains stochasticity to enable diverse trajectory sampling, while in optimization stage, LEPO constructs a unified gradient estimation for both latent representations and discrete tokens. Extensive experiments show that LEPO significantly outperforms existing RL methods for discrete and latent reasoning.

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 / 1 minor

Summary. The paper proposes LEPO, a framework that injects Gumbel-Softmax stochasticity into continuous latent reasoning in LLMs to prevent deterministic collapse and restore exploration. It then applies RL directly to latent representations via a unified gradient estimator that handles both continuous latents and discrete tokens. The central claim is that this yields significant outperformance over existing RL methods for discrete and latent reasoning, supported by extensive experiments.

Significance. If the central claims hold, the work would meaningfully advance latent reasoning by making it compatible with RL through controlled stochasticity, addressing a key limitation where latent methods lose exploratory capacity. The unified gradient construction and Gumbel-Softmax adaptation represent a technically interesting bridge between continuous and discrete spaces in policy optimization. Strengths include the explicit focus on restoring exploration without new invented entities and the potential for falsifiable predictions via the reported outperformance.

major comments (2)

[optimization stage / unified gradient estimation] The unified gradient estimation (described in the optimization stage) applies Gumbel-Softmax reparameterization to continuous latent representations. Gumbel-Softmax is canonically for categorical variables; its direct use here risks temperature-dependent bias that does not necessarily vanish in the policy-gradient estimator when rewards are defined only on discrete token sequences. No explicit bias analysis, variance bound, or stability proof for the combined estimator is provided, which is load-bearing for the claim that LEPO restores exploration without instability.
[Experiments] The abstract asserts that 'extensive experiments show that LEPO significantly outperforms existing RL methods,' yet supplies no details on baselines, datasets, metrics, ablation studies (e.g., on Gumbel-Softmax temperature), or statistical significance. Without these, the outperformance claim cannot be evaluated and the weakest assumption (stable, unbiased unified estimation) remains untested.

minor comments (1)

[Method] Notation for the latent representations and the Gumbel-Softmax temperature parameter should be introduced with explicit definitions and ranges before use in the method description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our work. We address each of the major comments below and outline the revisions we will make to the manuscript.

read point-by-point responses

Referee: [optimization stage / unified gradient estimation] The unified gradient estimation (described in the optimization stage) applies Gumbel-Softmax reparameterization to continuous latent representations. Gumbel-Softmax is canonically for categorical variables; its direct use here risks temperature-dependent bias that does not necessarily vanish in the policy-gradient estimator when rewards are defined only on discrete token sequences. No explicit bias analysis, variance bound, or stability proof for the combined estimator is provided, which is load-bearing for the claim that LEPO restores exploration without instability.

Authors: We appreciate the referee's scrutiny of the unified gradient estimation. In LEPO, Gumbel-Softmax is employed to reparameterize the continuous latent variables, introducing controlled stochasticity that allows diverse sampling while enabling end-to-end gradient flow. This creates a unified estimator applicable to both latent and token levels. We recognize that a dedicated analysis of bias and variance is absent from the current manuscript. Our empirical evaluations indicate stable optimization and effective exploration restoration. In the revised manuscript, we will add a subsection providing bias analysis, including discussion of temperature effects and a sketch of the estimator's properties. revision: yes
Referee: [Experiments] The abstract asserts that 'extensive experiments show that LEPO significantly outperforms existing RL methods,' yet supplies no details on baselines, datasets, metrics, ablation studies (e.g., on Gumbel-Softmax temperature), or statistical significance. Without these, the outperformance claim cannot be evaluated and the weakest assumption (stable, unbiased unified estimation) remains untested.

Authors: The full manuscript provides comprehensive details on the experimental setup, including baselines, datasets, metrics, ablation studies on the Gumbel-Softmax temperature, and statistical significance testing, within the Experiments section. To enhance the self-contained nature of the abstract and facilitate quicker evaluation of the claims, we will revise the abstract to incorporate a brief overview of the experimental methodology and key findings. revision: partial

Circularity Check

0 steps flagged

No significant circularity in LEPO derivation chain

full rationale

The paper's core contribution is the LEPO framework: injecting Gumbel-Softmax for stochasticity in latent reasoning, then applying RL with a unified gradient estimator over latents and tokens. These steps build on standard reparameterization tricks and policy optimization without self-defining the target performance metric in terms of the method itself, without renaming fitted parameters as predictions, and without load-bearing self-citations that reduce the central claim to an unverified prior result by the same authors. The abstract and description present the approach as an extension of existing RL and latent reasoning techniques, with outperformance demonstrated via experiments rather than by construction. No equations or steps reduce the claimed improvement to a tautology or fitted input.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract relies on standard techniques (Gumbel-Softmax, RL policy optimization) without detailing new axioms, free parameters, or invented entities; full paper would be needed to audit these.

pith-pipeline@v0.9.0 · 5478 in / 1041 out tokens · 75976 ms · 2026-05-12T03:54:33.433701+00:00 · methodology

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discussion (0)

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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

we inject controllable stochasticity into latent reasoning via Gumbel-Softmax... unified gradient estimation for both latent representations and discrete tokens

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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.

Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages · 3 internal anchors

[1]

Training Large Language Models to Reason in a Continuous Latent Space

Training large language models to rea- son in a continuous latent space. arXiv preprint arXiv:2412.06769. Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Ja- cob Steinhardt. 2021a. Measuring massive multitask language understanding. Proceedings of the International Conference on Learning Representations (ICLR). Dan Hen...

work page internal anchor Pith review Pith/arXiv arXiv 2016
[2]

DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Gpqa: A graduate-level google-proof q&a benchmark. In First Conference on Language Modeling. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, and 1 oth- ers. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300. Zhenyi ...

work page internal anchor Pith review Pith/arXiv arXiv 2024
[3]

arXiv preprint arXiv:2510.05069

Swireasoning: Switch-thinking in latent and explicit for pareto-superior reasoning llms. arXiv preprint arXiv:2510.05069. Jihoon Tack, Jack Lanchantin, Jane Yu, Andrew Co- hen, Ilia Kulikov, Janice Lan, Shibo Hao, Yuan- dong Tian, Jason Weston, and Xian Li. 2025. Llm pretraining with continuous concepts. arXiv preprint arXiv:2502.08524. Wenhui Tan, Jiaze ...

work page arXiv 2025
[4]

DAPO: An Open-Source LLM Reinforcement Learning System at Scale

Dapo: An open-source llm reinforce- ment learning system at scale. arXiv preprint arXiv:2503.14476. Zhenrui Yue, Bowen Jin, Huimin Zeng, Honglei Zhuang, Zhen Qin, Jinsung Yoon, Lanyu Shang, Jiawei Han, and Dong Wang. 2025. Hybrid la- tent reasoning via reinforcement learning. arXiv preprint arXiv:2505.18454. Zhen Zhang, Xuehai He, Weixiang Yan, Ao Shen, C...

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[5]

The sampling temperatures are set to 1.0 during training and 0.6 for testing

We apply top-p sampling with p= 0.95 and top-k sampling with k= 30 . The sampling temperatures are set to 1.0 during training and 0.6 for testing. All experiments are conducted with 8 Nvidia H20 GPUs. Training takes approx- imately 28 hours for Qwen2.5-7B, and 20 hours for Qwen2.5-3B and Llama-3.2-3B-Instruct. For LEPO, we conduct a grid search over Lg ∈ ...

work page 2048