ReGuLaR: Variational Latent Reasoning Guided by Rendered Chain-of-Thought

TL;DR

ReGuLaR introduces a variational latent reasoning framework where latent states $\mathbf{Z}$ are sampled from a posterior conditioned on prior steps and regularized by visual representations of rendered CoT. By rendering segments of the explicit reasoning chain into images and encoding them with a frozen visual encoder, ReGuLaR obtains dense visual-semantic priors $p_{\gamma}$ that preserve information while compressing reasoning. The method uses a VAE-like ELBO to jointly optimize latent reasoning, answer generation, and prior regularization, enabling multi-modal latent reasoning and strong scalability across LLM backbones. Empirically, ReGuLaR achieves state-of-the-art performance on several math reasoning benchmarks, reduces reasoning steps, and even surpasses explicit CoT in certain multi-modal scenarios, with an ability to perform extreme compression (e.g., $K=1$).

Abstract

While Chain-of-Thought (CoT) significantly enhances the performance of Large Language Models (LLMs), explicit reasoning chains introduce substantial computational redundancy. Recent latent reasoning methods attempt to mitigate this by compressing reasoning processes into latent space, but often suffer from severe performance degradation due to the lack of appropriate compression guidance. In this study, we propose Rendered CoT-Guided variational Latent Reasoning (ReGuLaR), a simple yet novel latent learning paradigm resolving this issue. Fundamentally, we formulate latent reasoning within the Variational Auto-Encoding (VAE) framework, sampling the current latent reasoning state from the posterior distribution conditioned on previous ones. Specifically, when learning this variational latent reasoning model, we render explicit reasoning chains as images, from which we extract dense visual-semantic representations to regularize the posterior distribution, thereby achieving efficient compression with minimal information loss. Extensive experiments demonstrate that ReGuLaR significantly outperforms existing latent reasoning methods across both computational efficiency and reasoning effectiveness, and even surpasses CoT through multi-modal reasoning, providing a new and insightful solution to latent reasoning. Code: https://github.com/FanmengWang/ReGuLaR.

Figures (7)

• Figure 1: Illustration of our modeling principle. Given an explicit reasoning chain of length $L$, we render it onto $K$ images ($K \ll L$) and extract corresponding visual representations to guide the latent reasoning process with $K$ steps.
• Figure 2: Comparison of CoT-based explicit reasoning and latent reasoning, where the autoregressive decoder corresponds to the underlying LLM.
• Figure 3: Illustration of the proposed ReGuLaR. Here, only the latent reasoning head, adapter, and LoRA module are trainable. The blue arrows "$\rightarrow$" indicate deterministic outputs, while the red arrows "$\rightarrow$" indicate probabilistic outputs achieved by sampling. The special token "###" triggers the transition from the reasoning process to answer generation during inference.
• Figure 4: (a) Generalizability analysis using DeepSeek-R1-Distill-Qwen-1.5B as the LLM backbone, where the left panel reports Accuracy and the right panel reports Reasoning Length. (b) Compression Analysis on the GSM8K-Aug dataset using LLaMA-3.2-1B-Instruct (left) and DeepSeek-R1-Distill-Qwen-1.5B (right) as the LLM backbone, where the compression rate represents the number of explicit reasoning tokens corresponding to a single latent reasoning state.
• Figure 5: Scalability analysis across varying model sizes, where we employ LLaMA-3.2 (1B, 3B) and LLaMA-3.1 (8B) Instruct variants as the LLM backbones. Comprehensive results, including reasoning length, are provided in Figure \ref{['fig: Full_Scalability']}.