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arXiv 提交日期: 2026-05-14
📄 Abstract - Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space

This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) in terms of combination of trajectory singularity, adjoint state vanishing, and gradient absence. To address these issues, we approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that acts as a closed-loop controller. To bypass the intractability of directly solving the HJB PDE, we employ Flow Matching as the optimal trajectory solver within the rectified latent control space. This allows our Manta-LM with Global Integral Operator to approximate the global vector field, effectively realizing a model that simultaneously achieves high-fidelity text generation and efficient, low-cost parallel sampling. Empirically, our method achieves strong performance on language modeling and conditional generation tasks, while exhibiting improved stability, efficiency, and controllability.

顶级标签: llm machine learning theory
详细标签: diffusion models optimal control autoregressive models flow matching language generation 或 搜索:

语言生成作为最优控制:潜在控制空间中的闭环扩散 / Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space


1️⃣ 一句话总结

本文提出将语言生成问题转化为随机最优控制问题,通过近似求解哈密顿-雅可比-贝尔曼方程得到闭环控制策略,并利用流匹配技术在潜在控制空间中进行高效并行采样,从而在保证生成文本质量的同时显著提升采样效率和稳定性。

源自 arXiv: 2605.14531