发表机构
Evercot AI（Evercot AI）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出张量场模型（TFMs），将其应用于生成状态流形，采用流匹配训练，可提升性能并通过可重用条件表示实现的分摊采样加速生成。
AI 中文摘要
本文介绍了张量场模型（Tensor Field Models, TFMs），这是一种实现级数学结构，其中学习到的算子将可容许分量-截面族的乘积映射到生成状态流形上规定的随时间变化的切截面族。解析和动力学约束通过可容许族的选择进行编码，而非由根本定义强加。构造的、分量可分的以及张量丛TFMs为该通用对象提供了结构化细化。在此考虑的条件实现中，结构化条件 $c=(c_1,\ldots,c_n)$ 被逐分量映射到可重用集合 $\mathbf H_c=(H_{c_1}^{(1)},\ldots,H_{c_n}^{(n)})$。在所评估的架构中，分量表示保持独立，仅通过场算子组合以生成向量场。所有学习模型均使用流匹配（Flow Matching）进行训练。实验表明，TFMs可提升性能，且由可重用条件表示实现的分摊采样可加速生成过程。
英文摘要
This paper introduces Tensor Field Models (TFMs), realization-level Mathematical Structures in which a learned Operator maps a product of admissible component-section families to a prescribed family of time-dependent tangent sections on a Generative State Manifold. Analytic and dynamical restrictions are encoded through the choice of admissible families rather than imposed by the root definition. Constructed, component-separable, and Tensor Bundle TFMs provide structured refinements of this common object. In the conditional realizations considered here, a structured condition $c=(c_1,\ldots,c_n)$ is mapped componentwise to a reusable collection $\mathbf H_c=(H_{c_1}^{(1)},\ldots,H_{c_n}^{(n)})$. In the architectures evaluated here, the component representations remain distinct and are combined only by the Field Operator to produce the generated Vector Field. All learned models are trained using Flow Matching. Experiments show that TFMs can improve performance and that amortized sampling enabled by reusable condition representations can accelerate generation.
