Yunpeng Mei, Xiaowen Zhu, Chenyu Wang, Chenbo Xin, Hongjie Cao, Jiamin Wang, Jie Chen, Gang Wang · 2026 · arXiv
DOI: 10.48550/arXiv.2610.30107 · open-access PDF
流相匹配会带来连续的速度回归问题,但通常会报告在交互时间内平均的损失,从而掩盖哪些区域受到内在的模糊性限制,而哪些区域仍然受到数据限制。我们引入了Velocity Ambiguity Profile(VAP),$\mathcal{A}_v(t)$,速度预测的时局Bayes风险地板,并将时间解决的损失分解为 $L_N(t)=\mathcal{A}_v(t)+R(t;N)$,其中只有过剩术语 $R(t;N)$可以通过更多的数据或不同的估计量来减少。
Machine translation (Meta M2M100); the English original follows.
Flow matching trains a continuum of velocity regression problems but usually reports a loss averaged over interpolation time, obscuring which regions are limited by intrinsic ambiguity and which remain data-limited. We introduce the Velocity Ambiguity Profile (VAP), $\mathcal{A}_v(t)$, the time-local Bayes-risk floor of velocity prediction, and decompose time-resolved loss as $L_N(t)=\mathcal{A}_v(t)+R(t;N)$, where only the excess term $R(t;N)$ is reducible by more data or a different estimator. For $N$ training samples and a $K$-component mixture in the structured example, we prove two statis
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