Yunpeng Mei, Xiaowen Zhu, Chenyu Wang, Chenbo Xin, Hongjie Cao, Jiamin Wang, Jie Chen, Gang Wang · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.30107 · cited by 0 works (OpenAlex) · open-access PDF
흐름 조정된 코어 조정된 데이터 코어 영역은 속도 흐름 문제의 연속을 개선하지만 일반적으로 인터폴레이션 시간에 평균적인 손실을보고, 내재적 불확실성에 의해 제한된 영역을 차단하고 데이터 제한되는 영역을 분리합니다. 우리는 속도 불확실성 프로파일 (VAP), $\mathcal{A}_v(N)$, 데이터의 로컬 트랜스폴레이션 위험 플랫폼의 속도 예측을 통해 시간을 감소시키고, $L_N(t)=\mathcal{A}_v(t)+R(t;N)$를 소개합니다. 단지 과도한 용어 $R(t;A)_v(n)$가 더 또는 다른 시간 계산자에 의해 감소될 수있는
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 statistical benchmarks. In an intrinsic local-regression benchmark, $\mathcal{A}_v(t)$ enters the time-dependent noise factor of the standard nonparametric rate. In separated isotropic Gaussian mixtures, the Bayes velocity becomes locally affine, and a label-oracle residual-regression benchmark has parametric excess-risk scale $K\mathcal{A}_v(t)/N$, matched within the same separated residual Gaussian-location subproblem. Controlled Gaussian-mixture experiments validate this diagnostic through a dense transition sweep, calibrated oracle-to-blind and empirical-proxy audits, and a local controlled time-sampler stress test in which a frozen reducible-error proxy reduces reducible loss while cross-cell sensitivity delimits aggressive sampling. On CIFAR-100 DINOv2 feature flow, guided time sampling reduces uniformly evaluated velocity loss by $6.78\%$ and global feature Fréchet distance (FD) by $23.6\%$, while class-conditional kernel inception distance (KID) shows no improvement. VAP turns an averaged flow-matching objective into a time-resolved diagnostic for locating ambiguity-limited and data-limited regions.
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Topics: Mathematics, Nonparametric statistics, Residual, Parametric statistics, Matching (statistics), Maxima and minima
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