Title: ReynoldsFlow: Spatiotemporal Flow Representations for Video Learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Video Representation Learning, Spatiotemporal Modeling, Physics-Inspired Flow, Helmholtz Decomposition, Reynolds Transport Theorem

Abstract: Representation learning for videos has largely relied on spatiotemporal modules embedded in deep architectures, which, while effective, often require heavy computation and heuristic design. Existing approaches, such as 3D convolutional modules or optical flow networks, may also overlook changes in illumination, scale variations, and structural deformations in video sequences. To address these challenges, we propose ReynoldsFlow, a physics-inspired flow representation that leverages the Helmholtz decomposition and the Reynolds transport theorem to derive principled spatiotemporal features directly from video data. Unlike classical optical flow, ReynoldsFlow captures both divergence-free and curl-free components under more general assumptions, enabling robustness to photometric variation while preserving intrinsic structure. Beyond its theoretical grounding, ReynoldsFlow remains lightweight and adaptable, combining frame intensity with flow magnitude to yield texture-preserving and dynamics-aware representations that substantially enhance tiny object detection. Experiments on benchmarks with various target scales demonstrate that ReynoldsFlow is consistently comparable to or outperforms existing flow-based features, while also improving interpretability and efficiency. These results position ReynoldsFlow as a compelling representation for video understanding and a strong foundation for downstream model learning. The code will be made publicly available.

TL;DR: We propose ReynoldsFlow, a physics-inspired spatiotemporal flow representation that is lightweight, interpretable, and robust to photometric and structural variations for efficient video representation learning.