# Unfolding Videos Dynamics via Taylor Expansion

arXiv: https://arxiv.org/abs/2409.02371 · HTML: https://mlsanity.com/paper/2409.02371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 74 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 30 of 61)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Training](https://mlsanity.com/paper/2203.12602/) (2022)
- [A Closer Look at Spatiotemporal Convolutions for Action Recognition](https://mlsanity.com/paper/1711.11248/) (2017)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Rethinking Spatiotemporal Feature Learning: Speed-Accuracy Trade-offs in Video Classification](https://mlsanity.com/paper/1712.04851/) (2017)
- [End-to-End Learning of Visual Representations from Uncurated Instructional Videos](https://mlsanity.com/paper/1912.06430/) (2019)
- [AVA: A Video Dataset of Spatio-temporally Localized Atomic Visual Actions](https://mlsanity.com/paper/1705.08421/) (2017)
- [Spatiotemporal Contrastive Video Representation Learning](https://mlsanity.com/paper/2008.03800/) (2020)
- [BMN: Boundary-Matching Network for Temporal Action Proposal Generation](https://mlsanity.com/paper/1907.09702/) (2019)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [Self-Supervised MultiModal Versatile Networks](https://mlsanity.com/paper/2006.16228/) (2020)
- [Cooperative Learning of Audio and Video Models from Self-Supervised Synchronization](https://mlsanity.com/paper/1807.00230/) (2018)
- [Space-Time Correspondence as a Contrastive Random Walk](https://mlsanity.com/paper/2006.14613/) (2020)
- [Self-supervised Co-training for Video Representation Learning](https://mlsanity.com/paper/2010.09709/) (2020)
- [Unsupervised Representation Learning by Sorting Sequences](https://mlsanity.com/paper/1708.01246/) (2017)
- [A Large-Scale Study on Unsupervised Spatiotemporal Representation Learning](https://mlsanity.com/paper/2104.14558/) (2021)
- [Video Representation Learning by Dense Predictive Coding](https://mlsanity.com/paper/1909.04656/) (2019)
- [SpeedNet: Learning the Speediness in Videos](https://mlsanity.com/paper/2004.06130/) (2020)
- [VideoMoCo: Contrastive Video Representation Learning with Temporally Adversarial Examples](https://mlsanity.com/paper/2103.05905/) (2021)
- [Self-Supervised Video Representation Learning with Space-Time Cubic Puzzles](https://mlsanity.com/paper/1811.09795/) (2018)
- [Self-supervised Video Representation Learning by Pace Prediction](https://mlsanity.com/paper/2008.05861/) (2020)
- [TCLR: Temporal Contrastive Learning for Video Representation](https://mlsanity.com/paper/2101.07974/) (2021)

## Built on by (most cited first, 3 of 3)

- [Explaining and Mitigating the Modality Gap in Contrastive Multimodal Learning](https://mlsanity.com/paper/2412.07909/) (2024)
- [Chirality in Action: Time-Aware Video Representation Learning by Latent Straightening](https://mlsanity.com/paper/2509.08502/) (2025)
- [Swift Sampling: Selecting Temporal Surprises via Taylor Series](https://mlsanity.com/paper/2605.22678/) (2026)

## Abstract (arXiv)

Taking inspiration from physical motion, we present a new self-supervised dynamics learning strategy for videos: Video Time-Differentiation for Instance Discrimination (ViDiDi). ViDiDi is a simple and data-efficient strategy, readily applicable to existing self-supervised video representation learning frameworks based on instance discrimination. At its core, ViDiDi observes different aspects of a video through various orders of temporal derivatives of its frame sequence. These derivatives, along with the original frames, support the Taylor series expansion of the underlying continuous dynamics at discrete times, where higher-order derivatives emphasize higher-order motion features. ViDiDi learns a single neural network that encodes a video and its temporal derivatives into consistent embeddings following a balanced alternating learning algorithm. By learning consistent representations for original frames and derivatives, the encoder is steered to emphasize motion features over static backgrounds and uncover the hidden dynamics in original frames. Hence, video representations are better separated by dynamic features. We integrate ViDiDi into existing instance discrimination frameworks (VICReg, BYOL, and SimCLR) for pretraining on UCF101 or Kinetics and test on standard benchmarks including video retrieval, action recognition, and action detection. The performances are enhanced by a significant margin without the need for large models or extensive datasets.