# Interpretable Representation Learning from Videos using Nonlinear Priors

arXiv: https://arxiv.org/abs/2410.18539 · HTML: https://mlsanity.com/paper/2410.18539/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Visual Interaction Networks](https://mlsanity.com/paper/1706.01433/) (2017)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [CoPhy: Counterfactual Learning of Physical Dynamics](https://mlsanity.com/paper/1909.12000/) (2019)
- [IntPhys: A Framework and Benchmark for Visual Intuitive Physics Reasoning](https://mlsanity.com/paper/1803.07616/) (2018)
- [Learning Physical Intuition of Block Towers by Example](https://mlsanity.com/paper/1603.01312/) (2016)
- [Learning Visual Predictive Models of Physics for Playing Billiards](https://mlsanity.com/paper/1511.07404/) (2015)
- [Reasoning About Physical Interactions with Object-Oriented Prediction and Planning](https://mlsanity.com/paper/1812.10972/) (2018)
- [Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning](https://mlsanity.com/paper/2110.15796/) (2021)
- [Newtonian Image Understanding: Unfolding the Dynamics of Objects in Static Images](https://mlsanity.com/paper/1511.04048/) (2015)
- [A Survey on Machine Learning Approaches for Modelling Intuitive Physics](https://mlsanity.com/paper/2202.06481/) (2022)
- [Unsupervised Learning of Latent Physical Properties Using Perception-Prediction Networks](https://mlsanity.com/paper/1807.09244/) (2018)

## Abstract (arXiv)

Learning interpretable representations of visual data is an important challenge, to make machines' decisions understandable to humans and to improve generalisation outside of the training distribution. To this end, we propose a deep learning framework where one can specify nonlinear priors for videos (e.g. of Newtonian physics) that allow the model to learn interpretable latent variables and use these to generate videos of hypothetical scenarios not observed at training time. We do this by extending the Variational Auto-Encoder (VAE) prior from a simple isotropic Gaussian to an arbitrary nonlinear temporal Additive Noise Model (ANM), which can describe a large number of processes (e.g. Newtonian physics). We propose a novel linearization method that constructs a Gaussian Mixture Model (GMM) approximating the prior, and derive a numerically stable Monte Carlo estimate of the KL divergence between the posterior and prior GMMs. We validate the method on different real-world physics videos including a pendulum, a mass on a spring, a falling object and a pulsar (rotating neutron star). We specify a physical prior for each experiment and show that the correct variables are learned. Once a model is trained, we intervene on it to change different physical variables (such as oscillation amplitude or adding air drag) to generate physically correct videos of hypothetical scenarios that were not observed previously.