Unsupervised Learning of Equivariant Structure from Sequences

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Takeru Miyato, Masanori Koyama, Kenji Fukumizu


In this study, we present \textit{meta-sequential prediction} (MSP), an unsupervised framework to learn the symmetry from the time sequence of length at least three. Our method leverages the stationary property~(e.g. constant velocity, constant acceleration) of the time sequence to learn the underlying equivariant structure of the dataset by simply training the encoder-decoder model to be able to predict the future observations. We will demonstrate that, with our framework, the hidden disentangled structure of the dataset naturally emerges as a by-product by applying \textit{simultaneous block-diagonalization} to the transition operators in the latent space, the procedure which is commonly used in representation theory to decompose the feature-space based on the type of response to group actions.We will showcase our method from both empirical and theoretical perspectives.Our result suggests that finding a simple structured relation and learning a model with extrapolation capability are two sides of the same coin. The code is available at https://github.com/takerum/metasequentialprediction.