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Effectively modeling long spatiotemporal sequences is challenging due to theneed to model complex spatial correlations and long-range temporal dependenciessimultaneously. ConvLSTMs attempt to address this by updating tensor-valuedstates with recurrent neural networks, but their sequential computation makesthem slow to train. In contrast, Transformers can process an entirespatiotemporal sequence, compressed into tokens, in parallel. However, the costof attention scales quadratically in length, limiting their scalability tolonger sequences. Here, we address the challenges of prior methods andintroduce convolutional state space models (ConvSSM) that combine the tensormodeling ideas of ConvLSTM with the long sequence modeling approaches of statespace methods such as S4 and S5. First, we demonstrate how parallel scans canbe applied to convolutional recurrences to achieve subquadratic parallelizationand fast autoregressive generation. We then establish an equivalence betweenthe dynamics of ConvSSMs and SSMs, which motivates parameterization andinitialization strategies for modeling long-range dependencies. The result isConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling.ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizonMoving-MNIST experiment while training 3X faster than ConvLSTM and generatingsamples 400X faster than Transformers. In addition, ConvS5 matches or exceedsthe performance of state-of-the-art methods on challenging DMLab, Minecraft andHabitat prediction benchmarks and enables new directions for modeling longspatiotemporal sequences.

Convolutional State Space Models for Long-Range Spatiotemporal Modeling