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A central problem in learning from sequential data is representing cumulativehistory in an incremental fashion as more data is processed. We introduce ageneral framework (HiPPO) for the online compression of continuous signals anddiscrete time series by projection onto polynomial bases. Given a measure thatspecifies the importance of each time step in the past, HiPPO produces anoptimal solution to a natural online function approximation problem. As specialcases, our framework yields a short derivation of the recent Legendre MemoryUnit (LMU) from first principles, and generalizes the ubiquitous gatingmechanism of recurrent neural networks such as GRUs. This formal frameworkyields a new memory update mechanism (HiPPO-LegS) that scales through time toremember all history, avoiding priors on the timescale. HiPPO-LegS enjoys thetheoretical benefits of timescale robustness, fast updates, and boundedgradients. By incorporating the memory dynamics into recurrent neural networks,HiPPO RNNs can empirically capture complex temporal dependencies. On thebenchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-artaccuracy of 98.3%. Finally, on a novel trajectory classification task testingrobustness to out-of-distribution timescales and missing data, HiPPO-LegSoutperforms RNN and neural ODE baselines by 25-40% accuracy.

HiPPO: Recurrent Memory with Optimal Polynomial Projections