Papers › HiPPO: Recurrent Memory with Optimal Polynomial Projections

HiPPO: Recurrent Memory with Optimal Polynomial Projections

17 Aug 2020NeurIPS 2020 12arXiv:2008.07669archive 2025-07-28

Albert Gu, Tri Dao, Stefano Ermon, Atri Rudra, Christopher Re

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

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HazyResearch/hippo-code officialmentioned in papermentioned on GitHubpytorchApache-2.0 report
ag1988/dss mentioned on GitHubpytorch report

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3ran · our draft was wrong
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bitreversal_permutation HazyResearch/hippo-code/model/unroll.py official repository ran fingerprinted Apache-2.0 (permissive) · 920218357ef96393 · report
bitreversal_po2 HazyResearch/hippo-code/model/unroll.py official repository ran fingerprinted Apache-2.0 (permissive) · 1c7d80fa5881a795 · report
shift_up HazyResearch/hippo-code/model/unroll.py official repository ran Apache-2.0 (permissive) · 3de2f7ab3e3dc431 · report
transition HazyResearch/hippo-code/model/op.py official repository ran · our draft was wrong Apache-2.0 (permissive) · 82ea253c64044e55 · report
Linear_ HazyResearch/hippo-code/model/components.py official repository unverified Apache-2.0 (permissive) · ba910cfe698ad603 · report
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get_initializer HazyResearch/hippo-code/model/components.py official repository unverified Apache-2.0 (permissive) · 261aab6fe51ea01d · report
pl_train HazyResearch/hippo-code/pl_runner.py official repository unverified Apache-2.0 (permissive) · 662bbcc5aee6ea80 · report
transition HazyResearch/hippo-code/tensorflow/hippo.py official repository unverified Apache-2.0 (permissive) · 46b2822b9e5411e0 · report
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Tasks

Sequential Image ClassificationTime SeriesTime Series Analysis

1 archive task tag without a task page not shown.

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Sequential Image Classification Sequential MNIST HiPPO-LegS Permuted Accuracy 98.3% #8 of 30 Archive leaderboard report

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