Papers › Simplified State Space Layers for Sequence Modeling

Simplified State Space Layers for Sequence Modeling

9 Aug 2022arXiv:2208.04933archive 2025-07-28

Jimmy T. H. Smith, Andrew Warrington, Scott W. Linderman

Models using structured state space sequence (S4) layers have achieved state-of-the-art performance on long-range sequence modeling tasks. An S4 layer combines linear state space models (SSMs), the HiPPO framework, and deep learning to achieve high performance. We build on the design of the S4 layer and introduce a new state space layer, the S5 layer. Whereas an S4 layer uses many independent single-input, single-output SSMs, the S5 layer uses one multi-input, multi-output SSM. We establish a connection between S5 and S4, and use this to develop the initialization and parameterization used by the S5 model. The result is a state space layer that can leverage efficient and widely implemented parallel scans, allowing S5 to match the computational efficiency of S4, while also achieving state-of-the-art performance on several long-range sequence modeling tasks. S5 averages 87.4% on the long range arena benchmark, and 98.5% on the most difficult Path-X task.

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lindermanlab/S5 officialmentioned in papermentioned on GitHubjaxMIT report
leonty1/deepldnn mentioned on GitHubpytorchApache-2.0 report
leonty1/essm mentioned on GitHubpytorch report
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Tasks

Computational EfficiencyListOpsLong-range modelingRetrievalState Space Models

2 archive task tags without a task page not shown.

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Long-range modeling LRA S5 Avg 87.46 #1 of 7 Archive leaderboard report
Long-range modeling LRA S5 Image 88 #1 of 7 Archive leaderboard report
Long-range modeling LRA S5 ListOps 62.15 #1 of 7 Archive leaderboard report
Long-range modeling LRA S5 Pathfinder 95.33 #1 of 7 Archive leaderboard report
Long-range modeling LRA S5 Pathfinder-X 98.58 #1 of 7 Archive leaderboard report
Long-range modeling LRA S5 Retrieval 91.4 #1 of 7 Archive leaderboard report
Long-range modeling LRA S5 Text 89.31 #1 of 7 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

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