{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/liquid-structural-state-space-models","title":"Liquid Structural State-Space Models","arxiv_id":"2209.12951","date":"2022-09-26","proceeding":null,"authors":["Ramin Hasani","Mathias Lechner","Tsun-Hsuan Wang","Makram Chahine","Alexander Amini","Daniela Rus"],"abstract":"A proper parametrization of state transition matrices of linear state-space models (SSMs) followed by standard nonlinearities enables them to efficiently learn representations from sequential data, establishing the state-of-the-art on a large series of long-range sequence modeling benchmarks. In this paper, we show that we can improve further when the structural SSM such as S4 is given by a linear liquid time-constant (LTC) state-space model. LTC neural networks are causal continuous-time neural networks with an input-dependent state transition module, which makes them learn to adapt to incoming inputs at inference. We show that by using a diagonal plus low-rank decomposition of the state transition matrix introduced in S4, and a few simplifications, the LTC-based structural state-space model, dubbed Liquid-S4, achieves the new state-of-the-art generalization across sequence modeling tasks with long-term dependencies such as image, text, audio, and medical time-series, with an average performance of 87.32% on the Long-Range Arena benchmark. On the full raw Speech Command recognition, dataset Liquid-S4 achieves 96.78% accuracy with a 30% reduction in parameter counts compared to S4. The additional gain in performance is the direct result of the Liquid-S4's kernel structure that takes into account the similarities of the input sequence samples during training and inference.","url_abs":"https://arxiv.org/abs/2209.12951v1","url_pdf":"https://arxiv.org/pdf/2209.12951v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"liquid-structural-state-space-models","repo_url":"https://github.com/raminmh/liquid-s4","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"heart-rate-estimation","task_name":"Heart rate estimation"},{"task_slug":"long-range-modeling","task_name":"Long-range modeling"},{"task_slug":"spo2-estimation","task_name":"SpO2 estimation"},{"task_slug":"speech-recognition","task_name":"Speech Recognition"},{"task_slug":"state-space-models","task_name":"State Space Models"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/heart-rate-estimation-on-bidmc","task":"Heart rate estimation","dataset":"BIDMC","model":"Liquid-S4","rank_in_archive_order":1,"of":2,"metrics":{"MAE [bpm, session-wise]":"0.303"},"uses_additional_data":false},{"leaderboard":"/sota/spo2-estimation-on-bidmc","task":"SpO2 estimation","dataset":"BIDMC","model":"Liquid-S4","rank_in_archive_order":1,"of":2,"metrics":{"MAE [bpm, session-wise]":"0.066"},"uses_additional_data":false},{"leaderboard":"/sota/speech-recognition-on-speech-commands-2","task":"Speech Recognition","dataset":"Speech Commands","model":"Liquid-S4","rank_in_archive_order":2,"of":3,"metrics":{"Accuracy (%)":"98.51"},"uses_additional_data":false}],"syntology":{"syntology_url":"https://syntology.ai/paper/2209.12951","atlas_url":"https://app.syntology.ai/?focus=2209.12951","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}