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Tuning Frequency Bias in State Space Models Poster

A conference poster detailing methods to tune frequency bias in State Space Models (SSMs) through initialization and training dynamics, including theoretical analysis and experimental results on long-range benchmarks.

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Paper title: Tuning Frequency Bias of State Space Models Abstract: A conference poster detailing methods to tune frequency bias in State Space Models (SSMs) through initialization and training dynamics, including theoretical analysis and experimental results on long-range benchmarks. Paper body (method & results): <!DOCTYPE html> <html lang="en"> <head> <meta content="text/html; charset=utf-8" http-equiv="content-type"/> <title>Tuning Frequency Bias of State Space Models</title>  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport"/> <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/css/bootstrap.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv-fonts.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/latexml_styles.css" rel="stylesheet" type="text/css"/> <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/js/bootstrap.bundle.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/html2canvas/1.3.3/html2canvas.min.js"></script> <script src="/static/browse/0.3.4/js/addons_new.js"></script> <script src="/static/browse/0.3.4/js/feedbackOverlay.js"></script> <base href="/html/2410.02035v1/"/></head> <body> <nav class="ltx_page_navbar"> <nav class="ltx_TOC"> <ol class="ltx_toclist"> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S1" title="In Tuning Frequency Bias of State Space Models">1 Introduction</a></li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S2" title="In Tuning Frequency Bias of State Space Models">2 What is the Frequency Bias of an SSM?</a></li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S3" title="In Tuning Frequency Bias of State Space Models">3 Frequency Bias of an SSM at Initialization</a></li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S4" title="In Tuning Frequency Bias of State Space Models">4 Frequency Bias of an SSM during Training</a></li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S5" title="In Tuning Frequency Bias of State Space Models">5 Tuning the Frequency Bias of an SSM</a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S5.SS1" title="In 5 Tuning the Frequency Bias of an SSM ‣ Tuning Frequency Bias of State Space Models">5.1 Tuning Frequency Bias by Scaling the Initialization</a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S5.SS2" title="In 5 Tuning the Frequency Bias of an SSM ‣ Tuning Frequency Bias of State Space Models">5.2 Tuning Frequency Bias by a Sobolev Filter</a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S6" title="In Tuning Frequency Bias of State Space Models">6 Experiments and Discussions</a></li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#S7" title="In Tuning Frequency Bias of State Space Models">7 Conclusion</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A1" title="In Tuning Frequency Bias of State Space Models">A Proofs</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A2" title="In Tuning Frequency Bias of State Space Models">B Functional Derivatives</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A3" title="In Tuning Frequency Bias of State Space Models">C Scaling Laws of the Initialization</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A4" title="In Tuning Frequency Bias of State Space Models">D More Numerical Experiments on the Illustrative Example</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"> <a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A5" title="In Tuning Frequency Bias of State Space Models">E Details of the Experiments</a> <ol class="ltx_toclist ltx_toclist_appendix"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A5.SS1" title="In Appendix E Details of the Experiments ‣ Tuning Frequency Bias of State Space Models">E.1 Denoising Sequential Autoencoder</a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A5.SS2" title="In Appendix E Details of the Experiments ‣ Tuning Frequency Bias of State Space Models">E.2 Long-Range Arena</a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_appendix"> <a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A6" title="In Tuning Frequency Bias of State Space Models">F Supplementary Experiments</a> <ol class="ltx_toclist ltx_toclist_appendix"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A6.SS1" title="In Appendix F Supplementary Experiments ‣ Tuning Frequency Bias of State Space Models">F.1 Predict the Magnitudes of Waves</a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.02035v1#A6.SS2" title="In Appendix F Supplementary Experiments ‣ Tuning Frequency Bias of State Space Models">F.2 Tuning Frequency Bias in Moving MNIST Video Prediction</a></li> </ol> </li> </ol></nav> </nav> <div class="ltx_page_main"> <div class="ltx_page_content"> <article class="ltx_document ltx_authors_1line"> <h1 class="ltx_title ltx_title_document">Tuning Frequency Bias of State Space Models</h1> <div class="ltx_authors"> Annan Yu 1 Dongwei Lyu Corresponding author: <a class="ltx_ref ltx_url ltx_font_typewriter" href="ay262@cornell.edu" title="">ay262@cornell.edu</a>. 2 Soon Hoe Lim 3,4 Michael W. Mahoney 5,6,7 N. Benjamin Erichson5,6 1 Center for Applied Mathematics Cornell University 2 Data Science Institute University of Chicago 3 Department of Mathematics KTH Royal Institute of Technology 4 Nordita KTH Royal Institute of Technology and Stockholm University 5 Lawrence Berkeley National Laboratory 6 International Computer Science Institute 7 Department of Statistics University of California at Berkeley </div> <div class="ltx_abstract"> <h6 cl

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