# From Generalization Analysis to Optimization Designs for State Space Models

arXiv: https://arxiv.org/abs/2405.02670 · HTML: https://mlsanity.com/paper/2405.02670/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 4 May 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [ListOps: A Diagnostic Dataset for Latent Tree Learning](https://mlsanity.com/paper/1804.06028/) (2018)
- [How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projections](https://mlsanity.com/paper/2206.12037/) (2022)
- [Learning long-range spatial dependencies with horizontal gated-recurrent units](https://mlsanity.com/paper/1805.08315/) (2018)
- [On Generalization Bounds of a Family of Recurrent Neural Networks](https://mlsanity.com/paper/1910.12947/) (2019)
- [Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterization](https://mlsanity.com/paper/1803.09327/) (2018)
- [On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis](https://mlsanity.com/paper/2009.07799/) (2020)
- [Can SGD Learn Recurrent Neural Networks with Provable Generalization?](https://mlsanity.com/paper/1902.01028/) (2019)
- [Inverse Approximation Theory for Nonlinear Recurrent Neural Networks](https://mlsanity.com/paper/2305.19190/) (2023)

## Built on by (most cited first, 11 of 11)

- [Tuning Frequency Bias of State Space Models](https://mlsanity.com/paper/2410.02035/) (2024)
- [HOPE for a Robust Parameterization of Long-memory State Space Models](https://mlsanity.com/paper/2405.13975/) (2024)
- [Provable Benefits of Complex Parameterizations for Structured State Space Models](https://mlsanity.com/paper/2410.14067/) (2024)
- [Block-Biased Mamba for Long-Range Sequence Processing](https://mlsanity.com/paper/2505.09022/) (2025)
- [Generalization Error Analysis for Selective State-Space Models Through the Lens of Attention](https://mlsanity.com/paper/2502.01473/) (2025)
- [On the Expressivity of Selective State-Space Layers: A Multivariate Polynomial Approach](https://mlsanity.com/paper/2502.02209/) (2025)
- [Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraints](https://mlsanity.com/paper/2405.20278/) (2024)
- [Demystifying the Token Dynamics of Deep Selective State Space Models](https://mlsanity.com/paper/2410.03292/) (2024)
- [Analysis of Long Range Dependency Understanding in State Space Models](https://mlsanity.com/paper/2601.13048/) (2026)
- [Aligning Inductive Bias for Data-Efficient Generalization in State Space Models](https://mlsanity.com/paper/2509.20789/) (2025)
- [Upper Generalization Bounds for Neural Oscillators](https://mlsanity.com/paper/2603.09742/) (2026)

## Abstract (arXiv)

A State Space Model (SSM) is a foundation model in time series analysis, which has recently been shown as an alternative to transformers in sequence modeling. In this paper, we theoretically study the generalization of SSMs and propose improvements to training algorithms based on the generalization results. Specifically, we give a textitdata-dependent generalization bound for SSMs, showing an interplay between the SSM parameters and the temporal dependencies of the training sequences. Leveraging the generalization bound, we (1) set up a scaling rule for model initialization based on the proposed generalization measure, which significantly improves the robustness of the output value scales on SSMs to different temporal patterns in the sequence data; (2) introduce a new regularization method for training SSMs to enhance the generalization performance. Numerical results are conducted to validate our results.