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Spectral State Space Models

This repository contains code for training and evaluating spectral state space models and accompanies the paper Spectral State Space Models.

The paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model.

Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Installation

Clone and navigate to the spectral_ssm directory containing setup.py. Run:

pip install -e .

Usage

The example.py file contains the full training pipeline. model.py contains code for the model itself, including the Spectral Temporal Unit (STU) block.

python3 example.py

Citing this work

@misc{agarwal2024spectral,
      title={Spectral State Space Models},
      author={Naman Agarwal and Daniel Suo and Xinyi Chen and Elad Hazan},
      year={2024},
      eprint={2312.06837},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

License and disclaimer

Copyright 2024 DeepMind Technologies Limited

All software is licensed under the Apache License, Version 2.0 (Apache 2.0); you may not use this file except in compliance with the Apache 2.0 license. You may obtain a copy of the Apache 2.0 license at: https://www.apache.org/licenses/LICENSE-2.0

All other materials are licensed under the Creative Commons Attribution 4.0 International License (CC-BY). You may obtain a copy of the CC-BY license at: https://creativecommons.org/licenses/by/4.0/legalcode

Unless required by applicable law or agreed to in writing, all software and materials distributed here under the Apache 2.0 or CC-BY licenses are distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the licenses for the specific language governing permissions and limitations under those licenses.

This is not an official Google product.