This 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.

翻译：本文研究具有长程依赖性的预测任务中的序列建模。我们基于谱滤波算法（Hazan等人，2017）学习线性动力系统，提出了一种新的状态空间模型（SSMs）构建方法。由此产生了一种新颖的序列预测架构，我们称之为谱态空间模型。谱态空间模型具有两个主要优势：首先，其性能既不依赖于底层动力系统的谱特性，也不受问题维度的影响，因而具备可证明的鲁棒性；其次，这些模型采用无需学习的固定卷积滤波器构建，在理论和实践上均优于传统SSMs。我们在合成动力系统和多模态长程预测任务上对所提模型进行评估。这些评估结果验证了谱滤波在需要极长程记忆任务中的理论优势。