SpectraLDS: Provable Distillation for Linear Dynamical Systems

TL;DR

SpectraLDS introduces a provable, efficient method for identifying symmetric linear dynamical systems that maintains accuracy and enables constant-time inference, regardless of sequence length.

Contribution

It provides the first provable, spectral-transform-based approach for symmetric LDS identification with guarantees independent of system dimension.

Findings

Achieves accurate LDS identification with spectral methods.

Enables constant-time, constant-space inference per token.

Improves inference efficiency in language modeling tasks.

Abstract

We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that represents symmetric LDSs as convolutions learnable via fixed spectral transformations. We show how to invert this representation, thereby recovering an LDS model from its spectral transform and yielding an end-to-end convex optimization procedure. This distillation preserves predictive accuracy while enabling constant-time and constant-space inference per token, independent of sequence length. We evaluate our method, SpectraLDS, as a component in sequence prediction architectures and demonstrate that accuracy is preserved while inference efficiency is improved on tasks such as language modeling.