SpectraLDS: New Method Enables Efficient Distillation of Linear Dynamical Systems with Provable Accuracy
Researchers have introduced SpectraLDS, the first method with provable accuracy guarantees for identifying and distilling symmetric linear dynamical systems (LDS) independent of state dimension or memory length. The approach leverages spectral transformations to convert LDS representations into a convex optimization problem, enabling recovery of a compact model from its spectral form. This matters because the resulting models achieve constant-time and constant-space inference per token regardless of sequence length, offering efficiency gains for applications like language modeling.
SpectraLDS is a novel algorithm that addresses a longstanding challenge in sequence modeling: identifying symmetric linear dynamical systems with accuracy guarantees that do not degrade as state dimension or effective memory grows. The method builds on prior work representing symmetric LDSs as convolutions learnable through fixed spectral transformations, and introduces a procedure to invert this representation, recovering a full LDS model from its spectral transform. This inversion yields an end-to-end convex optimization pipeline, which provides stronger theoretical guarantees than non-convex alternatives. Crucially, the distilled models support constant-time and constant-space inference per token, decoupling computational cost from sequence length. The authors evaluated SpectraLDS as a component within sequence prediction architectures and report that predictive accuracy is preserved while inference efficiency improves on benchmarks including language modeling tasks. The work sits at the intersection of machine learning theory and control systems, with potential implications for deploying recurrent-style models more efficiently in practice.
What's missing
The paper is a preprint and has not yet undergone formal peer review. Key open questions include how SpectraLDS performs on non-symmetric LDS settings and whether the convex optimization procedure scales tractably to very large models.
What different sources said
- arXiv cs.LGCenter
SpectraLDS: Provable Distillation for Linear Dynamical Systems
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