LISA: Laplacian In-context Spectral Analysis

TL;DR

LISA is a novel spectral analysis method that adapts Laplacian-based time-series models at inference time using only observed data, enhancing forecasting especially under changing dynamics.

Contribution

LISA introduces a new approach combining delay-coordinate embeddings, Laplacian spectral learning, and lightweight residual adapters for effective in-context adaptation of time-series models.

Findings

LISA outperforms baseline models in forecasting accuracy.

LISA is particularly effective under dynamic changes.

The method links in-context adaptation with spectral techniques for dynamical systems.

Abstract

We propose Laplacian In-context Spectral Analysis (LISA), a method for inference-time adaptation of Laplacian-based time-series models using only an observed prefix. LISA combines delay-coordinate embeddings and Laplacian spectral learning to produce diffusion-coordinate state representations, together with a frozen nonlinear decoder for one-step prediction. We introduce lightweight latent-space residual adapters based on either Gaussian-process regression or an attention-like Markov operator over context windows. Across forecasting and autoregressive rollout experiments, LISA improves over the frozen baseline and is often most beneficial under changing dynamics. This work links in-context adaptation to nonparametric spectral methods for dynamical systems.