LISA: Laplacian In-context Spectral Analysis

2026-02-03

AI Summary

This work addresses the challenge of adapting Laplacian-based time series models to dynamic changes during inference. To this end, the authors propose a context-adaptive approach that constructs a diffusion-coordinate state representation at inference time by leveraging the observed time series prefix, combining delay-coordinate embedding with Laplacian spectral learning. A lightweight latent-space residual adapter is introduced to fine-tune this representation adaptively, while a frozen nonlinear decoder performs the final one-step-ahead prediction. This method represents the first integration of context-adaptive mechanisms with nonparametric spectral techniques, demonstrating significantly improved performance over frozen baseline models when system dynamics undergo abrupt shifts, and exhibiting enhanced robustness and generalization capability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Natural Language Processing: Learning & Optimization for NLP
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

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.

Problem

• in-context adaptation
• Laplacian-based time-series models
• changing dynamics
• spectral methods
• dynamical systems

Innovation

• Laplacian spectral learning
• in-context adaptation
• delay-coordinate embedding
• diffusion coordinates
• nonparametric dynamics