Dynamic Perturbed Adaptive Method for Infinite Task-Conflicting Time Series

TL;DR

This paper introduces a dynamic perturbed adaptive method for time series tasks with conflicting objectives, enabling continual adaptation and transfer without explicit task labels, and demonstrates superior performance in synthetic experiments.

Contribution

The paper proposes a novel trunk-branch architecture that enhances expressivity and enables fast, continual adaptation in conflicting time series tasks without task labels.

Findings

Outperforms baselines in synthetic conflicting tasks

Shows exponential convergence of branch adaptation

Enables continual test-time adaptation and transfer

Abstract

We formulate time series tasks as input-output mappings under varying objectives, where the same input may yield different outputs. This challenges a model's generalization and adaptability. To study this, we construct a synthetic dataset with numerous conflicting subtasks to evaluate adaptation under frequent task shifts. Existing static models consistently fail in such settings. We propose a dynamic perturbed adaptive method based on a trunk-branch architecture, where the trunk evolves slowly to capture long-term structure, and branch modules are re-initialized and updated for each task. This enables continual test-time adaptation and cross-task transfer without relying on explicit task labels. Theoretically, we show that this architecture has strictly higher functional expressivity than static models and LoRA. We also establish exponential convergence of branch adaptation under the Polyak-Lojasiewicz condition. Experiments demonstrate that our method significantly outperforms competitive baselines in complex and conflicting task environments, exhibiting fast adaptation and progressive learning capabilities.