Koopman Operator Identification of Model Parameter Trajectories for Temporal Domain Generalization (KOMET)

2026-03-31 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

KOMET (Koopman Operator identification of Model parameter Evolution under Temporal drift) is a model-agnostic, data-driven framework designed to address temporal domain drift in parametric models. It treats the sequence of trained parameter vectors as a nonlinear dynamical system's trajectory, identifying its governing linear operator using Extended Dynamic Mode Decomposition (EDMD). The framework employs a warm-start sequential training protocol to ensure parameter-trajectory smoothness and a Fourier-augmented observable dictionary to leverage periodic structures in real-world distribution drifts. Once identified, KOMET's Koopman operator autonomously predicts future parameter trajectories without requiring future labeled data, enabling zero-retraining adaptation during deployment. Evaluated on six datasets with rotating, oscillating, and expanding distribution geometries, KOMET achieved mean autonomous-rollout accuracies between 0.981 and 1.000 over 100 held-out time steps. Spectral and coupling analyses further revealed interpretable dynamical structures consistent with the drifting decision boundary's geometry.

Key takeaway

For MLOps Engineers deploying models in non-stationary environments, KOMET offers a robust solution for continuous adaptation. By autonomously predicting model parameter evolution, you can maintain high accuracy (0.981-1.000) over extended periods without costly retraining. Consider integrating KOMET's two-phase pipeline to reduce operational overhead and ensure model performance under periodic or detrendable temporal drift.

Key insights

KOMET enables zero-retraining model adaptation by predicting parameter trajectories via Koopman operator identification.

Principles

• Treat parameter trajectories as dynamical systems.
• Smoothness and periodicity aid Koopman operator identification.
• PCA can compress high-dimensional weight spaces.

Method

KOMET uses a two-phase pipeline: warm-start sequential training with Adam moment continuity and smoothness regularization, followed by EDMD with a physics-informed Fourier dictionary on PCA-whitened parameter trajectories to identify and autonomously roll out the Koopman operator.

In practice

• Apply warm-start training to reduce epochs by 9x.
• Use weight decay for softmax networks to ensure Koopman compatibility.
• Detrend non-periodic drifts before applying Fourier-basis EDMD.

Topics

• KOMET Framework
• Temporal Domain Generalization
• Koopman Operator Theory
• Extended Dynamic Mode Decomposition
• Parameter Trajectory Analysis

Best for: MLOps Engineer, Research Scientist, AI Scientist, Machine Learning Engineer, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.