Spectral Saliency for Machine Unlearning

2026-08-16

AI Summary

This study addresses the trade-off between data removal and model utility in machine unlearning by proposing a Spectral Saliency Unlearning framework. Grounded in spectral theory, this method justifies thresholding strategies through spectral amplitude normalization, singular value decomposition to filter weak components, and selective gradient updates to precisely eliminate target data influence. Experiments demonstrate that the framework effectively balances unlearning efficacy with model performance across image classifiers, diffusion models, and large language models. By integrating theoretical rigor with empirical validation, this work provides a versatile solution for cross-modal machine unlearning, ensuring robust data erasure while preserving functional integrity in diverse generative and discriminative architectures.

Abstract

Machine unlearning (MU) aims to remove the influence of specific training data while preserving model utility. As the name suggests, MU can be viewed as the inverse of learning, using gradient-based updates to reduce the influence of a forget-set by counteracting the previously learned behavior. Recently, Muon, a gradient descent variant, has been introduced. Muon applies spectral magnitude normalization to encourage exploration of rare directions and demonstrates promising performance. Inspired by Muon, we adopt the spectral view for unlearning and propose Spectral Saliency Unlearning (SSU). SSU thresholds weak singular components and updates only those directions supported by a confident unlearning signal. We further provide theoretical justification for this thresholding approach from the perspective of the forgetting-retention trade-off. Experiments across image classifiers, diffusion models, and LLMs demonstrate SSU's effectiveness.

Problem

• Machine Unlearning
• Model Utility
• Forgetting-Retention Trade-off

Innovation

• Spectral Saliency Unlearning
• Machine Unlearning
• Singular Value Thresholding
• Forgetting-Retention Trade-off
• Muon