Stop Marginalizing My Dreams: Model Inversion via Laplace Kernel for Continual Learning

TL;DR

This paper introduces REMIX, a novel framework for model inversion in data-free continual learning that captures feature dependencies using a Laplace kernel, leading to more coherent synthetic samples and improved performance.

Contribution

REMIX enables scalable full-covariance modeling in model inversion for continual learning by leveraging a Laplace kernel, surpassing diagonal covariance limitations.

Findings

Modeling feature dependencies improves synthetic sample quality.

REMIX outperforms existing methods on standard benchmarks.

Scalable full-covariance modeling is feasible with linear memory complexity.

Abstract

Data-free continual learning (DFCIL) relies on model inversion to synthesize pseudo-samples and mitigate catastrophic forgetting. However, existing inversion methods are fundamentally limited by a simplifying assumption: they model feature distributions using diagonal covariance, effectively ignoring correlations that define the geometry of learned representations. As a result, synthesized samples often lack fidelity, limiting knowledge retention. In this work, we show that modeling feature dependencies is a key ingredient for effective DFCIL. We introduce REMIX, a structured covariance modeling framework that enables scalable full-covariance modeling without the prohibitive cost of dense matrix inversion and log-determinant computation. By leveraging a Laplace kernel parameterization, REMIX captures structured feature dependencies using memory that scales linearly with the feature dimensionality, while requiring only an additional logarithmic factor in computation. Modeling these correlations produces more coherent synthetic samples and consistently improves performance across standard DFCIL benchmarks. Our results demonstrate that moving beyond diagonal assumptions is essential for effective and scalable data-free continual learning. Our code is available at https://github. com/pkrukowski1/REMIX-Model-Inversion-via-Laplace-Kernel.