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

arXiv: https://arxiv.org/abs/2605.11804 · HTML: https://mlsanity.com/paper/2605.11804/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 20 of 20)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (2018)
- [Dreaming to Distill: Data-free Knowledge Transfer via DeepInversion](https://mlsanity.com/paper/1912.08795/) (2019)
- [Rainbow Memory: Continual Learning with a Memory of Diverse Samples](https://mlsanity.com/paper/2103.17230/) (2021)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [FearNet: Brain-Inspired Model for Incremental Learning](https://mlsanity.com/paper/1711.10563/) (2017)
- [Adaptive Aggregation Networks for Class-Incremental Learning](https://mlsanity.com/paper/2010.05063/) (2020)
- [Always Be Dreaming: A New Approach for Data-Free Class-Incremental Learning](https://mlsanity.com/paper/2106.09701/) (2021)
- [Zero-Shot Knowledge Distillation in Deep Networks](https://mlsanity.com/paper/1905.08114/) (2019)
- [FeTrIL: Feature Translation for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2211.13131/) (2022)
- [FeCAM: Exploiting the Heterogeneity of Class Distributions in Exemplar-Free Continual Learning](https://mlsanity.com/paper/2309.14062/) (2023)
- [GAN Memory with No Forgetting](https://mlsanity.com/paper/2006.07543/) (2020)
- [R-DFCIL: Relation-Guided Representation Learning for Data-Free Class Incremental Learning](https://mlsanity.com/paper/2203.13104/) (2022)
- [Learning latent representations across multiple data domains using Lifelong VAEGAN](https://mlsanity.com/paper/2007.10221/) (2020)
- [Task-recency bias strikes back: Adapting covariances in Exemplar-Free Class Incremental Learning](https://mlsanity.com/paper/2409.18265/) (2024)
- [Model Inversion with Layer-Specific Modeling and Alignment for Data-Free Continual Learning](https://mlsanity.com/paper/2510.26311/) (2025)

## Abstract (arXiv)

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.