# Convergence of Continual Learning in Homogeneous Deep Networks

arXiv: https://arxiv.org/abs/2606.30559 · HTML: https://mlsanity.com/paper/2606.30559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 63 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 30 of 43)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [Kernel and Rich Regimes in Overparametrized Models](https://mlsanity.com/paper/2002.09277/) (2020)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics](https://mlsanity.com/paper/2007.07400/) (2020)
- [Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel](https://mlsanity.com/paper/1810.05369/) (2018)
- [A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix](https://mlsanity.com/paper/2010.04003/) (2020)
- [Continual Learning in the Teacher-Student Setup: Impact of Task Similarity](https://mlsanity.com/paper/2107.04384/) (2021)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)
- [Nested Learning: The Illusion of Deep Learning Architectures](https://mlsanity.com/paper/2512.24695/) (2025)
- [Wide Neural Networks Forget Less Catastrophically](https://mlsanity.com/paper/2110.11526/) (2021)
- [A Closer Look at Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2203.17269/) (2022)
- [Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization](https://mlsanity.com/paper/2006.06560/) (2020)
- [Recent Advances of Foundation Language Models-based Continual Learning: A Survey](https://mlsanity.com/paper/2405.18653/) (2024)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Continual Learning in Linear Classification on Separable Data](https://mlsanity.com/paper/2306.03534/) (2023)
- [A Statistical Theory of Regularization-Based Continual Learning](https://mlsanity.com/paper/2406.06213/) (2024)
- [Analysis of Catastrophic Forgetting for Random Orthogonal Transformation Tasks in the Overparameterized Regime](https://mlsanity.com/paper/2207.06475/) (2022)
- [The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model](https://mlsanity.com/paper/2401.12617/) (2024)
- [Fixed Design Analysis of Regularization-Based Continual Learning](https://mlsanity.com/paper/2303.10263/) (2023)
- [Statistical Mechanical Analysis of Catastrophic Forgetting in Continual Learning with Teacher and Student Networks](https://mlsanity.com/paper/2105.07385/) (2021)
- [Challenging Common Assumptions about Catastrophic Forgetting](https://mlsanity.com/paper/2207.04543/) (2022)
- [How do Quadratic Regularizers Prevent Catastrophic Forgetting: The Role of Interpolation](https://mlsanity.com/paper/2102.02805/) (2021)
- [Maslow's Hammer for Catastrophic Forgetting: Node Re-Use vs Node Activation](https://mlsanity.com/paper/2205.09029/) (2022)

## Abstract (arXiv)

We characterize weakly regularized continual classification in homogeneous models as sequential projections onto task margin sets. This result generalizes prior analyses restricted to either stationary (single-task) deep models or continual linear models. We show that global convergence generally fails, even for simple models linear in data but nonlinear in parameters. Nevertheless, by leveraging results from nonconvex projection theory, we identify regularity properties of homogeneous deep networks that guarantee local linear convergence under random and cyclic task sequences. Finally, we extend our analysis to continual regression, unifying the framework for homogeneous models.