# Reactivation: Empirical NTK Dynamics Under Task Shifts

arXiv: https://arxiv.org/abs/2507.16039 · HTML: https://mlsanity.com/paper/2507.16039/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Feature Learning in Infinite-Width Neural Networks](https://mlsanity.com/paper/2011.14522/) (2020)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [The Break-Even Point on Optimization Trajectories of Deep Neural Networks](https://mlsanity.com/paper/2002.09572/) (2020)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix](https://mlsanity.com/paper/2010.04003/) (2020)
- [Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent](https://mlsanity.com/paper/2006.11942/) (2020)
- [A Theory of Neural Tangent Kernel Alignment and Its Influence on Training](https://mlsanity.com/paper/2105.14301/) (2021)
- [Learning Curves for Continual Learning in Neural Networks: Self-Knowledge Transfer and Forgetting](https://mlsanity.com/paper/2112.01653/) (2021)
- [On the Cone Effect in the Learning Dynamics](https://mlsanity.com/paper/2503.16316/) (2025)

## Abstract (arXiv)

The Neural Tangent Kernel (NTK) offers a powerful tool to study the functional dynamics of neural networks. In the so-called lazy, or kernel regime, the NTK remains static during training and the network function is linear in the static neural tangents feature space. The evolution of the NTK during training is necessary for feature learning, a key driver of deep learning success. The study of the NTK dynamics has led to several critical discoveries in recent years, in generalization and scaling behaviours. However, this body of work has been limited to the single task setting, where the data distribution is assumed constant over time. In this work, we present a comprehensive empirical analysis of NTK dynamics in continual learning, where the data distribution shifts over time. Our findings highlight continual learning as a rich and underutilized testbed for probing the dynamics of neural training. At the same time, they challenge the validity of static-kernel approximations in theoretical treatments of continual learning, even at large scale.