# Understanding Sparse Feature Updates in Deep Networks using Iterative Linearisation

arXiv: https://arxiv.org/abs/2211.12345 · HTML: https://mlsanity.com/paper/2211.12345/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 18 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [The large learning rate phase of deep learning: the catapult mechanism](https://mlsanity.com/paper/2003.02218/) (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)
- [Finite Versus Infinite Neural Networks: an Empirical Study](https://mlsanity.com/paper/2007.15801/) (2020)
- [Enhanced Convolutional Neural Tangent Kernels](https://mlsanity.com/paper/1911.00809/) (2019)
- [Limitations of the NTK for Understanding Generalization in Deep Learning](https://mlsanity.com/paper/2206.10012/) (2022)

## Abstract (arXiv)

Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and their corresponding kernels. However, these theoretical tools cannot fully explain finite networks as the empirical kernel changes significantly during gradient-descent-based training in contrast to infinite networks. In this work, we derive an iterative linearised training method as a novel empirical tool to further investigate this distinction, allowing us to control for sparse (i.e. infrequent) feature updates and quantify the frequency of feature learning needed to achieve comparable performance. We justify iterative linearisation as an interpolation between a finite analog of the infinite width regime, which does not learn features, and standard gradient descent training, which does. Informally, we also show that it is analogous to a damped version of the Gauss-Newton algorithm -- a second-order method. We show that in a variety of cases, iterative linearised training surprisingly performs on par with standard training, noting in particular how much less frequent feature learning is required to achieve comparable performance. We also show that feature learning is essential for good performance. Since such feature learning inevitably causes changes in the NTK kernel, we provide direct negative evidence for the NTK theory, which states the NTK kernel remains constant during training.