# An Application of the Holonomic Gradient Method to the Neural Tangent Kernel

arXiv: https://arxiv.org/abs/2410.23626 · HTML: https://mlsanity.com/paper/2410.23626/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity](https://mlsanity.com/paper/1602.05897/) (2016)
- [Fast Neural Kernel Embeddings for General Activations](https://mlsanity.com/paper/2209.04121/) (2022)
- [Avoiding Kernel Fixed Points: Computing with ELU and GELU Infinite Networks](https://mlsanity.com/paper/2002.08517/) (2020)

## Abstract (arXiv)

A holonomic system of linear partial differential equations is, roughly speaking, a system whose solution space is finite dimensional. A distribution that is a solution of a holonomic system is called a holonomic distribution. We give methods to numerically evaluate dual activations of holonomic activator distributions for neural tangent kernels. These methods are based on computer algebra algorithms for rings of differential operators.