An Application of the Holonomic Gradient Method to the Neural Tangent Kernel
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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.
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References · 6
- 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
- 2019On Exact Computation with an Infinitely Wide Neural Netcited by 572
- 2019Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivationcited by 146
- 2016Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivitycited by 138
- 2022Fast Neural Kernel Embeddings for General Activationscited by 18
- 2020Avoiding Kernel Fixed Points: Computing with ELU and GELU Infinite Networkscited by 6
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