Controlling the Inductive Bias of Wide Neural Networks by Modifying the Kernel's Spectrum

• URL: http://arxiv.org/abs/2307.14531v2
• Date: Wed, 20 Mar 2024 07:49:41 GMT
• Title: Controlling the Inductive Bias of Wide Neural Networks by Modifying the Kernel's Spectrum
• Authors: Amnon Geifman, Daniel Barzilai, Ronen Basri, Meirav Galun,
• Abstract summary: We introduce Modified Spectrum Kernels (MSKs) to approximate kernels with desired eigenvalues. We propose a preconditioned gradient descent method, which alters the trajectory of gradient descent. Our method is both computationally efficient and simple to implement.
• Score: 18.10812063219831
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Wide neural networks are biased towards learning certain functions, influencing both the rate of convergence of gradient descent (GD) and the functions that are reachable with GD in finite training time. As such, there is a great need for methods that can modify this bias according to the task at hand. To that end, we introduce Modified Spectrum Kernels (MSKs), a novel family of constructed kernels that can be used to approximate kernels with desired eigenvalues for which no closed form is known. We leverage the duality between wide neural networks and Neural Tangent Kernels and propose a preconditioned gradient descent method, which alters the trajectory of GD. As a result, this allows for a polynomial and, in some cases, exponential training speedup without changing the final solution. Our method is both computationally efficient and simple to implement.

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