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Wide neural networks are biased towards learning certain functions,influencing both the rate of convergence of gradient descent (GD) and thefunctions that are reachable with GD in finite training time. As such, there isa great need for methods that can modify this bias according to the task athand. To that end, we introduce Modified Spectrum Kernels (MSKs), a novelfamily of constructed kernels that can be used to approximate kernels withdesired eigenvalues for which no closed form is known. We leverage the dualitybetween wide neural networks and Neural Tangent Kernels and propose apreconditioned gradient descent method, which alters the trajectory of GD. As aresult, this allows for a polynomial and, in some cases, exponential trainingspeedup without changing the final solution. Our method is both computationallyefficient and simple to implement.

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