Quantifying the benefit of using differentiable learning over tangent kernels
International Conference on Machine Learning, 2021•proceedings.mlr.press
We study the relative power of learning with gradient descent on differentiable models, such
as neural networks, versus using the corresponding tangent kernels. We show that under
certain conditions, gradient descent achieves small error only if a related tangent kernel
method achieves a non-trivial advantage over random guessing (aka weak learning),
though this advantage might be very small even when gradient descent can achieve
arbitrarily high accuracy. Complementing this, we show that without these conditions …
as neural networks, versus using the corresponding tangent kernels. We show that under
certain conditions, gradient descent achieves small error only if a related tangent kernel
method achieves a non-trivial advantage over random guessing (aka weak learning),
though this advantage might be very small even when gradient descent can achieve
arbitrarily high accuracy. Complementing this, we show that without these conditions …
Abstract
We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (aka weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing.
proceedings.mlr.press