Reproducing kernel Hilbert space: Difference between revisions

Revision as of 12:12, 4 July 2023

Revision as of 08:40, 11 August 2023

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We lastly remark that the above theory can be further extended to spaces of functions with values in function spaces but obtaining kernels for these spaces is a more difficult task.<ref>Rosasco</ref>

== Connection between RKHSRKHSs withand the ReLU function ==

The [[Rectifier (neural networks)|ReLU function]] is commonly defined as <math>f(x)=\max \{0, x\}</math> and is a mainstay in the architecture of neural networks where it is used as an activation function. One can construct a ReLU-like nonlinear function using the theory of reproducing kernel Hilbert spaces. Below, we derive this construction and show how it implies the representation power of neural networks with ReLU activations.