Sigmoid kernel

The problem, from first principles

Linear kernel and Polynomial kernel both grow without bound as inputs grow. The sigmoid kernel squashes its output through a tanh, so every similarity lands strictly between -1 and 1. It resembles the activation of a single neural network neuron applied to a dot product, which is why it appears in SVM libraries as the kernel closest to a two-layer network.

Given X with shape (n, d) and Y with shape (m, d), return the (n, m) matrix of sigmoid similarities.

Constraints

• Return an array of shape (n, m) where entry [i, j] equals tanh(gamma * X[i] @ Y[j] + coef0).
• Defaults: gamma=1.0, coef0=0.0.
• Build it on top of linear_kernel from the earlier question, which is already available to load.
• Do not modify X or Y.

Hints

Open one at a time. Each gives away a little more than the last.