# -*- coding: utf-8 -*-
import autograd.numpy as np
def init_kaf_nn(layer_sizes, scale=0.01, rs=np.random.RandomState(0), dict_size=20, boundary=3.0):
"""
Initialize the parameters of a KAF feedforward network.
- dict_size: the size of the dictionary for every neuron.
- boundary: the boundary for the activation functions.
"""
# Initialize the dictionary
D = np.linspace(-boundary, boundary, dict_size).reshape(-1, 1)
# Rule of thumb for gamma
interval = D[1,0] - D[0,0];
gamma = 0.5/np.square(2*interval)
D = D.reshape(1, 1, -1)
# Initialize a list of parameters for the layer
w = [(rs.randn(insize, outsize) * scale, # Weight matrix
rs.randn(outsize) * scale, # Bias vector
rs.randn(1, outsize, dict_size) * 0.5) # Mixing coefficients
for insize, outsize in zip(layer_sizes[:-1], layer_sizes[1:])]
return w, (D, gamma)
def predict_kaf_nn(w, X, info):
"""
Compute the outputs of a KAF feedforward network.
"""
D, gamma = info
for W, b, alpha in w:
outputs = np.dot(X, W) + b
K = gauss_kernel(outputs, D, gamma)
X = np.sum(K*alpha, axis=2)
return X
def gauss_kernel(X, D, gamma=1.0):
"""
Compute the 1D Gaussian kernel between all elements of a
NxH matrix and a fixed L-dimensional dictionary, resulting in a NxHxL matrix of kernel
values.
"""
return np.exp(- gamma*np.square(X.reshape(-1, X.shape[1], 1) - D))
