NNGP

Neural Tangent Kernel(NTK) “In short, NTK represent the changes of the weights before and after the gradient descent update” Let’s start the journey of revealing the black-box neural networks. Setup a Neural Network First of all, we need to define a simple neural network with 2 hidden layers $$ y(x, w)$$ where $y$ is the neural network with weights $w \in \mathbb{R}^m$ and, ${ x, \bar{y} }_N$ is the dataset which is a set of the input data and the output data with $N$ data points....

Neural Network Gaussian Process(NNGP) Model the neural network as GP, aka neural network Gaussian Process(NNGP). Intuitively, the kernel of NNGP compute the distance between the output vectors of 2 input data points. We define the following functions as neural networks with fully-conntected layers: $$z_{i}^{1}(x) = b_i^{1} + \sum_{j=1}^{N_1} \ W_{ij}^{1}x_j^1(x), \ \ x_{j}^{1}(x) = \phi(b_i^{0} + \sum_{k=1}^{d_{in}} \ W_{ik}^{0}x_k(x))$$ where $b_i^{1}$ is the $i$th-bias of the second layer(the same as first hidden layer), $W_{ij}^{1}$ is the $i$th-weights of the first layer(the same as input layer) , function $\phi$ is the activation function, and $x$ is the input data of the neural network....