Neural Networks

Neural Network

Input Dimension
Number of Hidden Layers
Output Dimension
A typical Neural Network Structure

For Linear Models, target $Y$ (a number or a vector) are approximated by $$f(X) = W \cdot \hat{X} $$ where $\hat{X}= \begin{pmatrix}1\\X \end{pmatrix}$. A natural way to extend the linear model is to take the composition of a linear model with a non-linear function $\sigma$, $$g(X) =\sigma (W \cdot \hat{X}) $$ Here, $\sigma$ applies entry-wisely to the vector $W \cdot \hat{X}$. This extension gives us a single-layer neural network, the main goal is to approximate the weights matrix $W$ in the training process.

A multilayer neural network model with $k$ hidden layers is of the form $$X \mapsto (g_k \circ \cdots \circ g_2\circ g_1\circ g_0)(X),\qquad k \in \{0,1,2,3,4,5,\cdots\} $$ The weighs matrices $W_i$ associated to each layer are approximated in the training process.

Convolutional Neural Network

Model Loading


Common Structures