# Generalization Bounds for Neural Networks via Approximate Description Length

We investigate the sample complexity of networks with bounds on the magnitude of its weights. In particular, we consider the class $H=\left\{W_t\circ\rho\circ \ldots\circ\rho\circ W_{1} :W_1,\ldots,W_{t-1}\in M_{d, d}, W_t\in M_{1,d}\right\}$ where the spectral norm of each $W_i$ is bounded by $O(1)$, the Frobenius norm is bounded by $R$, and $\rho$ is the sigmoid function $\frac{e^x}{1+e^x}$ or the smoothened ReLU function $\ln (1+e^x)$... (read more)

PDF Abstract