Optimizing Connectivity through Network Gradients for Restricted Boltzmann Machines

Abstract: Leveraging sparse networks to connect successive layers in deep neural networks has recently been shown to provide benefits to large-scale state-of-the-art models. However, network connectivity also plays a significant role in the learning performance of shallow networks, such as the classic Restricted Boltzmann Machine (RBM). Efficiently finding sparse connectivity patterns that improve the learning performance of shallow networks is a fundamental problem. While recent principled approaches explicitly include network connections as model parameters that must be optimized, they often rely on explicit penalization or network sparsity as a hyperparameter. This work presents the Network Connectivity Gradients (NCG), an optimization method to find optimal connectivity patterns for RBMs. NCG leverages the idea of network gradients: given a specific connection pattern, it determines the gradient of every possible connection and uses the gradient to drive a continuous connection strength parameter that in turn is used to determine the connection pattern. Thus, learning RBM parameters and learning network connections is truly jointly performed, albeit with different learning rates, and without changes to the model's classic energy-based objective function. The proposed method is applied to the MNIST and other data sets showing that better RBM models are found for the benchmark tasks of sample generation and classification. Results also show that NCG is robust to network initialization and is capable of both adding and removing network connections while learning.