A topological insight into restricted Boltzmann machines
This work addresses computational bottlenecks in RBMs for applications like feature extraction and density estimation, offering a novel topological approach that is incremental but impactful for efficiency.
The authors tackled the computational inefficiency of Restricted Boltzmann Machines (RBMs) by analyzing their topology as bipartite graphs with small-world properties and proposing sparse, scale-free constrained models. They demonstrated that these models reduce the number of weights by orders of magnitude with minimal loss in generative performance and achieve better capabilities than standard RBMs for a fixed weight count.
Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep artificial neural networks for automatic features extraction, unsupervised weights initialization, but also as density estimators. Thus, their generative and discriminative capabilities, but also their computational time are instrumental to a wide range of applications. Our main contribution is to look at RBMs from a topological perspective, bringing insights from network science. Firstly, here we show that RBMs and Gaussian RBMs (GRBMs) are bipartite graphs which naturally have a small-world topology. Secondly, we demonstrate both on synthetic and real-world datasets that by constraining RBMs and GRBMs to a scale-free topology (while still considering local neighborhoods and data distribution), we reduce the number of weights that need to be computed by a few orders of magnitude, at virtually no loss in generative performance. Thirdly, we show that, for a fixed number of weights, our proposed sparse models (which by design have a higher number of hidden neurons) achieve better generative capabilities than standard fully connected RBMs and GRBMs (which by design have a smaller number of hidden neurons), at no additional computational costs.