Inherent Structure Capacity to design lean 2-layer RBM

This webpage includes description and details regarding experiments for our paper " Using Inherent Structures to design Lean 2-layer RBM" accepted at ICML 2018.

Abstract

Understanding the representational power of Restricted Boltzmann Machines (RBMs) with multiple layers is an ill-understood problem and is an area of active research. Motivated from the approach of Inherent Structure formalism (Stillinger & Weber, 1982), extensively used in analysing Spin Glasses, we propose a novel measure called Inherent Structure Capacity (ISC), which characterizes the representation capacity of a fixed architecture RBM by the expected number of modes of distributions emanating from the RBM with parameters drawn from a prior distribution. Though ISC is intractable, we show that for a single layer RBM architecture ISC approaches a finite constant as number of hidden units are increased and to further improve t ISC, one needs to add incorporate a second layer. Furthermore, we introduce Lean RBMs, which are multi-layer RBMs where each layer can have at-most O(n) units with the number of visible units being n. We show that for every single layer RBM with Omega(n^{2+r}), r >= 0, hidden units there exists a two-layered lean RBM with Theta(n^2) parameters with the same ISC, establishing that 2 layer RBMs can achieve the same representational power as single-layer RBMs but using far fewer number of parameters. To the best of our knowledge, this is the first result which quantitatively establishes the need for layering.

Resources

Paper link

Supplementary link

Experiments

Details regarding experiments can be found in the experiment page

Contact Details

Please feel free to contact Abhishek ( abhishekbansal2016@gmail.com) or Abhinav (abhinava@iisc.ac.in) for any details