Publication
ICML 2018
Conference paper

Using inherent structures to design lean 2-layer RBMs

Abstract

Understanding the representational power of Restricted Boltzmann Machines (RBMs) with mul-tiple 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 the ISC, one needs to add a second layer. Furthermore, we introduce Lean RBMs, which are multi-layer RBMs where each layer can have1 at-most 0(n) units with the number of visible units being n. We show that for every single layer RBM with ft(n2+r),r > 0, hidden units there exists a two-layered lean RBM with 0(n2) 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.

Date

10 Jul 2018

Publication

ICML 2018

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