Adversarial Training Methods for Boltzmann Machines

Jian Zhang,Nan Zhang,Shifei Ding,Weikuan Jia

doi:10.1109/access.2019.2962758

Abstract

A Restricted Boltzmann Machines (RBM) is a generative Neural Net that is typically trained to minimize KL divergence between data distribution P data and its model distribution P RBM . However, minimizing this KL divergence does not sufficiently penalize an RBM that place a high probability in regions where the data distribution has a low density, and therefore, RBMs always generate blurry images. In order to solve this problem, this paper extends the loss function of RBMs from KL divergence to adversarial loss and proposes an Adversarial Restricted Boltzmann Machine (ARBM) and an Adversarial Deep Boltzmann Machine (ADBM). Different from the other RBMs, an ARBM minimizes its adversarial loss between the data distribution and its model distribution without explicit gradients. Different from traditional DBMs, an ADBM minimizes its adversarial loss without a layer-by-layer pre-training. In order to generate highquality color images, this paper proposes an Adversarial Hybrid Deep Generative Net (AHDGN) based on an ADBM. The experiments verify that the adversarial loss can be minimized in our proposed models, and the generated images are comparable with the current state-of-the-art results.

Highlights

The last decade has witnessed revolutionary advances in machine learning, mainly due to the progress in training neural nets
We provide a theoretical analysis of the proposed Adversarial Restricted Boltzmann Machine (ARBM), that essentially shows that, given G, D1 and D2, at the optimal points, G can recover the data distributions by minimizing both a JS divergence of (Pdata(x), Pmodel (x)) and a JS divergence of (Pdata(h), Pmodel (h))
We aim to demonstrate 3 key results: 1) During ARBM training, both forward KL divergence and reverse KL divergence are decreasing with iterations

Summary

Introduction

The last decade has witnessed revolutionary advances in machine learning, mainly due to the progress in training neural nets. Neural generative models such as Restricted Boltzmann Machines (RBMs) [1]–[3], Variational Autoencoders (VAEs) [4], Generative Flow models (Glows) [5], and Generative Adversarial Networks (GANs) [6] have demonstrated promising results on image synthesis. GANs, in particular, are generally regarded as the current state-of-the-art [7]. The popularity of RBM-based generative models, including Deep Belief Nets and Deep Boltzmann Machines, has faded in recent years. RBMs and derived models generally have sufficient representational power to learn essentially any distribution [8], the difficulties must arise during training

Objectives

Methods

Conclusion