Ratio Divergence Learning Using Target Energy in Restricted Boltzmann Machines: Beyond Kullback--Leibler Divergence Learning

• URL: http://arxiv.org/abs/2409.07679v1
• Date: Thu, 12 Sep 2024 01:01:55 GMT
• Title: Ratio Divergence Learning Using Target Energy in Restricted Boltzmann Machines: Beyond Kullback--Leibler Divergence Learning
• Authors: Yuichi Ishida, Yuma Ichikawa, Aki Dote, Toshiyuki Miyazawa, Koji Hukushima,
• Abstract summary: We propose ratio divergence (RD) learning for discrete energy-based models. RD learning combines the strength of both forward and reverse Kullback-Leibler divergence (KLD) learning. Numerical experiments demonstrate that RD learning significantly outperforms other learning methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose ratio divergence (RD) learning for discrete energy-based models, a method that utilizes both training data and a tractable target energy function. We apply RD learning to restricted Boltzmann machines (RBMs), which are a minimal model that satisfies the universal approximation theorem for discrete distributions. RD learning combines the strength of both forward and reverse Kullback-Leibler divergence (KLD) learning, effectively addressing the "notorious" issues of underfitting with the forward KLD and mode-collapse with the reverse KLD. Since the summation of forward and reverse KLD seems to be sufficient to combine the strength of both approaches, we include this learning method as a direct baseline in numerical experiments to evaluate its effectiveness. Numerical experiments demonstrate that RD learning significantly outperforms other learning methods in terms of energy function fitting, mode-covering, and learning stability across various discrete energy-based models. Moreover, the performance gaps between RD learning and the other learning methods become more pronounced as the dimensions of target models increase.

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