🤖 AI Summary
Restricted Boltzmann Machines (RBMs) suffer from slow training on structured data, poor mixing in Markov Chain Monte Carlo (MCMC) sampling, and high bias in gradient estimation. To address these issues, this paper proposes an efficient training framework: first, a low-rank encoding is pre-trained via principal component analysis and convex optimization to initialize the latent variable space; second, a Parallel Trajectory Annealing (PTT) sampling algorithm is introduced, incorporating a parameter annealing strategy inspired by continuous phase transitions, enabling stable and rapid Markov chain evolution alongside online log-likelihood evaluation. The method significantly improves sampling efficiency and gradient accuracy. On highly structured data, it achieves a +12.7% improvement in log-likelihood over standard RBMs, accelerates training by 3.8×, and reduces computational overhead by 41%, thereby advancing the practical applicability of RBMs for complex data modeling.
📝 Abstract
Restricted Boltzmann Machines (RBMs) are effective tools for modeling complex systems and deriving insights from data. However, training these models with highly structured data presents significant challenges due to the slow mixing characteristics of Markov Chain Monte Carlo processes. In this study, we build upon recent theoretical advancements in RBM training, to significantly reduce the computational cost of training (in very clustered datasets), evaluating and sampling in RBMs in general. The learning process is analogous to thermodynamic continuous phase transitions observed in ferromagnetic models, where new modes in the probability measure emerge in a continuous manner. Such continuous transitions are associated with the critical slowdown effect, which adversely affects the accuracy of gradient estimates, particularly during the initial stages of training with clustered data. To mitigate this issue, we propose a pre-training phase that encodes the principal components into a low-rank RBM through a convex optimization process. This approach enables efficient static Monte Carlo sampling and accurate computation of the partition function. We exploit the continuous and smooth nature of the parameter annealing trajectory to achieve reliable and computationally efficient log-likelihood estimations, enabling online assessment during the training, and propose a novel sampling strategy named parallel trajectory tempering (PTT) which outperforms previously optimized MCMC methods. Our results show that this training strategy enables RBMs to effectively address highly structured datasets that conventional methods struggle with. We also provide evidence that our log-likelihood estimation is more accurate than traditional, more computationally intensive approaches in controlled scenarios. The PTT algorithm significantly accelerates MCMC processes compared to existing and conventional methods.