Generative and discriminative training of Boltzmann machine through Quantum annealing
This work addresses the challenge of training Boltzmann machines in quantum computing, offering a more efficient method for researchers in quantum machine learning, though it appears incremental as it builds on prior temperature estimation techniques.
The authors tackled the problem of learning Boltzmann machines for generative and discriminative tasks by proposing a hybrid quantum-classical method that uses quantum annealing to sample states, with a novel approach to estimate unknown hardware temperature from probability distributions instead of energies, enabling optimal parameter estimation in a single run.
A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as the reading site while the latter is used to manipulate visible states' probability. In Generative BM, the samples of visible data imitate the probability distribution of a given data set. In contrast, the visible sites of discriminative BM are treated as Input/Output (I/O) reading sites where the conditional probability of output state is optimized for a given set of input states. The cost function for learning BM is defined as a weighted sum of Kullback-Leibler (KL) divergence and Negative conditional Log-Likelihood (NCLL), adjusted using a hyperparamter. Here, the KL Divergence is the cost for generative learning, and NCLL is the cost for discriminative learning. A Stochastic Newton-Raphson optimization scheme is presented. The gradients and the Hessians are approximated using direct samples of BM obtained through Quantum annealing (QA). Quantum annealers are hardware representing the physics of the Ising model that operates on low but finite temperature. This temperature affects the probability distribution of the BM; however, its value is unknown. Previous efforts have focused on estimating this unknown temperature through regression of theoretical Boltzmann energies of sampled states with the probability of states sampled by the actual hardware. This assumes that the control parameter change does not affect the system temperature, however, this is not usually the case. Instead, an approach that works on the probability distribution of samples, instead of the energies, is proposed to estimate the optimal parameter set. This ensures that the optimal set can be obtained from a single run.