论文标题
通过量子退火对Boltzmann机器的生成和判别培训
Generative and discriminative training of Boltzmann machine through Quantum annealing
论文作者
论文摘要
提出了一种用于生成和歧视任务的学习玻尔兹曼机器(BM)的混合量子古典方法。 Boltzmann机器是无向图,具有可见和隐藏节点网络,前者用作阅读站点,而后者则用于操纵可见状态的概率。在生成BM中,可见数据的样本模仿给定数据集的概率分布。相比之下,判别BM的可见位点被视为输入/输出(I/O)读数位点,其中对给定的一组输入状态优化了输出状态的条件概率。学习BM的成本函数定义为使用高参数调整的Kullback-Leibler(KL)差异和负条件对数可能性(NCLL)的加权总和。在这里,KL分歧是生成学习的成本,而NCLL是歧视性学习的成本。提出了随机的牛顿 - 拉夫森优化方案。使用量子退火(QA)获得的直接样品BM近似梯度和Hessian。量子退火器是代表在低但有限温度下运行的ISING模型物理的硬件。该温度影响BM的概率分布;但是,其价值是未知的。先前的努力集中在通过实际硬件采样的态概率的理论玻尔兹曼能量来估算这种未知温度。假设控制参数变化不会影响系统温度,但是通常情况并非如此。取而代之的是,提出了一种用于样品的概率分布而不是能量的方法,以估计最佳参数集。这样可以确保可以从单个运行中获得最佳集合。
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.