Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer

Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit “bars and stripes” dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD.

The Remarkable Robustness of Surrogate Gradient Learning for Instilling Complex Function in Spiking Neural Networks

Brains process information in spiking neural networks. Their intricate connections shape the diverse functions these networks perform. Yet how network connectivity relates to function is poorly understood, and the functional capabilities of models of spiking networks are still rudimentary. The lack of both theoretical insight and practical algorithms to find the necessary connectivity poses a major impediment to both studying information processing in the brain and building efficient neuromorphic hardware systems. The training algorithms that solve this problem for artificial neural networks typically rely on gradient descent. But doing so in spiking networks has remained challenging due to the nondifferentiable nonlinearity of spikes. To avoid this issue, one can employ surrogate gradients to discover the required connectivity. However, the choice of a surrogate is not unique, raising the question of how its implementation influences the effectiveness of the method. Here, we use numerical simulations to systematically study how essential design parameters of surrogate gradients affect learning performance on a range of classification problems. We show that surrogate gradient learning is robust to different shapes of underlying surrogate derivatives, but the choice of the derivative's scale can substantially affect learning performance. When we combine surrogate gradients with suitable activity regularization techniques, spiking networks perform robust information processing at the sparse activity limit. Our study provides a systematic account of the remarkable robustness of surrogate gradient learning and serves as a practical guide to model functional spiking neural networks.

Cloud resource optimization based on poisson linear deep gradient learning for mobile cloud computing

Mobile Cloud Computing (MCC) addresses the drawbacks of Mobile Users (MU) where the in-depth evaluation of mobile applications is transferred to a centralized cloud via a wireless medium to reduce load, therefore optimizing resources. In this paper, we consider the resource (i.e., bandwidth and memory) allocation problem to support mobile applications in a MCC environment. In such an environment, Mobile Cloud Service Providers (MCSPs) form a coalition to create a resource pool to share their resources with the Mobile Cloud Users. To enhance the welfare of the MCSPs, a method for optimal resource allocation to the mobile users called, Poisson Linear Deep Resource Allocation (PL-DRA) is designed. For resource allocation between mobile users, we formulate and solve optimization models to acquire an optimal number of application instances while meeting the requirements of mobile users. For optimal application instances, the Poisson Distributed Queuing model is designed. The distributed resource management is designed as a multithreaded model where parallel computation is provided. Next, a Linear Gradient Deep Resource Allocation (LG-DRA) model is designed based on the constraints, bandwidth, and memory to allocate mobile user instances. This model combines the advantage of both decision making (i.e. Linear Programming) and perception ability (i.e. Deep Resource Allocation). Besides, a Stochastic Gradient Learning is utilized to address mobile user scalability. The simulation results show that the Poisson queuing strategy based on the improved Deep Learning algorithm has better performance in response time, response overhead, and energy consumption than other algorithms.

Developmental and evolutionary constraints on olfactory circuit selection

Across species, neural circuits show remarkable regularity, suggesting that their structure has been driven by underlying optimality principles. Here, we ask whether we can predict the neural circuitry of diverse species by optimizing the neural architecture to make learning as efficient as possible. We focus on the olfactory system, primarily because it has a relatively simple evolutionarily conserved structure, and because its input and intermediate layer sizes exhibits a tight allometric scaling. In mammals, it has been shown that the number of neurons in layer 2 of piriform cortex scales as the number of glomeruli (the input units) to the 3/2 power; in invertebrates, we show that the number of mushroom body Kenyon cells scales as the number of glomeruli to the 7/2 power. To understand these scaling laws, we model the olfactory system as a three layered nonlinear neural network, and analytically optimize the intermediate layer size for efficient learning from a limited number of samples. We find that the 3/2 scaling observed in mammals emerges naturally, both in full batch optimization and under stochastic gradient learning. We extended the framework to the case where a fraction of the olfactory circuit is genetically specified, not learned. We show numerically that this makes the scaling law steeper when the number of glomeruli is small, and we are able to recover the 7/2 scaling law observed in invertebrates. This study paves the way for a deeper understanding of the organization of brain circuits from an evolutionary perspective.