Universal representation by Boltzmann machines with Regularised Axons

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be numerically hard. Recently we proposed a regularisation of the connections of Boltzmann machines, in order to control the energy landscape of the model, paving a way for efficient sampling and training. Here we formally prove that such regularised Boltzmann machines preserve the ability to represent arbitrary distributions. This is in conjunction with controlling the number of energy local minima, thus enabling easy \emph{guided} sampling and training. Furthermore, we explicitly show that regularised Boltzmann machines can store exponentially many arbitrarily correlated visible patterns with perfect retrieval, and we connect them to the Dense Associative Memory networks.Comment: 12 pages. Updated reference

Event-Driven Contrastive Divergence for Spiking Neuromorphic Systems

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.Comment: (Under review

Short-Term Load Forecasting of Natural Gas with Deep Neural Network Regression

Deep neural networks are proposed for short-term natural gas load forecasting. Deep learning has proven to be a powerful tool for many classification problems seeing significant use in machine learning fields such as image recognition and speech processing. We provide an overview of natural gas forecasting. Next, the deep learning method, contrastive divergence is explained. We compare our proposed deep neural network method to a linear regression model and a traditional artificial neural network on 62 operating areas, each of which has at least 10 years of data. The proposed deep network outperforms traditional artificial neural networks by 9.83% weighted mean absolute percent error (WMAPE)

Towards Deeper Understanding in Neuroimaging

Neuroimaging is a growing domain of research, with advances in machine learning having tremendous potential to expand understanding in neuroscience and improve public health. Deep neural networks have recently and rapidly achieved historic success in numerous domains, and as a consequence have completely redefined the landscape of automated learners, giving promise of significant advances in numerous domains of research. Despite recent advances and advantages over traditional machine learning methods, deep neural networks have yet to have permeated significantly into neuroscience studies, particularly as a tool for discovery. This dissertation presents well-established and novel tools for unsupervised learning which aid in feature discovery, with relevant applications to neuroimaging. Through our works within, this dissertation presents strong evidence that deep learning is a viable and important tool for neuroimaging studies

Deep Neural Networks As Time Series Forecasters of Energy Demand

Short-term load forecasting is important for the day-to-day operation of natural gas utilities. Traditionally, short-term load forecasting of natural gas is done using linear regression, autoregressive integrated moving average models, and artificial neural networks. Many purchasing and operating decisions are made using these forecasts, and there can be high cost to both natural gas utilities and their customers if the short-term load forecast is inaccurate. Therefore, the GasDay lab continues to explore new ways to make better forecasts. Recently, deep neural networks (DNNs) have emerged as a powerful tool in machine learning problems. DNNs have been shown to greatly outperform traditional methods in many applications, and they have completely revolutionized some fields. Given their success in other machine learning problems, DNNs are evaluated in energy forecasting. This thesis examines many DNN parameters in the context of the short-term load forecasting problem including architecture, input features, and use of synthetic data. The performance of the model is compared against several traditional forecast strategies, including artificial neural networks and linear regression short-term load forecasting strategies. Additionally, the DNN forecaster is evaluated as part of the GasDay ensemble. The DNN forecaster proposed in this thesis offers an average 6.98% improvement in terms of weighted mean absolute percent error (WMAPE) when included as part of the GasDay ensemble. Finally, ideas for future work are discussed

Classification and reconstruction of optical quantum states with deep neural networks

We apply deep-neural-network-based techniques to quantum state classification and reconstruction. We demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feedforward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed [arXiv:2008.03240] QST technique with conditional generative adversarial networks (QST-CGAN). We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than a standard iterative maximum likelihood (iMLE) method. Further, the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than iMLE.Comment: 40 pages, 20 figures, 5 tables, code will be available at https://github.com/quantshah/qst-n