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1. From Boltzmann Machines to Neural Networks and Back Again

   Goel, S ; Klivans, A ; Koehler, F. ( January 2020 , Advances in neural information processing systems)

   null (Ed.)

   Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann Machines, probably the most well-studied class of latent variable models. Our results are based on new connections to learning two-layer neural networks under ℓ∞ bounded input; for both problems, we give nearly optimal results under the conjectured hardness of sparse parity with noise. Using the connection between RBMs and feedforward networks, we also initiate the theoretical study of supervised RBMs [Hinton, 2012], a version of neural-network learning that couples distributional assumptions induced from the underlying graphical model with the architecture of the unknown function class. We then give an algorithm for learning a natural class of supervised RBMs with better runtime than what is possible for its related class of networks without distributional assumptions. 

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2. Spike-train level backpropagation for training deep recurrent spiking neural networks

   Zhang, Wenrui ; Li, Peng ( December 2019 , Advances in neural information processing systems)

   Spiking neural networks (SNNs) well support spatio-temporal learning and energy-efficient event-driven hardware neuromorphic processors. As an important class of SNNs, recurrent spiking neural networks (RSNNs) possess great computational power. However, the practical application of RSNNs is severely limited by challenges in training. Biologically-inspired unsupervised learning has limited capability in boosting the performance of RSNNs. On the other hand, existing backpropagation (BP) methods suffer from high complexity of unfolding in time, vanishing and exploding gradients, and approximate differentiation of discontinuous spiking activities when applied to RSNNs. To enable supervised training of RSNNs under a well-defined loss function, we present a novel Spike-Train level RSNNs Backpropagation (ST-RSBP) algorithm for training deep RSNNs. The proposed ST-RSBP directly computes the gradient of a rate-coded loss function defined at the output layer of the network w.r.t tunable parameters. The scalability of ST-RSBP is achieved by the proposed spike-train level computation during which temporal effects of the SNN is captured in both the forward and backward pass of BP. Our ST-RSBP algorithm can be broadly applied to RSNNs with a single recurrent layer or deep RSNNs with multiple feedforward and recurrent layers. Based upon challenging speech and image datasets including TI46, N-TIDIGITS, Fashion-MNIST and MNIST, ST-RSBP is able to train SNNs with an accuracy surpassing that of the current state-of-the-art SNN BP algorithms and conventional non-spiking deep learning models. 

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3. Working Memory Augmentation for Improved Learning in Neural Adaptive Control

   https://doi.org/10.1109/CDC40024.2019.9029549  

   Muthirayan, Deepan ; Khargonekar, Pramod P. ( December 2019 , 2019 IEEE Conference on Decision and Control)

   In this paper, we propose a novel control architecture, inspired from neuroscience, for adaptive control of continuous time systems. The objective here is to design control architectures and algorithms that can learn and adapt quickly to changes that are even abrupt. The proposed architecture, in the setting of standard neural network (NN) based adaptive control, augments an external working memory to the NN. The learning system stores, in its external working memory, recently observed feature vectors from the hidden layer of the NN that are relevant and forgets the older irrelevant values. It retrieves relevant vectors from the working memory to modify the final control signal generated by the controller. The use of external working memory improves the context inducing the learning system to search in a particular direction. This directed learning allows the learning system to find a good approximation of the unknown function even after abrupt changes quickly. We consider two classes of controllers for illustration of our ideas (i) a model reference NN adaptive controller for linear systems with matched uncertainty (ii) backstepping NN controller for strict feedback systems. Through extensive simulations and specific metrics we show that memory augmentation improves learning significantly even when the system undergoes sudden changes. Importantly, we also provide evidence for the proposed mechanism by which this specific memory augmentation improves learning. 

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4. Disjunctive Threshold Networks for Tabular Data Classification

   https://doi.org/10.1109/OJCS.2023.3282948  

   Wang, Weijia ; Qiao, Litao ; Lin, Bill ( January 2023 , IEEE Open Journal of the Computer Society)

   IEEE Open Journal of the Computer Society (Ed.)

   While neural networks have been achieving increasingly significant excitement in solving classification tasks such as natural language processing, their lack of interpretability becomes a great challenge for neural networks to be deployed in certain high-stakes human-centered applications. To address this issue, we propose a new approach for generating interpretable predictions by inferring a simple three-layer neural network with threshold activations, so that it can benefit from effective neural network training algorithms and at the same time, produce human-understandable explanations for the results. In particular, the hidden layer neurons in the proposed model are trained with floating point weights and binary output activations. The output neuron is also trainable as a threshold logic function that implements a disjunctive operation, forming the logical-OR of the first-level threshold logic functions. This neural network can be trained using state-of-the-art training methods to achieve high prediction accuracy. An important feature of the proposed architecture is that only a simple greedy algorithm is required to provide an explanation with the prediction that is human-understandable. In comparison with other explainable decision models, our proposed approach achieves more accurate predictions on a broad set of tabular data classification datasets. 

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5. On the Equivalence between Neural Network and Support Vector Machine

   Chen, Y. ; Huang, W. ; Nguyen, L. ; Weng, T.-W. ( December 2021 , Advances in neural information processing systems)

   Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) [27]. Under the squared loss, the infinite-width NN trained by gradient descent with an infinitely small learning rate is equivalent to kernel regression with NTK [4]. However, the equivalence is only known for ridge regression currently [6], while the equivalence between NN and other kernel machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore, in this work, we propose to establish the equivalence between NN and SVM, and specifically, the infinitely wide NN trained by soft margin loss and the standard soft margin SVM with NTK trained by subgradient descent. Our main theoretical results include establishing the equivalence between NN and a broad family of L2 regularized KMs with finite width bounds, which cannot be handled by prior work, and showing that every finite-width NN trained by such regularized loss functions is approximately a KM. Furthermore, we demonstrate our theory can enable three practical applications, including (i) non-vacuous generalization bound of NN via the corresponding KM; (ii) nontrivial robustness certificate for the infinite-width NN (while existing robustness verification methods would provide vacuous bounds); (iii) intrinsically more robust infinite-width NNs than those from previous kernel regression. 

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