<div>Computing with Artificial Neural Networks (ANNs) is a branch of machine learning that has seen substantial growth over the last decade, significantly increasing the accuracy and capability of machine learning systems. ANNs are connected networks of computing elements inspired by the neuronal connectivity in the brain. Spiking Neural Networks (SNNs) are a type of ANN that operate with event-driven computation, inspired by the “spikes” or firing events of individual neurons in the brain. Neuromorphic computing—the implementation of neural networks in hardware—seeks to improve the energy efficiency of these machine learning systems either by computing directly with device physical primitives, by bypassing the software layer of logical implementations, or by operating with SNN event-driven computation. Such implementations may, however, have added restrictions, including weight-localized learning and hard-wired connections. Further obstacles, such as catastrophic forgetting, the lack of supervised error signals, and storage and energy constraints, are encountered when these systems need to perform autonomous online, real-time learning in an unknown, changing environment. </div><div><br></div><div>Adapting neural network learning algorithms for these constraints can help address these issues. Specifically, corrections to Spike Timing-Dependent Plasticity (STDP) can stabilize local, unsupervised learning; accounting for the statistical firing properties of spiking neurons may improve conversions from non-spiking to spiking networks; biologically-inspired dopaminergic and habituation adjustments to STDP can limit catastrophic forgetting; convolving temporally instead of spatially can provide for localized weight sharing with direct synaptic connections; and explicitly training for spiking sparsity can significantly reduce computational energy consumption.</div>

<div>Deep learning models have become the de-facto solution in various fields like computer vision, natural language processing, robotics, drug discovery, and many others. The skyrocketing performance and success of multi-layer neural networks comes at a significant power and energy cost. Thus, there is a need to rethink the current trajectory and explore different computing frameworks. One such option is spiking neural networks (SNNs) that is inspired from the spike-based processing observed in biological brains. SNNs operating with binary signals (or spikes), can potentially be an energy-efficient alternative to the power-hungry analog neural networks (ANNs) that operate on real-valued analog signals. The binary all-or-nothing spike-based communication in SNNs implemented on event-driven hardware offers a low-power alternative to ANNs. A spike is a Delta function with magnitude 1. With all its appeal for low power, training SNNs efficiently for high accuracy remains an active area of research. The existing ANN training methodologies when applied to SNNs, results in networks that have very high latency. Supervised training of SNNs with spikes is challenging (due to discontinuous gradients) and resource-intensive (time, compute, and memory).Thus, we propose compression methods, training methodologies, learning rules</div><div><br></div><div>First, we propose compression techniques for SNNs based on unsupervised spike timing dependent plasticity (STDP) model. We present a sparse SNN topology where non-critical connections are pruned to reduce the network size and the remaining critical synapses are weight quantized to accommodate for limited conductance levels in emerging in-memory computing hardware . Pruning is based on the power law weight-dependent</div><div>STDP model; synapses between pre- and post-neuron with high spike correlation are retained, whereas synapses with low correlation or uncorrelated spiking activity are pruned. The process of pruning non-critical connections and quantizing the weights of critical synapses is</div><div>performed at regular intervals during training.</div><div><br></div><div>Second, we propose a multimodal SNN that combines two modalities (image and audio). The two unimodal ensembles are connected with cross-modal connections and the entire network is trained with unsupervised learning. The network receives inputs in both modalities for the same class and</div><div>predicts the class label. The excitatory connections in the unimodal ensemble and the cross-modal connections are trained with STDP. The cross-modal connections capture the correlation between neurons of different modalities. The multimodal network learns features of both modalities and improves the classification accuracy compared to unimodal topology, even when one of the modality is distorted by noise. The cross-modal connections are only excitatory and do not inhibit the normal activity of the unimodal ensembles. </div><div><br></div><div>Third, we explore supervised learning methods for SNNs.Many works have shown that an SNN for inference can be formed by copying the weights from a trained ANN and setting the firing threshold for each layer as the maximum input received in that layer. These type of converted SNNs require a large number of time steps to achieve competitive accuracy which diminishes the energy savings. The number of time steps can be reduced by training SNNs with spike-based backpropagation from scratch, but that is computationally expensive and slow. To address these challenges, we present a computationally-efficient training technique for deep SNNs. We propose a hybrid training methodology:</div><div>1) take a converted SNN and use its weights and thresholds as an initialization step for spike-based backpropagation, and 2) perform incremental spike-timing dependent backpropagation (STDB) on this carefully initialized network to obtain an SNN that converges within few epochs and requires fewer time steps for input processing. STDB is performed with a novel surrogate gradient function defined using neuron’s spike time. The weight update is proportional to the difference in spike timing between the current time step and the most recent time step the neuron generated an output spike.</div><div><br></div><div>Fourth, we present techniques to further reduce the inference latency in SNNs. SNNs suffer from high inference latency, resulting from inefficient input encoding, and sub-optimal settings of the neuron parameters (firing threshold, and membrane leak). We propose DIET-SNN, a low-latency deep spiking network that is trained with gradient descent to optimize the membrane leak and the firing threshold along with other network parameters (weights). The membrane leak and threshold for each layer of the SNN are optimized with end-to-end backpropagation to achieve competitive accuracy at reduced latency. The analog pixel values of an image are directly applied to the input layer of DIET-SNN without the need to convert to spike-train. The first convolutional layer is trained to convert inputs into spikes where leaky-integrate-and-fire (LIF) neurons integrate the weighted inputs and generate an output spike when the membrane potential crosses the trained firing threshold. The trained membrane leak controls the flow of input information and attenuates irrelevant inputs to increase the activation sparsity in the convolutional and dense layers of the network. The reduced latency combined with high activation sparsity provides large improvements in computational efficiency.</div><div><br></div><div>Finally, we explore the application of SNNs in sequential learning tasks. We propose LITE-SNN, a lightweight SNN suitable for sequential learning tasks on data from dynamic vision sensors (DVS) and natural language processing (NLP). In general sequential data is processed with complex recurrent neural networks (like long short-term memory (LSTM), and gated recurrent unit (GRU)) with explicit feedback connections and internal states to handle the long-term dependencies. Whereas neuron models in SNNs - integrate-and-fire (IF) or leaky-integrate-and-fire (LIF) - have implicit feedback in their internal state (membrane potential) by design and can be leveraged for sequential tasks. The membrane potential in the IF/LIF neuron integrates the incoming current and outputs an event (or spike) when the potential crosses a threshold value. Since SNNs compute with highly sparse spike-based spatio-temporal data, the energy/inference is lower than LSTMs/GRUs. SNNs also have fewer parameters than LSTM/GRU resulting in smaller models and faster inference. We observe the problem of vanishing gradients in vanilla SNNs for longer sequences and implement a convolutional SNN with attention layers to perform sequence-to-sequence learning tasks. The inherent recurrence in SNNs, in addition to the fully parallelized convolutional operations, provides an additional mechanism to model sequential dependencies and leads to better accuracy than convolutional neural networks with ReLU activations.</div>

<p>Spiking Neural Networks (SNNs) have recently attracted significant research interest as the third generation of artificial neural networks that can enable low-power event-driven data analytics. We propose ANN-SNN conversion using “soft re-set” spiking neuron model, referred to as Residual Membrane Potential (RMP) spiking neuron, which retains the “resid- ual” membrane potential above threshold at the firing instants. In addition, we propose a time-based coding scheme, named Temporal-Switch-Coding (TSC), and a corresponding TSC spiking neuron model. Each input image pixel is presented using two spikes with opposite polarity and the timing between the two spiking instants is proportional to the pixel intensity. We demonstrate near loss-less ANN-SNN conversion using RMP neurons for VGG-16, ResNet-20, and ResNet-34 SNNs on challenging datasets including CIFAR-10, CIFAR-100, and ImageNet. With the help of TSC coding, it achieves 7-14.5× less inference latency, and 30-60× fewer addition operations and memory accesses per inference across datasets compared to the state of the art (SOTA) SNN models. In the second part of the thesis, we propose a new type of recurrent neural network (RNN) architecture, named Os- cillatory Fourier Neural Network (O-FNN). We demonstrate that O-FNN is mathematically equivalent to a simplified form of Discrete Fourier Transform applied onto periodical activa- tion. In particular, the computationally intensive back-propagation through time in training is eliminated, leading to faster training while achieving the SOTA inference accuracy in a diverse group of sequential tasks. For instance, applying the proposed model to sentiment analysis on IMDB review dataset reaches 89.4% test accuracy within 5 epochs, accompanied by over 35x reduction in the model size compared to Long Short-Term Memory (LSTM). The proposed novel RNN architecture is well poised for intelligent sequential processing in resource constrained hardware.</p>