Inference And Learning In Spiking Neural Networks For Neuromorphic Systems

Neuromorphic computing is a computing field that takes inspiration from the biological and physical characteristics of the neocortex system to motivate a new paradigm of highly parallel and distributed computing to take on the demands of the ever-increasing scale and computational complexity of machine intelligence esp. in energy-limited systems such as Edge devices, Internet-of-Things (IOT), and cyber physical systems (CPS). Spiking neural network (SNN) is often studied together with neuromorphic computing as the underlying computational model . Similar to the biological neural system, SNN is an inherently dynamic and stateful network. The state and output of SNN do not only dependent on the current input, but also dependent on the history information. Another distinct property of SNN is that the information is represented, transmitted, and processed as discrete spike events, also referred to as action potentials. All the processing happens in the neurons such that the computation itself is massively distributed and parallel. This enables low power information transmission and processing. However, it is inefficient to implement SNNs on traditional Von Neumann architecture due to the performance gap between memory and processor. This has led to the advent of energy-efficient large-scale neuromorphic hardware such as IBM\u27s TrueNorth and Intel\u27s Loihi that enables low power implementation of large-scale neural networks for real-time applications. And although spiking networks have theoretically been shown to have Turing-equivalent computing power, it remains a challenge to train deep SNNs; the threshold functions that generate spikes are discontinuous, so they do not have derivatives and cannot directly utilize gradient-based optimization algorithms for training. Biologically plausible learning mechanism spike-timing-dependent plasticity (STDP) and its variants are local in synapses and time but are unstable during training and difficult to train multi-layer SNNs. To better exploit the energy-saving features such as spike domain representation and stochastic computing provided by SNNs in neuromorphic hardware, and to address the hardware limitations such as limited data precision and neuron fan-in/fan-out constraints, it is necessary to re-design a neural network including its structure and computing. Our work focuses on low-level (activations, weights) and high-level (alternative learning algorithms) redesign techniques to enable inference and learning with SNNs in neuromorphic hardware. First, we focused on transforming a trained artificial neural network (ANN) to a form that is suitable for neuromorphic hardware implementation. Here, we tackle transforming Long Short-Term Memory (LSTM), a version of recurrent neural network (RNN) which includes recurrent connectivity to enable learning long temporal patterns. This is specifically a difficult challenge due to the inherent nature of RNNs and SNNs; the recurrent connectivity in RNNs induces temporal dynamics which require synchronicity, especially with the added complexity of LSTMs; and SNNs are asynchronous in nature. In addition, the constraints of the neuromorphic hardware provided a massive challenge for this realization. Thus, in this work, we invented a store-and-release circuit using integrate-and-fire neurons which allows the synchronization and then developed modules using that circuit to replicate various parts of the LSTM. These modules enabled implementation of LSTMs with spiking neurons on IBM’s TrueNorth Neurosynaptic processor. This is the first work to realize such LSTM networks utilizing spiking neurons and implement on a neuromorphic hardware. This opens avenues for the use of neuromorphic hardware in applications involving temporal patterns. Moving from mapping a pretrained ANN, we work on training networks on the neuromorphic hardware. Here, we first looked at the biologically plausible learning algorithm called STDP which is a Hebbian learning rule for learning without supervision. Simplified computational interpretations of STDP is either unstable and/or complex such that it is costly to implement on hardware. Thus, in this work, we proposed a stable version of STDP and applied intentional approximations for low-cost hardware implementation called Quantized 2-Power Shift (Q2PS) rule. With this version, we performed both unsupervised learning for feature extraction and supervised learning for classification in a multilayer SNN to achieve comparable to better accuracy on MNIST dataset compared to manually labelled two-layered networks. Next, we approached training multilayer SNNs on a neuromorphic hardware with backpropagation, a gradient-based optimization algorithm that forms the backbone of deep neural networks (DNN). Although STDP is biologically plausible, its not as robust for learning deep networks as backpropagation is for DNNs. However, backpropagation is not biologically plausible and not suitable to be directly applied to SNNs, neither can it be implemented on a neuromorphic hardware. Thus, in the first part of this work, we devise a set of approximations to transform backprogation to the spike domain such that it is suitable for SNNs. After the set of approximations, we adapted the connectivity and weight update rule in backpropagation to enable learning solely based on the locally available information such that it resembled a rate-based STDP algorithm. We called this Error-Modulated STDP (EMSTDP). In the next part of this work, we implemented EMSTDP on Intel\u27s Loihi neuromorphic chip to realize online in-hardware supervised learning of deep SNNs. This is the first realization of a fully spike-based approximation of backpropagation algorithm implemented on a neuromorphic processor. This is the first step towards building an autonomous machine that learns continuously from its environment and experiences

SuperSpike: Supervised learning in multi-layer spiking neural networks

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in-vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in-silico. Here we revisit the problem of supervised learning in temporally coding multi-layer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three factor learning rule capable of training multi-layer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike-time patterns

Inference and Learning in Spiking Neural Networks for Neuromorphic Systems

Neuromorphic computing is a computing field that takes inspiration from the biological and physical characteristics of the neocortex system to motivate a new paradigm of highly parallel and distributed computing to take on the demands of the ever-increasing scale and computational complexity of machine intelligence esp. in energy-limited systems such as Edge devices, Internet-of-Things (IOT), and cyber physical systems (CPS). Spiking neural network (SNN) is often studied together with neuromorphic computing as the underlying computational model . Similar to the biological neural system, SNN is an inherently dynamic and stateful network. The state and output of SNN do not only dependent on the current input, but also dependent on the history information. Another distinct property of SNN is that the information is represented, transmitted, and processed as discrete spike events, also referred to as action potentials. All the processing happens in the neurons such that the computation itself is massively distributed and parallel. This enables low power information transmission and processing. However, it is inefficient to implement SNNs on traditional Von Neumann architecture due to the performance gap between memory and processor. This has led to the advent of energy-efficient large-scale neuromorphic hardware such as IBM\u27s TrueNorth and Intel\u27s Loihi that enables low power implementation of large-scale neural networks for real-time applications. And although spiking networks have theoretically been shown to have Turing-equivalent computing power, it remains a challenge to train deep SNNs; the threshold functions that generate spikes are discontinuous, so they do not have derivatives and cannot directly utilize gradient-based optimization algorithms for training. Biologically plausible learning mechanism spike-timing-dependent plasticity (STDP) and its variants are local in synapses and time but are unstable during training and difficult to train multi-layer SNNs. To better exploit the energy-saving features such as spike domain representation and stochastic computing provided by SNNs in neuromorphic hardware, and to address the hardware limitations such as limited data precision and neuron fan-in/fan-out constraints, it is necessary to re-design a neural network including its structure and computing. Our work focuses on low-level (activations, weights) and high-level (alternative learning algorithms) redesign techniques to enable inference and learning with SNNs in neuromorphic hardware. First, we focused on transforming a trained artificial neural network (ANN) to a form that is suitable for neuromorphic hardware implementation. Here, we tackle transforming Long Short-Term Memory (LSTM), a version of recurrent neural network (RNN) which includes recurrent connectivity to enable learning long temporal patterns. This is specifically a difficult challenge due to the inherent nature of RNNs and SNNs; the recurrent connectivity in RNNs induces temporal dynamics which require synchronicity, especially with the added complexity of LSTMs; and SNNs are asynchronous in nature. In addition, the constraints of the neuromorphic hardware provided a massive challenge for this realization. Thus, in this work, we invented a store-and-release circuit using integrate-and-fire neurons which allows the synchronization and then developed modules using that circuit to replicate various parts of the LSTM. These modules enabled implementation of LSTMs with spiking neurons on IBM\u27s TrueNorth Neurosynaptic processor. This is the first work to realize such LSTM networks utilizing spiking neurons and implement on a neuromorphic hardware. This opens avenues for the use of neuromorphic hardware in applications involving temporal patterns. Moving from mapping a pretrained ANN, we work on training networks on the neuromorphic hardware. Here, we first looked at the biologically plausible learning algorithm called STDP which is a Hebbian learning rule for learning without supervision. Simplified computational interpretations of STDP is either unstable and/or complex such that it is costly to implement on hardware. Thus, in this work, we proposed a stable version of STDP and applied intentional approximations for low-cost hardware implementation called Quantized 2-Power Shift (Q2PS) rule. With this version, we performed both unsupervised learning for feature extraction and supervised learning for classification in a multilayer SNN to achieve comparable to better accuracy on MNIST dataset compared to manually labelled two-layered networks. Next, we approached training multilayer SNNs on a neuromorphic hardware with backpropagation, a gradient-based optimization algorithm that forms the backbone of deep neural networks (DNN). Although STDP is biologically plausible, its not as robust for learning deep networks as backpropagation is for DNNs. However, backpropagation is not biologically plausible and not suitable to be directly applied to SNNs, neither can it be implemented on a neuromorphic hardware. Thus, in the first part of this work, we devise a set of approximations to transform backprogation to the spike domain such that it is suitable for SNNs. After the set of approximations, we adapted the connectivity and weight update rule in backpropagation to enable learning solely based on the locally available information such that it resembled a rate-based STDP algorithm. We called this Error-Modulated STDP (EMSTDP). In the next part of this work, we implemented EMSTDP on Intel\u27s Loihi neuromorphic chip to realize online in-hardware supervised learning of deep SNNs. This is the first realization of a fully spike-based approximation of backpropagation algorithm implemented on a neuromorphic processor. This is the first step towards building an autonomous machine that learns continuously from its environment and experiences

A supervised learning algorithm for learning precise timing of multiple spikes in multilayer spiking neural networks

There is a biological evidence to prove information is coded through precise timing of spikes in the brain. However, training a population of spiking neurons in a multilayer network to fire at multiple precise times remains a challenging task. Delay learning and the effect of a delay on weight learning in a spiking neural network (SNN) have not been investigated thoroughly. This paper proposes a novel biologically plausible supervised learning algorithm for learning precisely timed multiple spikes in a multilayer SNNs. Based on the spike-timing-dependent plasticity learning rule, the proposed learning method trains an SNN through the synergy between weight and delay learning. The weights of the hidden and output neurons are adjusted in parallel. The proposed learning method captures the contribution of synaptic delays to the learning of synaptic weights. Interaction between different layers of the network is realized through biofeedback signals sent by the output neurons. The trained SNN is used for the classification of spatiotemporal input patterns. The proposed learning method also trains the spiking network not to fire spikes at undesired times which contribute to misclassification. Experimental evaluation on benchmark data sets from the UCI machine learning repository shows that the proposed method has comparable results with classical rate-based methods such as deep belief network and the autoencoder models. Moreover, the proposed method can achieve higher classification accuracies than single layer and a similar multilayer SNN

Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective

On metrics of density and power efficiency, neuromorphic technologies have the potential to surpass mainstream computing technologies in tasks where real-time functionality, adaptability, and autonomy are essential. While algorithmic advances in neuromorphic computing are proceeding successfully, the potential of memristors to improve neuromorphic computing have not yet born fruit, primarily because they are often used as a drop-in replacement to conventional memory. However, interdisciplinary approaches anchored in machine learning theory suggest that multifactor plasticity rules matching neural and synaptic dynamics to the device capabilities can take better advantage of memristor dynamics and its stochasticity. Furthermore, such plasticity rules generally show much higher performance than that of classical Spike Time Dependent Plasticity (STDP) rules. This chapter reviews the recent development in learning with spiking neural network models and their possible implementation with memristor-based hardware

Bidirectional Learning in Recurrent Neural Networks Using Equilibrium Propagation

Neurobiologically-plausible learning algorithms for recurrent neural networks that can perform supervised learning are a neglected area of study. Equilibrium propagation is a recent synthesis of several ideas in biological and artificial neural network research that uses a continuous-time, energy-based neural model with a local learning rule. However, despite dealing with recurrent networks, equilibrium propagation has only been applied to discriminative categorization tasks. This thesis generalizes equilibrium propagation to bidirectional learning with asymmetric weights. Simultaneously learning the discriminative as well as generative transformations for a set of data points and their corresponding category labels, bidirectional equilibrium propagation utilizes recurrence and weight asymmetry to share related but non-identical representations within the network. Experiments on an artificial dataset demonstrate the ability to learn both transformations, as well as the ability for asymmetric-weight networks to generalize their discriminative training to the untrained generative task