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

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

Biologically plausible deep learning -- but how far can we go with shallow networks?

Training deep neural networks with the error backpropagation algorithm is considered implausible from a biological perspective. Numerous recent publications suggest elaborate models for biologically plausible variants of deep learning, typically defining success as reaching around 98% test accuracy on the MNIST data set. Here, we investigate how far we can go on digit (MNIST) and object (CIFAR10) classification with biologically plausible, local learning rules in a network with one hidden layer and a single readout layer. The hidden layer weights are either fixed (random or random Gabor filters) or trained with unsupervised methods (PCA, ICA or Sparse Coding) that can be implemented by local learning rules. The readout layer is trained with a supervised, local learning rule. We first implement these models with rate neurons. This comparison reveals, first, that unsupervised learning does not lead to better performance than fixed random projections or Gabor filters for large hidden layers. Second, networks with localized receptive fields perform significantly better than networks with all-to-all connectivity and can reach backpropagation performance on MNIST. We then implement two of the networks - fixed, localized, random & random Gabor filters in the hidden layer - with spiking leaky integrate-and-fire neurons and spike timing dependent plasticity to train the readout layer. These spiking models achieve > 98.2% test accuracy on MNIST, which is close to the performance of rate networks with one hidden layer trained with backpropagation. The performance of our shallow network models is comparable to most current biologically plausible models of deep learning. Furthermore, our results with a shallow spiking network provide an important reference and suggest the use of datasets other than MNIST for testing the performance of future models of biologically plausible deep learning.Comment: 14 pages, 4 figure

Hardware-efficient on-line learning through pipelined truncated-error backpropagation in binary-state networks

Artificial neural networks (ANNs) trained using backpropagation are powerful learning architectures that have achieved state-of-the-art performance in various benchmarks. Significant effort has been devoted to developing custom silicon devices to accelerate inference in ANNs. Accelerating the training phase, however, has attracted relatively little attention. In this paper, we describe a hardware-efficient on-line learning technique for feedforward multi-layer ANNs that is based on pipelined backpropagation. Learning is performed in parallel with inference in the forward pass, removing the need for an explicit backward pass and requiring no extra weight lookup. By using binary state variables in the feedforward network and ternary errors in truncated-error backpropagation, the need for any multiplications in the forward and backward passes is removed, and memory requirements for the pipelining are drastically reduced. Further reduction in addition operations owing to the sparsity in the forward neural and backpropagating error signal paths contributes to highly efficient hardware implementation. For proof-of-concept validation, we demonstrate on-line learning of MNIST handwritten digit classification on a Spartan 6 FPGA interfacing with an external 1Gb DDR2 DRAM, that shows small degradation in test error performance compared to an equivalently sized binary ANN trained off-line using standard back-propagation and exact errors. Our results highlight an attractive synergy between pipelined backpropagation and binary-state networks in substantially reducing computation and memory requirements, making pipelined on-line learning practical in deep networks.Comment: Now also consider 0/1 binary activations. Memory access statistics reporte

An Efficient Threshold-Driven Aggregate-Label Learning Algorithm for Multimodal Information Processing

The aggregate-label learning paradigm tackles the long-standing temporary credit assignment (TCA) problem in neuroscience and machine learning, enabling spiking neural networks to learn multimodal sensory clues with delayed feedback signals. However, the existing aggregate-label learning algorithms only work for single spiking neurons, and with low learning efficiency, which limit their real-world applicability. To address these limitations, we first propose an efficient threshold-driven plasticity algorithm for spiking neurons, namely ETDP. It enables spiking neurons to generate the desired number of spikes that match the magnitude of delayed feedback signals and to learn useful multimodal sensory clues embedded within spontaneous spiking activities. Furthermore, we extend the ETDP algorithm to support multi-layer spiking neural networks (SNNs), which significantly improves the applicability of aggregate-label learning algorithms. We also validate the multi-layer ETDP learning algorithm in a multimodal computation framework for audio-visual pattern recognition. Experimental results on both synthetic and realistic datasets show significant improvements in the learning efficiency and model capacity over the existing aggregate-label learning algorithms. It, therefore, provides many opportunities for solving real-world multimodal pattern recognition tasks with spiking neural networks

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware

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