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

Supervised Learning in Spiking Neural Networks for Precise Temporal Encoding

Precise spike timing as a means to encode information in neural networks is biologically supported, and is advantageous over frequency-based codes by processing input features on a much shorter time-scale. For these reasons, much recent attention has been focused on the development of supervised learning rules for spiking neural networks that utilise a temporal coding scheme. However, despite significant progress in this area, there still lack rules that have a theoretical basis, and yet can be considered biologically relevant. Here we examine the general conditions under which synaptic plasticity most effectively takes place to support the supervised learning of a precise temporal code. As part of our analysis we examine two spike-based learning methods: one of which relies on an instantaneous error signal to modify synaptic weights in a network (INST rule), and the other one on a filtered error signal for smoother synaptic weight modifications (FILT rule). We test the accuracy of the solutions provided by each rule with respect to their temporal encoding precision, and then measure the maximum number of input patterns they can learn to memorise using the precise timings of individual spikes as an indication of their storage capacity. Our results demonstrate the high performance of FILT in most cases, underpinned by the rule's error-filtering mechanism, which is predicted to provide smooth convergence towards a desired solution during learning. We also find FILT to be most efficient at performing input pattern memorisations, and most noticeably when patterns are identified using spikes with sub-millisecond temporal precision. In comparison with existing work, we determine the performance of FILT to be consistent with that of the highly efficient E-learning Chronotron, but with the distinct advantage that FILT is also implementable as an online method for increased biological realism.Comment: 26 pages, 10 figures, this version is published in PLoS ONE and incorporates reviewer comment

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

Investigation of Synapto-dendritic Kernel Adapting Neuron models and their use in spiking neuromorphic architectures

The motivation for this thesis is idea that abstract, adaptive, hardware efficient, inter-neuronal transfer functions (or kernels) which carry information in the form of postsynaptic membrane potentials, are the most important (and erstwhile missing) element in neuromorphic implementations of Spiking Neural Networks (SNN). In the absence of such abstract kernels, spiking neuromorphic systems must realize very large numbers of synapses and their associated connectivity. The resultant hardware and bandwidth limitations create difficult tradeoffs which diminish the usefulness of such systems. In this thesis a novel model of spiking neurons is proposed. The proposed Synapto-dendritic Kernel Adapting Neuron (SKAN) uses the adaptation of their synapto-dendritic kernels in conjunction with an adaptive threshold to perform unsupervised learning and inference on spatio-temporal spike patterns. The hardware and connectivity requirements of the neuron model are minimized through the use of simple accumulator-based kernels as well as through the use of timing information to perform a winner take all operation between the neurons. The learning and inference operations of SKAN are characterized and shown to be robust across a range of noise environments. Next, the SKAN model is augmented with a simplified hardware-efficient model of Spike Timing Dependent Plasticity (STDP). In biology STDP is the mechanism which allows neurons to learn spatio-temporal spike patterns. However when the proposed SKAN model is augmented with a simplified STDP rule, where the synaptic kernel is used as a binary flag that enable synaptic potentiation, the result is a synaptic encoding of afferent Signal to Noise Ratio (SNR). In this combined model the neuron not only learns the target spatio-temporal spike patterns but also weighs each channel independently according to its signal to noise ratio. Additionally a novel approach is presented to achieving homeostatic plasticity in digital hardware which reduces hardware cost by eliminating the need for multipliers. Finally the behavior and potential utility of this combined model is investigated in a range of noise conditions and the digital hardware resource utilization of SKAN and SKAN + STDP is detailed using Field Programmable Gate Arrays (FPGA)

Supervised Learning in Multilayer Spiking Neural Networks

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.Comment: 38 pages, 4 figure

A Delay Learning Algorithm Based on Spike Train Kernels for Spiking Neurons

Neuroscience research confirms that the synaptic delays are not constant, but can be modulated. This paper proposes a supervised delay learning algorithm for spiking neurons with temporal encoding, in which both the weight and delay of a synaptic connection can be adjusted to enhance the learning performance. The proposed algorithm firstly defines spike train kernels to transform discrete spike trains during the learning phase into continuous analog signals so that common mathematical operations can be performed on them, and then deduces the supervised learning rules of synaptic weights and delays by gradient descent method. The proposed algorithm is successfully applied to various spike train learning tasks, and the effects of parameters of synaptic delays are analyzed in detail. Experimental results show that the network with dynamic delays achieves higher learning accuracy and less learning epochs than the network with static delays. The delay learning algorithm is further validated on a practical example of an image classification problem. The results again show that it can achieve a good classification performance with a proper receptive field. Therefore, the synaptic delay learning is significant for practical applications and theoretical researches of spiking neural networks

Nonparametric enrichment in computational and biological representations of distributions

This thesis proposes nonparametric techniques to enhance unsupervised learning methods in computational or biological contexts. Representations of intractable distributions and their relevant statistics are enhanced by nonparametric components trained to handle challenging estimation problems. The first part introduces a generic algorithm for learning generative latent variable models. In contrast to traditional variational learning, no representation for the intractable posterior distributions are computed, making it agnostic to the model structure and the support of latent variables. Kernel ridge regression is used to consistently estimate the gradient for learning. In many unsupervised tasks, this approach outperforms advanced alternatives based on the expectation-maximisation algorithm and variational approximate inference. In the second part, I train a model of data known as the kernel exponential family density. The kernel, used to describe smooth functions, is augmented by a parametric component trained using an efficient meta-learning procedure; meta-learning prevents overfitting as would occur using conventional routines. After training, the contours of the kernel become adaptive to the local geometry of the underlying density. Compared to maximum-likelihood learning, our method better captures the shape of the density, which is the desired quantity in many downstream applications. The final part sees how nonparametric ideas contribute to understanding uncertainty computation in the brain. First, I show that neural networks can learn to represent uncertainty using the distributed distributional code (DDC), a representation similar to the nonparametric kernel mean embedding. I then derive several DDC-based message-passing algorithms, including computations of filtering and real-time smoothing. The latter is a common neural computation embodied in many postdictive phenomena of perception in multiple modalities. The main idea behind these algorithms is least-squares regression, where the training data are simulated from an internal model. The internal model can be concurrently updated to follow the statistics in sensory stimuli, enabling adaptive inference