Fractionally Predictive Spiking Neurons

Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation. Here, we show that the actual neural spike-train itself can be considered as the fractional derivative, provided that the neural signal is approximated by a sum of power-law kernels. A simple standard thresholding spiking neuron suffices to carry out such an approximation, given a suitable refractory response. Empirically, we find that the online approximation of signals with a sum of power-law kernels is beneficial for encoding signals with slowly varying components, like long-memory self-similar signals. For such signals, the online power-law kernel approximation typically required less than half the number of spikes for similar SNR as compared to sums of similar but exponentially decaying kernels. As power-law kernels can be accurately approximated using sums or cascades of weighted exponentials, we demonstrate that the corresponding decoding of spike-trains by a receiving neuron allows for natural and transparent temporal signal filtering by tuning the weights of the decoding kernel.Comment: 13 pages, 5 figures, in Advances in Neural Information Processing 201

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

Adaptation to changes in higher-order stimulus statistics in the salamander retina

Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution

The remarkable robustness of surrogate gradient learning for instilling complex function in spiking neural networks

Brains process information in spiking neural networks. Their intricate connections shape the diverse functions these networks perform. In comparison, the functional capabilities of models of spiking networks are still rudimentary. This shortcoming is mainly due to the lack of insight and practical algorithms to construct the necessary connectivity. Any such algorithm typically attempts to build networks by iteratively reducing the error compared to a desired output. But assigning credit to hidden units in multi-layered spiking networks has remained challenging due to the non-differentiable nonlinearity of spikes. To avoid this issue, one can employ surrogate gradients to discover the required connectivity in spiking network models. However, the choice of a surrogate is not unique, raising the question of how its implementation influences the effectiveness of the method. Here, we use numerical simulations to systematically study how essential design parameters of surrogate gradients impact learning performance on a range of classification problems. We show that surrogate gradient learning is robust to different shapes of underlying surrogate derivatives, but the choice of the derivative’s scale can substantially affect learning performance. When we combine surrogate gradients with a suitable activity regularization technique, robust information processing can be achieved in spiking networks even at the sparse activity limit. Our study provides a systematic account of the remarkable robustness of surrogate gradient learning and serves as a practical guide to model functional spiking neural networks

Effective and Efficient Computation with Multiple-timescale Spiking Recurrent Neural Networks

The emergence of brain-inspired neuromorphic computing as a paradigm for edge AI is motivating the search for high-performance and efficient spiking neural networks to run on this hardware. However, compared to classical neural networks in deep learning, current spiking neural networks lack competitive performance in compelling areas. Here, for sequential and streaming tasks, we demonstrate how a novel type of adaptive spiking recurrent neural network (SRNN) is able to achieve state-of-the-art performance compared to other spiking neural networks and almost reach or exceed the performance of classical recurrent neural networks (RNNs) while exhibiting sparse activity. From this, we calculate a $>$100x energy improvement for our SRNNs over classical RNNs on the harder tasks. To achieve this, we model standard and adaptive multiple-timescale spiking neurons as self-recurrent neural units, and leverage surrogate gradients and auto-differentiation in the PyTorch Deep Learning framework to efficiently implement backpropagation-through-time, including learning of the important spiking neuron parameters to adapt our spiking neurons to the tasks.Comment: 11 pages,5 figure