Leaky integrate-and-fire

Since the popularization of GPUs for machine learning (ML) workloads, several dedicated accelerator chips have emerged, offering architectures optimized for common ML operations and requirements. The types of tasks targeted by such platforms however - often sparse and highly parallel - are not confined to the realm of traditional layer-based learning. Established simulators for large-scale spiking networks with biologically plausible connectivity and synaptic density have historically targeted CPUs, with GPU support and ports being a relatively recent development[1][2]. Here, we present a work

The ability to train spiking neural network models is essential for the modeling of biological neural networks as well as for neuromorphic computing. The standard approach when training non-spiking neural networks is gradient descent. In spiking neural networks, however, gradient descent learning is complicated by the all-or-none character of spikes (Fig. A). It can lead to unexpected (dis-)appearances of spikes during training, resulting in disruptive, discontinuous changes in the network dynamics [1]. Further, it seemingly prohibits exact gradients to systematically generate or remove spikes

A signature feature of cortical circuits is the irregularity of neuronal firing, which manifests itself in the high temporal variability of spiking and the broad distribution of rates. Theoretical works have shown that this feature emerges dynamically in network models if coupling between cells is strong, i.e. if the mean number of synapses per neuron K is large and synaptic efficacy is of order 1/\sqrt{K}. However, the degree to which these models capture the mechanisms underlying neuronal firing in cortical circuits is not fully understood. Results have been derived using neuron models with

Neurons in the brain communicate through action potentials (spikes) that are transmitted through chemical synapses. Throughout the last decades, the question how networks of spiking neurons represent and process information has remained an important challenge. Some progress has resulted from a recent family of supervised learning rules (tempotrons) for models of spiking neurons. However, these studies have viewed synaptic transmission as static and characterized synaptic efficacies as scalar quantities that change only on slow time scales of learning across trials but remain fixed on the fast

…for a recurrent network of spiking (leaky integrate-and-fire) neurons with hard thresholds and show that the backward dynamics amount to an event-based backpropagation of errors through time. Our derivation uses the jump condition

Engineered pattern-recognition systems strive for short time-to-solution and low energy-to-solution characteristics. This represents one of the main driving forces behind the development of neuromorphic devices. For both them and their biological archetypes, this corresponds to using as few spikes as early as possible. The concept of few and early spikes is used as the founding principle in the time-to-first-spike coding scheme. Within this framework, we have developed a spike-timing-based learning algorithm, which we used to train neuronal networks on the mixed-signal neuromorphic platform Br