SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks

Abstract

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 multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer 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.

A solution to the learning dilemma for recurrent networks of spiking neurons

“…The learning rule called Superspike (Zenke and Ganguli, 2018) was derived by applying RTRL in spiking neural networks without recurrent connections. In the absence of these connections RTRL is practicable and the resulting learning rule uses eligibility traces similar to those arising in e-prop with LIF neurons.…”

“…This approach requires non-local communication within the RNN, which we wanted to avoid in e-prop. In contrast to e-prop, none of the papers above (Zenke and Ganguli, 2018;Murray, 2019;Roth et al, 2019) derived a theory or a definition of eligibility traces that can be applied to neuron models with a non-trivial internal dynamics, such as adaptive neurons or LSTM units, that appear to be essential for solving tasks with demanding temporal credit assignment of errors.…”

A Spiking Neuron and Population Model based on the Growth Transform Dynamical System

“…The non-differentiable nature of spiking dynamics makes it hard to design energy-based learning models involving neural variables. Neuromorphic algorithms currently work around this problem in different ways, including mapping deep neural nets to spiking networks through rate-based techniques [43,44], formulating loss functions that penalize the difference between actual and desired spike-times [45,46], or approximating the derivatives of spike signals through various means [47,48,49]. However, formulating the spiking dynamics of the entire network using an energy function involving neural state variables across the network would enable us to directly use the energy function itself for learning weight parameters; and forms the basis for our future work.…”

Data and Power Efficient Intelligence with Neuromorphic Learning Machines

“…This rule is the basis of the superspike algorithm proposed by Zenke and Ganguli (2017) and can learn to recognize and generate arbitrary patterns of spikes. It consists of three factors: a modulatory component $\mathit{error}=\frac{\partial \mathcal{L}}{\partial s}$, a pre-synaptic component ( ϵ ∗ s j ), and a post-synaptic component ${\rho }^{\prime }\left(u\right)$.…”