An Exact Mapping From ReLU Networks to Spiking Neural Networks

Energy consumption of deep artificial neural networks (ANNs) with thousands of neurons poses a problem not only during training [1], but also during inference [2]. Among other alternatives [3, 4, 5], hardware implementations of spiking neural networks (SNNs) [6, 7, 8, 9, 10] have been proposed as an energy-efficient solution, not only for large centralized applications, but also for computing in edge devices [11, 12, 13]. In SNNs neurons communicate by ultra-short pulses, called action potentials or spikes, that can be considered as point-like events in continuous time. In deep multi-layer SNNs, if a neuron in layer n fires a spike, this event causes a change in the voltage trajectory of neurons in layer n + 1. If, after some time, the trajectory of a neuron in layer n + 1 reaches a threshold value, then this neuron fires a spike. While there is no general consensus on how to best decode spike trains in biology [14, 15, 16], multiple pieces of evidence indicate that immediately after an onset of a stimulus, populations of neurons in auditory, visual, or tactile sensory areas respond in such a way that the timing of the first spike of each neuron after stimulus onset contains a high amount of information about the stimulus features [17, 18, 19]. These and similar observations have triggered the idea that, immediately after stimulus onset, an initial wave of activity is triggered and travels across several brain areas in the sensory processing stream [20, 21, 22, 23, 24]. We take inspiration from these observations and assume in this paper that information is encoded in the exact spike times of each neuron and that spikes are transmitted in a wave-like manner across layers of a deep feedforward neural network. Specifically, we use coding by time-to-first-spike (TTFS) [15], a timing-based code originally proposed in neuroscience [15, 17, 18, 22], which has recently attracted substantial attention in the context of neuromorphic implementations [8, 9, 10, 25, 26, 27, 28, 29, 30].