Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. However, the supervised training of SNNs remains a hard problem due to the discontinuity of the spiking neuron model.

In our analysis, we considered population spiking activity of monkey-I in response to a gray-scale natural movie. The movie is about a monkey wading through water.

In our analysis, we considered population spiking activity of monkey-I in response to a gray-scale natural movie. The movie is about a monkey wading through water.

Input: Network parameters θ; Input data x; Label y; Time steps T; Other hyperparameters; Output: Trained network parameters θ . Calculate the output o and the loss L based on o and y . Update θ based on the gradient-based optimizer. We first prove Theorem 1. Then Theorem 2 is similarly proved. We omit repetitive details here.

Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. However, the supervised training of SNNs remains a hard problem due to the discontinuity of the spiking neuron model.

Spiking neural networks (SNNs) with event-based computation are promising brain-inspired models for energy-efficient applications on neuromorphic hardware. However, most supervised SNN training methods, such as conversion from artificial neural networks or direct training with surrogate gradients, require complex computation rather than spike-based operations of spiking neurons during training. In this paper, we study spike-based implicit differentiation on the equilibrium state (SPIDE) that extends the recently proposed training method, implicit differentiation on the equilibrium state (IDE), for supervised learning with purely spike-based computation, which demonstrates the potential for energy-efficient training of SNNs. Specifically, we introduce ternary spiking neuron couples and prove that implicit differentiation can be solved by spikes based on this design, so the whole training procedure, including both forward and backward passes, is made as event-driven spike computation, and weights are updated locally with two-stage average firing rates. Then we propose to modify the reset membrane potential to reduce the approximation error of spikes. With these key components, we can train SNNs with flexible structures in a small number of time steps and with firing sparsity during training, and the theoretical estimation of energy costs demonstrates the potential for high efficiency. Meanwhile, experiments show that even with these constraints, our trained models can still achieve competitive results on MNIST, CIFAR-10, CIFAR-100, and CIFAR10-DVS. Our code is available at https://github.com/pkuxmq/SPIDE-FSNN.

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured by the identity of the clusters rather than by individuals within clusters. We show how this intuition can be made precise using information theory, without any need to introduce a metric on the space of stimuli or responses. Applied to the retinal ganglion cells of the salamander, this approach recovers classical results, but also provides clear evidence for subclasses beyond those identified previously. Further, we find that each of the ganglion cells is functionally unique, and that even within the same subclass only a few spikes are needed to reliably distinguish between cells.

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured by the identity of the clusters rather than by individuals within clusters. We show how this intuition can be made precise using information theory, without any need to introduce a metric on the space of stimuli or responses. Applied to the retinal ganglion cells of the salamander, this approach recovers classical results, but also provides clear evidence for subclasses beyond those identified previously. Further, we find that each of the ganglion cells is functionally unique, and that even within the same subclass only a few spikes are needed to reliably distinguish between cells.

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured by the identity ofthe clusters rather than by individuals within clusters. We show how this intuition can be made precise using information theory, without anyneed to introduce a metric on the space of stimuli or responses. Applied to the retinal ganglion cells of the salamander, this approach recovers classicalresults, but also provides clear evidence for subclasses beyond those identified previously. Further, we find that each of the ganglion cellsis functionally unique, and that even within the same subclass only a few spikes are needed to reliably distinguish between cells.