State-of-the-art neural network training methods depend on the gradient of
the network function. Therefore, they cannot be applied to networks whose
activation functions do not have useful derivatives, such as binary and
discrete-time spiking neural networks. To overcome this problem, the activation
function's derivative is commonly substituted with a surrogate derivative,
giving rise to surrogate gradient learning (SGL). This method works well in
practice but lacks theoretical foundation. The neural tangent kernel (NTK) has
proven successful in the analysis of gradient descent. Here, we provide a
generalization of the NTK, which we call the surrogate gradient NTK, that
enables the analysis of SGL. First, we study a naive extension of the NTK to
activation functions with jumps, demonstrating that gradient descent for such
activation functions is also ill-posed in the infinite-width limit. To address
this problem, we generalize the NTK to gradient descent with surrogate
derivatives, i.e., SGL. We carefully define this generalization and expand the
existing key theorems on the NTK with mathematical rigor. Further, we
illustrate our findings with numerical experiments. Finally, we numerically
compare SGL in networks with sign activation function and finite width to
kernel regression with the surrogate gradient NTK; the results confirm that the
surrogate gradient NTK provides a good characterization of SGL.

研究了神经网络训练方法中激活函数导数不可用时的问题，提出了代理梯度学习（SGL）的理论基础，并利用神经切向核（NTK）的推广 —— 代理梯度 NTK 分析了 SGL，通过数值实验验证了 SGL 在具有有限宽度和符号激活函数的网络中的有效性。

一种用于替代梯度学习的广义神经切向核

A generalized neural tangent kernel for surrogate gradient learning

Automotive embedded algorithms have very high constraints in terms of
latency, accuracy and power consumption. In this work, we propose to train
spiking neural networks (SNNs) directly on data coming from event cameras to
design fast and efficient automotive embedded applications. Indeed, SNNs are
more biologically realistic neural networks where neurons communicate using
discrete and asynchronous spikes, a naturally energy-efficient and hardware
friendly operating mode. Event data, which are binary and sparse in space and
time, are therefore the ideal input for spiking neural networks. But to date,
their performance was insufficient for automotive real-world problems, such as
detecting complex objects in an uncontrolled environment. To address this
issue, we took advantage of the latest advancements in matter of spike
backpropagation - surrogate gradient learning, parametric LIF, SpikingJelly
framework - and of our new \textit{voxel cube} event encoding to train 4
different SNNs based on popular deep learning networks: SqueezeNet, VGG,
MobileNet, and DenseNet. As a result, we managed to increase the size and the
complexity of SNNs usually considered in the literature. In this paper, we
conducted experiments on two automotive event datasets, establishing new
state-of-the-art classification results for spiking neural networks. Based on
these results, we combined our SNNs with SSD to propose the first spiking
neural networks capable of performing object detection on the complex GEN1
Automotive Detection event dataset.

通过使用事件摄像头直接训练尖峰神经网络，以设计快速高效的汽车嵌入式应用程序，并且采用了最新的尖峰反向传播方法，成功地针对 GEN1 汽车检测事件数据集提出了尖峰神经网络实现目标检测的方法。

基于脉冲神经网络的汽车事件数据目标检测

Object Detection with Spiking Neural Networks on Automotive Event Data

Spiking Neural Networks (SNNs) have recently emerged as the low-power
alternative to Artificial Neural Networks (ANNs) because of their sparse,
asynchronous, and binary event-driven processing. Due to their energy
efficiency, SNNs have a high possibility of being deployed for real-world,
resource-constrained systems such as autonomous vehicles and drones. However,
owing to their non-differentiable and complex neuronal dynamics, most previous
SNN optimization methods have been limited to image recognition. In this paper,
we explore the SNN applications beyond classification and present semantic
segmentation networks configured with spiking neurons. Specifically, we first
investigate two representative SNN optimization techniques for recognition
tasks (i.e., ANN-SNN conversion and surrogate gradient learning) on semantic
segmentation datasets. We observe that, when converted from ANNs, SNNs suffer
from high latency and low performance due to the spatial variance of features.
Therefore, we directly train networks with surrogate gradient learning,
resulting in lower latency and higher performance than ANN-SNN conversion.
Moreover, we redesign two fundamental ANN segmentation architectures (i.e.,
Fully Convolutional Networks and DeepLab) for the SNN domain. We conduct
experiments on two public semantic segmentation benchmarks including the PASCAL
VOC2012 dataset and the DDD17 event-based dataset. In addition to showing the
feasibility of SNNs for semantic segmentation, we show that SNNs can be more
robust and energy-efficient compared to their ANN counterparts in this domain.

本论文探讨了脉冲神经网络在语义分割方面的应用，通过替代全连接层和使用替代梯度学习方法，将基本的全卷积网络和 DeepLab 架构重构为 SNN 域的网络。实验表明，相较于 ANN 网络，SNN 网络在这个领域更加稳健和节能。