Spiking neural network (SNN) is studied in multidisciplinary domains to (i)
enable order-of-magnitudes energy-efficient AI inference and (ii)
computationally simulate neuro-scientific mechanisms. The lack of discrete
theory obstructs the practical application of SNN by limiting its performance
and nonlinearity support. We present a new optimization-theoretic perspective
of the discrete dynamics of spiking neurons. We prove that a discrete dynamical
system of simple integrate-and-fire models approximates the sub-gradient method
over unconstrained optimization problems. We practically extend our theory to
introduce a novel sign gradient descent (signGD)-based neuronal dynamics that
can (i) approximate diverse nonlinearities beyond ReLU and (ii) advance
ANN-to-SNN conversion performance in low time steps. Experiments on large-scale
datasets show that our technique achieves (i) state-of-the-art performance in
ANN-to-SNN conversion and (ii) is the first to convert new DNN architectures,
e.g., ConvNext, MLP-Mixer, and ResMLP. We publicly share our source code at
this https URL .

离散动力学的一个新的优化理论视角证明了一个基本的集成和发射模型的离散动力系统能够近似于无约束优化问题的次梯度方法，这一理论的实际扩展引入了一种基于符号梯度下降的神经元动力学，可以近似于 ReLU 之外的多种非线性并提高 ANN 到 SNN 转换性能。通过在大型数据集上的实验证明，我们的技术在 ANN 到 SNN 的转换中取得了最先进的性能，并且首次转换了新的 DNN 架构，例如 ConvNext、MLP-Mixer 和 ResMLP。

基于梯度下降的神经元动力学：超越 ReLU 网络的 ANN 到 SNN 转换

Sign Gradient Descent-based Neuronal Dynamics: ANN-to-SNN Conversion  Beyond ReLU Network

The dynamics of affective decision making is considered for an intelligent
network composed of agents with different types of memory: long-term and
short-term memory. The consideration is based on probabilistic affective
decision theory, which takes into account the rational utility of alternatives
as well as the emotional alternative attractiveness. The objective of this
paper is the comparison of two multistep operational algorithms of the
intelligent network: one based on discrete dynamics and the other on continuous
dynamics. By means of numerical analysis, it is shown that, depending on the
network parameters, the characteristic probabilities for continuous and
discrete operations can exhibit either close or drastically different behavior.
Thus, depending on which algorithm is employed, either discrete or continuous,
theoretical predictions can be rather different, which does not allow for a
uniquely defined description of practical problems. This finding is important
for understanding which of the algorithms is more appropriate for the correct
analysis of decision-making tasks. A discussion is given, revealing that the
discrete operation seems to be more realistic for describing intelligent
networks as well as affective artificial intelligence.

该研究使用概率情感决策理论，考虑了长期记忆和短期记忆的智能网络中情感决策的动态，比较了基于离散动力学和连续动力学的两种多步操作算法，结果表明它们可能表现出相似或截然不同的特征概率，这揭示了离散操作更适合描述智能网络和情感人工智能。