不连续神经网络多吸引子理论与联想记忆研究

The research on the multiple attractors of discontinuous neural networks has received extensive attention in artificial intelligence, and associative memory of discontinuous neural networks is one of the hot issues in brain-like compution. Combining high-gain output、the perturbed input and memristor, this project establishes the mathematical model of discontinuous neural networks, and studies the problem of the multiple attractors and associative memory of the model. Firstly, aiming at the mathematical model of neural networks, the dynamic scheme of segmentation is proposed in the state space, and a series of criteria on attractors are established by using nonsmooth analysis and Filippov's theory to explore the stability and convergence of the multiple attractors, which develop the theory and method of the attractors of neural networks. Secondly, aiming at associative memory of neural networks, the new scheme of multi-mode sequence is proposed to partially solve the problems of excessive pseudo-mode and low fault tolerance of neural networks, which provides theoretical and technical support for exploring a new architecture of high-speed storage and large-capacity associative memory system. The results of this project, on the one hand, will provide the new idea for the research on attractors of discontinuous neural networks; on the other hand, it provides a new method for brain-like compution in the design of dynamic associative memory.

不连续神经网络多吸引子研究在人工智能领域受到广泛关注，其联想记忆是类脑计算领域的一个热点问题。本项目结合高增益的输出、扰动输入和忆阻，建立不连续神经网络数学模型，研究模型的多吸引子和联想记忆问题。首先，针对神经网络数学模型，拟提出状态空间的动态分割方案，利用非光滑分析和Filippov理论，建立一系列多吸引子判据，探索多吸引子的稳定性和收敛性，发展神经网络多吸引子理论和方法。然后，针对联想记忆的神经网络，拟提出多模式序列设计新方案，部分解决网络的伪模式过量和容错能力过低等问题，为探索全新构架的高速存储和大容量的联想记忆系统提供理论与技术支撑。本项目的成果，一方面为不连续神经网络多吸引子的研究提供新思路；另一方面为类脑计算在动态联想记忆的设计方面提供新方法。

由于神经网络的参数切换、信号传输的跳变及运算放大器的有限切换速度不一致等因素，不连续神经网络是客观存在的。与不连续神经网络的单吸引子研究相比，多吸引子作为网络的重要特征且呈现出复杂的动力学行为。本项目针对不连续神经网络，利用Filippov微分包含、集值映射原理、动力学分析方法、不动点理论等工具研究了神经网络吸引子的局部稳定性、吸引性、镇定与同步、鲁棒有界性等, 这些动力学分析结果为神经网络电路系统的应用奠定了理论基础。基于状态空间的动态分割方案，提出了混合单调方法，建立了多吸引子共存判据，揭示了分割集的顶点、边和超平面之间的联系。构建了比较原理，推广了整数阶神经网络的Gronwall不等式; 提出了吸引子的稳定性和收敛性准则，扩大了网络的吸引域; 估计了吸引域的范围，丰富了多吸引子的分析方法。利用获得的神经网络的多吸引子理论，提出了可联想网络的模式记忆新方案，实现了黑白条纹的设计，为神经网络的联想记忆研究提供了新思路。依托本项目，我们发表 SCI 源论文 5 篇和 EI 论文 1 篇，其中 IEEE Trans 论文4 篇，包括 IEEE Transactions on Cybernetics 一篇, IEEE Transactions on Neural Networks and Learning Systems 二篇, IEEE Transactions on Systems, Man, and Cybernetics: Systems 一篇。