多层前馈神经网络信号放大的研究

The ability of amplifying weak signals is a fundamental mechanism of nervous systems. However, which neural network structure supports such amplification is not well known yet. Previous studies have paid more attention to the single layer neural networks constituted by monostable neurons, ignoring two important features of real neural networks: multilayer feedforward structure and neuronal bistability. The former means signals are unidirectional processed through different functional layers in neural networks, while the latter denotes that certain types of neurons participating signal processing exhibit two stable resting states. Based on these two features, this project aims to propose a specific type of neural networks constituted by bistable neurons with multilayer feedforward structure, in which the signal is processed only in one direction starting from the first input layer and arriving at the final output layer via a series of intermediate layers. Based on the multilayer feedforward neural networks, the project examines the impacts of the multilayer feedforward structure and neuronal bistability on signal amplification so as to figure out the conditions under which a weak input signal could be amplified in the output layer, thereby proposing a new mechanism of signal amplification which only relies on the specific network structure and the feature of neuron itself. In addition, the robustness of this mechanism will be checked by studying the influences of noise and neuron failures. This project might help to understand not only the relationship of the function-structure of networks，but also the ability of signal processing in biological systems.

信号放大是生物神经系统的一项重要功能，但是何种神经网络结构支持这一功能尚未清楚。已知的工作集中在由单稳态神经元构成的单层神经网络，忽视了真实神经网络的两个重要特点：层级结构和神经元双稳性。前者是指信号在处理过程中会依次经过不同的功能层，后者则指负责信号处理的部分神经元存在两个稳定的休息态。鉴于此，本项目拟提出一种由双稳态神经元构成的多层前馈神经网络，其中信号由输入层输入，经若干中间层单向传输至输出层输出。通过研究多层前馈结构和神经元双稳性对信号放大的影响，找出在何种网络条件下输入的信号会在输出层放大输出，其目的在于提出一种基于网络拓扑结构和神经元自身特性的信号放大机制。进一步，项目还将从噪声以及网络中部分神经元病死入手研究信号放大机制的鲁棒性。本项目的研究可加深对网络功能与网络结构之间关系的理解，也可为认识生物的信号放大本领提供新思路。

本项目致力于提出一种新的基于网络结构和神经元自身特性的信号放大机制，着重从理论上分析所提机制的工作原理，并探讨这一机制的鲁棒性。目前已完成的研究内容基本涵盖项目的预期研究目标。在本项目的资助下，项目申请人及项目组成员围绕课题目标主要做了以下方面的工作：1）构造了由双稳态振子组成的Y-型单向链，发现弱信号可在该链上放大传输，且放大效果对噪声具有较强的鲁棒性，放大效率优于传统的随机共振信号放大机制；2）基于Y-型单向链的研究结果，提出了若干改进型的简单前馈模体结构，利用这些简单模体可实现弱信号的放大功能；3）揭示一定程度的相位噪声有助于耦合神经元放大亚阈值信号；4）系统地研究了弱耦合诱导混沌阵子进入不同的周期扩展态；5）研究了神经元内禀周期及耦合强度的异质性对生物节律的增强作用。.基于上述研究内容我们取得了较好的研究成果，完成了项目的预期指标。部分理论成果已经发表SCI论文7篇，已投稿1篇论文，准备中论文1篇。项目资助培养硕士生4名。