Analysis and Design of Multivalued High-Capacity Associative Memories Based on Delayed Recurrent Neural Networks
研究了基于异步和分布式延迟递归神经网络的多值高容量联想记忆，通过引入多值激活函数提高存储容量，并给出保证平衡点存在唯一性和全局指数稳定性的条件。
This article aims at analyzing and designing the multivalued high-capacity-associative memories based on recurrent neural networks with both asynchronous and distributed delays. In order to increase storage capacities, multivalued activation functions are introduced into associative memories. The stored patterns are retrieved by external input vectors instead of initial conditions, which can guarantee accurate associative memories by avoiding spurious equilibrium points. Some sufficient conditions are proposed to ensure the existence, uniqueness, and global exponential stability of the equilibrium point of neural networks with mixed delays. For neural networks with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> neurons, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional input vectors, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${2k}$ </tex-math></inline-formula> -valued activation functions, the autoassociative memories have <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${(2k)^{n}}$ </tex-math></inline-formula> storage capacities and heteroassociative memories have min <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\{(2k)^{n},(2k)^{m}\}}$ </tex-math></inline-formula> storage capacities. That is, the storage capacities of designed associative memories in this article are obviously higher than the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${2^{n}}$ </tex-math></inline-formula> and min <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\{2^{n},2^{m}\}}$ </tex-math></inline-formula> storage capacities of the conventional ones. Three examples are given to support the theoretical results.