A TECHNIQUE FOR ANALYZING NEURAL NETWORKS IN TERMS OF TERNARY LOGIC
A TECHNIQUE FOR ANALYZING NEURAL NETWORKS IN TERMS OF TERNARY LOGIC
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一种用三元逻辑分析神经网络的技术
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通讯作者：
N. Tomova
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作者：
A. Karpenko;N. Tomova
有一类广泛的神经网络，其功能可以用二进制逻辑来描述：描述输入状态的一组逻辑变量与表征输出状态的一组逻辑变量相关联。这种网络可以用逻辑函数来描述，特别是通过哲加尔金多项式来描述。这对神经元权重的可变性施加了显著的限制。从克服关于神经网络逻辑不透明度的论文的角度来看，这一事实具有重要的意义，该论文与最常见的神经网络训练方法有关，这些方法实际上是计算机实验的结果。因此，可以认为神经科学主要是一门经验科学，唯一的区别是它的基础不是实验室，而是计算机实验。克服神经网络逻辑不透明度的一个重要步骤是建立对权系数的可变性的限制，即证明事实上神经元只能执行可以简化为逻辑操作的有限集合的操作。与此同时，没有理由断言人工神经网络必须建立在二进制逻辑装置的基础上。本文指出，三值逻辑的应用与神经网络运算的几何解释相结合，使我们能够揭示神经网络权系数的变异性存在着比严格的限制更多的限制。对具有四个输入的神经元进行了详尽的描述，说明了所提出的方法如何扩展到具有任意数目的输入的神经元的分析。
There is an extensive class of neural networks, the functioning of which can be described in terms of binary logic: a set of logical variables describing the state of the inputs is associated with a set of logical variables characterizing the state of the outputs. Such networks can be described in terms of logical functions, in particular, through the Zhegalkin polynomial. This imposes significant restrictions on the variability of the neuron weights. This fact is of significant interest from the point of view of overcoming the thesis about the logical opacity of neural networks, which is associated with the most common approaches to training neural networks, which are actually the results of computer experiments. Therefore, it can be considered that neuroscience is predominantly an empirical science, with the only difference that its foundations are not laboratory, but computer experiments. An important step towards overcoming the thesis about the logical opacity of neural networks is to establish restrictions on the variability of the weight coefficients, i.e. proof of the fact that in reality neurons can perform only a limited set of operations that can be reduced to logical ones. At the same time, there is no reason to assert that artificial neural networks must necessarily be built on the basis of the apparatus of binary logic. This paper shows that appliance of ternary logic in combination with a geometric interpretation of the operation of neural networks allows us to reveal the existence of more than strict restrictions on the variability of the weight coefficients of a neural network. An exhaustive description of a neuron with four inputs, which shows how the proposed approach can be extended to the analysis of neurons with an arbitrary number of inputs.