Lu Wenhao, Zheng Yuanjin, Leung Chi-Sing
IEEE Trans Neural Netw Learn Syst. 2024 Dec;35(12):18922-18930. doi: 10.1109/TNNLS.2023.3317135. Epub 2024 Dec 2.
Among many -winners-take-all ( WTA) models, the dual-neural network (DNN- WTA) model is with significantly less number of connections. However, for analog realization, noise is inevitable and affects the operational correctness of the WTA process. Most existing results focus on the effect of additive noise. This brief studies the effect of time-varying multiplicative input noise. Two scenarios are considered. The first one is the bounded noise case, in which only the noise range is known. Another one is for the general noise distribution case, in which we either know the noise distribution or have noise samples. For each scenario, we first prove the convergence property of the DNN- WTA model under multiplicative input noise and then provide an efficient method to determine whether a noise-affected DNN- WTA network performs the correct WTA process for a given set of inputs. With the two methods, we can efficiently measure the probability of the network performing the correct WTA process. In addition, for the case of the inputs being uniformly distributed, we derive two closed-form expressions, one for each scenario, for estimating the probability of the model having correct operation. Finally, we conduct simulations to verify our theoretical results.
在众多赢家通吃（WTA）模型中，双神经网络（DNN-WTA）模型的连接数显著更少。然而，对于模拟实现而言，噪声是不可避免的，并且会影响WTA过程的操作正确性。大多数现有结果关注的是加性噪声的影响。本简报研究时变乘性输入噪声的影响。考虑了两种情况。第一种是有界噪声情况，其中仅噪声范围已知。另一种是一般噪声分布情况，其中我们要么知道噪声分布，要么有噪声样本。对于每种情况，我们首先证明乘性输入噪声下DNN-WTA模型的收敛特性，然后提供一种有效方法来确定受噪声影响的DNN-WTA网络对于给定的一组输入是否执行正确的WTA过程。通过这两种方法，我们可以有效地测量网络执行正确WTA过程的概率。此外，对于输入均匀分布的情况，我们针对每种情况推导了两个闭式表达式，用于估计模型正确运行的概率。最后，我们进行仿真以验证我们的理论结果。
