Lu Wenhao, Leung Chi-Sing, Sum John, Xiao Yi
IEEE Trans Neural Netw Learn Syst. 2022 Jul;33(7):3184-3192. doi: 10.1109/TNNLS.2021.3050493. Epub 2022 Jul 6.
The dual neural network-based k -winner-take-all (DNN- k WTA) is an analog neural model that is used to identify the k largest numbers from n inputs. Since threshold logic units (TLUs) are key elements in the model, offset voltage drifts in TLUs may affect the operational correctness of a DNN- k WTA network. Previous studies assume that drifts in TLUs follow some particular distributions. This brief considers that only the drift range, given by [-∆, ∆] , is available. We consider two drift cases: time-invariant and time-varying. For the time-invariant case, we show that the state of a DNN- k WTA network converges. The sufficient condition to make a network with the correct operation is given. Furthermore, for uniformly distributed inputs, we prove that the probability that a DNN- k WTA network operates properly is greater than (1-2∆) . The aforementioned results are generalized for the time-varying case. In addition, for the time-invariant case, we derive a method to compute the exact convergence time for a given data set. For uniformly distributed inputs, we further derive the mean and variance of the convergence time. The convergence time results give us an idea about the operational speed of the DNN- k WTA model. Finally, simulation experiments have been conducted to validate those theoretical results.
基于双神经网络的k胜者全得（DNN-k WTA）是一种模拟神经模型，用于从n个输入中识别出k个最大的数。由于阈值逻辑单元（TLU）是该模型的关键元件，TLU中的失调电压漂移可能会影响DNN-k WTA网络的运行正确性。先前的研究假设TLU中的漂移遵循某些特定分布。本简报认为，仅已知由[-∆, ∆]给出的漂移范围。我们考虑两种漂移情况：时不变和时变。对于时不变情况，我们证明了DNN-k WTA网络的状态会收敛。给出了使网络正确运行的充分条件。此外，对于均匀分布的输入，我们证明了DNN-k WTA网络正确运行的概率大于(1 - 2∆)。上述结果被推广到时变情况。另外，对于时不变情况，我们推导了一种计算给定数据集精确收敛时间的方法。对于均匀分布的输入，我们进一步推导了收敛时间的均值和方差。收敛时间结果让我们了解了DNN-k WTA模型的运行速度。最后，进行了仿真实验以验证这些理论结果。
