DNN-<i>k</i>WTA With Bounded Random Offset Voltage Drifts in Threshold Logic Units
Wenhao Lu, Chi-Sing Leung, John Sum, Yi Xiao
Abstract
The dual neural network-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -winner-take-all (DNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> WTA) is an analog neural model that is used to identify the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> largest numbers from <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> 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- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> WTA network. Previous studies assume that drifts in TLUs follow some particular distributions. This brief considers that only the drift range, given by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[-\Delta, \Delta]$ </tex-math></inline-formula> , 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- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> 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- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> WTA network operates properly is greater than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(1-2\Delta)^{n}$ </tex-math></inline-formula> . 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- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> WTA model. Finally, simulation experiments have been conducted to validate those theoretical results.