Length of Pseudorandom Binary Sequence Required to Train Artificial Neural Network Without Overfitting

The artificial neural network (ANN) has been applied to the various fields due to its capability to process complicated nonlinear functions involving a large amount of data. A pseudorandom binary sequence (PRBS) is commonly used to train the ANN since the PRBS is easily generated by using a linear feedback shift register and has a correlation function which is peaked at zero delay but is almost zero at other delays. However, when the PRBS length is not sufficiently long (compared to the input size of the ANN), the ANN trained by the PRBS could suffer from the overfitting where the ANN describes the behavior of the training sequence very well, but does poorly on new data inputs. In this paper, we provide a minimum length of the PRBS required by the ANN to avoid the overfitting for a given input size of the ANN. For this purpose, we analyze the minimum length of the input sequence required to estimate the PRBS pattern through theoretical study. These analyses are confirmed by numerical simulation. The findings of this paper would be used to select the PRBS length for training the ANN.