Deep Learning Optimization Using Self-Adaptive Weighted Auxiliary Variables

In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning because of the high non-convexity of loss functions and the vanishing gradient issue. Our idea is to introduce auxiliary variables to separate the layers of the deep neural networks and reformulate the loss functions for ease of optimization. We design the self-adaptive weights to preserve the consistency between the reformulated loss and the original mean squared loss, which guarantees that optimizing the new loss helps optimize the original problem. Numerical experiments are presented to verify the consistency and show the effectiveness and robustness of our models over gradient descent.

Convolutional Neural Networks with A Topographic Representation Module for EEG-Based Brain-Computer Interfaces

Objective: Convolutional Neural Networks (CNNs) have shown great potential in the field of Brain-Computer Interfaces (BCIs). The raw Electroencephalogram (EEG) signal is usually represented as 2-Dimensional (2-D) matrix composed of channels and time points, which ignores the spatial topological information. Our goal is to make the CNN with the raw EEG signal as input have the ability to learn EEG spatial topological features, and improve its performance while essentially maintaining its original structure. Methods:We propose an EEG Topographic Representation Module (TRM). This module consists of (1) a mapping block from the raw EEG signal to a 3-D topographic map and (2) a convolution block from the topographic map to an output of the same size as input. According to the size of the kernel used in the convolution block, we design 2 types of TRMs, namely TRM-(5,5) and TRM-(3,3). We embed the TRM into 3 widely used CNNs, and tested them on 2 publicly available datasets (Emergency Braking During Simulated Driving Dataset (EBDSDD), and High Gamma Dataset (HGD)). Results: The results show that the classification accuracies of all 3 CNNs are improved on both datasets after using the TRM. With TRM-(5,5), the average accuracies of DeepConvNet, EEGNet and ShallowConvNet are improved by 6.54%, 1.72% and 2.07% on EBDSDD, and by 6.05%, 3.02% and 5.14% on HGD, respectively; with TRM-(3,3), they are improved by 7.76%, 1.71% and 2.17% on EBDSDD, and by 7.61%, 5.06% and 6.28% on HGD, respectively. Significance: We improve the classification performance of 3 CNNs on 2 datasets by the use of TRM, indicating that it has the capability to mine the EEG spatial topological information. In addition, since the output of TRM has the same size as the input, CNNs with the raw EEG signal as input can use this module without changing their original structures.