Realtime MEG source localization

Iterative gradient methods like Levenberg-Marquardt (LM) are in widespread use for source localization from electroencephalographic (EEG) and magnetoencephalographic (MEG) signals. Unfortunately LM depends sensitively on the initial guess, particularly (and counterintuitively) at higher signal-to-noise ratios, necessitating repeated runs. This, combined with LM's high per-step cost, makes its computational burden quite high. To reduce this burden, we trained a multilayer perceptron (MLP) as a real-time localizer. We used an analytical model of quasistatic electromagnetic propagation through the head to map randomly chosen dipoles to sensor activities, and trained an MLP to invert this mapping in the presence of various sorts of noise. With realistic noise, our MLP is about five hundred times faster than n-start-LM with n = 4 to match accuracies, while our hybrid MLP-start-LM is about four times more accurate and thirteen times faster than 4-start-LM

Realtime MEG source localization

Iterative gradient methods like Levenberg-Marquardt (LM) are in widespread use for source localization from electroencephalographic (EEG) and magnetoencephalographic (MEG) signals. Unfortunately LM depends sensitively on the initial guess, particularly (and counterintuitively) at higher signal-to-noise ratios, necessitating repeated runs. This, combined with LM's high per-step cost, makes its computational burden quite high. To reduce this burden, we trained a multilayer perceptron (MLP) as a real-time localizer. We used an analytical model of quasistatic electromagnetic propagation through the head to map randomly chosen dipoles to sensor activities, and trained an MLP to invert this mapping in the presence of various sorts of noise. With realistic noise, our MLP is about five hundred times faster than n-start-LM with n = 4 to match accuracies, while our hybrid MLP-start-LM is about four times more accurate and thirteen times faster than 4-start-LM

Unleashing the Potential of Regularization Strategies in Learning with Noisy Labels

In recent years, research on learning with noisy labels has focused on devising novel algorithms that can achieve robustness to noisy training labels while generalizing to clean data. These algorithms often incorporate sophisticated techniques, such as noise modeling, label correction, and co-training. In this study, we demonstrate that a simple baseline using cross-entropy loss, combined with widely used regularization strategies like learning rate decay, model weights average, and data augmentations, can outperform state-of-the-art methods. Our findings suggest that employing a combination of regularization strategies can be more effective than intricate algorithms in tackling the challenges of learning with noisy labels. While some of these regularization strategies have been utilized in previous noisy label learning research, their full potential has not been thoroughly explored. Our results encourage a reevaluation of benchmarks for learning with noisy labels and prompt reconsideration of the role of specialized learning algorithms designed for training with noisy labels

Fast Robust Subject-Independent Magnetoencephalographic Source Localization Using an Artificial Neural Network

We describe a system that localizes a single dipole to reasonable accuracy from noisy magnetoencephalographic (MEG) measurements in real time. At its core is a multilayer perceptron (MLP) trained to map sensor signals and head position to dipole location. Including head position overcomes the previous need to retrain the MLP for each subject and session. The training dataset was generated by mapping randomly chosen dipoles and head positions through an analytic model and adding noise from real MEG recordings. After training, a localization took 0.7 ms with an average error of 0.90 cm. A few iterations of a Levenberg-Marquardt routine using the MLP output as its initial guess took 15 ms and improved accuracy to 0.53 cm, which approaches the natural limit on accuracy imposed by noise. We applied these methods to localize single dipole sources from MEG components isolated by blind source separation and compared the estimated locations to those generated by standard manually assisted commercial software

Layer-wise Conditioning Analysis in Exploring the Learning Dynamics of DNNs

Conditioning analysis uncovers the landscape of an optimization objective by exploring the spectrum of its curvature matrix. This has been well explored theoretically for linear models. We extend this analysis to deep neural networks (DNNs) in order to investigate their learning dynamics. To this end, we propose layer-wise conditioning analysis, which explores the optimization landscape with respect to each layer independently. Such an analysis is theoretically supported under mild assumptions that approximately hold in practice. Based on our analysis, we show that batch normalization (BN) can stabilize the training, but sometimes result in the false impression of a local minimum, which has detrimental effects on the learning. Besides, we experimentally observe that BN can improve the layer-wise conditioning of the optimization problem. Finally, we find that the last linear layer of a very deep residual network displays ill-conditioned behavior. We solve this problem by only adding one BN layer before the last linear layer, which achieves improved performance over the original and pre-activation residual networks.Comment: Accepted to ECCV 2020. The code is available at: https://github.com/huangleiBuaa/LayerwiseC

Theoretical Characterization of the Generalization Performance of Overfitted Meta-Learning

Meta-learning has arisen as a successful method for improving training performance by training over many similar tasks, especially with deep neural networks (DNNs). However, the theoretical understanding of when and why overparameterized models such as DNNs can generalize well in meta-learning is still limited. As an initial step towards addressing this challenge, this paper studies the generalization performance of overfitted meta-learning under a linear regression model with Gaussian features. In contrast to a few recent studies along the same line, our framework allows the number of model parameters to be arbitrarily larger than the number of features in the ground truth signal, and hence naturally captures the overparameterized regime in practical deep meta-learning. We show that the overfitted min $\ell_2$-norm solution of model-agnostic meta-learning (MAML) can be beneficial, which is similar to the recent remarkable findings on ``benign overfitting'' and ``double descent'' phenomenon in the classical (single-task) linear regression. However, due to the uniqueness of meta-learning such as task-specific gradient descent inner training and the diversity/fluctuation of the ground-truth signals among training tasks, we find new and interesting properties that do not exist in single-task linear regression. We first provide a high-probability upper bound (under reasonable tightness) on the generalization error, where certain terms decrease when the number of features increases. Our analysis suggests that benign overfitting is more significant and easier to observe when the noise and the diversity/fluctuation of the ground truth of each training task are large. Under this circumstance, we show that the overfitted min $\ell_2$-norm solution can achieve an even lower generalization error than the underparameterized solution