Zechen Zhang

Zechen Zhang, Haim Sompolinsky

The infinite width limit of random neural networks is known to result in Neural Networks as Gaussian Process (NNGP) (Lee et al. (2018)), characterized by task-independent kernels. It is widely accepted that larger network widths contribute to improved generalization (Park et al. (2019)). However, this work challenges this notion by investigating the narrow width limit of the Bayesian Parallel Branching Neural Network (BPB-NN), an architecture that resembles neural networks with residual blocks. We demonstrate that when the width of a BPB-NN is significantly smaller compared to the number of training examples, each branch exhibits more robust learning due to a symmetry breaking of branches in kernel renormalization. Surprisingly, the performance of a BPB-NN in the narrow width limit is generally superior to or comparable to that achieved in the wide width limit in bias-limited scenarios. Furthermore, the readout norms of each branch in the narrow width limit are mostly independent of the architectural hyperparameters but generally reflective of the nature of the data. We demonstrate such phenomenon primarily in the branching graph neural networks, where each branch represents a different order of convolutions of the graph; we also extend the results to other more general architectures such as the residual-MLP and demonstrate that the narrow width effect is a general feature of the branching networks. Our results characterize a newly defined narrow-width regime for parallel branching networks in general.

Xiran Xu, Bo Wang, Yujie Yan et al.

To investigate the processing of speech in the brain, simple linear models are commonly used to establish a relationship between brain signals and speech features. However, these linear models are ill-equipped to model a highly dynamic and complex non-linear system like the brain. Although non-linear methods with neural networks have been developed recently, reconstructing unseen stimuli from unseen subjects' EEG is still a highly challenging task. This work presents a novel method, ConvConcatNet, to reconstruct mel-specgrams from EEG, in which the deep convolution neural network and extensive concatenation operation were combined. With our ConvConcatNet model, the Pearson correlation between the reconstructed and the target mel-spectrogram can achieve 0.0420, which was ranked as No.1 in the Task 2 of the Auditory EEG Challenge. The codes and models to implement our work will be available on Github: https://github.com/xuxiran/ConvConcatNet

Jie Chen, Yousef Saad, Zechen Zhang

The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a broad look into coarsening techniques that have been successfully deployed in scientific computing and see how similar principles are finding their way in more recent applications related to machine learning. In scientific computing, coarsening plays a central role in algebraic multigrid methods as well as the related class of multilevel incomplete LU factorizations. In machine learning, graph coarsening goes under various names, e.g., graph downsampling or graph reduction. Its goal in most cases is to replace some original graph by one which has fewer nodes, but whose structure and characteristics are similar to those of the original graph. As will be seen, a common strategy in these methods is to rely on spectral properties to define the coarse graph.