Yihui Huang

Jian Cao, Chen Qian, Yihui Huang et al.

Implicit regularization is an important way to interpret neural networks. Recent theory starts to explain implicit regularization with the model of deep matrix factorization (DMF) and analyze the trajectory of discrete gradient dynamics in the optimization process. These discrete gradient dynamics are relatively small but not infinitesimal, thus fitting well with the practical implementation of neural networks. Currently, discrete gradient dynamics analysis has been successfully applied to shallow networks but encounters the difficulty of complex computation for deep networks. In this work, we introduce another discrete gradient dynamics approach to explain implicit regularization, i.e. landscape analysis. It mainly focuses on gradient regions, such as saddle points and local minima. We theoretically establish the connection between saddle point escaping (SPE) stages and the matrix rank in DMF. We prove that, for a rank-R matrix reconstruction, DMF will converge to a second-order critical point after R stages of SPE. This conclusion is further experimentally verified on a low-rank matrix reconstruction problem. This work provides a new theory to analyze implicit regularization in deep learning.

Dicheng Chen, Wanqi Hu, Huiting Liu et al.

Magnetic Resonance Spectroscopy (MRS) is a noninvasive tool to reveal metabolic information. One challenge of 1H-MRS is the low Signal-Noise Ratio (SNR). To improve the SNR, a typical approach is to perform Signal Averaging (SA) with M repeated samples. The data acquisition time, however, is increased by M times accordingly, and a complete clinical MRS scan takes approximately 10 minutes at a common setting M=128. Recently, deep learning has been introduced to improve the SNR but most of them use the simulated data as the training set. This may hinder the MRS applications since some potential differences, such as acquisition system imperfections, and physiological and psychologic conditions may exist between the simulated and in vivo data. Here, we proposed a new scheme that purely used the repeated samples of realistic data. A deep learning model, Refusion Long Short-Term Memory (ReLSTM), was designed to learn the mapping from the low SNR time-domain data (24 SA) to the high SNR one (128 SA). Experiments on the in vivo brain spectra of 7 healthy subjects, 2 brain tumor patients and 1 cerebral infarction patient showed that only using 20% repeated samples, the denoised spectra by ReLSTM could provide comparable estimated concentrations of metabolites to 128 SA. Compared with the state-of-the-art low-rank denoising method, the ReLSTM achieved the lower relative error and the Cramér-Rao lower bounds in quantifying some important biomarkers. In summary, ReLSTM can perform high-fidelity denoising of the spectra under fast acquisition (24 SA), which would be valuable to MRS clinical studies.

Xiaobo Qu, Yihui Huang, Hengfa Lu et al.

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental time. We present a proof-of-concept of application of deep learning and neural network for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signal, which lifts the prohibiting demand for a large volume of realistic training data usually required in the deep learning approach.