Yuncheng Gao

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.

Chen Qian, Haoyu Zhang, Yuncheng Gao et al.

Diffusion magnetic resonance imaging (MRI) is the only imaging modality for non-invasive movement detection of in vivo water molecules, with significant clinical and research applications. Diffusion weighted imaging (DWI) MRI acquired by multi-shot techniques can achieve higher resolution, better signal-to-noise ratio, and lower geometric distortion than single-shot, but suffers from inter-shot motion-induced artifacts. These artifacts cannot be removed prospectively, leading to the absence of artifact-free training labels. Thus, the potential of deep learning in multi-shot DWI reconstruction remains largely untapped. To break the training data bottleneck, here, we propose a Physics-Informed Deep DWI reconstruction method (PIDD) to synthesize high-quality paired training data by leveraging the physical diffusion model (magnitude synthesis) and inter-shot motion-induced phase model (motion phase synthesis). The network is trained only once with 100,000 synthetic samples, achieving encouraging results on multiple realistic in vivo data reconstructions. Advantages over conventional methods include: (a) Better motion artifact suppression and reconstruction stability; (b) Outstanding generalization to multi-scenario reconstructions, including multi-resolution, multi-b-value, multi-under-sampling, multi-vendor, and multi-center; (c) Excellent clinical adaptability to patients with verifications by seven experienced doctors (p<0.001). In conclusion, PIDD presents a novel deep learning framework by exploiting the power of MRI physics, providing a cost-effective and explainable way to break the data bottleneck in deep learning medical imaging.