Hongchao Li

Liu Ziyin, Hongchao Li, Masahito Ueda · mit

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this work, we show that the minibatch noise of SGD regularizes the solution towards a noise-balanced solution whenever the loss function contains a rescaling parameter symmetry. Because the difference between a simple diffusion process and SGD dynamics is the most significant when symmetries are present, our theory implies that the loss function symmetries constitute an essential probe of how SGD works. We then apply this result to derive the stationary distribution of stochastic gradient flow for a diagonal linear network with arbitrary depth and width. The stationary distribution exhibits complicated nonlinear phenomena such as phase transitions, broken ergodicity, and fluctuation inversion. These phenomena are shown to exist uniquely in deep networks, implying a fundamental difference between deep and shallow models.

Liu Ziyin, Mingze Wang, Hongchao Li et al. · mit

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries -- a broad subclass of continuous symmetries present in the model architecture or loss function -- interplay with stochastic gradient descent (SGD). We first prove that gradient noise creates a systematic motion (a ``Noether flow") of the parameters $θ$ along the degenerate direction to a unique initialization-independent fixed point $θ^*$. These points are referred to as the {\it noise equilibria} because, at these points, noise contributions from different directions are balanced and aligned. Then, we show that the balance and alignment of gradient noise can serve as a novel alternative mechanism for explaining important phenomena such as progressive sharpening/flattening and representation formation within neural networks and have practical implications for understanding techniques like representation normalization and warmup.

Hongchao Li, Xianmin Lin, Aihua Zheng et al.

Vehicle Re-ID has recently attracted enthusiastic attention due to its potential applications in smart city and urban surveillance. However, it suffers from large intra-class variation caused by view variations and illumination changes, and inter-class similarity especially for different identities with the similar appearance. To handle these issues, in this paper, we propose a novel deep network architecture, which guided by meaningful attributes including camera views, vehicle types and colors for vehicle Re-ID. In particular, our network is end-to-end trained and contains three subnetworks of deep features embedded by the corresponding attributes (i.e., camera view, vehicle type and vehicle color). Moreover, to overcome the shortcomings of limited vehicle images of different views, we design a view-specified generative adversarial network to generate the multi-view vehicle images. For network training, we annotate the view labels on the VeRi-776 dataset. Note that one can directly adopt the pre-trained view (as well as type and color) subnetwork on the other datasets with only ID information, which demonstrates the generalization of our model. Extensive experiments on the benchmark datasets VeRi-776 and VehicleID suggest that the proposed approach achieves the promising performance and yields to a new state-of-the-art for vehicle Re-ID.

Patrick Bilic, Patrick Christ, Hongwei Bran Li et al.

In this work, we report the set-up and results of the Liver Tumor Segmentation Benchmark (LiTS), which was organized in conjunction with the IEEE International Symposium on Biomedical Imaging (ISBI) 2017 and the International Conferences on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2017 and 2018. The image dataset is diverse and contains primary and secondary tumors with varied sizes and appearances with various lesion-to-background levels (hyper-/hypo-dense), created in collaboration with seven hospitals and research institutions. Seventy-five submitted liver and liver tumor segmentation algorithms were trained on a set of 131 computed tomography (CT) volumes and were tested on 70 unseen test images acquired from different patients. We found that not a single algorithm performed best for both liver and liver tumors in the three events. The best liver segmentation algorithm achieved a Dice score of 0.963, whereas, for tumor segmentation, the best algorithms achieved Dices scores of 0.674 (ISBI 2017), 0.702 (MICCAI 2017), and 0.739 (MICCAI 2018). Retrospectively, we performed additional analysis on liver tumor detection and revealed that not all top-performing segmentation algorithms worked well for tumor detection. The best liver tumor detection method achieved a lesion-wise recall of 0.458 (ISBI 2017), 0.515 (MICCAI 2017), and 0.554 (MICCAI 2018), indicating the need for further research. LiTS remains an active benchmark and resource for research, e.g., contributing the liver-related segmentation tasks in \url{http://medicaldecathlon.com/}. In addition, both data and online evaluation are accessible via \url{www.lits-challenge.com}.