Chenguang Liu

Kexin Jin, Jonas Latz, Chenguang Liu et al.

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become particularly widespread. The stochasticity arises from data subsampling which reduces computational cost. Both, momentum and stochasticity help the algorithm to converge globally. In this work, we propose and analyse a continuous-time model for stochastic gradient descent with momentum. This model is a piecewise-deterministic Markov process that represents the optimiser by an underdamped dynamical system and the data subsampling through a stochastic switching. We investigate longtime limits, the subsampling-to-no-subsampling limit, and the momentum-to-no-momentum limit. We are particularly interested in the case of reducing the momentum over time. Under convexity assumptions, we show convergence of our dynamical system to the global minimiser when reducing momentum over time and letting the subsampling rate go to infinity. We then propose a stable, symplectic discretisation scheme to construct an algorithm from our continuous-time dynamical system. In experiments, we study our scheme in convex and non-convex test problems. Additionally, we train a convolutional neural network in an image classification problem. Our algorithm {attains} competitive results compared to stochastic gradient descent with momentum.

Chenguang Liu, Chisheng Wang, Feifei Dong et al.

Edge detection is a long-standing problem in computer vision. Despite the efficiency of existing algorithms, their performance, however, rely heavily on the pre-trained weights of the backbone network on the ImageNet dataset. The use of pre-trained weights in previous methods significantly increases the difficulty to design new models for edge detection without relying on existing well-trained ImageNet models, as pre-training the model on the ImageNet dataset is expensive and becomes compulsory to ensure the fairness of comparison. Besides, the pre-training and fine-tuning strategy is not always useful and sometimes even inaccessible. For instance, the pre-trained weights on the ImageNet dataset are unlikely to be helpful for edge detection in Synthetic Aperture Radar (SAR) images due to strong differences in the statistics between optical images and SAR images. Moreover, no dataset has comparable size to the ImageNet dataset for SAR image processing. In this work, we study the performance achievable by state-of-the-art deep learning based edge detectors in publicly available datasets when they are trained from scratch, and devise a new network architecture, the multi-stream and multi-scale fusion net (msmsfnet), for edge detection. We show in our experiments that by training all models from scratch, our model outperforms state-of-the-art edge detectors in three publicly available datasets. We also demonstrate the efficiency of our model for edge detection in SAR images, where no useful pre-trained weight is available. Finally, We show that our model is able to achieve competitive performance on the BSDS500 dataset when the pre-trained weights are used.

Kexin Jin, Jonas Latz, Chenguang Liu et al.

Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target functions - integrated with respect to a probability measure. Such problems can often be solved by stochastic optimization methods: performing optimization steps with respect to the indexed target function with randomly switched indices. In this work, we study a continuous-time variant of the stochastic gradient descent algorithm for optimization problems with continuous data. This so-called stochastic gradient process consists in a gradient flow minimizing an indexed target function that is coupled with a continuous-time index process determining the index. Index processes are, e.g., reflected diffusions, pure jump processes, or other Lévy processes on compact spaces. Thus, we study multiple sampling patterns for the continuous data space and allow for data simulated or streamed at runtime of the algorithm. We analyze the approximation properties of the stochastic gradient process and study its longtime behavior and ergodicity under constant and decreasing learning rates. We end with illustrating the applicability of the stochastic gradient process in a polynomial regression problem with noisy functional data, as well as in a physics-informed neural network.