Shi Chen

Shi Chen, Qin Li, Oliver Tse et al.

The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within Euclidean space, the need to optimize over spaces of probability measures in machine learning motivates exploration of accelerated gradient methods in this context too. To this end, we introduce a Hamiltonian-flow approach analogous to momentum-based approaches in Euclidean space. We demonstrate that, in the continuous-time setting, algorithms based on this approach can achieve convergence rates of arbitrarily high order. We complement our findings with numerical examples.

Yifei Yuan, Chen Shi, Runze Wang et al.

Generative query rewrite generates reconstructed query rewrites using the conversation history while rely heavily on gold rewrite pairs that are expensive to obtain. Recently, few-shot learning is gaining increasing popularity for this task, whereas these methods are sensitive to the inherent noise due to limited data size. Besides, both attempts face performance degradation when there exists language style shift between training and testing cases. To this end, we study low-resource generative conversational query rewrite that is robust to both noise and language style shift. The core idea is to utilize massive unlabeled data to make further improvements via a contrastive co-training paradigm. Specifically, we co-train two dual models (namely Rewriter and Simplifier) such that each of them provides extra guidance through pseudo-labeling for enhancing the other in an iterative manner. We also leverage contrastive learning with data augmentation, which enables our model pay more attention on the truly valuable information than the noise. Extensive experiments demonstrate the superiority of our model under both few-shot and zero-shot scenarios. We also verify the better generalization ability of our model when encountering language style shift.

Zhiyan Ding, Shi Chen, Qin Li et al.

Finding the optimal configuration of parameters in ResNet is a nonconvex minimization problem, but first-order methods nevertheless find the global optimum in the overparameterized regime. We study this phenomenon with mean-field analysis, by translating the training process of ResNet to a gradient-flow partial differential equation (PDE) and examining the convergence properties of this limiting process. The activation function is assumed to be $2$-homogeneous or partially $1$-homogeneous; the regularized ReLU satisfies the latter condition. We show that if the ResNet is sufficiently large, with depth and width depending algebraically on the accuracy and confidence levels, first-order optimization methods can find global minimizers that fit the training data.