He Lyu

Avrajit Ghosh, He Lyu, Xitong Zhang et al.

It is well known that the finite step-size ($h$) in Gradient Descent (GD) implicitly regularizes solutions to flatter minima. A natural question to ask is "Does the momentum parameter $β$ play a role in implicit regularization in Heavy-ball (H.B) momentum accelerated gradient descent (GD+M)?". To answer this question, first, we show that the discrete H.B momentum update (GD+M) follows a continuous trajectory induced by a modified loss, which consists of an original loss and an implicit regularizer. Then, we show that this implicit regularizer for (GD+M) is stronger than that of (GD) by factor of $(\frac{1+β}{1-β})$, thus explaining why (GD+M) shows better generalization performance and higher test accuracy than (GD). Furthermore, we extend our analysis to the stochastic version of gradient descent with momentum (SGD+M) and characterize the continuous trajectory of the update of (SGD+M) in a pointwise sense. We explore the implicit regularization in (SGD+M) and (GD+M) through a series of experiments validating our theory.

He Lyu, Huolin Zeng, Junren Wang et al.

Real-world clinical data is inherently multimodal, providing complementary evidence that mirrors the practical necessity of jointly assessing multiple related outcomes. Although multi-task learning can improve efficiency by sharing information across outcomes, existing approaches often fail to balance shared representation learning with outcome-specific modeling. Hard parameter sharing can trigger negative transfer when task gradients conflict, while flexible sharing may still entangle shared and task-specific signals. To address this, we propose a multi-task framework built on a unified Transformer for multimodal fusion, augmented with Orthogonal Task Decomposition (OrthTD) to split patient representations into shared and task-specific subspaces and impose a geometric orthogonality constraint to reduce redundancy and isolate task-specific signals. We evaluated OrthTD on a real-world cohort of 12,430 surgical patients for predicting four outcomes. OrthTD achieved average AUC (area under the receiver operating characteristic curve) of 87.5% and average AUPRC (area under the precision-recall curve) of 37.2%, consistently outperformed advanced tabular and multi-task methods. Notably, OrthTD achieves substantial gains in AUPRC, indicating superior performance in identifying rare events within imbalanced clinical data. These results suggest that enforcing non-redundant shared and task-specific representations can improve multi-outcome prediction from multimodal clinical data.

Xikun Jiang, He Lyu, Chenhao Ying et al.

With the increasingly widespread application of machine learning, how to strike a balance between protecting the privacy of data and algorithm parameters and ensuring the verifiability of machine learning has always been a challenge. This study explores the intersection of reinforcement learning and data privacy, specifically addressing the Multi-Armed Bandit (MAB) problem with the Upper Confidence Bound (UCB) algorithm. We introduce zkUCB, an innovative algorithm that employs the Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARKs) to enhance UCB. zkUCB is carefully designed to safeguard the confidentiality of training data and algorithmic parameters, ensuring transparent UCB decision-making. Experiments highlight zkUCB's superior performance, attributing its enhanced reward to judicious quantization bit usage that reduces information entropy in the decision-making process. zkUCB's proof size and verification time scale linearly with the execution steps of zkUCB. This showcases zkUCB's adept balance between data security and operational efficiency. This approach contributes significantly to the ongoing discourse on reinforcing data privacy in complex decision-making processes, offering a promising solution for privacy-sensitive applications.

He Lyu, Ningyu Sha, Shuyang Qin et al.

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets.