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Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…

How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…

Machine learning training methods depend plentifully and intricately on hyperparameters, motivating automated strategies for their optimisation. Many existing algorithms restart training for each new hyperparameter choice, at considerable…

In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schr\"odinger equation). In this paper, we aim to reduce the generalization error without…

During the last decades, many studies have been dedicated to improving the performance of neural networks, for example, the network architectures, initialization, and activation. However, investigating the importance and effects of…

Traditional CNN models are trained and tested on relatively low resolution images (<300 px), and cannot be directly operated on large-scale images due to compute and memory constraints. We propose Patch Gradient Descent (PatchGD), an…

Optimization with matrix gradient orthogonalization has recently demonstrated impressive results in the training of deep neural networks (Jordan et al., 2024; Liu et al., 2025). In this paper, we provide a theoretical analysis of this…

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic…

Prompt-based continual learning methods fine-tune only a small set of additional learnable parameters while keeping the pre-trained model's parameters frozen. It enables efficient adaptation to new tasks while mitigating the risk of…

Recent paradigms in Random Projection Layer (RPL)-based continual representation learning have demonstrated superior performance when building upon a pre-trained model (PTM). These methods insert a randomly initialized RPL after a PTM to…

We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…

We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a…

In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss…

Gradient-free optimizers allow for tackling problems regardless of the smoothness or differentiability of their objective function, but they require many more iterations to converge when compared to gradient-based algorithms. This has made…

Stochastic gradient descent (SGD) has achieved great success in training deep neural network, where the gradient is computed through back-propagation. However, the back-propagated values of different layers vary dramatically. This…

Fine-tuning pretrained language models (PLMs) for downstream tasks is a large-scale optimization problem, in which the choice of the training algorithm critically determines how well the trained model can generalize to unseen test data,…

Likelihood-based deep generative models (DGMs) have gained significant attention for their ability to approximate the distributions of high-dimensional data. However, these models lack a performance guarantee in assigning higher likelihood…

When evaluating the performance of a pre-trained model transferred to a downstream task, it is imperative to assess not only the in-distribution (ID) accuracy of the downstream model but also its capacity to generalize and identify…

Fine-tuning pretrained self-supervised language models is widely adopted for transfer learning to downstream tasks. Fine-tuning can be achieved by freezing gradients of the pretrained network and only updating gradients of a newly added…