Related papers: Improved Generalization Bound and Learning of Spar…
Deep learning has achieved significant success in single hyperspectral image super-resolution (SHSR); however, the high spectral dimensionality leads to a heavy computational burden, thus making it difficult to deploy in real-time…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning.…
Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…
We initiate the study of data dimensionality reduction, or sketching, for the $q\to p$ norms. Given an $n \times d$ matrix $A$, the $q\to p$ norm, denoted $\|A\|_{q \to p} = \sup_{x \in \mathbb{R}^d \backslash \vec{0}}…
The fundamental learning theory behind neural networks remains largely open. What classes of functions can neural networks actually learn? Why doesn't the trained network overfit when it is overparameterized? In this work, we prove that…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…
Low-Rank Adaptation (LoRA) is a widely adopted parameter-efficient fine-tuning (PEFT) method validated across NLP and CV domains. However, LoRA faces an inherent low-rank bottleneck: narrowing its performance gap with full finetuning…
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…
Averaging iterations of Stochastic Gradient Descent (SGD) have achieved empirical success in training deep learning models, such as Stochastic Weight Averaging (SWA), Exponential Moving Average (EMA), and LAtest Weight Averaging (LAWA).…
The Lottery Ticket Hypothesis (LTH) suggests that over-parameterized neural networks contain sparse subnetworks ("winning tickets") capable of matching full model performance when trained from scratch. With the growing reliance on…
Linear Quadratic Regulators (LQR) achieve enormous successful real-world applications. Very recently, people have been focusing on efficient learning algorithms for LQRs when their dynamics are unknown. Existing results effectively learn to…
The Statistical Learning Theory (SLT) provides the theoretical guarantees for supervised machine learning based on the Empirical Risk Minimization Principle (ERMP). Such principle defines an upper bound to ensure the uniform convergence of…
Low-rank adaptation (LoRA) has emerged as the de facto standard for parameter-efficient fine-tuning (PEFT) of foundation models, enabling the adaptation of billion-parameter networks with minimal computational and memory overhead. Despite…
Fine-tuning large language models (LLMs) on resource-constrained clients remains a challenging problem. Recent works have fused low-rank adaptation (LoRA) techniques with federated fine-tuning to mitigate challenges associated with client…
Deep neural networks (DNNs) for supervised learning can be viewed as a pipeline of the feature extractor (i.e., last hidden layer) and a linear classifier (i.e., output layer) that are trained jointly with stochastic gradient descent (SGD)…
The substantial computational demands of modern large-scale deep learning present significant challenges for efficient training and deployment. Recent research has revealed a widespread phenomenon wherein deep networks inherently learn…
The theory of greedy low-rank learning (GLRL) aims to explain the impressive generalization capabilities of deep learning. It proves that stochastic gradient-based training implicitly regularizes neural networks towards low-rank solutions…
In this work we study generalization guarantees for the metric learning problem, where the metric is induced by a neural network type embedding of the data. Specifically, we provide uniform generalization bounds for two regimes -- the…
Broad, open source availability of large pretrained foundation models on the internet through platforms such as HuggingFace has taken the world of practical deep learning by storm. A classical pipeline for neural network training now…