24 accepted papers
We present a rigorous asymptotic analysis of Echo State Networks (ESNs) in a teacher student setting with a linear teacher with oracle weights. Leveraging random matrix theory, we derive closed form expressions for the asymptotic bias, variance, and mean-squared error (MSE) as functions of the input…
We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min–Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min–max characterization of key statistics, enabling approximation of th…
Kronecker adapters have emerged as a promising approach for fine-tuning large-scale models, enabling high-rank updates through tunable component structures. However, existing work largely treats the component structure as a fixed or heuristic design choice, leaving the dimensions and number of Krone…
Millimeter-wave (mmWave) sensing enables privacy-preserving, always-on edge perception, but its measurements are often sparse, temporally irregular, and corrupted by high-frequency noise. Existing mmWave pipelines predominantly rely on artificial neural networks (ANNs), which achieve robustness thro…
Most edge-cloud collaboration frameworks rely on the substantial computational and storage capabilities of cloud-based artificial neural networks (ANNs). However, this reliance results in significant communication overhead between edge devices and the cloud, as well as high computational energy cons
A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis using Johnson--Lindenstrauss and subspace embedding techniqu…
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To relax this restrictive assumption, subsequent efforts have been…
Deep equilibrium models (DEQs), as typical implicit neural networks, have demonstrated remarkable success on various tasks. There is, however, a lack of theoretical understanding of the connections and differences between implicit DEQs and explicit neural network models. In this paper, leveraging re…
Participating in sports is of great significance to people's physical and mental well-being. While physical activity is commonplace for healthy individuals, it presents challenges for those with visual impairments, as they can not rely on visual cues to perceive essential information related to spor
Modern deep neural networks (DNNs) are extremely powerful; however, this comes at the price of increased depth and having more parameters per layer, making their training and inference more computationally challenging. In an attempt to address this key limitation, efforts have been devoted to the c…
In this article, we investigate the spectral behavior of random features kernel matrices of the type ${\bf K} = \mathbb{E}_{{\bf w}} \left[\sigma\left({\bf w}^{\sf T}{\bf x}_i\right)\sigma\left({\bf w}^{\sf T}{\bf x}_j\right)\right]_{i,j=1}^n$, with nonlinear function $\sigma(\cdot)$, data ${\bf x}_…
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models and non-convex problems are considered, strong simplifying a…
In this paper, we provide a precise characterization of generalization properties of high dimensional kernel ridge regression across the under- and over-parameterized regimes, depending on whether the number of training data n exceeds the feature dimension d. By establishing a bias-variance decompos…
For the visually impaired people, some outdoor activities like running or soccer are difficult, due to not being able to clearly see the environment. Recently, multiple researchers have contributed to help the visually impaired people run outdoors using robotic systems with different types of feedba…
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing nonlinear filters to design state-of-the-art neural network mo…
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and comparable. In this regime, the random RFF Gram matrix no longer c…
Deep neural networks with adaptive configurations have gained increasing attention due to the instant and flexible deployment of these models on platforms with different resource budgets. In this paper, we investigate a novel option to achieve this goal by enabling adaptive bit-widths of weights and…
In recent years, multiple navigation systems using vibrotactile feedback have been studied, due to their ability to convey information while keeping free the visual and auditory channels, besides eliciting rapid responses from users. In the current stage, most navigation systems with vibrotactile fe
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even though there is an extensive literature on the worst-case…
This paper focuses on learning transferable adversarial examples specifically against defense models (models to defense adversarial attacks). In particular, we show that a simple universal perturbation can fool a series of state-of-the-art defenses.
Logistic regression, one of the most popular machine learning binary classification methods, has been long believed to be unbiased. In this paper, we consider the "hard" classification problem of separating high dimensional Gaussian vectors, where the data dimension p and the sample size n are both…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral…
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we introduce a random matrix-based framework to analyze the learning…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data p and their number n grow large at the same rate. Under a two-class Gaussian mixture model for the input data, we p…