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We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for…

Training language models to produce both correct answers and sound reasoning remains an open challenge. Reinforcement learning with verifiable rewards typically optimizes only final outcomes, which can lead to a failure mode where task…

The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…

We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not…

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…

The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When…

Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…

We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential…

A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…

Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions…

In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers $V_{\lambda}^{\otimes N}$ of an irreducible representation $V_{\lambda}$ of a compact connected Lie group $G$. The weights are…

In this paper, we introduce a new class of optimization problems whose objective functions are weakly homogeneous relative to the constraint sets. By using the normalization argument in asymptotic analysis, we prove two criteria for the…

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…

Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, $L(\boldsymbol{\theta})$, with respect to a parameter vector $\boldsymbol{\theta}$, when…

There has been a growing interest in using end-to-end acoustic models for singing voice synthesis (SVS). Typically, these models require an additional vocoder to transform the generated acoustic features into the final waveform. However,…

Several fully end-to-end text-to-speech (TTS) models have been proposed that have shown better performance compared to cascade models (i.e., training acoustic and vocoder models separately). However, they often generate unstable pitch…

Subspace identification methods (SIMs) are known for their simple parameterization for MIMO systems and robust numerical properties. However, a comprehensive statistical analysis of SIMs remains an open problem. Following a three-step…