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In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical…

We show that training a single $d$-dimensional steering vector per layer with reinforcement learning, while freezing all base weights, matches the accuracy of fully RL-tuned reasoning models on mathematical-reasoning tasks. On an 8…

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

The goal of (stable) sparse recovery is to recover a $k$-sparse approximation $x*$ of a vector $x$ from linear measurements of $x$. Specifically, the goal is to recover $x*$ such that ||x-x*||_p <= C min_{k-sparse x'} ||x-x'||_q for some…

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any…

In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support…

Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

We consider the problem of learning generalized first-order representations of concepts from a single example. To address this challenging problem, we augment an inductive logic programming learner with two novel algorithmic contributions.…

Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals…

This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…

We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…

In this paper, we address the problem of reconstruction of support of a measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure…

In continual learning, a model learns incrementally over time while minimizing interference between old and new tasks. One of the most widely used approaches in continual learning is referred to as replay. Replay methods support interleaved…

Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number…

Let A be an m-dimensional vector with positive real entries. Let A_{i,j} be the vector obtained from A on deleting the entries A_i and A_j. We investigate some invariant and near invariants related to the solutions E (m-2 dimensional…

This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…

In this paper, we investigate continual learning performance metrics used in class incremental learning strategies for continual learning (CL) using some high performing methods. We investigate especially mean task accuracy. First, we show…

We study the problem of reconstructing a positive discrete measure on a compact set $K \subseteq \mathbb{R}^n$ from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new…