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We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
Production LLM systems increasingly require machine-readable outputs: JSON objects, typed traces, regex-constrained fields, and tool-call schemas. This paper targets on-device and low-cost small language model (SLM) deployments, where…
We propose a model to tackle classification tasks in the presence of very little training data. To this aim, we approximate the notion of exact match with a theoretically sound mechanism that computes a probability of matching in the input…
Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…
We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower…
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Classes of set functions along with a choice of ground set are a bedrock to determine and develop corresponding variants of greedy algorithms to obtain efficient solutions for combinatorial optimization problems. The class of approximate…
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
We introduce an enumeration-free method based on mathematical programming to precisely characterize various properties such as fairness or sparsity within the set of "good models", known as Rashomon set. This approach is generically…
The vast majority of techniques to train fair models require access to the protected attribute (e.g., race, gender), either at train time or in production. However, in many important applications this protected attribute is largely…
Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be…
Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
Submodularity in combinatorial optimization has been a topic of many studies and various algorithmic techniques exploiting submodularity of a studied problem have been proposed. It is therefore natural to ask, in cases where the cost…
Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…