Related papers: Logic-based Benders decomposition for large-scale …
The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot…
The reconstruction of the history of evolutionary genome-wide events among a set of related organisms is of great biological interest. A simplified model that captures only content modifying operations was introduced recently. It allows the…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
Inference scaling methods for LLMs often rely on decomposing problems into steps (or groups of tokens), followed by sampling and selecting the best next steps. However, these steps and their sizes are often predetermined or manually…
This article describes a novel language task, the Blackbird Language Matrices (BLM) task, inspired by intelligence tests, and illustrates the BLM datasets, their construction and benchmarking, and targeted experiments on chunking and…
Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…
Large language models (LLMs) have exhibited remarkable reasoning and planning capabilities. Most prior work in this area has used LLMs to reason through steps from an initial to a goal state or criterion, thereby effectively reasoning in a…
Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order…
The explosive growth of scientific publications has created an urgent need for automated methods that facilitate knowledge synthesis and hypothesis generation. Literature-based discovery (LBD) addresses this challenge by uncovering…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
When gradient-based methods are impractical, black-box optimization (BBO) provides a valuable alternative. However, BBO often struggles with high-dimensional problems and limited trial budgets. In this work, we propose a novel approach…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
We present the derivation reduction problem for SLD-resolution, the undecidable problem of finding a finite subset of a set of clauses from which the whole set can be derived using SLD-resolution. We study the reducibility of various…
Operator splitting methods have been successfully used in computational sciences, statistics, learning and vision areas to reduce complex problems into a series of simpler subproblems. However, prevalent splitting schemes are mostly…
Nowadays, Large Language Models (LLMs) have been gradually employed to solve complex tasks. To face the challenge, task decomposition has become an effective way, which proposes to divide a complex task into multiple simpler subtasks and…
Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this paper we deal with chains of normal subgroups $1 \triangleleft G_1 \triangleleft \cdots…