Related papers: An Algebraic Formalization of Forward and Forward-…

We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…

This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…

Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…

Deep generative models for graphs have exhibited promising performance in ever-increasing domains such as design of molecules (i.e, graph of atoms) and structure prediction of proteins (i.e., graph of amino acids). Existing work typically…

We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive…

Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…

In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…

Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…

We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a structure that is desirable in many aspects. While much…

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…

We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

An algebraic formalism, developped with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…

The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is…