Related papers: Full normalization for transfinite stacks
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed…
Let $J\subset S=K[x_0,...,x_n]$ be a monomial strongly stable ideal. The collection $\Mf(J)$ of the homogeneous polynomial ideals $I$, such that the monomials outside $J$ form a $K$-vector basis of $S/I$, is called a {\em $J$-marked…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…
In this paper, we build on recent results by Chauve et al. (2014) and Bahrani and Lumbroso (2017), which combined the split-decomposition, as exposed by Gioan and Paul, with analytic combinatorics, to produce new enumerative results on…
The aim of this paper is to give natural examples of $\mathbf{\Sigma}_1^1$-complete and $\mathbf{\Pi}_1^1$-complete sets. In the first part, we consider ideals on $\omega$. In particular, we show that the Hindman ideal $\mathcal{H}$ is…
Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
We construct and solve a complete system of differential equations for general tree-level inflation correlators with an arbitrary number of massive scalar exchanges and time-dependent couplings. Any massive tree correlators can be uniquely…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (STOC 2017). The combinatorial object underlying these approaches is a universal tree, as identified by Czerwi\'nski et al.…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…
In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated…
Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of…
We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical…
We propose a tree regularization framework, which enables many tree models to perform feature selection efficiently. The key idea of the regularization framework is to penalize selecting a new feature for splitting when its gain (e.g.…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
Checking infinite-state systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can…
The strong correlation between neurons or filters can significantly weaken the generalization ability of neural networks. Inspired by the well-known Tammes problem, we propose a novel diversity regularization method to address this issue,…