Related papers: Revisiting virtual difference ideals
In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Groebner basis of Z[x]-lattices, regular and coherent difference ascending…
Visual search, recommendation, and contrastive similarity learning power technologies that impact billions of users worldwide. Modern model architectures can be complex and difficult to interpret, and there are several competing techniques…
Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
The principal result is a primary decomposition of ideals generated by the (2x2)-subpermanents of a generic matrix. These permanental ideals almost always have embedded components and their minimal primes are of three distinct heights. Thus…
A famous result due to I. M. Isaacs states that if a commutative ring $R$ has the property that every prime ideal is principal, then every ideal of $R$ is principal. This motivates ring theorists to study commutative rings for which every…
The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of…
Inspired by the large success of Transformers in Large Language Models, these architectures are increasingly applied to tabular data. This is achieved by embedding tabular data into low-dimensional Euclidean spaces resulting in similar…
Lenstra's concept of Euclidean ideals generalizes the Euclidean algorithm; a domain with a Euclidean ideal has cyclic class group, while a domain with a Euclidean algorithm has trivial class group. This paper generalizes Harper's variation…
The generic initial ideals of a given ideal are rather recent invariants. Not much is known about these objects, and it turns out to be very difficult to compute them. The main purpose of this paper is to study the behaviour of generic…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
Despite massive empirical evaluations, one of the fundamental questions in imitation learning is still not fully settled: does AIL (adversarial imitation learning) provably generalize better than BC (behavioral cloning)? We study this open…
Bell inequalities follow from a set of seemingly natural assumptions about how to provide a causal model of a Bell experiment. In the face of their violation, two types of causal models that modify some of these assumptions have been…
In this note we highlight a common origin for many ubiquitous geometric structures, as well as several new ones by using only the functors of differential calculus in A.M Vinogradov's original sense, adapted to special classes of (graded)…
We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell…
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…
Learning the causal structure behind data is invaluable for improving generalization and obtaining high-quality explanations. We propose a novel framework, Invariant Structure Learning (ISL), that is designed to improve causal structure…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…