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We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…
For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector…
Fine-grained visual categorization (FGVC) is an important but challenging task due to high intra-class variances and low inter-class variances caused by deformation, occlusion, illumination, etc. An attention convolutional binary neural…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
In the monotone integer dualization problem, we are given two sets of vectors in an integer box such that no vector in the first set is dominated by a vector in the second. The question is to check if the two sets of vectors cover the…
Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…
In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…
Visual Entailment with natural language explanations aims to infer the relationship between a text-image pair and generate a sentence to explain the decision-making process. Previous methods rely mainly on a pre-trained vision-language…
Vision-language models benefit from high-resolution images, but the increase in visual-token count incurs high compute overhead. Humans resolve this tension via foveation: a coarse view guides "where to look", while selectively acquired…
The goal of image ordinal estimation is to estimate the ordinal label of a given image with a convolutional neural network. Existing methods are mainly based on ordinal regression and particularly focus on modeling the ordinal mapping from…
Convolutional neural networks have recently shown excellent results in general object detection and many other tasks. Albeit very effective, they involve many user-defined design choices. In this paper we want to better understand these…
Learning deep discrete latent presentations offers a promise of better symbolic and summarized abstractions that are more useful to subsequent downstream tasks. Inspired by the seminal Vector Quantized Variational Auto-Encoder (VQ-VAE),…
Motivated by the concept of "generating operators" for a countable family of operators introduced in the recent paper (arXiv:2306.16800), we find a method to reconstruct the Rankin--Cohen brackets from a very simple multivariable contour…
In this paper we address the following questions: (i) Let $C\subset \mathbb C^2$ be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is $C$ contained in an algebraic curve? (ii) What can be said of a…
Convex neural codes are combinatorial structures describing the intersection pattern of a collection of convex sets. Inductively pierced codes are a particularly nice subclass of neural codes introduced in the information visualization…
Vision transformers using self-attention or its proposed alternatives have demonstrated promising results in many image related tasks. However, the underpinning inductive bias of attention is not well understood. To address this issue, this…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…
Convolutional neural nets (convnets) trained from massive labeled datasets have substantially improved the state-of-the-art in image classification and object detection. However, visual understanding requires establishing correspondence on…