相关论文: InfoMod: A visual and computational approach to Ga…

In recent years, cross-modal retrieval has drawn much attention due to the rapid growth of multimodal data. It takes one type of data as the query to retrieve relevant data of another type. For example, a user can use a text to retrieve…

I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational…

Higher genus modular invariance of two-dimensional conformal field theories (CFTs) is a largely unexplored area. In this paper, we derive explicit expressions for the higher genus partition functions of a specific class of CFTs: code CFTs,…

Advancements in text-to-image generative AI with large multimodal models are spreading into the field of image compression, creating high-quality representation of images at extremely low bit rates. This work introduces novel components to…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

Knowledge Graphs (KGs) play a pivotal role in advancing various AI applications, with the semantic web community's exploration into multi-modal dimensions unlocking new avenues for innovation. In this survey, we carefully review over 300…

This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework that…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…

In this essay we discuss the recent trends in visual analysis and exploration of Knowledge Graphs, particularly in conjunction with Knowledge Graph Embedding techniques. We present an overview of the current state of visualization…

We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…

We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…

We consider the problem of computation and deformation of group orbits of solutions of the complex Ginzburg-Landau equation (CGLE) with cubic nonlinearity in $1\!+\!1$ space-time dimension invariant under the action of the three-dimensional…

Multi-modal embeddings form the foundation for vision-language models, such as CLIP embeddings, the most widely used text-image embeddings. However, these embeddings are vulnerable to subtle misalignment of cross-modal features, resulting…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

Statistical Shape Models of faces and various body parts are heavily used in medical image analysis, computer vision and visualization. Whilst the field is well explored with many existing tools, all of them aim at experts, which limits…

Link prediction aims to identify potential missing triples in knowledge graphs. To get better results, some recent studies have introduced multimodal information to link prediction. However, these methods utilize multimodal information…

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style…

In this paper we develop a theory of class invariants associated to $p$-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to…