Related papers: How Functorial Are (Deep) GADTs?

This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial…

Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…

Graph Neural Networks (GNNs) have achieved great success in various graph mining tasks.However, drastic performance degradation is always observed when a GNN is stacked with many layers. As a result, most GNNs only have shallow…

Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…

Requirements on subsystems have been made clear in this paper for a linear time invariant (LTI) networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS,…

Gradient Boosted Decision Trees (GBDTs) are widely used for building ranking and relevance models in search and recommendation. Considerations such as latency and interpretability dictate the use of as few features as possible to train…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…

Up-to-date High-Definition (HD) maps are essential for self-driving cars. To achieve constantly updated HD maps, we present a deep neural network (DNN), Diff-Net, to detect changes in them. Compared to traditional methods based on object…

Functional dependence graph (FDG) is an important class of directed graph that captures the dominance relationship among a set of variables. FDG is frequently used in calculating network coding capacity bounds. However, the order of FDG is…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element. Essentially, this theory encompasses the study of a functor which maps certain geometries…

We present and discuss a new method to extract parton distribution functions from hard scattering processes based on an alternative type of neural network, the Self-Organizing Map. Quantitative results including a detailed treatment of…

Modern IC complexity drives test pattern growth, with the majority of patterns targeting a small set of hard-to-detect (HTD) faults. This motivates new ATPG algorithms to improve test effectiveness specifically for HTD faults. This paper…

The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges…

Multi-agent pathfinding (MAPF) is a common abstraction of multi-robot trajectory planning problems, where multiple homogeneous robots simultaneously move in the shared environment. While solving MAPF optimally has been proven to be NP-hard,…

Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D…

Graph anomaly detection (GAD), which aims to identify abnormal nodes that deviate from the majority, has become increasingly important in high-stakes Web domains. However, existing GAD methods follow a "one model per dataset" paradigm,…

The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…

While foundation models have revolutionized such fields as natural language processing and computer vision, their potential in graph machine learning remains largely unexplored. One of the key challenges in designing graph foundation models…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…