Related papers: How Functorial Are (Deep) GADTs?

With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…

Graph learning aims to convert data into graph representations, which are fundamental to many problems in machine learning for CAD, where circuits, layouts, designs, and optimization states are often modeled as graph-structured objects.…

Graph neural networks (GNN) has been successfully applied to operate on the graph-structured data. Given a specific scenario, rich human expertise and tremendous laborious trials are usually required to identify a suitable GNN architecture.…

Applying AI foundation models directly to geospatial datasets remains challenging due to their limited ability to represent and reason with geographical entities, specifically vector-based geometries and natural language descriptions of…

Deep graph embedding is an important approach for community discovery. Deep graph neural network with self-supervised mechanism can obtain the low-dimensional embedding vectors of nodes from unlabeled and unstructured graph data. The…

Topological maps are favorable for their small storage compared to geometric map. However, they are limited in relocalization and path planning capabilities. To solve this problem, a feature-based hierarchical topological map (FHT-Map) is…

Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…

Neuromorphic systems or dedicated hardware for neuromorphic computing is getting popular with the advancement in research on different device materials for synapses, especially in crossbar architecture and also algorithms specific or…

We study the problem of finding a minimum-distortion embedding of the shortest path metric of an unweighted graph into a "simpler" metric $X$. Computing such an embedding (exactly or approximately) is a non-trivial task even when $X$ is the…

In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…

This paper is concerned with realizing Lattes maps as subdivision maps of finite subdivision rules. The main result is that the Lattes maps in all but finitely many analytic conjugacy classes can be realized as subdivision maps of finite…

The problem of finding the general classification of geodetic graphs is still open. We believe that one of the obstacles to attain this goal is that geodetic graphs lack a structural description. In other words, their fundamental properties…

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…

Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is…

The functional graph of a function $g:X\rightarrow X$ is the directed graph with vertex set $X$ the edges of which are of the form $x\rightarrow g(x)$ for $x\in X$. Functional graphs are heavily studied because they allow one to understand…

Graph Transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to…

Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…

Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…