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Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
Along with the rapid development of deep learning in practice, the theoretical explanations for its success become urgent. Generalization and expressivity are two widely used measurements to quantify theoretical behaviors of deep learning.…
Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains…
Why do deep networks generalize well? In contrast to classical generalization theory, we approach this fundamental question by examining not only inputs and outputs, but the evolution of internal features. Our study suggests a phenomenon of…
As a general type of machine learning approach, artificial neural networks have established state-of-art benchmarks in many pattern recognition and data analysis tasks. Among various kinds of neural networks architectures, polynomial neural…
Graph Neural Networks (GNNs) are proposed without considering the agnostic distribution shifts between training and testing graphs, inducing the degeneration of the generalization ability of GNNs on Out-Of-Distribution (OOD) settings. The…
Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them…
Compositional generalization is a basic mechanism in human language learning, which current neural networks struggle with. A recently proposed Disentangled sequence-to-sequence model (Dangle) shows promising generalization capability by…
The equation for QCD string proposed earlier is reviewed. This equation appears when we examine the gonihedric string model and the corresponding transfer matrix. Arguing that string equation should have a generalized Dirac form we found…
Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from…
In this paper, we propose a novel variable selection approach in the framework of high-dimensional linear models where the columns of the design matrix are highly correlated. It consists in rewriting the initial high-dimensional linear…
In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are…
The binary string matching problem consists in finding all the occurrences of a pattern in a text where both strings are built on a binary alphabet. This is an interesting problem in computer science, since binary data are omnipresent in…
An $\ell$-page stack layout (also known as an $\ell$-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into $\ell$ stacks (or pages), such that the endpoints of no two edges on the…
Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do…
Subgraph GNNs enhance message-passing GNNs expressivity by representing graphs as sets of subgraphs, demonstrating impressive performance across various tasks. However, their scalability is hindered by the need to process large numbers of…
Deep learning models struggle with compositional generalization, i.e. the ability to recognize or generate novel combinations of observed elementary concepts. In hopes of enabling compositional generalization, various unsupervised learning…
This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems,…
Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we…
When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, what…