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We study the power of negation in the Boolean and algebraic settings and show the following results. * We construct a family of polynomials $P_n$ in $n$ variables, all of whose monomials have positive coefficients, such that $P_n$ can be…
Graph neural networks (GNNs) are a widely used class of machine learning models for graph-structured data, based on local aggregation over neighbors. GNNs have close connections to logic. In particular, their expressive power is linked to…
We study the spectrum generating closed nonlinear superconformal algebra that describes $\mathcal{N}=2$ super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant $g=m(m+1)$,…
Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes of odd dimension are shown to be consta-dihedral. Exact counting formulae are derived for DN codes. The special class of…
Constructing high-quality features is critical to any quantitative data analysis. While feature engineering was historically addressed by carefully hand-crafting data representations based on domain expertise, deep neural networks (DNNs)…
While deep neural networks (DNN) have become an effective computational tool, the prediction results are often criticized by the lack of interpretability, which is essential in many real-world applications such as health informatics.…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
Deep neural networks (DNNs) are widely used as surrogate models in geophysical applications; incorporating theoretical guidance into DNNs has improved the generalizability. However, most of such approaches define the loss function based on…
In recent years, the remarkable success of graph neural networks (GNNs) on graph-structured data has prompted a surge of methods for explaining GNN predictions. However, the state-of-the-art for GNN explainability remains in flux. Different…
Deep neural networks (DNNs) are notoriously hard to understand and difficult to defend. Extracting representative paths (including the neuron activation values and the connections between neurons) from DNNs using software engineering…
Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods…
Deep neural networks (DNNs), especially deep convolutional neural networks (CNNs), have emerged as the powerful technique in various machine learning applications. However, the large model sizes of DNNs yield high demands on computation…
Given the increasing promise of graph neural networks (GNNs) in real-world applications, several methods have been developed for explaining their predictions. Existing methods for interpreting predictions from GNNs have primarily focused on…
Deep learning has been a groundbreaking technology in various fields as well as in communications systems. In spite of the notable advancements of deep neural network (DNN) based technologies in recent years, the high computational…
Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…
External difference families (EDFs) are combinatorial objects which were introduced in the early 2000s, motivated by information security applications such as the construction of AMD codes. Various generalizations have since been defined…
This paper studies Dropout Graph Neural Networks (DropGNNs), a new approach that aims to overcome the limitations of standard GNN frameworks. In DropGNNs, we execute multiple runs of a GNN on the input graph, with some of the nodes randomly…
Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired…
This paper focuses on the study of recognizing discontiguous entities. Motivated by a previous work, we propose to use a novel hypergraph representation to jointly encode discontiguous entities of unbounded length, which can overlap with…
In this paper, we provide a uniform framework for investigating small circuit classes and bounds through the lens of ordinary differential equations (ODEs). Following an approach recently introduced to capture the class of polynomial-time…