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Random 3CNF formulas constitute an important distribution for measuring the average-case behavior of propositional proof systems. Lower bounds for random 3CNF refutations in many propositional proof systems are known. Most notably are the…
Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The…
While message passing Graph Neural Networks (GNNs) have become increasingly popular architectures for learning with graphs, recent works have revealed important shortcomings in their expressive power. In response, several higher-order GNNs…
An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…
Learning tasks such as those involving genomic data often poses a serious challenge: the number of input features can be orders of magnitude larger than the number of training examples, making it difficult to avoid overfitting, even when…
Tensor factorization has become an increasingly popular approach to knowledge graph completion(KGC), which is the task of automatically predicting missing facts in a knowledge graph. However, even with a simple model like…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…
This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely…
Eigenvalues of 1-particle reduced density matrices of $N$-fermion states are upper bounded by $1/N$, resulting in a lower bound on entanglement entropy. We generalize these bounds to all other subspaces defined by Young diagrams in the…
The cumulative distribution network (CDN) is a recently developed class of probabilistic graphical models (PGMs) permitting a copula factorization, in which the CDF, rather than the density, is factored. Despite there being much recent…
Hypercomplex neural networks have proven to reduce the overall number of parameters while ensuring valuable performance by leveraging the properties of Clifford algebras. Recently, hypercomplex linear layers have been further improved by…
Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every…
For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in…
The latest theoretical advances in the field of unlimited sampling framework (USF) show the potential to avoid clipping problems of analog-to-digital converters (ADC). To date, most of the related works have focused on real-valued modulo…
We introduce a new graph parameter called linear upper maximum induced matching width \textsc{lu-mim width}, denoted for a graph $G$ by $lu(G)$. We prove that the smallest size of the \textsc{obdd} for $\varphi$, the monotone 2-\textsc{cnf}…
Previous work has shown that DNNs with large depth $L$ and $L_{2}$-regularization are biased towards learning low-dimensional representations of the inputs, which can be interpreted as minimizing a notion of rank $R^{(0)}(f)$ of the learned…
Graph neural networks (GNNs) are often trained on individual datasets, requiring specialized models and significant hyperparameter tuning due to the unique structures and features of each dataset. This approach limits the scalability and…
We study the effects of planarization (the construction of a planar diagram $D$ from a non-planar graph $G$ by replacing each crossing by a new vertex) on graph width parameters. We show that for treewidth, pathwidth, branchwidth,…
In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula, which can be…
It has been shown that the effectiveness of graph convolutional network (GCN) for recommendation is attributed to the spectral graph filtering. Most GCN-based methods consist of a graph filter or followed by a low-rank mapping optimized…