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High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases…
We study two global structural properties of a graph $\Gamma$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erd\"os--R\'enyi random graph model G(n,p), proving a sharp…
We study robust properties of zero sets of continuous maps $f:X\to\mathbb{R}^n$. Formally, we analyze the family $Z_r(f)=\{g^{-1}(0):\,\,\|g-f\|<r\}$ of all zero sets of all continuous maps $g$ closer to $f$ than $r$ in the max-norm. The…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
A growing body of research has shown that many classifiers are susceptible to {\em{adversarial examples}} -- small strategic modifications to test inputs that lead to misclassification. In this work, we study general non-parametric methods,…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
Robust generalization under distribution shift remains difficult to monitor and optimize in the absence of target-domain labels, as models with similar in-distribution accuracy can exhibit markedly different out-of-distribution (OOD)…
There has been recent growing interest in graph theoretical properties known as r- and (r,s)-robustness. These properties serve as sufficient conditions guaranteeing the success of certain consensus algorithms in networks with misbehaving…
We give characterizations of the structure and degree sequences of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree sequence. The class of hereditary unigraphs properly contains the…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…
Machine Learning (ML) has the potential to accelerate discovery of new materials and shed light on useful properties of existing materials. A key difficulty when applying ML in Materials Science is that experimental datasets of material…
Property Directed Reachability (\textsc{Pdr}), also known as IC3, is a state-of-the-art model checking algorithm widely used for verifying safety properties. While \textsc{Pdr} is effective in finding inductive invariants, its underlying…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
We study the structure learning problem for $H$-colorings, an important class of Markov random fields that capture key combinatorial structures on graphs, including proper colorings and independent sets, as well as spin systems from…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…