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The energy landscapes of proteins have evolved to be different from most random heteropolymers. Many studies have concluded that evolutionary selection for rapid and reliable folding to a given structure that is stable at biological…

Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…

We analyze the optimization landscapes of deep learning with wide networks. We highlight the importance of constraints for such networks and show that constraint -- as well as unconstraint -- empirical-risk minimization over such networks…

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the…

The stability of chemically complex nanoparticles is governed by an immense configurational space arising from heterogeneous local atomic environments across surface and interior regions. Efficiently identifying low-energy configurations…

When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to…

We examine several issues pertaining to statistical predictivity of the string theory landscape for weak scale supersymmetry (SUSY). We work within a predictive landscape wherein super-renormalizable terms scan while renormalizable terms do…

In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize…

We revisit the various measures of naturalness for models of weak scale supersymmetry including 1. electroweak (EW) naturalness, 2. naturalness via sensitivity to high scale parameters (EENZ/BG), 3. sensitivity of Higgs soft term due to…

We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most…

Neural Architecture Search (NAS) aims to optimize deep neural networks' architecture for better accuracy or smaller computational cost and has recently gained more research interests. Despite various successful approaches proposed to solve…

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…

Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…

Exploring unknown environments is a fundamental task in many domains, e.g., robot navigation, network security, and internet search. We initiate the study of a learning-augmented variant of the classical, notoriously hard online graph…

We analyze the performance of graph neural network (GNN) architectures from the perspective of random graph theory. Our approach promises to complement existing lenses on GNN analysis, such as combinatorial expressive power and worst-case…

(1) The enhanced capability of Graph Neural Networks (GNNs) in unsupervised community detection of clustered nodes is attributed to their capacity to encode both the connectivity and feature information spaces of graphs. The identification…

Using Large Language Models (LLMs) in an evolutionary or other iterative search framework have demonstrated significant potential in automated algorithm design. However, the underlying fitness landscape, which is critical for understanding…

Numerous explainability methods have been proposed to shed light on the inner workings of GNNs. Despite the inclusion of empirical evaluations in all the proposed algorithms, the interrogative aspects of these evaluations lack diversity. As…