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This paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to…

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…

The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…

With the proliferation of Deep Machine Learning into real-life applications, a particular property of this technology has been brought to attention: robustness Neural Networks notoriously present low robustness and can be highly sensitive…

Graph Neural Networks (GNNs) have shown their great ability in modeling graph structured data. However, real-world graphs usually contain structure noises and have limited labeled nodes. The performance of GNNs would drop significantly when…

Convolutional neural networks (CNNs) are known for their good performance and generalization in vision-related tasks and have become state-of-the-art in both application and research-based domains. However, just like other neural network…

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization…

As Large Language Models (LLMs) become more powerful and autonomous, they increasingly face conflicts and dilemmas in many scenarios. We first summarize and taxonomize these diverse conflicts. Then, we model the LLM's preferences to make…

Scene recognition, particularly for aerial and underwater images, often suffers from various types of degradation, such as blurring or overexposure. Previous works that focus on convolutional neural networks have been shown to be able to…

We consider the problem of selecting a subset of alternatives given noisy evaluations of the relative strength of different alternatives. We wish to select a k-subset (for a given k) that provides a maximum likelihood estimate for one of…

Graph neural networks (GNNs) learn node representations by passing and aggregating messages between neighboring nodes. GNNs have been applied successfully in several application domains and achieved promising performance. However, GNNs…

Landmarks$\unicode{x2013}$conditions that must be satisfied at some point in every solution plan$\unicode{x2013}$have contributed to major advancements in classical planning, but they have seldom been used in stochastic domains. We…

Graph neural networks (GNNs) have shown great potential in learning on graphs, but they are known to perform sub-optimally on link prediction tasks. Existing GNNs are primarily designed to learn node-wise representations and usually fail to…

Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for…

We study the saddle-points of the $p$-spin model -- the best understood example of a `complex' (rugged) landscape -- when its $N$ variables are complex. These points are the solutions to a system of $N$ random equations of degree $p-1$. We…

Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximization becomes polynomially solvable. From…

Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between…

In this paper we study the problem of learning a shallow artificial neural network that best fits a training data set. We study this problem in the over-parameterized regime where the number of observations are fewer than the number of…