相关论文: On the Mathematical Impossibility of Safe Universa…

Autonomous robots that rely on deep neural network controllers pose critical challenges for safety prediction, especially under partial observability and distribution shift. Traditional model-based verification techniques are limited in…

Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are an exciting development in computational physics. For example, the force-based quasicontinuum approximation is the only known pointwise…

We develop a mean-field theory of dropout as a perturbation of critical signal propagation at the edge of chaos. Dropout shifts the perfect-alignment fixed point, making the depth scale for information propagation finite even at critical…

We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate…

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…

Large language models now write software, draft legal documents, and produce clinical notes, yet fundamental limits, from Turing and Arrow to the No Free Lunch theorems, shape what computation can do. This thesis turns such impossibility…

This paper addresses the growing need to process non-Euclidean data, by introducing a geometric deep learning (GDL) framework for building universal feedforward-type models compatible with differentiable manifold geometries. We show that…

Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…

The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a universal nonperturbative method leading…

This paper studies the asymptotic convergence of computed dynamic models when the shock is unbounded. Most dynamic economic models lack a closed-form solution. As such, approximate solutions by numerical methods are utilized. Since the…

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…

Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…

Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

We introduce a class of fully-connected neural networks whose activation functions, rather than being pointwise, rescale feature vectors by a function depending only on their norm. We call such networks radial neural networks, extending…

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…

This manuscript establishes information-theoretic limitations for robustness of AI security and alignment by extending G\"odel's incompleteness theorem to AI. Knowing these limitations and preparing for the challenges they bring is…

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…