Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis

Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase--space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical r\^ole of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non--standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments.Comment: 20 pages, 13 figure

Universality classes for horizon instabilities

We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the shortest unstable mode diverges as one approaches the cross-over point from above, with a simple critical exponent which is the same in all three cases.Comment: 23 pages, latex2e, 4 figure

Bounds for avalanche critical values of the Bak-Sneppen model

We study the Bak-Sneppen model on locally finite transitive graphs $G$, in particular on Z^d and on T_Delta, the regular tree with common degree Delta. We show that the avalanches of the Bak-Sneppen model dominate independent site percolation, in a sense to be made precise. Since avalanches of the Bak-Sneppen model are dominated by a simple branching process, this yields upper and lower bounds for the so-called avalanche critical value $p_c^{BS}(G)$. Our main results imply that 1/(Delta+1) <= \leq p_c^{BS}(T_Delta) \leq 1/(Delta -1)$, and that$1/(2d+1)\leq p_c^{BS}(Z^d)\leq 1/(2d)+ 1/(2d)^2+O(d^{-3}), as d\to\infty.Comment: 19 page

Multiparty Dynamics and Failure Modes for Machine Learning and Artificial Intelligence

An important challenge for safety in machine learning and artificial intelligence systems is a~set of related failures involving specification gaming, reward hacking, fragility to distributional shifts, and Goodhart's or Campbell's law. This paper presents additional failure modes for interactions within multi-agent systems that are closely related. These multi-agent failure modes are more complex, more problematic, and less well understood than the single-agent case, and are also already occurring, largely unnoticed. After motivating the discussion with examples from poker-playing artificial intelligence (AI), the paper explains why these failure modes are in some senses unavoidable. Following this, the paper categorizes failure modes, provides definitions, and cites examples for each of the modes: accidental steering, coordination failures, adversarial misalignment, input spoofing and filtering, and goal co-option or direct hacking. The paper then discusses how extant literature on multi-agent AI fails to address these failure modes, and identifies work which may be useful for the mitigation of these failure modes.Comment: 12 Pages, This version re-submitted to Big Data and Cognitive Computing, Special Issue "Artificial Superintelligence: Coordination & Strategy