Related papers: On the geometry of flat minima

This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective…

The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical…

We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…

Mixtures of quantum fluids, that is gases or liquids, are considered with the emphasis on the conditions characterizing the stability of the mixtures. The mixtures, that can be formed by cold atoms or molecules, are assumed to be quantum…

We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a…

Proximity measurements probe whether pairs of particles are close to one another. We consider the impact of post-selected random proximity measurements on a quantum fluid of many distinguishable particles. We show that such measurements…

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is…

A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…

A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…

When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…

The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…

I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April,…

Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have…

We use a generic notion of flatness in the enriched context to define various completions of metric spaces -- enrichments over [0,\infty] -- and preorders -- enrichments over 2. We characterize the weights of colimits commuting in…

An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by velocity field {\bf and} the thermodynamic variables of an inviscid fluid. The kinetic-energy…