The Hierarchy of Stable Distributions and Operators to Trade Off Stability and Performance

Recent work addressing model reliability and generalization has resulted in a variety of methods that seek to proactively address differences between the training and unknown target environments. While most methods achieve this by finding distributions that will be invariant across environments, we will show they do not necessarily find the same distributions which has implications for performance. In this paper we unify existing work on prediction using stable distributions by relating environmental shifts to edges in the graph underlying a prediction problem, and characterize stable distributions as those which effectively remove these edges. We then quantify the effect of edge deletion on performance in the linear case and corroborate the findings in a simulated and real data experiment

Changing shapes: adiabatic dynamics of composite solitary waves

We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite non-linear non-dispersive waves points to variations in shape.Comment: 21 pages, 15 figures. To appear in Physica D: Nonlinear Phenomen