Related papers: Representation Stability
We present the first experimental observation of modulation instability of partially spatially incoherent light beams in non-instantaneous nonlinear media. We show that even in such a nonlinear partially coherent system (of…
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
The paper investigates the stability properties of restrictions of irreducible representations of the symmetric group to the hyperoctahedral subgroup. A stability result is obtained, analogous to the classical Murnaghan theorem on the…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
We consider two families X_n of varieties on which the symmetric group S_n acts: the configuration space of n points in C and the space of n linearly independent lines in C^n. Given an irreducible S_n-representation V, one can ask how the…
The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away…
Adversarial examples resulting from instability of current computer vision models are an extremely important topic due to their potential to compromise any application. In this paper we demonstrate that instability is inevitable due to a)…
In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…
We present a new family of deep neural network-based dynamic systems. The presented dynamics are globally stable and can be conditioned with an arbitrary context state. We show how these dynamics can be used as structured robot policies.…
In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is stable if no coalition of voters can deviate and choose a committee of proportional size, so that all…
We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.
In this paper we study stability patterns in the homology of the ordered configuration space of the once-punctured torus. In the last decade Church and Church-Ellenberg-Farb proved that the homology groups of the ordered configuration space…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
In this essay I aim to investigate and discuss the process through which bundles of things "self-organize" into other things. In particular, I engage in such investigation by trying to apply a framework of analysis of structural stability…