Related papers: Efficiently stable presentations from error-correc…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of $n$ nodes with up to $t$ Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily…
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
Graph cut problems are fundamental in Combinatorial Optimization, and are a central object of study in both theory and practice. Furthermore, the study of \emph{fairness} in Algorithmic Design and Machine Learning has recently received…
Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains…
Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…
The strong exponential-time hypothesis (SETH) is a commonly used conjecture in the field of complexity theory. It states that CNF formulas cannot be analyzed for satisfiability with a speedup over exhaustive search. This hypothesis and its…
This paper considers the problem of stabilizing a discrete-time non-linear stochastic system over a finite capacity noiseless channel. Our focus is on systems which decompose into a stable and unstable component, and the stability notion…
The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data…
This expository article is based on two lectures given by the first author at the Fields Institute in the Fall 2021 Thematic Program on Trends in Pure and Applied Model Theory. We give a detailed proof of a qualitative version of the…
For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this…
We define and study exact, efficient representations of realization spaces of a natural class of underconstrained 2D Euclidean Distance Constraint Systems(EDCS) or Frameworks based on 1-dof Henneberg-I graphs. Each representation…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
A practical approach is proposed to construct short presentations for Euclidean crystallographic groups in terms of generators and relations. For our purposes a short presentation is the one with a small number of short relators for a given…
Training stability is typically regarded as a prerequisite for reliable optimization in large language models. In this work, we analyze how stabilizing training dynamics affects the induced generation distribution. We show that under…