Related papers: On Approximate Classification of Theories

A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.

We present a new strictification method for type-theoretic structures that are only weakly stable under substitution. Given weakly stable structures over some model of type theory, we construct equivalent strictly stable structures by…

Was paper 839 in the author's list until winter 2023 when it was divided into three. Part I: We would like to generalize imaginary elements, weight of ortp$(a,M,N), {\mathbf P}$-weight, ${\mathbf P}$-simple types, etc. from [She90, Ch.…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

Fair classification has been a topic of intense study in machine learning, and several algorithms have been proposed towards this important task. However, in a recent study, Friedler et al. observed that fair classification algorithms may…

A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…

We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

We prove that in a theory $T$ stable over a predicate $P$, for any $\lambda > |T|$, there is a $\lambda$-prime model over any complete set A with a $\lambda$-saturated $P$-part.

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…

This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…

We investigate the presence of twinlike models in theories described by several real scalar fields. We focus on the first-order formalism, and we show how to build distinct scalar field theories that support the same extended solution, with…

The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…

We propose an approach to lifted approximate inference for first-order probabilistic models, such as Markov logic networks. It is based on performing exact lifted inference in a simplified first-order model, which is found by relaxing…

We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak…

We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…

Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…