Related papers: A separation theorem for simple theories
Answering a question of Goode, we show that $k$-triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a relational language of bounded arity is trivial. We use our…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple…
We show that in supersymmetric theories, knowing the soft theorem for a single particle in a supermultiplet allows one to immediately determine soft theorems for the remainder of the supermultiplet. While soft theorems in supersymmetric…
We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…
Historically, meteorological and climate studies have been prompted by the need for understanding precipitation to have better logistics in food production. Despite all efforts, nonlinearity in atmosphere dynamics is still a source of…
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scenarios. This paper studies simplicial distributions on…
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in…
Our main result (Theorem 1) suggests a possible dividing line ($\mu$-superstable $+$ $\mu$-symmetric) for abstract elementary classes without using extra set-theoretic assumptions or tameness. This theorem illuminates the structural side of…
Scale-separated AdS compactifications of string theory can be constructed at the two-derivative supergravity level in the presence of smeared orientifold planes. The unsmearing corrections are known to leading order in the large volume,…
In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework. In the embedding spaces,…
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…
Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…
In the framework of the Time Dependent Scattering Theory we discuss three forms of Cluster Separability as well as the conditions for the representation of the scattering system dynamics implied by their respective use.
We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.
A variety of techniques have been proposed to train machine learning classifiers that are independent of a given feature. While this can be an essential technique for enabling background estimation, it may also be useful for reducing…
We introduce and develop the theory of metaparticles. At the classical level, this is a world-line theory with the usual reparameterization invariance and two additional features. The theory is motivated by string theory on compact targets,…
We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…
Causation discovery without manipulation is considered a crucial problem to a variety of applications. The state-of-the-art solutions are applicable only when large numbers of samples are available or the problem domain is sufficiently…
The simplicial condition and other stronger conditions that imply it have recently played a central role in developing polynomial time algorithms with provable asymptotic consistency and sample complexity guarantees for topic estimation in…