Related papers: A Generalized Typicality for Abstract Alphabets
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
We construct a word-theoretic framework for generalized Markov numbers, that is, positive integers appearing in positive integer solutions of the generalized Markov equation $x^2+y^2+z^2+k_1yz+k_2zx+k_3xy=(3+k_1+k_2+k_3)xyz$. For each…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
We prove a new asymptotic un-equipartition property for the perplexity of long texts generated by a language model and present supporting experimental evidence from open-source models. Specifically we show that the logarithmic perplexity of…
This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract…
Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…
In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are…
Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…
Coding Theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. Such codes over rings had important applications and many interesting mathematical…
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal coding as the problem of universal…
Experimental studies are a cornerstone of Machine Learning (ML) research. A common and often implicit assumption is that the study's results will generalize beyond the study itself, e.g., to new data. That is, repeating the same study under…
We consider a notion of relative homology (and cohomology) for surfaces with two types of boundaries. Using this tool, we study a generalization of Kitaev's code based on surfaces with mixed boundaries. This construction includes both…
Random simplicial complexes, as generalizations of random graphs, have become increasingly popular in the literature in recent years. In this paper, we consider a new model for a random simplicial complex that was introduced in…
We generalize L\'evy's lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a much more general class of measures, so-called GAP measures. For any given density matrix $\rho$ on a…
Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we…