Related papers: Generalization of the Ball-Collision Algorithm
In this work, we examine a generic class of simple distributed balls-into-bins algorithms. Exploiting the strong concentration bounds that apply to balls-into-bins games, we provide an iterative method to compute accurate estimates of the…
Empirical evidence reveals existence of partial D-operators for the generalized IBP (BT) reduction algorithms that are, counterintuitively, much simpler and much easier to find than the complete D-operators from the foundational Bernstein…
We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and…
Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomenon holds in these generalized quantum cluster algebras. We…
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
Algorithm- and data-dependent generalization bounds are required to explain the generalization behavior of modern machine learning algorithms. In this context, there exists information theoretic generalization bounds that involve (various…
We propose a generalization of the collective field theory hamiltonian, including interactions between the original bosonic collective field $w_0 (z)$ and supplementary fields ${\bar w}_j (z)$ realizing classically a $w_\infty$ algebra. The…
Ensemble algorithms offer state of the art performance in many machine learning applications. A common explanation for their excellent performance is due to the bias-variance decomposition of the mean squared error which shows that the…
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…
We present a PAC-Bayes-style generalization bound which enables the replacement of the KL-divergence with a variety of Integral Probability Metrics (IPM). We provide instances of this bound with the IPM being the total variation metric and…
We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to…
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may…
Building on the Renormalization Group (RG) method the beam-beam interaction in circular colliders is studied. A regularized symplectic RG beam-beam map, that describes successfully the long-time asymptotic behavior of the original system…
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential…
We present a new model-based integrative method for clustering objects given both vectorial data, which describes the feature of each object, and network data, which indicates the similarity of connected objects. The proposed general model…
We obtain the rigorous uniform asymptotics of a particular integral where a stationary point is close to an endpoint. There exists a general method introduced by Bleistein for obtaining uniform asymptotics in this situation. However, this…
Traditional clustering algorithms often focus on the most fine-grained information and achieve clustering by calculating the distance between each pair of data points or implementing other calculations based on points. This way is not…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…