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Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten type classes are obtained. Some upper asymptotic estimates for…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex…
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
While neural machine translation (NMT) has achieved state-of-the-art translation performance, it is unable to capture the alignment between the input and output during the translation process. The lack of alignment in NMT models leads to…
A short proof of the linear nested Artin approximation property of the algebraic power series rings is given here.
This paper considers the problem of estimating the covariance of roto-translations computed by the Iterative Closest Point (ICP) algorithm. The problem is relevant for localization of mobile robots and vehicles equipped with depth-sensing…
In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
The previously developed n-vicinity method allows us to calculate accurately critical values of inverse temperatures for Ising models with short-range interaction. We generalize the method to the case of long-range interactions in spin…
Retrieval-Augmented Machine Translation (RAMT) is attracting growing attention. This is because RAMT not only improves translation metrics, but is also assumed to implement some form of domain adaptation. In this contribution, we study…
Continuous-output neural machine translation (CoNMT) replaces the discrete next-word prediction problem with an embedding prediction. The semantic structure of the target embedding space (i.e., closeness of related words) is intuitively…
We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete…
Nearest Neighbor Machine Translation ($k$NN-MT) has achieved great success in domain adaptation tasks by integrating pre-trained Neural Machine Translation (NMT) models with domain-specific token-level retrieval. However, the reasons…
We improve the approximation ratio for the Asymmetric TSP to less than 15. We also obtain improved ratios for the special case of unweighted digraphs and the generalization where we ask for a minimum-cost tour with given (distinct)…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
We survey the classical results of the Dirichlet Approximation Theorem.