Results 251 to 260 of about 6,431,216 (308)

Continuity of Best Hankel Approximation and Convergence of Near-Best Approximants

SIAM Journal on Control and Optimization, 1994
Summary: Consider a bounded Hankel operator \(\Gamma\) with \(s\)-numbers \(s_ 0\geq s_ 1\geq\cdots\) and a sequence of bounded Hankel operators \(\Gamma_ n\) converging to \(\Gamma\) in the operator norm. In this paper, it is shown that for each \(k\) with \(s_{k-1}> s_ k\geq s_{k+1}\geq\cdots\), the rational symbols of the best rank-\(k\) Hankel ...
Chui, Charles K., Li, Xin
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Theoretical guarantees on the best-of-n alignment policy

International Conference on Machine Learning
A simple and effective method for the inference-time alignment and scaling test-time compute of generative models is best-of-$n$ sampling, where $n$ samples are drawn from a reference policy, ranked based on a reward function, and the highest ranking one
Ahmad Beirami, Alekh Agarwal, Jonathan Berant, A. D'Amour, Jacob Eisenstein, Chirag Nagpal, A. Suresh   +6 more
semanticscholar   +1 more source

Variational Best-of-N Alignment

International Conference on Learning Representations
Best-of-N (BoN) is a popular and effective algorithm for aligning language models to human preferences. The algorithm works as follows: at inference time, N samples are drawn from the language model, and the sample with the highest reward, as judged by a
Afra Amini, Tim Vieira, Ryan Cotterell
semanticscholar   +1 more source

An algorithm for best rational approximation based on barycentric rational interpolation

Numerical Algorithms, 2021
C. Hofreither
semanticscholar   +1 more source

EMBEDDING THEOREMS AND BEST APPROXIMATIONS

Mathematics of the USSR-Sbornik, 1975
We establish necessary and sufficient conditions, in terms of best approximations, for a function in () to belong to (p$ SRC=http://ej.iop.org/images/0025-5734/26/2/A04/tex_sm_2477_img4.gif/>). The proofs depend on the properties of equimeasurable functions, which were applied by Ul'janov in the theory of the embedding of certain classes for (MR 37
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The Best Interpolating Approximation is a Limit of Best Weighted Approximations

Canadian Mathematical Bulletin, 1982
AbstractUnder appropriate conditions it is shown that the best interpolating approximation to a given function in the uniform norm is a limit of best unconstrained approximations with respect to a certain sequence of discontinuous weight functions.
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Best approximations by rational functions

Mathematical Notes of the Academy of Sciences of the USSR, 1971
Description of a general class of real continuous functions cn a segment Δ of the real line for which a best rational approximation with complex coefficients is not unique.
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Best Approximation with Walsh Atoms

Constructive Approximation, 1997
The author connects the theoretical algorithmic approximation rate in \(L^2 (\overline R)\) for the model case where \(W\) consist of Walsh atoms. The main result stated implies that a linear combination of \(K\) atoms can be approximated to relative error \(e\) with linear combination of \(O(K^2 \log(1/E)\)-orthogonal atoms. In finite dimension \(N\),
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Connectedness and solarity in problems of best and near-best approximation

, 2016
A. Alimov, I. G. Tsar'kov
semanticscholar   +1 more source

Best Rotated Approximation

SSRN Electronic Journal, 1971
The central theme of this paper is the minimax approximation of a function rotated by an angle about the origin and the study of the optimal angle of rotation of least minimax error. Existence theorems indicate validity for any choice of norm. In the following formulation of the problem we will include, with obvious modifications, the cases when the ...
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