We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.

It is shown that polynomially bounded operators on Banach spaces have polynomially bounded dilations which have spectrum in the unit circle and are generalized scalar. The proof also yields a description of all compressions of generalized scalar operators with spectrum in the unit circle.

We propose a generalized class of multimodal fusion operators for the task of visual question answering (VQA). We identify generalizations of existing multimodal fusion operators based on the Hadamard product, and show that specific nontrivial instantiations of this generalized fusion operator exhibit superior performance in terms of OpenEnded accuracy on the VQA task. In particular, we introdu...

Different types of aggregation operators such as the ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and the normalized Hamming distance are studied. We introduce the use of the OWA operator in generalized distances such as the quasiarithmetic distance. We will call these new distance aggregation the ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator. We develop a gene...