Related papers: Unguarded Recursion on Coinductive Resumptions
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We extend Barr's well-known characterization of the final coalgebra of a $Set$-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a $Set$-monad $\mathbf{M}$ for functors arising as liftings.…
Starting from any operad P, one can consider on one hand the free operad on P, and on the other hand the Baez--Dolan construction on P. These two new operads have the same space of operations, but with very different notions of arity and…
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Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…
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Generative transformers have experienced rapid popularity growth in the computer vision community in synthesizing high-fidelity and high-resolution images. The best generative transformer models so far, however, still treat an image naively…
In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…
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Monads and their composition via distributive laws have many applications in program semantics and functional programming. For many interesting monads, distributive laws fail to exist, and this has motivated investigations into weaker…
Flow-based generative models have shown an excellent ability to explicitly learn the probability density function of data via a sequence of invertible transformations. Yet, learning attentions in generative flows remains understudied, while…
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Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then…
We investigate the observational consequences of the light-like deformations of the Poincar\'e algebra induced by the jordanian and the extended jordanian classes of Drinfel'd twists. Twist-deformed generators belonging to a Universal…