586 research outputs found
Homotopy morphisms between convolution homotopy Lie algebras
In previous works by the authors, a bifunctor was associated to any operadic
twisting morphism, taking a coalgebra over a cooperad and an algebra over an
operad, and giving back the space of (graded) linear maps between them endowed
with a homotopy Lie algebra structure. We build on this result by using a more
general notion of -morphism between (co)algebras over a (co)operad
associated to a twisting morphism, and show that this bifunctor can be extended
to take such -morphisms in either one of its two slots. We also provide
a counterexample proving that it cannot be coherently extended to accept
-morphisms in both slots simultaneously. We apply this theory to
rational models for mapping spaces.Comment: 37 pages; v2: minor typo corrections, updated bibliography, final
versio
Convolution algebras and the deformation theory of infinity-morphisms
Given a coalgebra C over a cooperad, and an algebra A over an operad, it is
often possible to define a natural homotopy Lie algebra structure on hom(C,A),
the space of linear maps between them, called the convolution algebra of C and
A. In the present article, we use convolution algebras to define the
deformation complex for infinity-morphisms of algebras over operads and
coalgebras over cooperads. We also complete the study of the compatibility
between convolution algebras and infinity-morphisms of algebras and coalgebras.
We prove that the convolution algebra bifunctor can be extended to a bifunctor
that accepts infinity-morphisms in both slots and which is well defined up to
homotopy, and we generalize and take a new point of view on some other already
known results. This paper concludes a series of works by the two authors
dealing with the investigation of convolution algebras.Comment: 17 pages, 1 figure; (v2): Expanded some proofs, corrected typos,
updated references. Final versio
Evolino for recurrent support vector machines
Traditional Support Vector Machines (SVMs) need pre-wired finite time windows
to predict and classify time series. They do not have an internal state
necessary to deal with sequences involving arbitrary long-term dependencies.
Here we introduce a new class of recurrent, truly sequential SVM-like devices
with internal adaptive states, trained by a novel method called EVOlution of
systems with KErnel-based outputs (Evoke), an instance of the recent Evolino
class of methods. Evoke evolves recurrent neural networks to detect and
represent temporal dependencies while using quadratic programming/support
vector regression to produce precise outputs. Evoke is the first SVM-based
mechanism learning to classify a context-sensitive language. It also
outperforms recent state-of-the-art gradient-based recurrent neural networks
(RNNs) on various time series prediction tasks.Comment: 10 pages, 2 figure
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