327 research outputs found
The complex gradient inequality with parameter
We prove that given a holomorphic family of holomorphic functions with
isolated singularities at zero and constant Milnor number, it is possible to
obtain the gradient inequality with a uniform exponent.Comment: A remark was added at the end and some misprints were correcte
Testing Lipschitz non normally embedded complex spaces
We introduce a sectional criterion for testing if complex analytic germs
(X,0) \subset (\bC^n, 0) are Lipschitz non normally embedded.Comment: title changed; more introduction. revised before printin
Stronger Baselines for Trustable Results in Neural Machine Translation
Interest in neural machine translation has grown rapidly as its effectiveness
has been demonstrated across language and data scenarios. New research
regularly introduces architectural and algorithmic improvements that lead to
significant gains over "vanilla" NMT implementations. However, these new
techniques are rarely evaluated in the context of previously published
techniques, specifically those that are widely used in state-of-theart
production and shared-task systems. As a result, it is often difficult to
determine whether improvements from research will carry over to systems
deployed for real-world use. In this work, we recommend three specific methods
that are relatively easy to implement and result in much stronger experimental
systems. Beyond reporting significantly higher BLEU scores, we conduct an
in-depth analysis of where improvements originate and what inherent weaknesses
of basic NMT models are being addressed. We then compare the relative gains
afforded by several other techniques proposed in the literature when starting
with vanilla systems versus our stronger baselines, showing that experimental
conclusions may change depending on the baseline chosen. This indicates that
choosing a strong baseline is crucial for reporting reliable experimental
results.Comment: To appear at the Workshop on Neural Machine Translation (WNMT
The Kuratowski convergence of medial axes and conflict sets
This paper consists of two parts. In the first one we study the behaviour of
medial axes (skeletons) of closed, definable (in some o-minimal structure) sets
in {\Rz}^n under deformations. The second one is devoted to a similar study
of conflict sets in definable families. We apply a new approach to the
deformation process. Instead of seeing it as a `jump' from the initial to the
final state, we perceive it as a continuous process, expressed using the
Kuratowski convergence of sets (hence, unlike other authors, we do not require
any regularity of the deformation). Our main `medial axis inner
semi-continuity' result has already proved useful, as it was used to compute
the tangent cone of the medial axis with application in singularity theory.Comment: The preprint has been extended to include also the study of the
behaviour of the conflict set of a continuous family of definable sets
performed with a new co-author. Therefore the title has slightly been
changed, too. Besides that, the references have also been updated and in the
last version we strengthened the statement of Theorem 5.1
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