4,499 research outputs found
Vertex Algebras and Mirror Symmetry
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now
well established. However, previous approaches to it did not uncover the
underlying reason for mirror varieties to be mirror. We are able to calculate
explicitly vertex algebras that correspond to holomorphic parts of A and B
models of Calabi-Yau hypersurfaces and complete intersections in toric
varieties. We establish the relation between these vertex algebras for mirror
Calabi-Yau manifolds. This should eventually allow us to rewrite the whole
story of toric Mirror Symmetry in the language of sheaves of vertex algebras.
Our approach is purely algebraic and involves simple techniques from toric
geometry and homological algebra, as well as some basic results of the theory
of vertex algebras. Ideas of this paper may also be useful in other problems
related to maps from curves to algebraic varieties. This paper could also be of
interest to physicists, because it contains explicit descriptions of A and B
models of Calabi-Yau hypersurfaces and complete intersection in terms of free
bosons and fermions.Comment: 45 pages, Late
Learning Discriminative Features with Class Encoder
Deep neural networks usually benefit from unsupervised pre-training, e.g.
auto-encoders. However, the classifier further needs supervised fine-tuning
methods for good discrimination. Besides, due to the limits of full-connection,
the application of auto-encoders is usually limited to small, well aligned
images. In this paper, we incorporate the supervised information to propose a
novel formulation, namely class-encoder, whose training objective is to
reconstruct a sample from another one of which the labels are identical.
Class-encoder aims to minimize the intra-class variations in the feature space,
and to learn a good discriminative manifolds on a class scale. We impose the
class-encoder as a constraint into the softmax for better supervised training,
and extend the reconstruction on feature-level to tackle the parameter size
issue and translation issue. The experiments show that the class-encoder helps
to improve the performance on benchmarks of classification and face
recognition. This could also be a promising direction for fast training of face
recognition models.Comment: Accepted by CVPR2016 Workshop of Robust Features for Computer Visio
Probabilities in the inflationary multiverse
Inflationary cosmology leads to the picture of a "multiverse," involving an
infinite number of (spatially infinite) post-inflationary thermalized regions,
called pocket universes. In the context of theories with many vacua, such as
the landscape of string theory, the effective constants of Nature are
randomized by quantum processes during inflation. We discuss an analytic
estimate for the volume distribution of the constants within each pocket
universe. This is based on the conjecture that the field distribution is
approximately ergodic in the diffusion regime, when the dynamics of the fields
is dominated by quantum fluctuations (rather than by the classical drift). We
then propose a method for determining the relative abundances of different
types of pocket universes. Both ingredients are combined into an expression for
the distribution of the constants in pocket universes of all types.Comment: 18 pages, RevTeX 4, 2 figures. Discussion of the full probability in
Sec.VI is sharpened; the conclusions are strengthened. Note added explaining
the relation to recent work by Easther, Lim and Martin. Some references adde
Bounded-Distortion Metric Learning
Metric learning aims to embed one metric space into another to benefit tasks
like classification and clustering. Although a greatly distorted metric space
has a high degree of freedom to fit training data, it is prone to overfitting
and numerical inaccuracy. This paper presents {\it bounded-distortion metric
learning} (BDML), a new metric learning framework which amounts to finding an
optimal Mahalanobis metric space with a bounded-distortion constraint. An
efficient solver based on the multiplicative weights update method is proposed.
Moreover, we generalize BDML to pseudo-metric learning and devise the
semidefinite relaxation and a randomized algorithm to approximately solve it.
We further provide theoretical analysis to show that distortion is a key
ingredient for stability and generalization ability of our BDML algorithm.
Extensive experiments on several benchmark datasets yield promising results
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