31,198 research outputs found
Deep Directional Statistics: Pose Estimation with Uncertainty Quantification
Modern deep learning systems successfully solve many perception tasks such as
object pose estimation when the input image is of high quality. However, in
challenging imaging conditions such as on low-resolution images or when the
image is corrupted by imaging artifacts, current systems degrade considerably
in accuracy. While a loss in performance is unavoidable, we would like our
models to quantify their uncertainty in order to achieve robustness against
images of varying quality. Probabilistic deep learning models combine the
expressive power of deep learning with uncertainty quantification. In this
paper, we propose a novel probabilistic deep learning model for the task of
angular regression. Our model uses von Mises distributions to predict a
distribution over object pose angle. Whereas a single von Mises distribution is
making strong assumptions about the shape of the distribution, we extend the
basic model to predict a mixture of von Mises distributions. We show how to
learn a mixture model using a finite and infinite number of mixture components.
Our model allows for likelihood-based training and efficient inference at test
time. We demonstrate on a number of challenging pose estimation datasets that
our model produces calibrated probability predictions and competitive or
superior point estimates compared to the current state-of-the-art
Learning to Understand by Evolving Theories
In this paper, we describe an approach that enables an autonomous system to
infer the semantics of a command (i.e. a symbol sequence representing an
action) in terms of the relations between changes in the observations and the
action instances. We present a method of how to induce a theory (i.e. a
semantic description) of the meaning of a command in terms of a minimal set of
background knowledge. The only thing we have is a sequence of observations from
which we extract what kinds of effects were caused by performing the command.
This way, we yield a description of the semantics of the action and, hence, a
definition.Comment: KRR Workshop at ICLP 201
Generalized Lattice Gauge Theory, Spin Foams and State Sum Invariants
We construct a generalization of pure lattice gauge theory (LGT) where the
role of the gauge group is played by a tensor category. The type of tensor
category admissible (spherical, ribbon, symmetric) depends on the dimension of
the underlying manifold (<=3, <=4, any). Ordinary LGT is recovered if the
category is the (symmetric) category of representations of a compact Lie group.
In the weak coupling limit we recover discretized BF-theory in terms of a
coordinate free version of the spin foam formulation. We work on general
cellular decompositions of the underlying manifold.
In particular, we are able to formulate LGT as well as spin foam models of
BF-type with quantum gauge group (in dimension <=4) and with supersymmetric
gauge group (in any dimension).
Technically, we express the partition function as a sum over diagrams
denoting morphisms in the underlying category. On the LGT side this enables us
to introduce a generalized notion of gauge fixing corresponding to a
topological move between cellular decompositions of the underlying manifold. On
the BF-theory side this allows a rather geometric understanding of the state
sum invariants of Turaev/Viro, Barrett/Westbury and Crane/Yetter which we
recover.
The construction is extended to include Wilson loop and spin network type
observables as well as manifolds with boundaries. In the topological (weak
coupling) case this leads to TQFTs with or without embedded spin networks.Comment: 58 pages, LaTeX with AMS and XY-Pic macros; typos corrected and
references update
Localized mirror functor constructed from a Lagrangian torus
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we
define a holomorphic function W known as the Floer potential. We construct a
canonical A-infinity functor from the Fukaya category of X to the category of
matrix factorizations of W. It provides a unified way to construct matrix
factorizations from Lagrangian Floer theory. The technique is applied to toric
Fano manifolds to transform Lagrangian branes to matrix factorizations. Using
the method, we also obtain an explicit expression of the matrix factorization
mirror to the real locus of the complex projective space.Comment: 52 pages, 14 figures, Theorem 9.1 adde
Localized mirror functor constructed from a Lagrangian torus
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold , we define a holomorphic function known as the Floer potential. We construct a canonical â -functor from the Fukaya category of to the category of matrix factorizations of . It provides a unified way to construct matrix factorizations from Lagrangian Floer theory. The technique is applied to toric Fano manifolds to transform Lagrangian branes to matrix factorizations and prove homological mirror symmetry. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space.Accepted manuscrip
New Directions in Non-Relativistic and Relativistic Rotational and Multipole Kinematics for N-Body and Continuous Systems
In non-relativistic mechanics the center of mass of an isolated system is
easily separated out from the relative variables. For a N-body system these
latter are usually described by a set of Jacobi normal coordinates, based on
the clustering of the centers of mass of sub-clusters. The Jacobi variables are
then the starting point for separating {\it orientational} variables, connected
with the angular momentum constants of motion, from {\it shape} (or {\it
vibrational}) variables. Jacobi variables, however, cannot be extended to
special relativity. We show by group-theoretical methods that two new sets of
relative variables can be defined in terms of a {\it clustering of the angular
momenta of sub-clusters} and directly related to the so-called {\it dynamical
body frames} and {\it canonical spin bases}. The underlying group-theoretical
structure allows a direct extension of such notions from a non-relativistic to
a special- relativistic context if one exploits the {\it rest-frame instant
form of dynamics}. The various known definitions of relativistic center of mass
are recovered. The separation of suitable relative variables from the so-called
{\it canonical internal} center of mass leads to the correct kinematical
framework for the relativistic theory of the orbits for a N-body system with
action -at-a-distance interactions. The rest-frame instant form is also shown
to be the correct kinematical framework for introducing the Dixon multi-poles
for closed and open N-body systems, as well as for continuous systems,
exemplified here by the configurations of the Klein-Gordon field that are
compatible with the previous notions of center of mass.Comment: Latex, p.75, Invited contribution for the book {\it Atomic and
Molecular Clusters: New Research} (Nova Science
A geometric discretisation scheme applied to the Abelian Chern-Simons theory
We give a detailed general description of a recent geometrical discretisation
scheme and illustrate, by explicit numerical calculation, the scheme's ability
to capture topological features. The scheme is applied to the Abelian
Chern-Simons theory and leads, after a necessary field doubling, to an
expression for the discrete partition function in terms of untwisted
Reidemeister torsion and of various triangulation dependent factors. The
discrete partition function is evaluated computationally for various
triangulations of and of lens spaces. The results confirm that the
discretisation scheme is triangulation independent and coincides with the
continuum partition functionComment: 27 pages, 5 figures, 6 tables. in late
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