34,195 research outputs found
Revealing quantum chaos with machine learning
Understanding properties of quantum matter is an outstanding challenge in
science. In this paper, we demonstrate how machine-learning methods can be
successfully applied for the classification of various regimes in
single-particle and many-body systems. We realize neural network algorithms
that perform a classification between regular and chaotic behavior in quantum
billiard models with remarkably high accuracy. We use the variational
autoencoder for autosupervised classification of regular/chaotic wave
functions, as well as demonstrating that variational autoencoders could be used
as a tool for detection of anomalous quantum states, such as quantum scars. By
taking this method further, we show that machine learning techniques allow us
to pin down the transition from integrability to many-body quantum chaos in
Heisenberg XXZ spin chains. For both cases, we confirm the existence of
universal W shapes that characterize the transition. Our results pave the way
for exploring the power of machine learning tools for revealing exotic
phenomena in quantum many-body systems.Comment: 12 pages, 12 figure
Extended Object Tracking: Introduction, Overview and Applications
This article provides an elaborate overview of current research in extended
object tracking. We provide a clear definition of the extended object tracking
problem and discuss its delimitation to other types of object tracking. Next,
different aspects of extended object modelling are extensively discussed.
Subsequently, we give a tutorial introduction to two basic and well used
extended object tracking approaches - the random matrix approach and the Kalman
filter-based approach for star-convex shapes. The next part treats the tracking
of multiple extended objects and elaborates how the large number of feasible
association hypotheses can be tackled using both Random Finite Set (RFS) and
Non-RFS multi-object trackers. The article concludes with a summary of current
applications, where four example applications involving camera, X-band radar,
light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are
highlighted.Comment: 30 pages, 19 figure
Deformation Quantization of Poisson Structures Associated to Lie Algebroids
In the present paper we explicitly construct deformation quantizations of
certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although
the considered Poisson structures in general are far from being regular or even
symplectic, our construction gets along without Kontsevich's formality theorem
but is based on a generalized Fedosov construction. As the whole construction
merely uses geometric structures of E we also succeed in determining the
dependence of the resulting star products on these data in finding appropriate
equivalence transformations between them. Finally, the concreteness of the
construction allows to obtain explicit formulas even for a wide class of
derivations and self-equivalences of the products. Moreover, we can show that
some of our products are in direct relation to the universal enveloping algebra
associated to the Lie algebroid. Finally, we show that for a certain class of
star products on E^* the integration with respect to a density with vanishing
modular vector field defines a trace functional
Graph Element Networks: adaptive, structured computation and memory
We explore the use of graph neural networks (GNNs) to model spatial processes
in which there is no a priori graphical structure. Similar to finite element
analysis, we assign nodes of a GNN to spatial locations and use a computational
process defined on the graph to model the relationship between an initial
function defined over a space and a resulting function in the same space. We
use GNNs as a computational substrate, and show that the locations of the nodes
in space as well as their connectivity can be optimized to focus on the most
complex parts of the space. Moreover, this representational strategy allows the
learned input-output relationship to generalize over the size of the underlying
space and run the same model at different levels of precision, trading
computation for accuracy. We demonstrate this method on a traditional PDE
problem, a physical prediction problem from robotics, and learning to predict
scene images from novel viewpoints.Comment: Accepted to ICML 201
Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis
We introduce a data-driven approach to complete partial 3D shapes through a
combination of volumetric deep neural networks and 3D shape synthesis. From a
partially-scanned input shape, our method first infers a low-resolution -- but
complete -- output. To this end, we introduce a 3D-Encoder-Predictor Network
(3D-EPN) which is composed of 3D convolutional layers. The network is trained
to predict and fill in missing data, and operates on an implicit surface
representation that encodes both known and unknown space. This allows us to
predict global structure in unknown areas at high accuracy. We then correlate
these intermediary results with 3D geometry from a shape database at test time.
In a final pass, we propose a patch-based 3D shape synthesis method that
imposes the 3D geometry from these retrieved shapes as constraints on the
coarsely-completed mesh. This synthesis process enables us to reconstruct
fine-scale detail and generate high-resolution output while respecting the
global mesh structure obtained by the 3D-EPN. Although our 3D-EPN outperforms
state-of-the-art completion method, the main contribution in our work lies in
the combination of a data-driven shape predictor and analytic 3D shape
synthesis. In our results, we show extensive evaluations on a newly-introduced
shape completion benchmark for both real-world and synthetic data
NetLSD: Hearing the Shape of a Graph
Comparison among graphs is ubiquitous in graph analytics. However, it is a
hard task in terms of the expressiveness of the employed similarity measure and
the efficiency of its computation. Ideally, graph comparison should be
invariant to the order of nodes and the sizes of compared graphs, adaptive to
the scale of graph patterns, and scalable. Unfortunately, these properties have
not been addressed together. Graph comparisons still rely on direct approaches,
graph kernels, or representation-based methods, which are all inefficient and
impractical for large graph collections.
In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD):
the first, to our knowledge, permutation- and size-invariant, scale-adaptive,
and efficiently computable graph representation method that allows for
straightforward comparisons of large graphs. NetLSD extracts a compact
signature that inherits the formal properties of the Laplacian spectrum,
specifically its heat or wave kernel; thus, it hears the shape of a graph. Our
evaluation on a variety of real-world graphs demonstrates that it outperforms
previous works in both expressiveness and efficiency.Comment: KDD '18: The 24th ACM SIGKDD International Conference on Knowledge
Discovery & Data Mining, August 19--23, 2018, London, United Kingdo
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