4,964 research outputs found
Beam Profiler Network (BPNet) -- A Deep Learning Approach to Mode Demultiplexing of Laguerre-Gaussian Optical Beams
The transverse field profile of light is being recognized as a resource for
classical and quantum communications for which reliable methods of sorting or
demultiplexing spatial optical modes are required. Here, we demonstrate,
experimentally, state-of-the-art mode demultiplexing of Laguerre-Gaussian beams
according to both their orbital angular momentum and radial topological numbers
using a flow of two concatenated deep neural networks. The first network serves
as a transfer function from experimentally-generated to ideal
numerically-generated data, while using a unique "Histogram Weighted Loss"
function that solves the problem of images with limited significant
information. The second network acts as a spatial-modes classifier. Our method
uses only the intensity profile of modes or their superposition, making the
phase information redundant
Graph Filtration Learning
We propose an approach to learning with graph-structured data in the problem
domain of graph classification. In particular, we present a novel type of
readout operation to aggregate node features into a graph-level representation.
To this end, we leverage persistent homology computed via a real-valued,
learnable, filter function. We establish the theoretical foundation for
differentiating through the persistent homology computation. Empirically, we
show that this type of readout operation compares favorably to previous
techniques, especially when the graph connectivity structure is informative for
the learning problem
Classifying Signals on Irregular Domains via Convolutional Cluster Pooling
We present a novel and hierarchical approach for supervised classification of
signals spanning over a fixed graph, reflecting shared properties of the
dataset. To this end, we introduce a Convolutional Cluster Pooling layer
exploiting a multi-scale clustering in order to highlight, at different
resolutions, locally connected regions on the input graph. Our proposal
generalises well-established neural models such as Convolutional Neural
Networks (CNNs) on irregular and complex domains, by means of the exploitation
of the weight sharing property in a graph-oriented architecture. In this work,
such property is based on the centrality of each vertex within its
soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS
demonstrate the effectiveness of the proposed technique in capturing both local
and global patterns in graph-structured data out of different domains.Comment: 12 pages, 6 figures. To appear in the Proceedings of the 22nd
International Conference on Artificial Intelligence and Statistics (AISTATS)
2019, Naha, Okinawa, Japan. PMLR: Volume 8
Network Horizon Dynamics I: Qualitative Aspects
Mostly acyclic directed networks, treated mathematically as directed graphs,
arise in machine learning, biology, social science, physics, and other
applications. Newman [1] has noted the mathematical challenges of such
networks. In this series of papers, we study their connectivity properties,
focusing on three types of phase transitions that affect horizon sizes for
typical nodes. The first two types involve the familiar emergence of giant
components as average local connectivity increases, while the third type
involves small-world horizon growth at variable distance from a typical node.
In this first paper, we focus on qualitative behavior, simulations, and
applications, leaving formal considerations for subsequent papers. We explain
how such phase transitions distinguish deep neural networks from shallow
machine learning architectures, and propose hybrid local/random network designs
with surprising connectivity advantages. We also propose a small-world approach
to the horizon problem in the cosmology of the early universe as a novel
alternative to the inflationary hypothesis of Guth and Linde.Comment: 45 pages, 22 figure
Adversary Detection in Neural Networks via Persistent Homology
We outline a detection method for adversarial inputs to deep neural networks.
By viewing neural network computations as graphs upon which information flows
from input space to out- put distribution, we compare the differences in graphs
induced by different inputs. Specifically, by applying persistent homology to
these induced graphs, we observe that the structure of the most persistent
subgraphs which generate the first homology group differ between adversarial
and unperturbed inputs. Based on this observation, we build a detection
algorithm that depends only on the topological information extracted during
training. We test our algorithm on MNIST and achieve 98% detection adversary
accuracy with F1-score 0.98.Comment: 16 page
Profile approach for recognition of three-dimensional magnetic structures
We propose an approach for low-dimensional visualisation and classification
of complex topological magnetic structures formed in magnetic materials. Within
the approach one converts a three-dimensional magnetic configuration to a
vector containing the only components of the spins that are parallel to the z
axis. The next crucial step is to sort the vector elements in ascending or
descending order. Having visualized profiles of the sorted spin vectors one can
distinguish configurations belonging to different phases even with the same
total magnetization. For instance, spin spiral and paramagnetic states with
zero total magnetic moment can be easily identified. Being combined with a
simplest neural network our profile approach provides a very accurate phase
classification for three-dimensional magnets characterized by complex
multispiral states even in the critical areas close to phases transitions. By
the example of the skyrmionic configurations we show that profile approach can
be used to separate the states belonging to the same phase
A Growing Self-Organizing Network for Reconstructing Curves and Surfaces
Self-organizing networks such as Neural Gas, Growing Neural Gas and many
others have been adopted in actual applications for both dimensionality
reduction and manifold learning. Typically, in these applications, the
structure of the adapted network yields a good estimate of the topology of the
unknown subspace from where the input data points are sampled. The approach
presented here takes a different perspective, namely by assuming that the input
space is a manifold of known dimension. In return, the new type of growing
self-organizing network presented gains the ability to adapt itself in way that
may guarantee the effective and stable recovery of the exact topological
structure of the input manifold
Mesoscopic analysis of networks: applications to exploratory analysis and data clustering
We investigate the adaptation and performance of modularity-based algorithms,
designed in the scope of complex networks, to analyze the mesoscopic structure
of correlation matrices. Using a multi-resolution analysis we are able to
describe the structure of the data in terms of clusters at different
topological levels. We demonstrate the applicability of our findings in two
different scenarios: to analyze the neural connectivity of the nematode {\em
Caenorhabditis elegans}, and to automatically classify a typical benchmark of
unsupervised clustering, the Iris data set, with considerable success.Comment: Chaos (2011) in pres
On a lower bound for sorting signed permutations by reversals
Computing the reversal distances of signed permutations is an important topic
in Bioinformatics. Recently, a new lower bound for the reversal distance was
obtained via the plane permutation framework. This lower bound appears
different from the existing lower bound obtained by Bafna and Pevzner through
breakpoint graphs. In this paper, we prove that the two lower bounds are equal.
Moreover, we confirm a related conjecture on skew-symmetric plane permutations,
which can be restated as follows: let
and let
be any long cycle on the set . Then,
and are always in the same cycle of the product .
Furthermore, we show the new lower bound via plane permutations can be
interpreted as the topological genera of orientable surfaces associated to
signed permutations.Comment: slightly update
Learning Vertex Convolutional Networks for Graph Classification
In this paper, we develop a new aligned vertex convolutional network model to
learn multi-scale local-level vertex features for graph classification. Our
idea is to transform the graphs of arbitrary sizes into fixed-sized aligned
vertex grid structures, and define a new vertex convolution operation by
adopting a set of fixed-sized one-dimensional convolution filters on the grid
structure. We show that the proposed model not only integrates the precise
structural correspondence information between graphs but also minimises the
loss of structural information residing on local-level vertices. Experiments on
standard graph datasets demonstrate the effectiveness of the proposed model.Comment: arXiv admin note: text overlap with arXiv:1809.0109
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