Neural Networks with Complex-Valued Weights Have No Spurious Local
Minima
January 31, 2021
Computer Science
Statistics
Machine Learning
Machine Learning
We study the benefits of complex-valued weights for neural networks. We prove
that shallow complex neural networks with quadratic activations have no
spurious local minima. In contrast, shallow real neural networks with quadratic
activation...
Polyphone Disambiguation in Mandarin Chinese with Semi-Supervised
Learning
January 31, 2021
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Computer Science
Computation and Language
Artificial Intelligence
The majority of Chinese characters are monophonic, while a special group of
characters, called polyphonic characters, have multiple pronunciations. As a
prerequisite of performing speech-related generative tasks, the correct
pronunciation m...
A Matrix-based Distance of Pythagorean Fuzzy Set and its Application in
Medical Diagnosis
January 31, 2021
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Computer Science
Artificial Intelligence
The pythagorean fuzzy set (PFS) which is developed based on intuitionistic
fuzzy set, is more efficient in elaborating and disposing uncertainties in
indeterminate situations, which is a very reason of that PFS is applied in
various kinds o...
Energy in Fourth Order Gravity
January 31, 2021
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Mathematics
Physics
Differential Geometry
Mathematical Physics
Mathematical Physics
In this paper we make a detailed analysis of conservation principles in the
context of a family of fourth-order gravitational theories generated via a
quadratic Lagrangian. In particular, we focus on the associated notion of
energy and star...
Schubert puzzles and integrability II: multiplying motivic Segre classes
January 31, 2021
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Mathematics
Physics
Algebraic Geometry
Mathematical Physics
Combinatorics
Mathematical Physics
In Schubert Puzzles and Integrability I we proved several "puzzle rules" for
computing products of Schubert classes in K-theory (and sometimes equivariant
K-theory) of d-step flag varieties. The principal tool was "quantum
integrability", i...
Monotone additive statistics
January 31, 2021
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Economics
Mathematics
Statistics
Theoretical Economics
Probability
Statistics Theory
Statistics Theory
The expectation is an example of a descriptive statistic that is monotone
with respect to stochastic dominance, and additive for sums of independent
random variables. We provide a complete characterization of such statistics,
and explore a ...
On the Universal Coefficient Formula and Derived lim(i)
Functor
January 31, 2021
|
Mathematics
Algebraic Topology
It is known that homology and inverse limit functors do not commute. In the
paper we consider this very problem and find its application for various
homology theories. In particular, on the category of general topological
spaces, there are ...
Edge states for second order elliptic operators in a channel
January 30, 2021
Mathematics
Physics
Mathematical Physics
Mathematical Physics
Materials Science
Analysis of PDEs
We present a general framework to study edge states for second order elliptic
operators in a half channel. We associate an integer valued index to some bulk
materials, and we prove that for any junction between two such materials,
localised...
Acoustic Structure Inverse Design and Optimization Using Deep Learning
January 29, 2021
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Computer Science
Physics
Sound
Machine Learning
Applied Physics
From ancient to modern times, acoustic structures have been used to control
the propagation of acoustic waves. However, the design of the acoustic
structures has remained widely a time-consuming and computational
resource-consuming iterativ...
A long-distance quantum-capable internet testbed
January 29, 2021
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Physics
Quantum Physics
Building a Quantum Internet requires the development of innovative
quantum-enabling networking architectures that integrate advanced communication
systems with long-distance quantum communication hardware. Here, we present the
implementatio...