Expand-and-Cluster: Parameter Recovery of Neural Networks
April 25, 2023
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Computer Science
Neural and Evolutionary Computing
Can we identify the weights of a neural network by probing its input-output
mapping? At first glance, this problem seems to have many solutions because of
permutation, overparameterisation and activation function symmetries. Yet, we
show th...
The mod-2 cohomology groups of low-dimensional unordered flag manifolds
and Auerbach bases
April 25, 2023
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Mathematics
Algebraic Topology
Functional Analysis
Unordered flag manifolds are the manifolds of unordered n-tuple of mutually
orthogonal lines in Rn. In this paper, we develop some basic tools
to compute the mod-2 cohomology groups of these spaces, and apply them for
explic...
Succinct quantum testers for closeness and k-wise uniformity of
probability distributions
April 25, 2023
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Physics
Quantum Physics
We explore potential quantum speedups for the fundamental problem of testing
the properties of closeness and k-wise uniformity of probability
distributions.
\textit{Closeness testing} is the problem of distinguishing whether two
n-dim...
Exact values and improved bounds on the clique number of cyclotomic
graphs
April 25, 2023
Mathematics
Combinatorics
Number Theory
Let q be an odd power of a prime p, and S⊂Fq∗ such
that S=−S and S/S=Fq∗. We show that the clique number of
the Cayley graph Cay(Fq+,S) is at most
$\sqrt{|S/S|}+\sqrt{...
Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
April 25, 2023
Physics
Strongly Correlated Electrons
Quantum Physics
Realizing topological orders and topological quantum computation is a central
task of modern physics. An important but notoriously hard question in this
endeavor is how to diagnose topological orders that lack conventional order
parameters....
Nonlocality and Nonlinearity Implies Universality in Operator Learning
April 25, 2023
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Mathematics
Computer Science
Numerical Analysis
Machine Learning
Numerical Analysis
Neural operator architectures approximate operators between
infinite-dimensional Banach spaces of functions. They are gaining increased
attention in computational science and engineering, due to their potential both
to accelerate traditiona...
Homotopy Prefactorization Algebras
April 25, 2023
|
Mathematics
Algebraic Topology
Quantum Algebra
We apply the theory of operadic Koszul duality to provide a cofibrant
resolution of the colored operad whose algebras are prefactorization algebras
on a fixed space M. his allows us to describe a notion of prefactorization
algebra up to hom...
Normal forms for quasi-elliptic Enriques surfaces and applications
April 25, 2023
|
Mathematics
Algebraic Geometry
We work out normal forms for quasi-elliptic Enriques surfaces and give
several applications. These include torsors and numerically trivial
automorphisms, but our main application is the completion of the classification
of Enriques surfaces ...
MRI Recovery with Self-Calibrated Denoisers without Fully-Sampled Data
April 25, 2023
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Electrical Engineering and Systems Science
Image and Video Processing
Objective: Acquiring fully sampled training data is challenging for many MRI
applications. We present a self-supervised image reconstruction method, termed
ReSiDe, capable of recovering images solely from undersampled data.
Materials and ...
Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra
across Symmetries, Constraints, and Long-Range Interactions
April 25, 2023
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Physics
Strongly Correlated Electrons
Statistical Mechanics
Quantum Physics
We identify emergent hydrodynamics governing charge transport in Brownian
random circuits with various symmetries, constraints, and ranges of
interactions. This is accomplished via a mapping between the averaged dynamics
and the low energy ...