Construction of Hierarchically Semi-Separable matrix Representation
using Adaptive Johnson-Lindenstrauss Sketching
February 3, 2023
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
Numerical Analysis
Numerical Analysis
We present an extension of an adaptive, partially matrix-free, Hierarchically
Semi-Separable (HSS) matrix construction algorithm by Gorman et al. [SIAM J.
Sci. Comput. 41(5), 2019] which uses Gaussian sketching operators to a broader
class ...
Many-body enhancement in a spin-chain quantum heat engine
February 3, 2023
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Physics
Quantum Physics
Quantum Gases
Quantum Physics
Quantum Gases
We show that ferromagnetic interactions can enhance the adiabatic performance
of a quantum spin chain engine at low temperatures. The enhancement in work
output is particular pronounced, increasing exponentially with interaction
strength. T...
Sample Complexity of Probability Divergences under Group Symmetry
February 3, 2023
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Mathematics
Statistics
Statistics Theory
Machine Learning
Statistics Theory
Statistics Theory
Machine Learning
Statistics Theory
We rigorously quantify the improvement in the sample complexity of
variational divergence estimations for group-invariant distributions. In the
cases of the Wasserstein-1 metric and the Lipschitz-regularized
α-divergences, the reduct...
Evaluating Large Language Models in Theory of Mind Tasks
February 3, 2023
Computer Science
Computation and Language
Computers and Society
Human-Computer Interaction
Eleven Large Language Models (LLMs) were assessed using a custom-made battery
of false-belief tasks, considered a gold standard in testing Theory of Mind
(ToM) in humans. The battery included 640 prompts spread across 40 diverse
tasks, each...
Covariance Matrix Estimation for High-Throughput Biomedical Data with
Interconnected Communities
February 3, 2023
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Statistics
Methodology
Estimating a covariance matrix is central to high-dimensional data analysis.
Empirical analyses of high-dimensional biomedical data, including genomics,
proteomics, microbiome, and neuroimaging, among others, consistently reveal
strong modu...
Flat fully augmented links are determined by their complements
February 3, 2023
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Mathematics
Geometric Topology
In this paper, we show that two flat fully augmented links with homeomorphic
complements must be equivalent as links in S3. This requires a
careful analysis of how totally geodesic surfaces and cusps intersect in these
link co...
Degenerate Complex Monge Ampere Equation Part I
February 3, 2023
Mathematics
Differential Geometry
Analysis of PDEs
We describe the behavior of the singularities of solutions to degenerate
complex Monge-Amp`ere equations on K\"ahler manifolds. This was not resolved
since the fundamental paper of S-T Yau \cite{y} on this subject....
The Role of Game Networking in the Fusion of Physical and Digital Worlds
through 6G Wireless Networks
February 3, 2023
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Electrical Engineering and Systems Science
Computer Science
Signal Processing
Networking and Internet Architecture
The sixth generation (6G) of wireless technology is seen as one of the
enablers of real-time fusion of the physical and digital realms, as in Digital
Twin, eXtended reality, or the Metaverse. This would allow people to interact,
work, and e...
Blockwise Self-Supervised Learning at Scale
February 3, 2023
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Computer Science
Computer Vision and Pattern Recognition
Artificial Intelligence
Machine Learning
Current state-of-the-art deep networks are all powered by backpropagation. In
this paper, we explore alternatives to full backpropagation in the form of
blockwise learning rules, leveraging the latest developments in self-supervised
learnin...
Tubings, chord diagrams, and Dyson--Schwinger equations
February 3, 2023
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Mathematics
Physics
Combinatorics
High Energy Physics - Theory
Mathematical Physics
Mathematical Physics
We give series solutions to single insertion place propagator-type systems of
Dyson--Schwinger equations using binary tubings of rooted trees. These
solutions are combinatorially transparent in the sense that each tubing has a
straightforwa...