Exponential convergence rates for momentum stochastic gradient descent
in the overparametrized setting
February 7, 2023
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Mathematics
Computer Science
Statistics
Optimization and Control
Machine Learning
Probability
Machine Learning
We prove explicit bounds on the exponential rate of convergence for the
momentum stochastic gradient descent scheme (MSGD) for arbitrary, fixed
hyperparameters (learning rate, friction parameter) and its continuous-in-time
counterpart in th...
Polyhedral Clinching Auctions with a Single Sample
February 7, 2023
Computer Science
Computer Science and Game Theory
We address auctions in two-sided markets with budget constraints on buyers, a
fundamental setting also crucial for applications such as display advertising.
Our goal is to design efficient mechanisms that satisfy dominant strategy
incentive...
Kerr-fully Diving into the Abyss: Analytic Solutions to Plunging
Geodesics in Kerr
February 7, 2023
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Physics
General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
We present closed-form solutions for plunging geodesics in the extended Kerr
spacetime using Boyer-Lindquist coordinates. Our solutions directly solve for
the dynamics of generic timelike plunges, we also specialise to the case of
test part...
NeuronsGym: A Hybrid Framework and Benchmark for Robot Tasks with
Sim2Real Policy Learning
February 7, 2023
| | | | |
Computer Science
Robotics
The rise of embodied AI has greatly improved the possibility of general
mobile agent systems. At present, many evaluation platforms with rich scenes,
high visual fidelity and various application scenarios have been developed. In
this paper,...
Conformal measure rigidity for representations via self-joinings
February 7, 2023
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Mathematics
Geometric Topology
Dynamical Systems
Group Theory
Let Γ be a Zariski dense discrete subgroup of a connected simple real
algebraic group G1. We discuss a rigidity problem for discrete faithful
representations ρ:Γ→G2 and a surprising role played by higher
rank conform...
Fluctuations of Schensted row insertion
February 7, 2023
|
Mathematics
Probability
Combinatorics
We investigate asymptotic probabilistic phenomena arising from the
application of the Schensted row insertion algorithm, a key component of the
Robinson-Schensted-Knuth (RSK) correspondence, to random inputs. Our analysis
centers on a rando...
The Harer-Zagier and Jackson formulas and new results for one-face
bipartite maps
February 7, 2023
Mathematics
Combinatorics
The study of bipartite maps (or Grothendieck's dessins d'enfants) is closely
connected with geometry, mathematical physics and free probability. Here we
study these objects from their permutation factorization formulation using a
novel char...
Decompositions and Terracini loci of cubic forms of low rank
February 7, 2023
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Mathematics
Algebraic Geometry
We study Waring rank decompositions for cubic forms of rank n+2 in n+1
variables. In this setting, we prove that if a concise form has more than one
non-redundant decomposition of length n+2, then all such decompositions share
at leas...
Structured Generative Models for Scene Understanding
February 7, 2023
Computer Science
Computer Vision and Pattern Recognition
This position paper argues for the use of \emph{structured generative models}
(SGMs) for the understanding of static scenes. This requires the reconstruction
of a 3D scene from an input image (or a set of multi-view images), whereby the
con...
Sums of Powers by L'Hopital's Rule
February 7, 2023
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Mathematics
Number Theory
For a positive integer d, let pd(n):=0d+1d+2d+⋯+nd;
i.e., pd(n) is the sum of the first dth-powers up to n. It's
well known that pd(n) is a polynomial of degree d+1 in n. While this is
usual...