942 research outputs found
Thermofield Duality for Higher Spin Rindler Gravity
We study the Thermo-field realization of the duality between the Rindler-AdS
higher spin theory and vector theory. The CFT represents a decoupled
pair of free vector field theories. It is shown how this decoupled
domain CFT is capable of generating the connected Rindler-AdS background with
the full set of Higher Spin fields.Comment: 23 pages, 1 figure; v2 reference added; v3 presentation modified and
typos correcte
Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks
Convolutional neural networks (CNNs) have been shown to achieve optimal
approximation and estimation error rates (in minimax sense) in several function
classes. However, previous analyzed optimal CNNs are unrealistically wide and
difficult to obtain via optimization due to sparse constraints in important
function classes, including the H\"older class. We show a ResNet-type CNN can
attain the minimax optimal error rates in these classes in more plausible
situations -- it can be dense, and its width, channel size, and filter size are
constant with respect to sample size. The key idea is that we can replicate the
learning ability of Fully-connected neural networks (FNNs) by tailored CNNs, as
long as the FNNs have \textit{block-sparse} structures. Our theory is general
in a sense that we can automatically translate any approximation rate achieved
by block-sparse FNNs into that by CNNs. As an application, we derive
approximation and estimation error rates of the aformentioned type of CNNs for
the Barron and H\"older classes with the same strategy.Comment: 8 pages + References 2 pages + Supplemental material 18 page
Space-Time in the SYK Model
We consider the question of identifying the bulk space-time of the SYK model.
Focusing on the signature of emergent space-time of the (Euclidean) model, we
explain the need for non-local (Radon-type) transformations on external legs of
-point Green's functions. This results in a dual theory with Euclidean AdS
signature with additional leg-factors. We speculate that these factors
incorporate the coupling of additional bulk states similar to the discrete
states of 2d string theory.Comment: 24 pages, 1 figure; v2: published version in JHEP with minor
correction
Higher order Painleve systems of type , Drinfeld-Sokolov hierarchies and Fuchsian systems (Progress in Mathematics of Integrable Systems)
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