936 research outputs found
Off-shell hydrodynamics from holography
We outline a program for obtaining an action principle for dissipative fluid
dynamics by considering the holographic Wilsonian renormalization group applied
to systems with a gravity dual. As a first step, in this paper we restrict to
systems with a non-dissipative horizon. By integrating out gapped degrees of
freedom in the bulk gravitational system between an asymptotic boundary and a
horizon, we are led to a formulation of hydrodynamics where the dynamical
variables are not standard velocity and temperature fields, but the relative
embedding of the boundary and horizon hypersurfaces. At zeroth order, this
action reduces to that proposed by Dubovsky et al. as an off-shell formulation
of ideal fluid dynamics.Comment: 34 pages, 2 figures; v2: references added, clarifications added in
Sec. I
Nationality Classification Using Name Embeddings
Nationality identification unlocks important demographic information, with
many applications in biomedical and sociological research. Existing name-based
nationality classifiers use name substrings as features and are trained on
small, unrepresentative sets of labeled names, typically extracted from
Wikipedia. As a result, these methods achieve limited performance and cannot
support fine-grained classification.
We exploit the phenomena of homophily in communication patterns to learn name
embeddings, a new representation that encodes gender, ethnicity, and
nationality which is readily applicable to building classifiers and other
systems. Through our analysis of 57M contact lists from a major Internet
company, we are able to design a fine-grained nationality classifier covering
39 groups representing over 90% of the world population. In an evaluation
against other published systems over 13 common classes, our F1 score (0.795) is
substantial better than our closest competitor Ethnea (0.580). To the best of
our knowledge, this is the most accurate, fine-grained nationality classifier
available.
As a social media application, we apply our classifiers to the followers of
major Twitter celebrities over six different domains. We demonstrate stark
differences in the ethnicities of the followers of Trump and Obama, and in the
sports and entertainments favored by different groups. Finally, we identify an
anomalous political figure whose presumably inflated following appears largely
incapable of reading the language he posts in.Comment: 10 pages, 9 figures, 4 table, accepted by CIKM 2017, Demo and free
API: www.name-prism.co
Joint multiple dictionary learning for tensor sparse coding
Traditional dictionary learning algorithms are used for finding a sparse representation on high dimensional
data by transforming samples into a one-dimensional (1D)
vector. This 1D model loses the inherent spatial structure property of data. An alternative solution is to employ Tensor Decomposition for dictionary learning on their original structural form —a tensor— by learning multiple dictionaries along each mode and the corresponding sparse representation in respect to the Kronecker product of these dictionaries. To learn tensor
dictionaries along each mode, all the existing methods update each dictionary iteratively in an alternating manner. Because atoms from each mode dictionary jointly make contributions to the sparsity of tensor, existing works ignore atoms correlations between different mode dictionaries by treating each mode dictionary independently. In this paper, we propose a joint multiple dictionary learning method for tensor sparse coding,
which explores atom correlations for sparse representation and updates multiple atoms from each mode dictionary simultaneously. In this algorithm, the Frequent-Pattern Tree (FP-tree) mining algorithm is employed to exploit frequent atom patterns in the sparse representation. Inspired by the idea of K-SVD, we develop a new dictionary update method that jointly updates
elements in each pattern. Experimental results demonstrate our method outperforms other tensor based dictionary learning algorithms
Tensor regression based on linked multiway parameter analysis
Classical regression methods take vectors as covariates
and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to
efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the
regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm,
the number of independent parameters along each mode is
constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets
Is Stochastic Gradient Descent Near Optimal?
The success of neural networks over the past decade has established them as
effective models for many relevant data generating processes. Statistical
theory on neural networks indicates graceful scaling of sample complexity. For
example, Joen & Van Roy (arXiv:2203.00246) demonstrate that, when data is
generated by a ReLU teacher network with parameters, an optimal learner
needs only samples to attain expected error .
However, existing computational theory suggests that, even for
single-hidden-layer teacher networks, to attain small error for all such
teacher networks, the computation required to achieve this sample complexity is
intractable. In this work, we fit single-hidden-layer neural networks to data
generated by single-hidden-layer ReLU teacher networks with parameters drawn
from a natural distribution. We demonstrate that stochastic gradient descent
(SGD) with automated width selection attains small expected error with a number
of samples and total number of queries both nearly linear in the input
dimension and width. This suggests that SGD nearly achieves the
information-theoretic sample complexity bounds of Joen & Van Roy
(arXiv:2203.00246) in a computationally efficient manner. An important
difference between our positive empirical results and the negative theoretical
results is that the latter address worst-case error of deterministic
algorithms, while our analysis centers on expected error of a stochastic
algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:2203.0024
Quantum teleportation implies symmetry-protected topological order
We constrain a broad class of teleportation protocols using insights from
locality. In the "standard" teleportation protocols we consider, all
outcome-dependent unitaries are Pauli operators conditioned on linear functions
of the measurement outcomes. We find that all such protocols involve preparing
a "resource state" exhibiting symmetry-protected topological (SPT) order with
Abelian protecting symmetry . The logical states are teleported between the edges of
the chain by measuring the corresponding string order parameters in the
bulk and applying outcome-dependent Paulis. Hence, this single class of
nontrivial SPT states is both necessary and sufficient for the standard
teleportation of qubits. We illustrate this result with several examples,
including a nonstabilizer hypergraph state.Comment: 33 pages, 8 figure
Long-range-enhanced surface codes
The surface code is a quantum error-correcting code for one logical qubit,
protected by spatially localized parity checks in two dimensions. Due to
fundamental constraints from spatial locality, storing more logical qubits
requires either sacrificing the robustness of the surface code against errors
or increasing the number of physical qubits. We bound the minimal number of
spatially non-local parity checks necessary to add logical qubits to a surface
code while maintaining, or improving, robustness to errors. We asymptotically
saturate this bound using a family of hypergraph product codes, interpolating
between the surface code and constant-rate low-density parity-check codes.
Fault-tolerant protocols for logical operations generalize naturally to these
longer-range codes, based on those from ordinary surface codes. We provide
near-term practical implementations of this code for hardware based on trapped
ions or neutral atoms in mobile optical tweezers. Long-range-enhanced surface
codes outperform conventional surface codes using hundreds of physical qubits,
and represent a practical strategy to enhance the robustness of logical qubits
to errors in near-term devices.Comment: 16 pages, 12 figures; v2 changes: fixed typos and added citation
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