13,353 research outputs found
Distributed Stochastic Optimization of the Regularized Risk
Many machine learning algorithms minimize a regularized risk, and stochastic
optimization is widely used for this task. When working with massive data, it
is desirable to perform stochastic optimization in parallel. Unfortunately,
many existing stochastic optimization algorithms cannot be parallelized
efficiently. In this paper we show that one can rewrite the regularized risk
minimization problem as an equivalent saddle-point problem, and propose an
efficient distributed stochastic optimization (DSO) algorithm. We prove the
algorithm's rate of convergence; remarkably, our analysis shows that the
algorithm scales almost linearly with the number of processors. We also verify
with empirical evaluations that the proposed algorithm is competitive with
other parallel, general purpose stochastic and batch optimization algorithms
for regularized risk minimization
WordRank: Learning Word Embeddings via Robust Ranking
Embedding words in a vector space has gained a lot of attention in recent
years. While state-of-the-art methods provide efficient computation of word
similarities via a low-dimensional matrix embedding, their motivation is often
left unclear. In this paper, we argue that word embedding can be naturally
viewed as a ranking problem due to the ranking nature of the evaluation
metrics. Then, based on this insight, we propose a novel framework WordRank
that efficiently estimates word representations via robust ranking, in which
the attention mechanism and robustness to noise are readily achieved via the
DCG-like ranking losses. The performance of WordRank is measured in word
similarity and word analogy benchmarks, and the results are compared to the
state-of-the-art word embedding techniques. Our algorithm is very competitive
to the state-of-the- arts on large corpora, while outperforms them by a
significant margin when the training set is limited (i.e., sparse and noisy).
With 17 million tokens, WordRank performs almost as well as existing methods
using 7.2 billion tokens on a popular word similarity benchmark. Our multi-node
distributed implementation of WordRank is publicly available for general usage.Comment: Conference on Empirical Methods in Natural Language Processing
(EMNLP), November 1-5, 2016, Austin, Texas, US
Sine-Gordon Soliton on a Cnoidal Wave Background
The method of Darboux transformation, which is applied on cnoidal wave
solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave
background. Interesting characteristics of the solution, i.e., the velocity of
solitons and the shift of crests of cnoidal waves along a soliton, are
calculated. Solutions are classified into three types (Type-1A, Type-1B,
Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change
Screened hybrid functional applied to 3d^0-->3d^8 transition-metal perovskites LaMO3 (M=Sc-Cu): influence of the exchange mixing parameter on the structural, electronic and magnetic properties
We assess the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened
hybrid density functional scheme applied to the perovskite family LaMO3
(M=Sc-Cu) and discuss the role of the mixing parameter alpha (which determines
the fraction of exact Hartree-Fock exchange included in the density functional
theory (DFT) exchange-correlation functional) on the structural, electronic,
and magnetic properties. The physical complexity of this class of compounds,
manifested by the largely varying electronic characters
(band/Mott-Hubbard/charge-transfer insulators and metals), magnetic orderings,
structural distortions (cooperative Jahn-Teller like instabilities), as well as
by the strong competition between localization/delocalization effects
associated with the gradual filling of the t_2g and e_g orbitals, symbolize a
critical and challenging case for theory. Our results indicates that HSE is
able to provide a consistent picture of the complex physical scenario
encountered across the LaMO3 series and significantly improve the standard DFT
description. The only exceptions are the correlated paramagnetic metals LaNiO3
and LaCuO3, which are found to be treated better within DFT. By fitting the
ground state properties with respect to alpha we have constructed a set of
'optimum' values of alpha from LaScO3 to LaCuO3: it is found that the 'optimum'
mixing parameter decreases with increasing filling of the d manifold (LaScO3:
0.25; LaTiO3 & LaVO3: 0.10-0.15; LaCrO3, LaMnO3, and LaFeO3: 0.15; LaCoO3:
0.05; LaNiO3 & LaCuO3: 0). This trend can be nicely correlated with the
modulation of the screening and dielectric properties across the LaMO3 series,
thus providing a physical justification to the empirical fitting procedure.Comment: 32 pages, 29 figure
Atomic correlations in itinerant ferromagnets: quasi-particle bands of nickel
We measure the band structure of nickel along various high-symmetry lines of
the bulk Brillouin zone with angle-resolved photoelectron spectroscopy. The
Gutzwiller theory for a nine-band Hubbard model whose tight-binding parameters
are obtained from non-magnetic density-functional theory resolves most of the
long-standing discrepancies between experiment and theory on nickel. Thereby we
support the view of itinerant ferromagnetism as induced by atomic correlations.Comment: 4 page REVTeX 4.0, one figure, one tabl
Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory
In this paper, using a Hopf-algebraic method, we construct deformed
Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this
twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can
see the consistency between the algebra and non(anti)commutative relation among
(super)coordinates and interpret that symmetry of non(anti)commutative QFT is
in fact twisted one. The key point is validity of our new twist element that
guarantees non(anti)commutativity of space. It is checked in this paper for N=1
case. We also comment on the possibility of noncommutative central charge
coordinate. Finally, because our twist operation does not break the original
algebra, we can claim that (twisted) SUSY is not broken in contrast to the
string inspired SUSY in N=1 non(anti)commutative superspace.Comment: 15 pages, LaTeX. v3:One section added, typos corrected, to appear in
Int. J. Mod. Phys.
A new class of non-Hermitian Hamiltonians with real spectra
We construct a new class of non-Hermitian Hamiltonians with real spectra. The
Hamiltonians possess one explicitly known eigenfunction.Comment: 6 page
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