1,743 research outputs found
Multi-bump solutions of on lattices in
We consider critical exponent semi-linear elliptic equation with coefficient
K(x) periodic in its first k variables, with 2k smaller than n-2. Under some
natural conditions on K near a critical point, we prove the existence of
multi-bump solutions where the centers of bumps can be placed in some lattices
in Rk, including infinite lattices. We also show that for 2k greater than or
equal to n-2, no such solutions exist.Comment: Final version. Some typo corrected. To appear inJournal fur die reine
und angewandte Mathematik (Crelle's Journal
Development of a sub-milimeter position sensitive gas detector
A position sensitive thin gap chamber has been developed. The position
resolution was measured using the cosmic muons. This paper presents the
structure of this detector, position resolution measurement method and results
Test of the prototype of electron detector for LHAASO project using cosmic rays
LHAASO project is to be built in south-west China, which use an array of 5137
election detectors for the measurement of the incident electrons arriving at
the detector plane. For the quality control of the big quantity of electron
detectors, a cosmic ray hodoscope with two-dimensional spacial sensitivity and
good time resolution has been developed. The first prototype of electron
detector is tested with the hodoscope and the performance of the detector is
validated to be consistent with the design.Comment: submitted to Chinese physics C. arXiv admin note: substantial text
overlap with arXiv:1308.575
DeepRank: A New Deep Architecture for Relevance Ranking in Information Retrieval
This paper concerns a deep learning approach to relevance ranking in
information retrieval (IR). Existing deep IR models such as DSSM and CDSSM
directly apply neural networks to generate ranking scores, without explicit
understandings of the relevance. According to the human judgement process, a
relevance label is generated by the following three steps: 1) relevant
locations are detected, 2) local relevances are determined, 3) local relevances
are aggregated to output the relevance label. In this paper we propose a new
deep learning architecture, namely DeepRank, to simulate the above human
judgment process. Firstly, a detection strategy is designed to extract the
relevant contexts. Then, a measure network is applied to determine the local
relevances by utilizing a convolutional neural network (CNN) or two-dimensional
gated recurrent units (2D-GRU). Finally, an aggregation network with sequential
integration and term gating mechanism is used to produce a global relevance
score. DeepRank well captures important IR characteristics, including
exact/semantic matching signals, proximity heuristics, query term importance,
and diverse relevance requirement. Experiments on both benchmark LETOR dataset
and a large scale clickthrough data show that DeepRank can significantly
outperform learning to ranking methods, and existing deep learning methods.Comment: Published as a conference paper at CIKM 2017, CIKM'17, November
6--10, 2017, Singapore TextNet (https://github.com/pl8787/textnet-release)
PyTorch (https://github.com/pl8787/DeepRank_PyTorch
Selfishness need not be bad
We investigate the price of anarchy (PoA) in non-atomic congestion games when
the total demand gets very large.
First results in this direction have recently been obtained by
\cite{Colini2016On, Colini2017WINE, Colini2017arxiv} for routing games and show
that the PoA converges to 1 when the growth of the total demand satisfies
certain regularity conditions. We extend their results by developing a
\Wuuu{new} framework for the limit analysis of \Wuuuu{the PoA that offers
strong techniques such as the limit of games and applies to arbitrary growth
patterns of .} \Wuuu{We} show that the PoA converges to 1 in the limit game
regardless of the type of growth of for a large class of cost functions
that contains all polynomials and all regularly varying functions.
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For routing games with BPR \Wuu{cost} functions, we show in addition that
socially optimal strategy profiles converge to \Wuu{equilibria} in the limit
game, and that PoA, where is the degree of the
\Wuu{BPR} functions. However, the precise convergence rate depends crucially on
the the growth of , which shows that a conjecture proposed by
\cite{O2016Mechanisms} need not hold
Learning of Human-like Algebraic Reasoning Using Deep Feedforward Neural Networks
There is a wide gap between symbolic reasoning and deep learning. In this
research, we explore the possibility of using deep learning to improve symbolic
reasoning. Briefly, in a reasoning system, a deep feedforward neural network is
used to guide rewriting processes after learning from algebraic reasoning
examples produced by humans. To enable the neural network to recognise patterns
of algebraic expressions with non-deterministic sizes, reduced partial trees
are used to represent the expressions. Also, to represent both top-down and
bottom-up information of the expressions, a centralisation technique is used to
improve the reduced partial trees. Besides, symbolic association vectors and
rule application records are used to improve the rewriting processes.
Experimental results reveal that the algebraic reasoning examples can be
accurately learnt only if the feedforward neural network has enough hidden
layers. Also, the centralisation technique, the symbolic association vectors
and the rule application records can reduce error rates of reasoning. In
particular, the above approaches have led to 4.6% error rate of reasoning on a
dataset of linear equations, differentials and integrals.Comment: 8 pages, 7 figure
Locally Smoothed Neural Networks
Convolutional Neural Networks (CNN) and the locally connected layer are
limited in capturing the importance and relations of different local receptive
fields, which are often crucial for tasks such as face verification, visual
question answering, and word sequence prediction. To tackle the issue, we
propose a novel locally smoothed neural network (LSNN) in this paper. The main
idea is to represent the weight matrix of the locally connected layer as the
product of the kernel and the smoother, where the kernel is shared over
different local receptive fields, and the smoother is for determining the
importance and relations of different local receptive fields. Specifically, a
multi-variate Gaussian function is utilized to generate the smoother, for
modeling the location relations among different local receptive fields.
Furthermore, the content information can also be leveraged by setting the mean
and precision of the Gaussian function according to the content. Experiments on
some variant of MNIST clearly show our advantages over CNN and locally
connected layer.Comment: In Proceedings of 9th Asian Conference on Machine Learning (ACML2017
Spherical Paragraph Model
Representing texts as fixed-length vectors is central to many language
processing tasks. Most traditional methods build text representations based on
the simple Bag-of-Words (BoW) representation, which loses the rich semantic
relations between words. Recent advances in natural language processing have
shown that semantically meaningful representations of words can be efficiently
acquired by distributed models, making it possible to build text
representations based on a better foundation called the Bag-of-Word-Embedding
(BoWE) representation. However, existing text representation methods using BoWE
often lack sound probabilistic foundations or cannot well capture the semantic
relatedness encoded in word vectors. To address these problems, we introduce
the Spherical Paragraph Model (SPM), a probabilistic generative model based on
BoWE, for text representation. SPM has good probabilistic interpretability and
can fully leverage the rich semantics of words, the word co-occurrence
information as well as the corpus-wide information to help the representation
learning of texts. Experimental results on topical classification and sentiment
analysis demonstrate that SPM can achieve new state-of-the-art performances on
several benchmark datasets.Comment: 10 page
A Study of MatchPyramid Models on Ad-hoc Retrieval
Deep neural networks have been successfully applied to many text matching
tasks, such as paraphrase identification, question answering, and machine
translation. Although ad-hoc retrieval can also be formalized as a text
matching task, few deep models have been tested on it. In this paper, we study
a state-of-the-art deep matching model, namely MatchPyramid, on the ad-hoc
retrieval task. The MatchPyramid model employs a convolutional neural network
over the interactions between query and document to produce the matching score.
We conducted extensive experiments to study the impact of different pooling
sizes, interaction functions and kernel sizes on the retrieval performance.
Finally, we show that the MatchPyramid models can significantly outperform
several recently introduced deep matching models on the retrieval task, but
still cannot compete with the traditional retrieval models, such as BM25 and
language models.Comment: Neu-IR '16 SIGIR Workshop on Neural Information Retrieva
Semantic Regularities in Document Representations
Recent work exhibited that distributed word representations are good at
capturing linguistic regularities in language. This allows vector-oriented
reasoning based on simple linear algebra between words. Since many different
methods have been proposed for learning document representations, it is natural
to ask whether there is also linear structure in these learned representations
to allow similar reasoning at document level. To answer this question, we
design a new document analogy task for testing the semantic regularities in
document representations, and conduct empirical evaluations over several
state-of-the-art document representation models. The results reveal that neural
embedding based document representations work better on this analogy task than
conventional methods, and we provide some preliminary explanations over these
observations.Comment: 6 page
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