Convolutional Neural Networks for Sentence Classification

We report on a series of experiments with convolutional neural networks (CNN) trained on top of pre-trained word vectors for sentence-level classification tasks. We show that a simple CNN with little hyperparameter tuning and static vectors achieves excellent results on multiple benchmarks. Learning task-specific vectors through fine-tuning offers further gains in performance. We additionally propose a simple modification to the architecture to allow for the use of both task-specific and static vectors. The CNN models discussed herein improve upon the state of the art on 4 out of 7 tasks, which include sentiment analysis and question classification.Comment: To appear in EMNLP 201

M-furcations in coupled maps

We study the scaling behavior of $M$-furcation $(M\!=\!2, 3, 4,\dots)$ sequences of $M^n$-period $(n=1,2,\dots)$ orbits in two coupled one-dimensional (1D) maps. Using a renormalization method, how the scaling behavior depends on $M$ is particularly investigated in the zero-coupling case in which the two 1D maps become uncoupled. The zero-coupling fixed map of the $M$-furcation renormalization transformation is found to have three relevant eigenvalues $\delta$, $\alpha$, and $M$ ($\delta$ and $\alpha$ are the parameter and orbital scaling factors of 1D maps, respectively). Here the second and third ones, $\alpha$ and $M$, called the ``coupling eigenvalues'', govern the scaling behavior associated with coupling, while the first one $\delta$ governs the scaling behavior of the nonlinearity parameter like the case of 1D maps. The renormalization results are also confirmed by a direct numerical method.Comment: 18 pages + 2 figures (available upon request), Revtex 3.

Octahedral developing of knot complement II: Ptolemy coordinates and applications

It is known that a knot complement (minus two points) decomposes into ideal octahedra with respect to a given knot diagram. In this paper, we study the Ptolemy variety for such an octahedral decomposition in perspective of Thurston's gluing equation variety. More precisely, we compute explicit Ptolemy coordinates in terms of segment and region variables, the coordinates of the gluing equation variety motivated from the volume conjecture. As a consequence, we present an explicit formula for computing the obstruction to lifting a $(\mathrm{PSL}(2,\mathbb{C}),P)$-representation of the knot group to a $(\mathrm{SL}(2,\mathbb{C}),P)$-representation. We also present a diagrammatic algorithm to compute a holonomy representation of the knot group.Comment: 32 pages, 21 figue

Credibility Adjusted Term Frequency: A Supervised Term Weighting Scheme for Sentiment Analysis and Text Classification

We provide a simple but novel supervised weighting scheme for adjusting term frequency in tf-idf for sentiment analysis and text classification. We compare our method to baseline weighting schemes and find that it outperforms them on multiple benchmarks. The method is robust and works well on both snippets and longer documents