SNU_IDS at SemEval-2018 Task 12: Sentence Encoder with Contextualized Vectors for Argument Reasoning Comprehension

We present a novel neural architecture for the Argument Reasoning Comprehension task of SemEval 2018. It is a simple neural network consisting of three parts, collectively judging whether the logic built on a set of given sentences (a claim, reason, and warrant) is plausible or not. The model utilizes contextualized word vectors pre-trained on large machine translation (MT) datasets as a form of transfer learning, which can help to mitigate the lack of training data. Quantitative analysis shows that simply leveraging LSTMs trained on MT datasets outperforms several baselines and non-transferred models, achieving accuracies of about 70% on the development set and about 60% on the test set.Comment: SemEval 201

Slopes of smooth curves on Fano manifolds

Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension $n\geq 3$ with respect to smooth curves. The question turns out to be easy for curves of genus $\geq 1$ and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold $(X, -K_X)$ is not slope stable with respect to a smooth curve. Our result also states that a Fano threefold $X$ with Picard number 1 is slope stable with respect to every smooth curve unless $X$ is the projective space.Comment: 13 pages, Theorems in the original version were modified. This paper will be published in the Bulletin of the London Mathematical Societ

Weighted inhomogeneous regularization for inverse problems with indirect and incomplete measurement data

Regularization promotes well-posedness in solving an inverse problem with incomplete measurement data. The regularization term is typically designed based on a priori characterization of the unknown signal, such as sparsity or smoothness. The standard inhomogeneous regularization incorporates a spatially changing exponent $p$ of the standard $\ell_p$ norm-based regularization to recover a signal whose characteristic varies spatially. This study proposes a weighted inhomogeneous regularization that extends the standard inhomogeneous regularization through new exponent design and weighting using spatially varying weights. The new exponent design avoids misclassification when different characteristics stay close to each other. The weights handle another issue when the region of one characteristic is too small to be recovered effectively by the $\ell_p$ norm-based regularization even after identified correctly. A suite of numerical tests shows the efficacy of the proposed weighted inhomogeneous regularization, including synthetic image experiments and real sea ice recovery from its incomplete wave measurements

Learning a Manifold-Constrained Map between Image Sets: Applications to Matching and Pose Estimation

This paper proposes a method for matching two sets of images given a small number of training examples by exploiting the underlying structure of the image manifolds. A nonlinear map from one manifold to another is constructed by combining linear maps locally defined on the tangent spaces of the manifolds. This construction imposes strong constraints on the choice of the maps, and makes possible good generalization of correspondences between all of the image sets. This map is flexible enough to approximate an arbitrary diffeomorphism between manifolds and can serve many purposes for applications. The underlying algorithm is a non-iterative efficient procedure whose complexity mainly depends on the number of matched training examples and the dimensionality of the manifold, and not on the number of samples nor on the dimensionality of the images. Several experiments were performed to demonstrate the potential of our method in image analysis and pose estimation. The first example demonstrates how images from a rotating camera can be mapped to the underlying pose manifold. Second, computer generated images from articulating toy figures are matched using the underlying 4 dimensional manifold to generate image-driven animations. Finally, two sets of actual lip images during speech are matched by their appearance manifold. In all these cases, our algorithm is able to obtain reasonable matches between thousands of large-dimensional images, with a minimum of computation