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Hsin-Yuan Huang

Publications and source records attributed to Hsin-Yuan Huang.

76 records · Page 5Linked to original sources

FusionNet: Fusing via Fully-Aware Attention with Application to Machine Comprehension

This paper introduces a new neural structure called FusionNet, which extends existing attention approaches from three perspectives. First, it puts forward a novel concept of "history of word" to characterize attention information from the lowest word-level embedding up to the highest semantic-level representation. Second, it introduces an improved attention scoring function that better utilizes the "history of word" concept. Third, it proposes a fully-aware multi-level attention mechanism to capture the complete information in one text (such as a question) and exploit it in its counterpart (such as context or passage) layer by layer. We apply FusionNet to the Stanford Question Answering Dataset (SQuAD) and it achieves the first position for both single and ensemble model on the official SQuAD leaderboard at the time of writing (Oct. 4th, 2017). Meanwhile, we verify the generalization of FusionNet with two adversarial SQuAD datasets and it sets up the new state-of-the-art on both datasets: on AddSent, FusionNet increases the best F1 metric from 46.6% to 51.4%; on AddOneSent, FusionNet boosts the best F1 metric from 56.0% to 60.7%.

cs.CL↗

The domain geometry and the bubbling phenomenon of rank two Gauge theory

Let $Ω$ be a flat torus and $G$ be the green's function of $-Δ$ on $Ω$. One intriguing mystery of $G$ is how the number of its critical points is related to blowup solutions of certain PDEs. In this article we prove that for the following equation that describes a Chern-Simons model in Gauge theory: \begin{equation}\label{e103} \left\{ \begin{array}{ll} Δu_1+\frac{1}{\varepsilon^2}e^{u_2}(1-e^{u_1})=8πδ_{p_{1}} Δu_2+\frac{1}{\varepsilon^2}e^{u_1}(1-e^{u_2})=8πδ_{p_{2}} \end{array} \text{ in }\quad Ω\right., \quad p_1-p_2 \mbox{ is a half period}, \end{equation} if fully bubbling solutions of Liouville type exist, $G$ has exactly three critical points. In addition we establish necessary conditions for the existence of fully bubbling solutions with multiple bubbles.

math.AP↗

Uniqueness of topological multi-vortex solutions for a skew-symmetric Chern-Simons system

Consider the following skew-symmetric Chern-Simons system \begin{equation*}\left \{ \begin{split} &Δu_{1}+\frac{1}{\varepsilon^2} e^{u_{2}}(1-e^{u_{1}})=4π\sum^{N_1}_{j=1}δ_{p_{j,1}}\\ &Δu_{2}+\frac{1}{\varepsilon^2} e^{u_{1}}(1-e^{u_{2}})=4π\sum^{N_2}_{j=1}δ_{p_{j,2}} \end{split}\right.\quad\text{ in }\quadΩ, \end{equation*} where $Ω$ is a flat 2-dimensional torus $\mathbb{T}^2$ or $\mathbb{R}^2$, $\varepsilon> 0$ is a coupling parameter, and $δ_p$ denotes the Dirac measure concentrated at $p$. In this paper, we prove that, when the coupling parameter $\varepsilon$ is small, the topological type solutions to the above system are uniquely determined by the location of their vortex points. This result follows by the bubbling analysis and the non-degency of linearized equations.

math.AP↗

On the Entire Radial Solutions of the Chern-Simons SU(3) System

In this paper, we study the entire radial solutions of the self-dual equations arising from the relativistic SU(3) Chern-Simons model proposed by Kao-Lee and Dunne. Understanding the structure of entire radial solutions is one of fundamental issues for the system of nonlinear equations. In this paper, we prove any entire radial solutions must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at infinity of these solutions. Even for radial solutions, this classification has remained an open problem for many years. As an application of this classification, we prove that the two components u and v have intersection at most finite times.

math.AP↗