12,655 research outputs found
On Tree-Based Neural Sentence Modeling
Neural networks with tree-based sentence encoders have shown better results
on many downstream tasks. Most of existing tree-based encoders adopt syntactic
parsing trees as the explicit structure prior. To study the effectiveness of
different tree structures, we replace the parsing trees with trivial trees
(i.e., binary balanced tree, left-branching tree and right-branching tree) in
the encoders. Though trivial trees contain no syntactic information, those
encoders get competitive or even better results on all of the ten downstream
tasks we investigated. This surprising result indicates that explicit syntax
guidance may not be the main contributor to the superior performances of
tree-based neural sentence modeling. Further analysis show that tree modeling
gives better results when crucial words are closer to the final representation.
Additional experiments give more clues on how to design an effective tree-based
encoder. Our code is open-source and available at
https://github.com/ExplorerFreda/TreeEnc.Comment: To Appear at EMNLP 201
Matrix-valued -deformed bi-orthogonal polynomials, Non-commutative Toda theory and B\"acklund transformation
This paper is devoted to revealing the relationship between matrix-valued
-deformed bi-orthogonal polynomials and non-commutative Toda-type
hierarchies. In this procedure, Wronski quasi-determinants are widely used and
play the role of non-commutative -functions. At the same time, B\"acklund
transformations are realized by using a moment modification method and
non-commutative -deformed Volterra hierarchies are obtained, which
contain the known examples of the Itoh-Narita-Bogoyavlensky lattices and the
fractional Volterra hierarchy.Comment: 30 pages. Comments are welcom
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin
chain associated with the R-matrix and generic integrable
non-diagonal boundary conditions. By using the fusion technique, certain closed
operator identities among the fused transfer matrices at the inhomogeneous
points are derived. The corresponding asymptotic behaviors of the transfer
matrices and their values at some special points are given in detail. Based on
the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz
equations of the system are obtained. These results can be naturally
generalized to cases related to the algebra.Comment: published version, 27 pages, 1 table, 1 figur
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