755 research outputs found
On the refined counting of graphs on surfaces
Ribbon graphs embedded on a Riemann surface provide a useful way to describe
the double line Feynman diagrams of large N computations and a variety of other
QFT correlator and scattering amplitude calculations, e.g in MHV rules for
scattering amplitudes, as well as in ordinary QED. Their counting is a special
case of the counting of bi-partite embedded graphs. We review and extend
relevant mathematical literature and present results on the counting of some
infinite classes of bi-partite graphs. Permutation groups and representations
as well as double cosets and quotients of graphs are useful mathematical tools.
The counting results are refined according to data of physical relevance, such
as the structure of the vertices, faces and genus of the embedded graph. These
counting problems can be expressed in terms of observables in three-dimensional
topological field theory with S_d gauge group which gives them a topological
membrane interpretation.Comment: 57 pages, 12 figures; v2: Typos corrected; references adde
Graph-to-Sequence Learning using Gated Graph Neural Networks
Many NLP applications can be framed as a graph-to-sequence learning problem.
Previous work proposing neural architectures on this setting obtained promising
results compared to grammar-based approaches but still rely on linearisation
heuristics and/or standard recurrent networks to achieve the best performance.
In this work, we propose a new model that encodes the full structural
information contained in the graph. Our architecture couples the recently
proposed Gated Graph Neural Networks with an input transformation that allows
nodes and edges to have their own hidden representations, while tackling the
parameter explosion problem present in previous work. Experimental results show
that our model outperforms strong baselines in generation from AMR graphs and
syntax-based neural machine translation.Comment: ACL 201
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