12,513 research outputs found
Hashing based Answer Selection
Answer selection is an important subtask of question answering (QA), where
deep models usually achieve better performance. Most deep models adopt
question-answer interaction mechanisms, such as attention, to get vector
representations for answers. When these interaction based deep models are
deployed for online prediction, the representations of all answers need to be
recalculated for each question. This procedure is time-consuming for deep
models with complex encoders like BERT which usually have better accuracy than
simple encoders. One possible solution is to store the matrix representation
(encoder output) of each answer in memory to avoid recalculation. But this will
bring large memory cost. In this paper, we propose a novel method, called
hashing based answer selection (HAS), to tackle this problem. HAS adopts a
hashing strategy to learn a binary matrix representation for each answer, which
can dramatically reduce the memory cost for storing the matrix representations
of answers. Hence, HAS can adopt complex encoders like BERT in the model, but
the online prediction of HAS is still fast with a low memory cost. Experimental
results on three popular answer selection datasets show that HAS can outperform
existing models to achieve state-of-the-art performance
Indecomposable representations and oscillator realizations of the exceptional Lie algebra G_2
In this paper various representations of the exceptional Lie algebra G_2 are
investigated in a purely algebraic manner, and multi-boson/multi-fermion
realizations are obtained. Matrix elements of the master representation, which
is defined on the space of the universal enveloping algebra of G_2, are
explicitly determined. From this master representation, different
indecomposable representations defined on invariant subspaces or quotient
spaces with respect to these invariant subspaces are discussed. Especially, the
elementary representations of G_2 are investigated in detail, and the
corresponding six-boson realization is given. After obtaining explicit forms of
all twelve extremal vectors of the elementary representation with the highest
weight {\Lambda}, all representations with their respective highest weights
related to {\Lambda} are systematically discussed. For one of these
representations the corresponding five-boson realization is constructed.
Moreover, a new three-fermion realization from the fundamental representation
(0,1) of G_2 is constructed also.Comment: 29 pages, 4 figure
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