22,589 research outputs found
On the support of measures in multiplicative free convolution semigroups
In this paper, we study the supports of measures in multiplicative free
semigroups on the positive real line and on the unit circle. We provide
formulas for the density of the absolutely continuous parts of measures in
these semigroups. The descriptions rely on the characterizations of the images
of the upper half-plane and the unit disc under certain subordination
functions. These subordination functions are -transforms of infinitely
divisible measures with respect to multiplicative free convolution. The
characterizations also help us study the regularity properties of these
measures. One of the main results is that the number of components in the
support of measures in the semigroups is a decreasing function of the semigroup
parameter
Large Margin Neural Language Model
We propose a large margin criterion for training neural language models.
Conventionally, neural language models are trained by minimizing perplexity
(PPL) on grammatical sentences. However, we demonstrate that PPL may not be the
best metric to optimize in some tasks, and further propose a large margin
formulation. The proposed method aims to enlarge the margin between the "good"
and "bad" sentences in a task-specific sense. It is trained end-to-end and can
be widely applied to tasks that involve re-scoring of generated text. Compared
with minimum-PPL training, our method gains up to 1.1 WER reduction for speech
recognition and 1.0 BLEU increase for machine translation.Comment: 9 pages. Accepted as a long paper in EMNLP201
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