888 research outputs found
Sampling from Stochastic Finite Automata with Applications to CTC Decoding
Stochastic finite automata arise naturally in many language and speech
processing tasks. They include stochastic acceptors, which represent certain
probability distributions over random strings. We consider the problem of
efficient sampling: drawing random string variates from the probability
distribution represented by stochastic automata and transformations of those.
We show that path-sampling is effective and can be efficient if the
epsilon-graph of a finite automaton is acyclic. We provide an algorithm that
ensures this by conflating epsilon-cycles within strongly connected components.
Sampling is also effective in the presence of non-injective transformations of
strings. We illustrate this in the context of decoding for Connectionist
Temporal Classification (CTC), where the predictive probabilities yield
auxiliary sequences which are transformed into shorter labeling strings. We can
sample efficiently from the transformed labeling distribution and use this in
two different strategies for finding the most probable CTC labeling
Area-Universal Rectangular Layouts
A rectangular layout is a partition of a rectangle into a finite set of
interior-disjoint rectangles. Rectangular layouts appear in various
applications: as rectangular cartograms in cartography, as floorplans in
building architecture and VLSI design, and as graph drawings. Often areas are
associated with the rectangles of a rectangular layout and it might hence be
desirable if one rectangular layout can represent several area assignments. A
layout is area-universal if any assignment of areas to rectangles can be
realized by a combinatorially equivalent rectangular layout. We identify a
simple necessary and sufficient condition for a rectangular layout to be
area-universal: a rectangular layout is area-universal if and only if it is
one-sided. More generally, given any rectangular layout L and any assignment of
areas to its regions, we show that there can be at most one layout (up to
horizontal and vertical scaling) which is combinatorially equivalent to L and
achieves a given area assignment. We also investigate similar questions for
perimeter assignments. The adjacency requirements for the rectangles of a
rectangular layout can be specified in various ways, most commonly via the dual
graph of the layout. We show how to find an area-universal layout for a given
set of adjacency requirements whenever such a layout exists.Comment: 19 pages, 16 figure
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