2,459 research outputs found
Linear Bounded Composition of Tree-Walking Tree Transducers: Linear Size Increase and Complexity
Compositions of tree-walking tree transducers form a hierarchy with respect
to the number of transducers in the composition. As main technical result it is
proved that any such composition can be realized as a linear bounded
composition, which means that the sizes of the intermediate results can be
chosen to be at most linear in the size of the output tree. This has
consequences for the expressiveness and complexity of the translations in the
hierarchy. First, if the computed translation is a function of linear size
increase, i.e., the size of the output tree is at most linear in the size of
the input tree, then it can be realized by just one, deterministic,
tree-walking tree transducer. For compositions of deterministic transducers it
is decidable whether or not the translation is of linear size increase. Second,
every composition of deterministic transducers can be computed in deterministic
linear time on a RAM and in deterministic linear space on a Turing machine,
measured in the sum of the sizes of the input and output tree. Similarly, every
composition of nondeterministic transducers can be computed in simultaneous
polynomial time and linear space on a nondeterministic Turing machine. Their
output tree languages are deterministic context-sensitive, i.e., can be
recognized in deterministic linear space on a Turing machine. The membership
problem for compositions of nondeterministic translations is nondeterministic
polynomial time and deterministic linear space. The membership problem for the
composition of a nondeterministic and a deterministic tree-walking tree
translation (for a nondeterministic IO macro tree translation) is log-space
reducible to a context-free language, whereas the membership problem for the
composition of a deterministic and a nondeterministic tree-walking tree
translation (for a nondeterministic OI macro tree translation) is possibly
NP-complete
Macro tree transducers
Macro tree transducers are a combination of top-down tree transducers and macro grammars. They serve as a model for syntax-directed semantics in which context information can be handled. In this paper the formal model of macro tree transducers is studied by investigating typical automata theoretical topics like composition, decomposition, domains, and ranges of the induced translation classes. The extension with regular look-ahead is considered
Gradient-based Inference for Networks with Output Constraints
Practitioners apply neural networks to increasingly complex problems in
natural language processing, such as syntactic parsing and semantic role
labeling that have rich output structures. Many such structured-prediction
problems require deterministic constraints on the output values; for example,
in sequence-to-sequence syntactic parsing, we require that the sequential
outputs encode valid trees. While hidden units might capture such properties,
the network is not always able to learn such constraints from the training data
alone, and practitioners must then resort to post-processing. In this paper, we
present an inference method for neural networks that enforces deterministic
constraints on outputs without performing rule-based post-processing or
expensive discrete search. Instead, in the spirit of gradient-based training,
we enforce constraints with gradient-based inference (GBI): for each input at
test-time, we nudge continuous model weights until the network's unconstrained
inference procedure generates an output that satisfies the constraints. We
study the efficacy of GBI on three tasks with hard constraints: semantic role
labeling, syntactic parsing, and sequence transduction. In each case, the
algorithm not only satisfies constraints but improves accuracy, even when the
underlying network is state-of-the-art.Comment: AAAI 201
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