2,380 research outputs found
Combining Language and Vision with a Multimodal Skip-gram Model
We extend the SKIP-GRAM model of Mikolov et al. (2013a) by taking visual
information into account. Like SKIP-GRAM, our multimodal models (MMSKIP-GRAM)
build vector-based word representations by learning to predict linguistic
contexts in text corpora. However, for a restricted set of words, the models
are also exposed to visual representations of the objects they denote
(extracted from natural images), and must predict linguistic and visual
features jointly. The MMSKIP-GRAM models achieve good performance on a variety
of semantic benchmarks. Moreover, since they propagate visual information to
all words, we use them to improve image labeling and retrieval in the zero-shot
setup, where the test concepts are never seen during model training. Finally,
the MMSKIP-GRAM models discover intriguing visual properties of abstract words,
paving the way to realistic implementations of embodied theories of meaning.Comment: accepted at NAACL 2015, camera ready version, 11 page
Local strong maximal monotonicity and full stability for parametric variational systems
The paper introduces and characterizes new notions of Lipschitzian and
H\"olderian full stability of solutions to general parametric variational
systems described via partial subdifferential and normal cone mappings acting
in Hilbert spaces. These notions, postulated certain quantitative properties of
single-valued localizations of solution maps, are closely related to local
strong maximal monotonicity of associated set-valued mappings. Based on
advanced tools of variational analysis and generalized differentiation, we
derive verifiable characterizations of the local strong maximal monotonicity
and full stability notions under consideration via some positive-definiteness
conditions involving second-order constructions of variational analysis. The
general results obtained are specified for important classes of variational
inequalities and variational conditions in both finite and infinite dimensions
Constraint Qualifications and Optimality Conditions for Nonconvex Semi-Infinite and Infinite Programs
The paper concerns the study of new classes of nonlinear and nonconvex
optimization problems of the so-called infinite programming that are generally
defined on infinite-dimensional spaces of decision variables and contain
infinitely many of equality and inequality constraints with arbitrary (may not
be compact) index sets. These problems reduce to semi-infinite programs in the
case of finite-dimensional spaces of decision variables. We extend the
classical Mangasarian-Fromovitz and Farkas-Minkowski constraint qualifications
to such infinite and semi-infinite programs. The new qualification conditions
are used for efficient computing the appropriate normal cones to sets of
feasible solutions for these programs by employing advanced tools of
variational analysis and generalized differentiation. In the further
development we derive first-order necessary optimality conditions for infinite
and semi-infinite programs, which are new in both finite-dimensional and
infinite-dimensional settings.Comment: 28 page
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