2,305 research outputs found
The Structure Transfer Machine Theory and Applications
Representation learning is a fundamental but challenging problem, especially
when the distribution of data is unknown. We propose a new representation
learning method, termed Structure Transfer Machine (STM), which enables feature
learning process to converge at the representation expectation in a
probabilistic way. We theoretically show that such an expected value of the
representation (mean) is achievable if the manifold structure can be
transferred from the data space to the feature space. The resulting structure
regularization term, named manifold loss, is incorporated into the loss
function of the typical deep learning pipeline. The STM architecture is
constructed to enforce the learned deep representation to satisfy the intrinsic
manifold structure from the data, which results in robust features that suit
various application scenarios, such as digit recognition, image classification
and object tracking. Compared to state-of-the-art CNN architectures, we achieve
the better results on several commonly used benchmarks\footnote{The source code
is available. https://github.com/stmstmstm/stm }
An expressive completeness theorem for coalgebraic modal mu-calculi
Generalizing standard monadic second-order logic for Kripke models, we
introduce monadic second-order logic interpreted over coalgebras for an
arbitrary set functor. We then consider invariance under behavioral equivalence
of MSO-formulas. More specifically, we investigate whether the coalgebraic
mu-calculus is the bisimulation-invariant fragment of the monadic second-order
language for a given functor. Using automatatheoretic techniques and building
on recent results by the third author, we show that in order to provide such a
characterization result it suffices to find what we call an adequate uniform
construction for the coalgebraic type functor. As direct applications of this
result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the
modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation
invariance results for the bag functor (graded modal logic) and all exponential
polynomial functors (including the "game functor"). As a more involved
application, involving additional non-trivial ideas, we also derive a
characterization theorem for the monotone modal mu-calculus, with respect to a
natural monadic second-order language for monotone neighborhood models.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0721
New Principles for Auxetic Periodic Design
We show that, for any given dimension d ≥ 2, the range of distinct possible designs for periodic frameworks with auxetic capabilities is infinite. We rely on a purely geometric approach to auxetic trajectories developed within our general theory of deformations of periodic frameworks
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