14,548 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
Synthesis of Data Word Transducers
In reactive synthesis, the goal is to automatically generate an
implementation from a specification of the reactive and non-terminating
input/output behaviours of a system. Specifications are usually modelled as
logical formulae or automata over infinite sequences of signals
(-words), while implementations are represented as transducers. In the
classical setting, the set of signals is assumed to be finite. In this paper,
we consider data -words instead, i.e., words over an infinite alphabet.
In this context, we study specifications and implementations respectively given
as automata and transducers extended with a finite set of registers. We
consider different instances, depending on whether the specification is
nondeterministic, universal or deterministic, and depending on whether the
number of registers of the implementation is given or not.
In the unbounded setting, we show undecidability for both universal and
nondeterministic specifications, while decidability is recovered in the
deterministic case. In the bounded setting, undecidability still holds for
nondeterministic specifications, but can be recovered by disallowing tests over
input data. The generic technique we use to show the latter result allows us to
reprove some known result, namely decidability of bounded synthesis for
universal specifications
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