60,409 research outputs found
A continuous-time analysis of distributed stochastic gradient
We analyze the effect of synchronization on distributed stochastic gradient
algorithms. By exploiting an analogy with dynamical models of biological quorum
sensing -- where synchronization between agents is induced through
communication with a common signal -- we quantify how synchronization can
significantly reduce the magnitude of the noise felt by the individual
distributed agents and by their spatial mean. This noise reduction is in turn
associated with a reduction in the smoothing of the loss function imposed by
the stochastic gradient approximation. Through simulations on model non-convex
objectives, we demonstrate that coupling can stabilize higher noise levels and
improve convergence. We provide a convergence analysis for strongly convex
functions by deriving a bound on the expected deviation of the spatial mean of
the agents from the global minimizer for an algorithm based on quorum sensing,
the same algorithm with momentum, and the Elastic Averaging SGD (EASGD)
algorithm. We discuss extensions to new algorithms which allow each agent to
broadcast its current measure of success and shape the collective computation
accordingly. We supplement our theoretical analysis with numerical experiments
on convolutional neural networks trained on the CIFAR-10 dataset, where we note
a surprising regularizing property of EASGD even when applied to the
non-distributed case. This observation suggests alternative second-order
in-time algorithms for non-distributed optimization that are competitive with
momentum methods.Comment: 9/14/19 : Final version, accepted for publication in Neural
Computation. 4/7/19 : Significant edits: addition of simulations, deep
network results, and revisions throughout. 12/28/18: Initial submissio
Stringent Constraints on Cosmological Neutrino-Antineutrino Asymmetries from Synchronized Flavor Transformation
We assess a mechanism which can transform neutrino-antineutrino asymmetries
between flavors in the early universe, and confirm that such transformation is
unavoidable in the near bi-maximal framework emerging for the neutrino mixing
matrix. We show that the process is a standard Mikheyev-Smirnov-Wolfenstein
flavor transformation dictated by a synchronization of momentum states. We also
show that flavor ``equilibration'' is a special feature of maximal mixing, and
carefully examine new constraints placed on neutrino asymmetries. In
particular, the big bang nucleosynthesis limit on electron neutrino degeneracy
xi_e < 0.04 does not apply directly to all flavors, yet confirmation of the
large-mixing-angle solution to the solar neutrino problem will eliminate the
possibility of degenerate big bang nucleosynthesis.Comment: 11 pages, 6 figures; minor changes to match PRD versio
Eigenvector Synchronization, Graph Rigidity and the Molecule Problem
The graph realization problem has received a great deal of attention in
recent years, due to its importance in applications such as wireless sensor
networks and structural biology. In this paper, we extend on previous work and
propose the 3D-ASAP algorithm, for the graph realization problem in
, given a sparse and noisy set of distance measurements. 3D-ASAP
is a divide and conquer, non-incremental and non-iterative algorithm, which
integrates local distance information into a global structure determination.
Our approach starts with identifying, for every node, a subgraph of its 1-hop
neighborhood graph, which can be accurately embedded in its own coordinate
system. In the noise-free case, the computed coordinates of the sensors in each
patch must agree with their global positioning up to some unknown rigid motion,
that is, up to translation, rotation and possibly reflection. In other words,
to every patch there corresponds an element of the Euclidean group Euc(3) of
rigid transformations in , and the goal is to estimate the group
elements that will properly align all the patches in a globally consistent way.
Furthermore, 3D-ASAP successfully incorporates information specific to the
molecule problem in structural biology, in particular information on known
substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a
faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a
preprocessing step for dividing the initial graph into smaller subgraphs. Our
extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very
robust to high levels of noise in the measured distances and to sparse
connectivity in the measurement graph, and compare favorably to similar
state-of-the art localization algorithms.Comment: 49 pages, 8 figure
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Percolation scheduling for non-VLIW machines
Percolation Scheduling, a technique for compile-time code parallelization, has proven very successful for exploiting fine-grain irregular parallelism in ordinary programs. Currently, this technology is targeted only to VLIW (Very Long Instruction Word) machines, which have the advantages of 'free' synchronization and communication. Shared memory multi-processors can simulate the execution characteristics of VLIW machines with the use of static barriers. Preliminary results show that Percolation Scheduling can be used with good results on this type of architecture by increasing the granularity from operation level to source statement level, removing any redundant synchronization, and providing an efficient implementation of multi-way jumps
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