Depth Descent Synchronization in $\mathrm{SO}(D)$

2020-02-13 · Tyler Maunu, Gilad Lerman

We give robust recovery results for synchronization on the rotation group, $\mathrm{SO}(D)$. In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We give a novel algorithm that exploits Tukey depth in the tangent space, which exactly recovers the underlying rotations up to an outlier percentage of $1/(D(D-1)+2)$. This corresponds to an outlier fraction of $1/4$ for $\mathrm{SO}(2)$ and $1/8$ for $\mathrm{SO}(3)$. In the case of $D=2$, we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We finish by discussing this result in relation to a simpler nonconvex energy minimization framework based on least absolute deviations, which exhibits spurious fixed points.

📄 PDF Abstract BibTeX arXiv:2002.05299

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On the Convergence of Gradient Descent in GANs: MMD GAN As a Gradient Flow

2020-11-04 · Youssef Mroueh, Truyen Nguyen

We consider the maximum mean discrepancy ($\mathrm{MMD}$) GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized $\mathrm{MMD}$ GAN. We show that this flow prov…

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2026-06-10 · Fabio Pasqualetti, Taosha Guo arxiv

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Performance Optimization on Model Synchronization in Parallel Stochastic Gradient Descent Based SVM

2019-05-03 · Vibhatha Abeykoon, Geoffrey Fox, Minje Kim

Understanding the bottlenecks in implementing stochastic gradient descent (SGD)-based distributed support vector machines (SVM) algorithm is important in training larger data sets. The communication time to do the model …

Model Optimization

The Effective Depth Paradox: Evaluating the Relationship between Architectural Topology and Trainability in Deep CNNs

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