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no code implementations • ICML 2020 • Sai Ganesh Nagarajan, David Balduzzi, Georgios Piliouras

Even simple games learning dynamics can yield chaotic behavior.

no code implementations • 17 Jun 2020 • Arnab Bhattacharyya, Rathin Desai, Sai Ganesh Nagarajan, Ioannis Panageas

We show that ${\mu}$ and ${\Sigma}$ can be estimated with error $\epsilon$ in the Frobenius norm, using $\tilde{O}\left(\frac{\textrm{nz}({\Sigma}^{-1})}{\epsilon^2}\right)$ samples from a truncated $\mathcal{N}({\mu},{\Sigma})$ and having access to a membership oracle for $S$.

no code implementations • ICML 2020 • Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas

The expressivity of neural networks as a function of their depth, width and type of activation units has been an important question in deep learning theory.

no code implementations • 17 Feb 2020 • Qi Lei, Sai Ganesh Nagarajan, Ioannis Panageas, Xiao Wang

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games.

no code implementations • ICLR 2020 • Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas, Xiao Wang

Motivated by our observation that the triangle waves used in Telgarsky's work contain points of period 3 - a period that is special in that it implies chaotic behavior based on the celebrated result by Li-Yorke - we proceed to give general lower bounds for the width needed to represent periodic functions as a function of the depth.

no code implementations • 19 Feb 2019 • Sai Ganesh Nagarajan, Ioannis Panageas

Moreover, for $d>1$ we show EM almost surely converges to the true mean for any measurable set $S$ when the map of EM has only three fixed points, namely $-\vec{\mu}, \vec{0}, \vec{\mu}$ (covariance matrix $\vec{\Sigma}$ is known), and prove local convergence if there are more than three fixed points.

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