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no code implementations • 18 Jul 2022 • Boaz Barak, Benjamin L. Edelman, Surbhi Goel, Sham Kakade, Eran Malach, Cyril Zhang

There is mounting empirical evidence of emergent phenomena in the capabilities of deep learning methods as we scale up datasets, model sizes, and training times.

1 code implementation • 20 Feb 2022 • Gal Kaplun, Nikhil Ghosh, Saurabh Garg, Boaz Barak, Preetum Nakkiran

In this work, we propose a new approach: we measure the performance of a collection of models when evaluated on a $\textit{single input point}$.

no code implementations • NeurIPS 2021 • Yamini Bansal, Preetum Nakkiran, Boaz Barak

We revisit and extend model stitching (Lenc & Vedaldi 2015) as a methodology to study the internal representations of neural networks.

1 code implementation • 25 Feb 2021 • David Chiang, Alexander M. Rush, Boaz Barak

We propose a notation for tensors with named axes, which relieves the author, reader, and future implementers from the burden of keeping track of the order of axes and the purpose of each.

2 code implementations • ICLR 2021 • Yamini Bansal, Gal Kaplun, Boaz Barak

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation $r$ of the training data, and then fitting a simple (e. g., linear) classifier $g$ to the labels.

3 code implementations • ICLR 2020 • Preetum Nakkiran, Gal Kaplun, Yamini Bansal, Tristan Yang, Boaz Barak, Ilya Sutskever

We show that a variety of modern deep learning tasks exhibit a "double-descent" phenomenon where, as we increase model size, performance first gets worse and then gets better.

1 code implementation • NeurIPS 2019 • Preetum Nakkiran, Gal Kaplun, Dimitris Kalimeris, Tristan Yang, Benjamin L. Edelman, Fred Zhang, Boaz Barak

We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks.

no code implementations • NeurIPS 2019 • Boaz Barak, Chi-Ning Chou, Zhixian Lei, Tselil Schramm, Yueqi Sheng

Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a pair of $\gamma$-correlated $G(n, p)$ graphs $G_0, G_1$ with average degree between $n^{\varepsilon}$ and $n^{1/153}$ for $\varepsilon = o(1)$, recovers the "ground truth" permutation $\pi\in S_n$ that matches the vertices of $G_0$ to the vertices of $G_n$ in the way that minimizes the number of mismatched edges.

no code implementations • 26 Jan 2015 • Boaz Barak, Ankur Moitra

This is also the first algorithm for tensor completion that works in the overcomplete case when $r > n$, and in fact it works all the way up to $r = n^{3/2-\epsilon}$.

no code implementations • 6 Jul 2014 • Boaz Barak, Jonathan A. Kelner, David Steurer

We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in $\mathbb R^m$ with at most $\tau m$ nonzero coordinates, and $e$ is a random noise vector in $\mathbb R^n$ with bounded magnitude.

no code implementations • 21 Apr 2014 • Boaz Barak, David Steurer

Two recent developments, the Unique Games Conjecture (UGC) and the Sum-of-Squares (SOS) method, surprisingly suggest that this tailoring is not necessary and that a single efficient algorithm could achieve best possible guarantees for a wide range of different problems.

no code implementations • 23 Dec 2013 • Boaz Barak, Jonathan Kelner, David Steurer

Aside from being a natural relaxation, this is also motivated by a connection to the Small Set Expansion problem shown by Barak et al. (STOC 2012) and our results yield a certain improvement for that problem.

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