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1 code implementation • 24 Feb 2021 • Meena Jagadeesan, Ilya Razenshteyn, Suriya Gunasekar

We provide a function space characterization of the inductive bias resulting from minimizing the $\ell_2$ norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting hypothesis on ReLU networks trained using gradient descent.

1 code implementation • 3 May 2020 • Yihe Dong, Yu Gao, Richard Peng, Ilya Razenshteyn, Saurabh Sawlani

We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph.

no code implementations • 23 Apr 2020 • Sepideh Mahabadi, Ilya Razenshteyn, David P. Woodruff, Samson Zhou

Adaptive sampling is a useful algorithmic tool for data summarization problems in the classical centralized setting, where the entire dataset is available to the single processor performing the computation.

no code implementations • 21 Mar 2020 • Michael Kapralov, Navid Nouri, Ilya Razenshteyn, Ameya Velingker, Amir Zandieh

Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing.

1 code implementation • ICML 2020 • Greg Yang, Tony Duan, J. Edward Hu, Hadi Salman, Ilya Razenshteyn, Jerry Li

Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks.

1 code implementation • ICML 2020 • Arturs Backurs, Yihe Dong, Piotr Indyk, Ilya Razenshteyn, Tal Wagner

Our extensive experiments, on real-world text and image datasets, show that Flowtree improves over various baselines and existing methods in either running time or accuracy.

Data Structures and Algorithms

3 code implementations • NeurIPS 2019 • Hadi Salman, Greg Yang, Jerry Li, Pengchuan Zhang, huan zhang, Ilya Razenshteyn, Sebastien Bubeck

In this paper, we employ adversarial training to improve the performance of randomized smoothing.

no code implementations • 3 Apr 2019 • Hao Chen, Ilaria Chillotti, Yihe Dong, Oxana Poburinnaya, Ilya Razenshteyn, M. Sadegh Riazi

In this paper, we introduce SANNS, a system for secure $k$-NNS that keeps client's query and the search result confidential.

1 code implementation • ICLR 2020 • Yihe Dong, Piotr Indyk, Ilya Razenshteyn, Tal Wagner

Space partitions of $\mathbb{R}^d$ underlie a vast and important class of fast nearest neighbor search (NNS) algorithms.

no code implementations • 15 Nov 2018 • Sébastien Bubeck, Yin Tat Lee, Eric Price, Ilya Razenshteyn

In our recent work (Bubeck, Price, Razenshteyn, arXiv:1805. 10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem.

no code implementations • 8 Nov 2018 • Sepideh Mahabadi, Konstantin Makarychev, Yury Makarychev, Ilya Razenshteyn

We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces.

no code implementations • 8 Nov 2018 • Konstantin Makarychev, Yury Makarychev, Ilya Razenshteyn

Further, the cost of every clustering is preserved within $(1+\varepsilon)$.

no code implementations • 26 Jun 2018 • Alexandr Andoni, Piotr Indyk, Ilya Razenshteyn

The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X, D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).

no code implementations • 25 May 2018 • Sébastien Bubeck, Eric Price, Ilya Razenshteyn

First we prove that, for a broad set of classification tasks, the mere existence of a robust classifier implies that it can be found by a possibly exponential-time algorithm with relatively few training examples.

no code implementations • NeurIPS 2017 • Piotr Indyk, Ilya Razenshteyn, Tal Wagner

We introduce a new distance-preserving compact representation of multi-dimensional point-sets.

no code implementations • 18 Nov 2016 • Alexandr Andoni, Huy L. Nguyen, Aleksandar Nikolov, Ilya Razenshteyn, Erik Waingarten

We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation.

no code implementations • 9 Oct 2015 • Thomas D. Ahle, Rasmus Pagh, Ilya Razenshteyn, Francesco Silvestri

* New upper and lower bounds for (A)LSH-based algorithms.

1 code implementation • NeurIPS 2015 • Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig Schmidt

Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

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