# Seminars & Colloquia Calendar

## Time-Space Hardness of Learning Sparse Parities

#### Avishay Tal: IAS

Location: ** CoRE 301**

Date & time: Wednesday, 01 March 2017 at 11:00AM - 11:11AM

One approach is to gather \[O(n)\]random examples and perform Gaussian-elimination. This requires a memory of size \[O(n^2)\]and \[poly(n)\]time. Another approach is to go over all possible \[2^n\]parity functions and to verify them by checking \[O(n)\]random examples for each guess. This requires a memory of size \[O(n)\], but \[O(2^n * n)\]time.

In a recent work, Raz [FOCS, 2016] shows that if an algorithm has memory of size much smaller than \[n^2\], then it has to spend exponential time in order to learn a parity function. In other words, fast learning requires good memory.

In this work, we show that even if the parity function is known to be extremely sparse, where only log(n) of the a_i's are nonzero, then the learning task is still time-space hard. That is, we show that any algorithm with linear size memory and polynomial time fails to learn log(n)-sparse parities.

Consequently, the classical tasks of learning linear-size DNF formulae, linear-size decision trees, and logarithmic-size juntas are all time-space hard.

Based on joint work with Gillat Kol and Ran Raz.

R. Shapiro Organizer's Page

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

Organizer's webpage: Organizer's webpage

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