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Electronic Colloquium on Computational Complexity

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All reports by Author Sumegha Garg:

TR19-071 | 14th May 2019
Sumegha Garg, Ran Raz, Avishay Tal

Time-Space Lower Bounds for Two-Pass Learning

A line of recent works showed that for a large class of learning problems, any learning algorithm requires either super-linear memory size or a super-polynomial number of samples [Raz16,KRT17,Raz17,MM18,BOGY18,GRT18]. For example, any algorithm for learning parities of size $n$ requires either a memory of size $\Omega(n^{2})$ or an exponential number ... more >>>

TR17-161 | 30th October 2017
Mark Braverman, Gil Cohen, Sumegha Garg

Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>

TR17-121 | 31st July 2017
Sumegha Garg, Ran Raz, Avishay Tal

Extractor-Based Time-Space Lower Bounds for Learning

Revisions: 1

A matrix $M: A \times X \rightarrow \{-1,1\}$ corresponds to the following learning problem: An unknown element $x \in X$ is chosen uniformly at random. A learner tries to learn $x$ from a stream of samples, $(a_1, b_1), (a_2, b_2) \ldots$, where for every $i$, $a_i \in A$ is chosen ... more >>>

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