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Electronic Colloquium on Computational Complexity

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All reports by Author Srinivasan Arunachalam:

TR21-178 | 3rd December 2021
Srinivasan Arunachalam, Oded Regev, Penghui Yao

On the Gaussian surface area of spectrahedra

We show that for sufficiently large $n\geq 1$ and $d=C n^{3/4}$ for some universal constant $C>0$, a random spectrahedron with matrices drawn from Gaussian orthogonal ensemble has Gaussian surface area $\Theta(n^{1/8})$ with high probability.

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TR21-130 | 7th September 2021
Srinivasan Arunachalam, João F. Doriguello

Matrix hypercontractivity, streaming algorithms and LDCs: the large alphabet case

Hypercontractive inequalities for real-valued functions over the Boolean cube play an important role in theoretical computer science. In this work, we prove a hypercontractive inequality for matrix-valued functions defined over large alphabets, generalizing the result of Ben-Aroya, Regev, de Wolf (FOCS'08) for the Boolean alphabet. To obtain our result we ... more >>>

TR21-013 | 20th January 2021
Srinivasan Arunachalam, Penghui Yao

Positive spectrahedrons: Geometric properties, Invariance principles and Pseudorandom generators

In a recent work, O'Donnell, Servedio and Tan (STOC 2019) gave explicit pseudorandom generators (PRGs) for arbitrary $m$-facet polytopes in $n$ variables with seed length poly-logarithmic in $m,n$, concluding a sequence of works in the last decade, that was started by Diakonikolas, Gopalan, Jaiswal, Servedio, Viola (SICOMP 2010) and Meka, ... more >>>

TR20-185 | 1st December 2020
Srinivasan Arunachalam, Alex Grilo, Tom Gur, Igor Oliveira, Aarthi Sundaram

Quantum learning algorithms imply circuit lower bounds

Revisions: 1

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathrm{C}$ be a class of polynomial-size concepts, and suppose that $\mathrm{C}$ can be PAC-learned with membership queries under the uniform distribution with error $1/2 - \gamma$ by a time $T$ quantum algorithm. ... more >>>

TR19-041 | 7th March 2019
Srinivasan Arunachalam, Alex Bredariol Grilo, Aarthi Sundaram

Quantum hardness of learning shallow classical circuits

In this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum learning and quantum-secure cryptosystems. We then achieve the following results.

1) Hardness of learning ... more >>>

TR18-167 | 25th September 2018
Srinivasan Arunachalam, Sourav Chakraborty, Michal Koucky, Nitin Saurabh, Ronald de Wolf

Improved bounds on Fourier entropy and Min-entropy

Revisions: 1

Given a Boolean function $f: \{-1,1\}^n\rightarrow \{-1,1\}$, define the Fourier distribution to be the distribution on subsets of $[n]$, where each $S\subseteq [n]$ is sampled with probability $\widehat{f}(S)^2$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96] seeks to relate two fundamental measures associated with the Fourier distribution: does ... more >>>

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