All reports by Author Jiapeng Zhang:

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TR19-110
| 23rd August 2019
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Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang#### Improved bounds for the sunflower lemma

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TR19-028
| 1st March 2019
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Shachar Lovett, Noam Solomon, Jiapeng Zhang#### From DNF compression to sunflower theorems via regularity

Revisions: 1

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TR18-190
| 5th November 2018
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Shachar Lovett, Jiapeng Zhang#### DNF sparsification beyond sunflowers

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TR18-119
| 21st June 2018
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YiHsiu Chen, Mika G\"o{\"o}s, Salil Vadhan, Jiapeng Zhang#### A Tight Lower Bound for Entropy Flattening

Revisions: 1

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TR18-087
| 20th April 2018
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Kun He, Qian Li, Xiaoming Sun, Jiapeng Zhang#### Quantum Lov{\'a}sz Local Lemma: Shearer's Bound is Tight

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TR18-082
| 21st April 2018
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Xin Li, Shachar Lovett, Jiapeng Zhang#### Sunflowers and Quasi-sunflowers from Randomness Extractors

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TR17-085
| 4th May 2017
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Daniel Kane, Shachar Lovett, Shay Moran, Jiapeng Zhang#### Active classification with comparison queries

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TR16-161
| 26th October 2016
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Shachar Lovett, Jiapeng Zhang#### Robust sensitivity

Revisions: 1

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TR16-118
| 31st July 2016
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Shachar Lovett, Jiapeng Zhang#### On the impossibility of entropy reversal, and its application to zero-knowledge proofs

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TR16-021
| 11th February 2016
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Shachar Lovett, Jiapeng Zhang#### Noisy Population Recovery from Unknown Noise

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TR15-180
| 4th November 2015
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Bo Tang, Jiapeng Zhang#### Barriers to Black-Box Constructions of Traitor Tracing Systems

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TR14-123
| 7th October 2014
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Shachar Lovett, Jiapeng Zhang#### Improved noisy population recovery, and reverse Bonami-Beckner inequality for sparse functions

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TR11-038
| 10th March 2011
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Jiapeng Zhang#### On the query complexity for Showing Dense Model

Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang

A sunflower with $r$ petals is a collection of $r$ sets so that the

intersection of each pair is equal to the intersection of all. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must ...
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Shachar Lovett, Noam Solomon, Jiapeng Zhang

The sunflower conjecture is one of the most well-known open problems in combinatorics. It has several applications in theoretical computer science, one of which is DNF compression, due to Gopalan, Meka and Reingold [Computational Complexity 2013]. In this paper, we show that improved bounds for DNF compression imply improved bounds ... more >>>

Shachar Lovett, Jiapeng Zhang

There are two natural complexity measures associated with DNFs: their size, which is the number of clauses; and their width, which is the maximal number of variables in a clause. It is a folklore result that DNFs of small size can be approximated by DNFs of small width (logarithmic in ... more >>>

YiHsiu Chen, Mika G\"o{\"o}s, Salil Vadhan, Jiapeng Zhang

We study \emph{entropy flattening}: Given a circuit $\mathcal{C}_X$ implicitly describing an $n$-bit source $X$ (namely, $X$ is the output of $\mathcal{C}_X$ on a uniform random input), construct another circuit $\mathcal{C}_Y$ describing a source $Y$ such that (1) source $Y$ is nearly \emph{flat} (uniform on its support), and (2) the Shannon ... more >>>

Kun He, Qian Li, Xiaoming Sun, Jiapeng Zhang

Lov{\'a}sz Local Lemma (LLL) is a very powerful tool in combinatorics and probability theory to show the possibility of avoiding all ``bad" events under some ``weakly dependent" condition. Over the last decades, the algorithmic aspect of LLL has also attracted lots of attention in theoretical computer science \cite{moser2010constructive, kolipaka2011moser, harvey2015algorithmic}. ... more >>>

Xin Li, Shachar Lovett, Jiapeng Zhang

The Erdos-Rado sunflower theorem (Journal of Lond. Math. Soc. 1960) is a fundamental result in combinatorics, and the corresponding sunflower conjecture is a central open problem. Motivated by applications in complexity theory, Rossman (FOCS 2010) extended the result to quasi-sunflowers, where similar conjectures emerge about the optimal parameters for which ... more >>>

Daniel Kane, Shachar Lovett, Shay Moran, Jiapeng Zhang

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a ... more >>>

Shachar Lovett, Jiapeng Zhang

The sensitivity conjecture is one of the central open problems in boolean complexity. A recent work of Gopalan et al. [CCC 2016] conjectured a robust analog of the sensitivity conjecture, which relates the decay of the Fourier mass of a boolean function to moments of its sensitivity. We prove this ... more >>>

Shachar Lovett, Jiapeng Zhang

Zero knowledge proof systems have been widely studied in cryptography. In the statistical setting, two classes of proof systems studied are Statistical Zero Knowledge (SZK) and Non-Interactive Statistical Zero Knowledge (NISZK), where the difference is that in NISZK only very limited communication is allowed between the verifier and the prover. ... more >>>

Shachar Lovett, Jiapeng Zhang

The noisy population recovery problem is a statistical inference problem, which is a special case of the problem of learning mixtures of product distributions. Given an unknown distribution on $n$-bit strings with support of size $k$, and given access only to noisy samples from it, where each bit is flipped ... more >>>

Bo Tang, Jiapeng Zhang

Reducibility between different cryptographic primitives is a fundamental problem in modern cryptography. As one of the primitives, traitor tracing systems help content distributors recover the identities of users that collaborated in the pirate construction by tracing pirate decryption boxes. We present the first negative result on designing efficient traitor tracing ... more >>>

Shachar Lovett, Jiapeng Zhang

The noisy population recovery problem is a basic statistical inference problem. Given an unknown distribution in $\{0,1\}^n$ with support of size $k$,

and given access only to noisy samples from it, where each bit is flipped independently with probability $1/2-\eps$,

estimate the original probability up to an additive error of ...
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Jiapeng Zhang

A theorem of Green, Tao, and Ziegler can be stated as follows: if $R$ is a pseudorandom distribution, and $D$ is a dense distribution of $R,$ then $D$ can be modeled as a distribution $M$ which is dense in uniform distribution such that $D$ and $M$ are indistinguishable. The reduction ... more >>>