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Constructive Discrepancy Minimization by Walking on the Edges
TLDR
A new randomized algorithm to find a coloring as in Spencer's result based on a restricted random walk which is “truly” constructive in that it does not appeal to the existential arguments, giving a new proof of Spencer's theorem and the partial coloring lemma.
Bilinear Classes: A Structural Framework for Provable Generalization in RL
TLDR
This work provides an RL algorithm which has polynomial sample complexity for Bilinear Classes, a new structural framework which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation.
On cryptography with auxiliary input
TLDR
CPA/CCA secure symmetric encryption schemes that remain secure with exponentially hard-to-invert auxiliary input are constructed, based on a new cryptographic assumption, Learning Subspace-with-Noise (LSN), which is related to the well known Learning Parity- with-noise (LPN) assumption.
Bias vs structure of polynomials in large fields, and applications in effective algebraic geometry and coding theory
TLDR
Improved bounds are obtained for a suite of problems in effective algebraic geometry, including Hilbert nullstellensatz, radical membership and counting rational points in low degree varieties.
Subspace evasive sets
TLDR
The main technical ingredient is the construction of k low-degree polynomials whose common set of zeros has small intersection with any k-dimensional subspace.
Inverse conjecture for the gowers norm is false
TLDR
This paper shows the inverse conjecture to be false for p=2 and for d=4, by presenting an explicit function whose 4-th Gowers norm is non-negligible, but whose correlation with any polynomial of degree 3 is exponentially small.
The analytic rank of tensors and its applications
The analytic rank of tensors and its applications, Discrete Analysis 2019:7, 10 pp. There are several arguments in additive combinatorics concerning two-variable functions taking values in a field
MDS Matrices over Small Fields: A Proof of the GM-MDS Conjecture
  • Shachar Lovett
  • Mathematics, Computer Science
    IEEE 59th Annual Symposium on Foundations of…
  • 7 March 2018
TLDR
This work proves the conjecture that the MDS condition is sufficient over small fields as well as over very large fields by a probabilistic argument.
Non-malleable codes from additive combinatorics
Non-malleable codes provide a useful and meaningful security guarantee in situations where traditional errorcorrection (and even error-detection) is impossible; for example, when the attacker can
Weight Distribution and List-Decoding Size of Reed–Muller Codes
TLDR
A new connection is made between computer science techniques used to study low-degree polynomials and coding theory questions to resolve the weight distribution and list-decoding size of Reed-Muller codes for all distances.
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