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Property Testing Bounds for Linear and Quadratic Functions via Parity Decision Trees
TLDR
It is observed that the query complexity of testing properties of linear and quadratic functions can be characterized in terms of complexity in another model of computation called parity decision trees.
Torus polynomials: an algebraic approach to ACC lower bounds
TLDR
It is shown that MAJORITY cannot be approximated by low-degree symmetric torus polynomials, a step towards proving ACC0 lower bounds for the majority function via this approach.
On testing bent functions
TLDR
This work shows that testing whether a given Boolean function on n variables is bent, or 1 8 -far from being bent, requires Ω(n) queries, and remarks that this problem is equivalent to testing affine-isomorphism to the inner product function.
On polynomial approximations over ℤ/2kℤ
On Multilinear Forms: Bias, Correlation, and Tensor Rank
TLDR
The bias vs tensor-rank connection is proved and the finite field multiplication tensor has tensor rank at least at least $3.52 k$ matching the best known lower bound for any explicit tensor in three dimensions over $GF(2)".
On polynomial approximations over Z/2kZ
TLDR
It is observed that the model the authors study subsumes the model of non-classical polynomials in the sense that proving bounds in the model implies bounds on the agreement ofNon- classical poynomials with Boolean functions.
Towards understanding the approximation of Boolean functions by nonclassical polynomials
TLDR
The ability of nonclassical polynomials to approximate Boolean functions with respect to both previously studied and new notions of approximation is investigated.
Lecture 11 : Random variables II : mutual independence , k-wise independence , some obvious facts about random variables , expectation of a random variable , linearity of expectation
Definition 1. Let X1, . . . , Xn be random variables defined on a probability space (Ω, P ). Then X1, . . . , Xn are said to mutually independent if for all a1, a2, . . . , an ∈ R, the events [X1 =
Lecture 3: Finding integer solutions to systems of linear equations
TLDR
It turns out that the algorithm implicit in the constructive proof is not efficient since the intermediate entries can blow up, and thus an efficient algorithm is proposed to find the Hermite Normal Form (HNF) of a given integer matrix, which shall be the stepping to stone to the algorithm for finding integer solutions to a system of linear equation.
CS 598 : Theoretical Machine Learning
TLDR
It is shown that by combining these weak learning in some specific way the authors can achieve a strong learner, which is clear from previous argument, strong PAC learning implies weak PAC learning.
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