Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardness of learning noisy halfspaces using polynomial thresholds   We prove the hardness of weakly learning halfspaces in the presence of
adversarial noise using polynomial threshold functions (PTFs). In particular,
we prove that for any constants $d \in \mathbb{Z}^+$ and $\varepsilon > 0$, it
is NP-hard to decide: given a set of $\{-1,1\}$-labeled points in
$\mathbb{R}^n$ whether (YES Case) there exists a halfspace that classifies
$(1-\varepsilon)$-fraction of the points correctly, or (NO Case) any degree-$d$
PTF classifies at most $(1/2 + \varepsilon)$-fraction of the points correctly.
This strengthens to all constant degrees the previous NP-hardness of learning
using degree-$2$ PTFs shown by Diakonikolas et al. (2011). The latter result
had remained the only progress over the works of Feldman et al. (2006) and
Guruswami et al. (2006) ruling out weakly proper learning adversarially noisy
halfspaces.

35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an