Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Improved learning of AC0 functions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
PP is closed under intersection
Selected papers of the 23rd annual ACM symposium on Theory of computing
When do extra majority gates help?: polylog(N) majority gates are equivalent to one
Computational Complexity - Special issue on circuit complexity
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
On the power of a threshold gate at the top
Information Processing Letters
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
Learning functions of k relevant variables
Journal of Computer and System Sciences - Special issue: STOC 2003
Learning Monotone Decision Trees in Polynomial Time
SIAM Journal on Computing
Testing for Concise Representations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Agnostically Learning Halfspaces
SIAM Journal on Computing
Efficient learning algorithms yield circuit lower bounds
Journal of Computer and System Sciences
Learning Geometric Concepts via Gaussian Surface Area
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
The Intersection of Two Halfspaces Has High Threshold Degree
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Computing symmetric boolean functions by circuits with few exact threshold gates
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Correlation bounds for poly-size AC0 circuits with n1-o(1) symmetric gates
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Exponential lower bound for bounded depth circuits with few threshold gates
Information Processing Letters
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In 2002 Jackson et al. [JKS02] asked whether AC0 circuits augmented with a threshold gate at the output can be efficiently learned from uniform random examples. We answer this question affirmatively by showing that such circuits have fairly strong Fourier concentration; hence the low-degree algorithm of Linial, Mansour and Nisan [LMN93] learns such circuits in sub-exponential time. Under a conjecture of Gotsman and Linial [GL94] which upper bounds the total influence of low-degree polynomial threshold functions, the running time is quasi-polynomial. Our results extend to AC0 circuits augmented with a small super-constant number of threshold gates at arbitrary locations in the circuit. We also establish some new structural properties of AC0 circuits augmented with threshold gates, which allow us to prove a range of separation results and lower bounds.