Communications of the ACM
On the degree of Boolean functions as real polynomials
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Approximating threshold circuits by rational functions
Information and Computation
An introduction to computational learning theory
An introduction to computational learning theory
PP is closed under intersection
Selected papers of the 23rd annual ACM symposium on Theory of computing
Boosting a weak learning algorithm by majority
Information and Computation
Perceptrons, PP, and the polynomial hierarchy
Computational Complexity - Special issue on circuit complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the power of a threshold gate at the top
Information Processing Letters
Computing Boolean functions by polynomials and threshold circuits
Computational Complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Machine Learning
Machine Learning
Learning Intersections and Thresholds of Halfspaces
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Toward Attribute Efficient Learning of Decision Lists and Parities
The Journal of Machine Learning Research
Separating AC0 from depth-2 majority circuits
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Unconditional lower bounds for learning intersections of halfspaces
Machine Learning
Learning intersections of halfspaces with a margin
Journal of Computer and System Sciences
Extremal properties of polynomial threshold functions
Journal of Computer and System Sciences
Polynomials that Sign Represent Parity and Descartes' Rule of Signs
Computational Complexity
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
SIAM Journal on Computing
Any AND-OR Formula of Size $N$ Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
SIAM Journal on Computing
Improved lower bounds for learning intersections of halfspaces
COLT'06 Proceedings of the 19th annual conference on Learning Theory
On PAC learning algorithms for rich boolean function classes
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
On the complexity of depth-2 circuits with threshold gates
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
SIAM Journal on Computing
| Hi-index | 0.00 |
We give new upper and lower bounds on the degree of real multivariate polynomials which sign-represent Boolean functions. Our upper bounds for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs.