Communications of the ACM
Computational limitations on learning from examples
Journal of the ACM (JACM)
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Cryptographic hardness of distribution-specific learning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Structural analysis of polynomial-time query learnability
Mathematical Systems Theory
Learning Arithmetic Read-Once Formulas
SIAM Journal on Computing
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
On interpolating arithmetic read-once formulas with exponentiation
Journal of Computer and System Sciences
On learning width two branching programs
Information Processing Letters
On pseudorandomness and resource-bounded measure
Theoretical Computer Science
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Randomness vs time: derandomization under a uniform assumption
Journal of Computer and System Sciences
Machine Learning
Machine Learning
Hiding Instances in Multioracle Queries
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
On the applications of multiplicity automata in learning
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Learnability and Automatizability
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Cryptographic Hardness for Learning Intersections of Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Circuit lower bounds for Merlin-Arthur classes
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Online Learning and Resource-Bounded Dimension: Winnow Yields New Lower Bounds for Hard Sets
SIAM Journal on Computing
Super-polynomial versus half-exponential circuit size in the exponential hierarchy
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Learning and lower bounds for AC0 with threshold gates
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Exact learning algorithms, betting games, and circuit lower bounds
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Exact Learning Algorithms, Betting Games, and Circuit Lower Bounds
ACM Transactions on Computation Theory (TOCT)
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We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circuit class C in Angluin's model of exact learning from membership and equivalence queries or in Valiant's PAC model yields a lower bound against C. More specifically, we prove that any subexponential time, deterministic exact learning algorithm for C (from membership and equivalence queries) implies the existence of a function f in EXP^N^P such that f@?C. If C is PAC learnable with membership queries under the uniform distribution or exact learnable in randomized polynomial-time, we prove that there exists a function f@?BPEXP (the exponential time analog of BPP) such that f@?C. For C equal to polynomial-size, depth-two threshold circuits (i.e., neural networks with a polynomial number of hidden nodes), our result shows that efficient learning algorithms for this class would solve one of the most challenging open problems in computational complexity theory: proving the existence of a function in EXP^N^P or BPEXP that cannot be computed by circuits from C. We are not aware of any representation-independent hardness results for learning depth-2, polynomial-size neural networks with respect to the uniform distribution. Our approach uses the framework of the breakthrough result due to Kabanets and Impagliazzo showing that derandomizing BPP yields non-trivial circuit lower bounds.