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Quantum learning algorithms imply circuit lower bounds
This result is optimal in both $\gamma$ and $T$, since it is not hard to learn any class $\mathfrak{C}$ of functions in (classical) time $T = 2^n$ (with no error), or in quantum time $T = \mathsf{poly}(n)$ with error at most $1/2 - \Omega(2^{-n/2})$ via Fourier sampling.
Conspiracies between Learning Algorithms, Circuit Lower Bounds and Pseudorandomness
We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness.
Learning circuits with few negations
In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions.
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