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. Among other results, we show a generic learning speedup lemma, equivalences between various learning models in the exponential time and subexponential time regimes, a dichotomy between learning and pseudorandomness, consequences of non-trivial learning for circuit lower bounds, Karp-Lipton theorems for probabilistic exponential time, and NC$^1$-hardness for the Minimum Circuit Size Problem.

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