Conspiracies between Learning Algorithms, Circuit Lower Bounds and Pseudorandomness

TL;DR

This paper explores deep theoretical links between learning algorithms, circuit complexity lower bounds, and pseudorandomness, revealing new equivalences, speedups, and hardness results in computational complexity.

Contribution

It introduces a generic learning speedup lemma, establishes equivalences between learning models, and connects non-trivial learning to circuit lower bounds and hardness results.

Findings

A generic learning speedup lemma is established.

Equivalences between exponential and subexponential time learning models are shown.

Non-trivial learning implies circuit lower bounds and hardness for certain problems.

Abstract

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.