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On the Power of Interactive Proofs for Learning
- We construct an interactive protocol for learning the $t$ largest Fourier characters of a given function $f \colon \{0, 1\}^n \to \{0, 1\}$ up to an arbitrarily small error, wherein the verifier uses $\mathsf{poly}(t)$ random examples.
Information-theoretic generalization bounds for learning from quantum data
Learning tasks play an increasingly prominent role in quantum information and computation.
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.
An Adaptivity Hierarchy Theorem for Property Testing
More accurately, we say that a tester is $k$-(round) adaptive if it makes queries in $k+1$ rounds, where the queries in the $i$'th round may depend on the answers obtained in the previous $i-1$ rounds.
