Universal masking channels generalize hardcore lemma
Original title: Universal Hardness From Masking Channels
Masking channels certify hardness of non-Boolean function learning via convex duality on fidelity.
The paper generalizes the hardcore lemma using masking channels that inject randomness into output distributions. Classic hardcore measure equates to an input-dependent masking channel. Framework uses convex duality to certify learning difficulty for any function class C and loss notion. Maximum fidelity of the channel measures least noise needed to hide f structure. Derives multiclass hardcore generalizations and constructs a universal masking channel for multiple hardness notions simultaneously. Symmetry holds with pseudoentropy and MaxEnt algorithm.
- Hardcore measure equivalent to masking channel
- Fidelity via convex duality characterizes learning difficulty
- Multiclass generalizations of hardcore lemma
- Universal masking channel for many hardness notions
- Tight pseudoentropy characterization using MaxEnt
From the original article
1 min read at arxiv.orgWe prove a broad learning-theoretic generalization of the celebrated hardcore lemma concerning the average-case complexity of computing a Boolean function (Impagliazzo, 1995).
By Parikshit Gopalan · arxiv.org
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