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A matrix $M: A \times X \rightarrow \{-1,1\}$ corresponds to the following learning problem: An unknown element $x \in X$ is chosen uniformly at random.
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Gillat Kol, Ran Raz, Avishay Tal: Time-Space Hardness of Learning Sparse Parities. STOC 2017: 1067-1080
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Dana Moshkovitz, Michal Moshkovitz: Mixing Implies Strong Lower Bounds for Space Bounded Learning. Electronic Colloquium on Computational Complexity (ECCC) 24: 116 (2017)
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Jacob Steinhardt, Gregory Valiant, Stefan Wager: Memory, Communication, and Statistical Queries. COLT 2016: 1490-1516
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Ran Raz: A Time-Space Lower Bound for a Large Class of Learning Problems. FOCS 2017 (to appear). Also in: Electronic Colloquium on Computational Complexity (ECCC) 24: 20 (2017)
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