# Fast Learning Requires Good Memory

@article{Raz2019FastLR,
title={Fast Learning Requires Good Memory},
author={Ran Raz},
journal={Journal of the ACM (JACM)},
year={2019},
volume={66},
pages={1 - 18}
}
• R. Raz
• Published 12 December 2018
• Computer Science, Mathematics
• Journal of the ACM (JACM)
We prove that any algorithm for learning parities requires either a memory of quadratic size or an exponential number of samples. This proves a recent conjecture of Steinhardt et al. (2016) and shows that for some learning problems, a large storage space is crucial. More formally, in the problem of parity learning, an unknown string x ∈ {0,1}n was chosen uniformly at random. A learner tries to learn x from a stream of samples (a1, b1), (a2, b2) …, where each at is uniformly distributed over {0…
3 Citations
A Time-Space Lower Bound for a Large Class of Learning Problems
• R. Raz
• Mathematics, Computer Science
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
• 2017
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This paper describes natural prediction problems in which every sufficiently accurate training algorithm must encode essentially all the information about a large subset of its training examples, which remains true even when the examples are high-dimensional and have entropy much higher than the sample size.

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Fast Learning Requires Good Memory: A Time-Space Lower Bound for Parity Learning
• R. Raz
• Computer Science, Mathematics
2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
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It is proved that any algorithm for learning parities requires either a memory of quadratic size or an exponential number of samples, and an encryption scheme that requires a private key of length n, as well as time complexity of n per encryption/decryption of each bit is provenly and unconditionally secure.
A Time-Space Lower Bound for a Large Class of Learning Problems
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• Mathematics, Computer Science
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We prove a general time-space lower bound that applies for a large class of learning problems and shows that for every problem in that class, any learning algorithm requires either a memory of
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