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TR23-006
| 20th January 2023
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Nader Bshouty#### Superpolynomial Lower Bounds for Learning Monotone Classes

Revisions: 1

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TR23-005
| 13th January 2023
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Paul Beame, Niels Kornerup#### Cumulative Memory Lower Bounds for Randomized and Quantum Computation

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TR23-004
| 13th January 2023
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Yinan Li, Youming Qiao, Avi Wigderson, Yuval Wigderson, Chuanqi Zhang#### On linear-algebraic notions of expansion

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Nader Bshouty

Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$ DNF, size-$s$ Decision Tree, and $\log s$-Junta by DNF (that returns a DNF hypothesis). Assuming a natural ... more >>>

Paul Beame, Niels Kornerup

Cumulative memory---the sum of space used over the steps of a computation---is a fine-grained measure of time-space complexity that is a more accurate measure of cost for algorithms with infrequent spikes in memory usage in the context of technologies such as cloud computing that allow dynamic allocation and de-allocation of ... more >>>

Yinan Li, Youming Qiao, Avi Wigderson, Yuval Wigderson, Chuanqi Zhang

A fundamental fact about bounded-degree graph expanders is that three notions of expansion---vertex expansion, edge expansion, and spectral expansion---are all equivalent. In this paper, we study to what extent such a statement is true for linear-algebraic notions of expansion.

There are two well-studied notions of linear-algebraic expansion, namely dimension expansion ... more >>>

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