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Creators/Authors contains: "Valiant, Gregory"

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  1. ; ; ; (, Journal of the ACM)
    We show that any memory-constrained, first-order algorithm which minimizes d-dimensional, 1-Lipschitz convex functions over the unit ball to 1/poly(d) accuracy using at most $$d^{1.25-\delta}$$ bits of memory must make at least $$\tilde{Omega}(d^{1+(4/3)\delta})$$ first-order queries (for any constant $$\delta in [0,1/4]$$). Consequently, the performance of such memory-constrained algorithms are a polynomial factor worse than the optimal $$\tilde{O}(d)$$ query bound for this problem obtained by cutting plane methods that use $$\tilde{O}(d^2)$$ memory. This resolves a COLT 2019 open problem of Woodworth and Srebro. 
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    Free, publicly-accessible full text available December 31, 2025
  2. ; ; ; ; (, The Annals of Statistics)
    Free, publicly-accessible full text available December 1, 2025
  3. ; (, ACM)
    Full Text Available 
  4. (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Guruswami, Venkatesan (Ed.)
    We describe two algorithms for multiplying n × n matrices using time and energy Õ(n²) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different algorithm, is for Boolean matrix multiplication. We hope this work inspires a deeper consideration of physically plausible/realizable models of computing that might allow for algorithms which improve upon the runtimes and energy usages suggested by the parallel RAM model in which each operation requires one unit of time and one unit of energy. 
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    Full Text Available 
  5. ; (, Leibniz international proceedings in informatics)
    Accepted Manuscript Full Text Available
  6. ; ; (, ICML)
    Accepted Manuscript Full Text Available
  7. ; ; ; (, Advances in Neural Information Processing Systems 35 (NeurIPS 2022))
    Accepted Manuscript Full Text Available
  8. ; ; ; (, Conference on Learning Theory (COLT))
    We show that any memory-constrained, first-order algorithm which minimizes d-dimensional, 1-Lipschitz convex functions over the unit ball to 1/ poly(d) accuracy using at most d^(1.25-delta) bits of memory must make at least d^(1+ 4 delta / 3) first-order queries (for any constant delta in (0,1/4). Consequently, the performance of such memory-constrained algorithms are a polynomial factor worse than the optimal O(d polylog d) query bound for this problem obtained by cutting plane methods that use >d^2 memory. This resolves one of the open problems in the COLT 2019 open problem publication of Woodworth and Srebro. 
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    Accepted Manuscript Full Text Available
  9. ; ; ; (, Conference on Learning Theory (COLT))
    Accepted Manuscript Full Text Available
  10. ; ; ; ; ; (, Conference on Learning Theory)
    Accepted Manuscript Full Text Available