The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform
Matthew Legendre - One of the best experts on this subject based on the ideXlab platform.
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automatically adapting programs for mixed precision floating Point Computation
International Conference on Supercomputing, 2013Co-Authors: Jeffrey K Hollingsworth, Bronis R De Supinski, Matthew LegendreAbstract:As scientific Computation continues to scale, efficient use of floating-Point arithmetic processors is critical. Lower precision allows streaming architectures to perform more operations per second and can reduce memory bandwidth pressure on all architectures. However, using a precision that is too low for a given algorithm and data set leads to inaccurate results. In this paper, we present a framework that uses binary instrumentation and modification to build mixed-precision configurations of existing binaries that were originally developed to use only double-precision. This framework allows developers to explore mixed-precision configurations without modifying their source code, and it permits autotuning of floating-Point precision. We include a simple search algorithm to automate identification of code regions that can use lower precision. Our results for several benchmarks show that our framework is effective and incurs low overhead (less than 10X in most cases). In addition, we demonstrate that our tool can replicate manual conversions and suggest further optimization; in one case, we achieve a speedup of 2X.
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ICS - Automatically adapting programs for mixed-precision floating-Point Computation
Proceedings of the 27th international ACM conference on International conference on supercomputing - ICS '13, 2013Co-Authors: Jeffrey K Hollingsworth, Bronis R De Supinski, Matthew LegendreAbstract:As scientific Computation continues to scale, efficient use of floating-Point arithmetic processors is critical. Lower precision allows streaming architectures to perform more operations per second and can reduce memory bandwidth pressure on all architectures. However, using a precision that is too low for a given algorithm and data set leads to inaccurate results. In this paper, we present a framework that uses binary instrumentation and modification to build mixed-precision configurations of existing binaries that were originally developed to use only double-precision. This framework allows developers to explore mixed-precision configurations without modifying their source code, and it permits autotuning of floating-Point precision. We include a simple search algorithm to automate identification of code regions that can use lower precision. Our results for several benchmarks show that our framework is effective and incurs low overhead (less than 10X in most cases). In addition, we demonstrate that our tool can replicate manual conversions and suggest further optimization; in one case, we achieve a speedup of 2X.
Cedric Langbort - One of the best experts on this subject based on the ideXlab platform.
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on incremental approximate saddle Point Computation in zero sum matrix games
Automatica, 2016Co-Authors: Shaunak D Bopardikar, Cedric LangbortAbstract:We consider the problem of approximately computing saddle-Point of a zero-sum matrix game when either the columns of the matrix are revealed incrementally in time or the matrix is too large to apply traditional methods. We leverage the established adaptive multiplicative weights algorithm but introduce a novel simple criterion to determine whether the approximately computed minimizer's best strategy needs to be re-computed when a new column of the matrix is introduced. Our main results are two-fold. First, we show that our proposed incremental approach achieves the same accuracy as applying the adaptive multiplicative weights algorithm on the entire matrix, if known a priori. Second, when the columns of the matrix are generated independently and from the same distribution, we show that the expected number of times the approximate strategy is re-computed grows at most logarithmically with the number of columns of the matrix, thereby being Computationally efficient.
Jeffrey K Hollingsworth - One of the best experts on this subject based on the ideXlab platform.
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automatically adapting programs for mixed precision floating Point Computation
International Conference on Supercomputing, 2013Co-Authors: Jeffrey K Hollingsworth, Bronis R De Supinski, Matthew LegendreAbstract:As scientific Computation continues to scale, efficient use of floating-Point arithmetic processors is critical. Lower precision allows streaming architectures to perform more operations per second and can reduce memory bandwidth pressure on all architectures. However, using a precision that is too low for a given algorithm and data set leads to inaccurate results. In this paper, we present a framework that uses binary instrumentation and modification to build mixed-precision configurations of existing binaries that were originally developed to use only double-precision. This framework allows developers to explore mixed-precision configurations without modifying their source code, and it permits autotuning of floating-Point precision. We include a simple search algorithm to automate identification of code regions that can use lower precision. Our results for several benchmarks show that our framework is effective and incurs low overhead (less than 10X in most cases). In addition, we demonstrate that our tool can replicate manual conversions and suggest further optimization; in one case, we achieve a speedup of 2X.
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ICS - Automatically adapting programs for mixed-precision floating-Point Computation
Proceedings of the 27th international ACM conference on International conference on supercomputing - ICS '13, 2013Co-Authors: Jeffrey K Hollingsworth, Bronis R De Supinski, Matthew LegendreAbstract:As scientific Computation continues to scale, efficient use of floating-Point arithmetic processors is critical. Lower precision allows streaming architectures to perform more operations per second and can reduce memory bandwidth pressure on all architectures. However, using a precision that is too low for a given algorithm and data set leads to inaccurate results. In this paper, we present a framework that uses binary instrumentation and modification to build mixed-precision configurations of existing binaries that were originally developed to use only double-precision. This framework allows developers to explore mixed-precision configurations without modifying their source code, and it permits autotuning of floating-Point precision. We include a simple search algorithm to automate identification of code regions that can use lower precision. Our results for several benchmarks show that our framework is effective and incurs low overhead (less than 10X in most cases). In addition, we demonstrate that our tool can replicate manual conversions and suggest further optimization; in one case, we achieve a speedup of 2X.
Shaunak D Bopardikar - One of the best experts on this subject based on the ideXlab platform.
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on incremental approximate saddle Point Computation in zero sum matrix games
Automatica, 2016Co-Authors: Shaunak D Bopardikar, Cedric LangbortAbstract:We consider the problem of approximately computing saddle-Point of a zero-sum matrix game when either the columns of the matrix are revealed incrementally in time or the matrix is too large to apply traditional methods. We leverage the established adaptive multiplicative weights algorithm but introduce a novel simple criterion to determine whether the approximately computed minimizer's best strategy needs to be re-computed when a new column of the matrix is introduced. Our main results are two-fold. First, we show that our proposed incremental approach achieves the same accuracy as applying the adaptive multiplicative weights algorithm on the entire matrix, if known a priori. Second, when the columns of the matrix are generated independently and from the same distribution, we show that the expected number of times the approximate strategy is re-computed grows at most logarithmically with the number of columns of the matrix, thereby being Computationally efficient.
Shang-hua Teng - One of the best experts on this subject based on the ideXlab platform.
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Quantum Separation of Local Search and Fixed Point Computation
Algorithmica, 2009Co-Authors: Xi Chen, Shang-hua TengAbstract:We give a lower bound of Ω(n (d−1)/2) on the quantum query complexity for finding a fixed Point of a discrete Brouwer function over grid [n] d . Our lower bound is nearly tight, as Grover Search can be used to find a fixed Point with O(n d/2) quantum queries. Our result establishes a nearly tight bound for the Computation of d-dimensional approximate Brouwer fixed Points defined by Scarf and by Hirsch, Papadimitriou, and Vavasis. It can be extended to the quantum model for Sperner’s Lemma in any dimensions: The quantum query complexity of finding a panchromatic cell in a Sperner coloring of a triangulation of a d-dimensional simplex with n d cells is Ω(n (d−1)/2). For d=2, this result improves the bound of Ω(n 1/4) of Friedl, Ivanyos, Santha, and Verhoeven. More significantly, our result provides a quantum separation of local search and fixed Point Computation over [n]d , for d≥4. Aaronson’s local search algorithm for grid [n]d , using Aldous Sampling and Grover Search, makes O(n d/3) quantum queries. Thus, the quantum query model over [n]d for d≥4 strictly separates these two fundamental search problems.
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COCOON - Quantum Separation of Local Search and Fixed Point Computation
Lecture Notes in Computer Science, 2008Co-Authors: Xi Chen, Shang-hua TengAbstract:We give a lower bound of i¾?(n(di¾? 1)/2) on the quantum query complexity for finding a fixed Point of a discrete Brouwer function over grid [n]d. Our lower bound is nearly tight, as Grover Search can be used to find a fixed Point with O(nd/2) quantum queries. Our result establishes a nearly tight bound for the Computation of d-dimensional approximate Brouwer fixed Points defined by Scarf and by Hirsch, Papadimitriou, and Vavasis. It can be extended to the quantum model for Sperner's Lemma in any dimensions: The quantum query complexity of finding a panchromatic cell in a Sperner coloring of a triangulation of a d-dimensional simplex with ndcells is i¾?(n(di¾? 1)/2). For d= 2, this result improves the bound of i¾?(n1/4) of Friedl, Ivanyos, Santha, and Verhoeven. More significantly, our result provides a quantum separation of local search and fixed Point Computation over [n]d, for di¾? 4. Aaronson's local search algorithm for grid [n]d, using Aldous Sampling and Grover Search, makes O(nd/3) quantum queries. Thus, the quantum query model over [n]dfor di¾? 4 strictly separates these two fundamental search problems.
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FOCS - Paths Beyond Local Search: A Tight Bound for Randomized Fixed-Point Computation
48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), 2007Co-Authors: Xi Ghen, Shang-hua TengAbstract:In 1983, Akhus proved that randomization can speedup local search. For example, it reduces the query complexity of local search over grid [1 : n]d from ominus(nd-1) to 0(d1/2nd/2). It remains open whether randomisation helps fixed-Point Computation. Inspired by the recent advances on the complexity of equilibrium Computation, we solve this open problem by giving an asymptotically tight bound of (Omega(n))d-1 on the randomized query complexity for computing a fixed Point of a discrete Brouwer function over grid [1 : n]d. Our result can be extended to the black-box query model for Sperner's I&mma in any dimension. It also yields a tight bound for the Computation of d-dimensional approximate Brouwer fixed Points as defined by Scarf and by Hirsch, Papadimitriou, and Vavasis. Since the randomized query complexity of global optimization over [1 : n]d is ominus(nd), the randomized query model over [ 1 : n]d strictly separates these three important search problems: Global optimization is harder than fixed-Point Computation, and fixed-Point Computation is harder than local search. Our result indeed demonstrates that randomization does not help much in fixed-Point Computation in the black-box query model. Our randomized lower bound matches the deterministic complexity of this problem, which is ominus(nd-1).
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Paths Beyond Local Search: A Nearly Tight Bound for Randomized Fixed-Point Computation
arXiv: Computer Science and Game Theory, 2007Co-Authors: Xi Chen, Shang-hua TengAbstract:In 1983, Aldous proved that randomization can speedup local search. For example, it reduces the query complexity of local search over [1:n]^d from Theta (n^{d-1}) to O (d^{1/2}n^{d/2}). It remains open whether randomization helps fixed-Point Computation. Inspired by this open problem and recent advances on equilibrium Computation, we have been fascinated by the following question: Is a fixed-Point or an equilibrium fundamentally harder to find than a local optimum? In this paper, we give a nearly-tight bound of Omega(n)^{d-1} on the randomized query complexity for computing a fixed Point of a discrete Brouwer function over [1:n]^d. Since the randomized query complexity of global optimization over [1:n]^d is Theta (n^{d}), the randomized query model over [1:n]^d strictly separates these three important search problems: Global optimization is harder than fixed-Point Computation, and fixed-Point Computation is harder than local search. Our result indeed demonstrates that randomization does not help much in fixed-Point Computation in the query model; the deterministic complexity of this problem is Theta (n^{d-1}).