The Complexity of Gradient Descent: CLS = PPAD ∩ PLS

Fearnley, John; Goldberg, Paul W.; Hollender, Alexandros; Savani, Rahul

doi:10.1145/3568163

Cited by 11 publications

(2 citation statements)

References 49 publications

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“…k = k + 1 13: end while pipelines and instruction sets [35]. At the same time, FPGAs undoubtedly offer greater advantages due to their reconfigurability and flexible memory hierarchy [36]. Although MCU+FPGA architecture can provide a diverse combination of scalar and spatial computing architectures for the instrumentation and improve the in-situ analysis capability of the instrumentation.…”

Section: Overall Structurementioning

confidence: 99%

FPGA-Based Real-time T2 Spectrum Inversion Algorithm for LWD-NMR Logging with Periodic Thermal Management

Fan

Liu

et al. 2023

Preprint

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The LWD-NMR instruments are limited by the telemetry bandwidth and logging timing requirements, so the echo T2 spectrum inversion function must be implemented at downhole logging instruments. Firstly, the inversion problem of T2 spectrum is converted to a non-negative least squares problem and solved by the accelerated projective gradient descent (APGD) algorithm. Secondly, the distributed structure is used in FPGA design to shorten the time for the APGD algorithm. Finally, a software cooling method based on a multi-core structure and periodic thermal management technology is deployed. Therefore, the inversion algorithm of echo T2 spectrum deployed on FPGA not only meets the requirements of real-time inversion calculation but also reduces the temperature effectively by means of software cooling. It provides a useful reference for the research of the downhole data processing technology of LWD.

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Section: Overall Structurementioning

confidence: 99%

FPGA-Based Real-time T2 Spectrum Inversion Algorithm for LWD-NMR Logging with Periodic Thermal Management

Fan

Liu

et al. 2023

Preprint

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“…We use the term "PL arithmetic circuit" for circuits over the basis {+, −, max, min, ×ζ} with rational constants. Some recent works call them "linear" arithmetic circuits instead[Deligkas et al, 2021;Fearnley et al, 2022].…”

mentioning

confidence: 99%

FIXP-membership via Convex Optimization: Games, Cakes, and Markets

Filos-Ratsikas

Hansen

Høgh

et al. 2022

2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)

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We introduce a new technique for proving membership of problems in FIXP -the class capturing the complexity of computing a fixed-point of an algebraic circuit. Our technique constructs a "pseudogate" which can be used as a black box when building FIXP circuits. This pseudogate, which we term the "OPT-gate", can solve most convex optimization problems. Using the OPT-gate, we prove new FIXP-membership results, and we generalize and simplify several known results from the literature on fair division, game theory and competitive markets.In particular, we prove complexity results for two classic problems: computing a market equilibrium in the Arrow-Debreu model with general concave utilities is in FIXP, and computing an envy-free division of a cake with very general valuations is FIXP-complete. We further showcase the wide applicability of our technique, by using it to obtain simplified proofs and extensions of known FIXP-membership results for equilibrium computation for various types of strategic games, as well as the pseudomarket mechanism of Hylland and Zeckhauser.

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