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Bilinearly indexed random processes -- \emph{stationarization} of fully lifted interpolation

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arxiv 2311.18097 v1 pith:Y7L5PR6I submitted 2023-11-29 math.PR cond-mat.dis-nncs.ITmath-phmath.ITmath.MPmath.STstat.TH

classification math.PRcond-mat.dis-nncs.ITmath-phmath.ITmath.MPmath.STstat.TH
keywords interpolatingrandombilinearlyemphfullyhereindexedintroduced
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Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful \emph{fully lifted} (fl) statistical interpolating/comparison mechanism for bilinearly indexed random processes. Here, we present a particular realization of such fl mechanism that relies on a stationarization along the interpolating path concept. A collection of very fundamental relations among the interpolating parameters is uncovered, contextualized, and presented. As a nice bonus, in particular special cases, we show that the introduced machinery allows various simplifications to forms readily usable in practice. Given how many well known random structures and optimization problems critically rely on the results of the type considered here, the range of applications is pretty much unlimited. We briefly point to some of these opportunities as well.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. CLuP practically achieves $\sim 1.77$ positive and $\sim 0.33$ negative Hopfield model ground state free energy

    cond-mat.dis-nn 2025-07 conditional novelty 6.0 of 10

    CLuP±Hop approximates Hopfield ground state free energies to within about 0.3% using simple gradient descent, backed by the author's fully lifted random duality theory.

  2. Deep ReLU networks -- injectivity capacity upper bounds

    stat.ML 2024-12 reject novelty 6.0 of 10

    For deep ReLU networks with random Gaussian weights, the paper gives upper bounds on the layer expansion needed for injectivity and finds the expansion need saturates by four layers.

  3. A CLuP algorithm to practically achieve $\sim 0.76$ SK--model ground state free energy

    cond-mat.dis-nn 2025-07 conditional novelty 5.0 of 10

    The authors propose a CLuP-SK barrier-descent algorithm and report it achieves approximately 0.76 of the SK ground state free energy for n around 2000 to 8000, approaching the theoretical Parisi limit of about 0.763.

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