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Fully lifted interpolating comparisons of bilinearly indexed random processes
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A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly indexed) comparative alternatives. Despite on occasion very involved technical considerations, the final interpolating forms and their underlying relations admit rather elegant expressions that provide conceivably highly desirable and useful tool for further studying various different aspects of random processes and their applications. We also discuss the generality of the considered models and show that they encompass many well known random structures and optimization problems to which then the obtained results automatically apply.
Forward citations
Cited by 7 Pith papers
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Ground state energies of multipartite $p$-spin models -- partially lifted RDT view
The paper uses partially lifted random duality theory to derive matching ground-state-energy bounds for spherical multipartite pure p-spin models and proves the Subag and Dartois-McKenna formulas agree exactly.
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CLuP practically achieves $\sim 1.77$ positive and $\sim 0.33$ negative Hopfield model ground state free energy
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.
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Deep ReLU networks -- injectivity capacity upper bounds
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.
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A CLuP algorithm to practically achieve $\sim 0.76$ SK--model ground state free energy
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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Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDT
For the asymmetric binary perceptron, the worst-case local entropy breaks down for constraint density alpha in (0.77, 0.78), matching replica predictions and the range where fast algorithms stop working.
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Fully lifted \emph{blirp} interpolation -- a large deviation view
A large-deviation upgrade of fully lifted blirp interpolation is derived, yielding explicit derivative identities that the author links to local entropy and computational gaps in perceptron models.
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A large deviation view of \emph{stationarized} fully lifted blirp interpolation
The paper derives new derivative identities for a stationarized fully lifted bilinearly indexed random process interpolator and states an equality between large deviation limits at the opposite ends of an interpolation path.
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