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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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1122 · Dec 202319922001200920172026
13 results for fl-RDT

New method lowers spherical perceptron capacity using fully lifted random duality theory.

problem Tackles the negative spherical perceptron capacity, a long-standing open problem.
method Develops fully lifted random duality theory (fl RDT) to characterize capacity.
result Shows remarkable closed-form analytical relations for practical capacity values.

New insights into binary perceptron reveal phase transitions and algorithmic thresholds.

problem Understanding the statistical-computational gap in binary perceptron models.
method Application of fully lifted random duality theory (fl RDT) to uncover structural changes.
result Numerical estimates of constraint density thresholds align with theoretical predictions.

Study on theoretical limits of 0\ell_0 sparse-regression algorithms using Fl RDT.

problem Understanding the performance limits of 0\ell_0 norm based optimization algorithms in compressed sensing and sparse regression.
method Utilized Fully lifted random duality theory (Fl RDT) to analyze the maximum-likelihood (ML) decoding performance.
result Uncovered phase-transition (PT) and descending 0\ell_0 (d0\ell_0) curves that separate successful and unsuccessful algorithm performance.

Study potential computational gaps in symmetric binary perceptrons using fl-RDT.

problem Potential statistical-computational gaps in symmetric binary perceptrons.
method Parametric utilization of fully lifted random duality theory (fl-RDT).
result Observation of a computational gap SCG=αcαaSCG=α_c-α_a in SBP.

Wide hidden layer TCM nets capacity analyzed using RDT and fl RDT.

problem Capacity analysis of wide hidden layer TCM nets.
method Employed Fully Lifted Random Duality Theory (fl RDT) for capacity characterization.
result Explicit, closed form capacity characterizations for a generic class of hidden layer activations.

Study binary perceptrons' capacity using random duality theory.

problem Characterize the capacity of binary perceptrons with general thresholds.
method Utilized fully lifted random duality theory (fl RDT) to characterize the capacity.
result Characterizations match replica symmetry breaking predictions and uncover the capacity for zero-threshold scenario.

The study calculates the injectivity capacity of ReLU networks using a novel mathematical approach.

problem Determining the injectivity capacity of ReLU networks layers.
method Employing fully lifted random duality theory (fl RDT) to handle the 0\ell_0 spherical perceptron and implicitly the ReLU layers injectivity.
result The lifting mechanism converges remarkably fast with relative corrections not exceeding 0.1%.

Improved neural network capacity analysis using simplified RDT.

problem Analyzing the memorization capabilities of sign perceptron neural networks.
method Developed a simplified, partially lifted Random Duality Theory (fl RDT) approach.
result Concrete capacity bounds universally improve over previous best known ones.

The study revisits Hopfield's associative memory model and calculates its capacity for two specific pattern basins.

problem Determining the capacity of a Hebbian-Hopfield network for storing binary patterns.
method Using fully lifted random duality theory and numerical analysis, the study calculates the capacity for two specific pattern basins.
result Explicit characterizations of the capacity for the AGS and NLT pattern basins, with remarkable fast lifting convergence.

New algorithm nearly achieves ground state free energy of SK model.

problem Determining the ground state free energy of the SK model.
method Controlled Loosening-up (CLuP) algorithm applied to SK models.
result Achieves ground state free energy of ~0.76 for n in the thousands.

CLuP achieves near optimal ground state energies for positive and negative Hopfield models.

problem Finding near optimal ground state energies for positive and negative Hopfield models.
method Controlled Loosening-up (CLuP) algorithm with fully lifted random duality theory (fl RDT).
result Achieves ground state free energies of 1.771.77 and 0.330.33 for positive and negative Hopfield models respectively.

New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.

problem Resolving algorithmic hardness in asymmetric binary perceptrons.
method Fully lifted random duality theory (fl RDT) and large deviation upgrade (sfl LD RDT).
result Local entropy breaks down for constraint densities in (0.77, 0.78) interval, matching current solver limits.

This paper connects ultrametric overlap gap properties to parametric RDT for symmetric binary perceptrons.

problem Characterizing statistical computational gaps in symmetric binary perceptrons.
method Developed an analytical union-bounding program to rigorously upper-bound constraint densities of ultrametric overlap gap properties.
result Obtained tightest bounds at the first two levels of ultrametric overlap gap properties, closely approaching parametric RDT estimates.