Deep Networks and the Multiple Manifold Problem

Authors: Sam Buchanan, Dar Gilboa, John Wright

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Reproducibility Variable Result LLM Response
Research Type Theoretical Our main result is an analysis of the one-dimensional case of the multiple manifold problem, which reduces the analysis of the gradient descent dynamics to the construction of a certificate showing that a certain deterministic integral equation involving the network architecture and the structure of the data admits a solution of small norm.
Researcher Affiliation Academia Sam Buchanan Columbia University sdb2157@columbia.edu Dar Gilboa Harvard University dar_gilboa@fas.harvard.edu John Wright Columbia University jw2966@columbia.edu
Pseudocode No The paper does not contain structured pseudocode or algorithm blocks.
Open Source Code No The paper does not provide concrete access to source code (e.g., a repository link or explicit code release statement) for the methodology described in this paper.
Open Datasets No The paper describes a theoretical model problem where data is generated based on mathematical properties ('N i.i.d. samples from a distribution supported on the manifolds') rather than using a publicly available dataset.
Dataset Splits No The paper is theoretical and does not describe experimental validation or dataset splits.
Hardware Specification No The paper is theoretical and does not report on running experiments that would require specific hardware.
Software Dependencies No The paper is theoretical and does not describe experimental implementations requiring specific software dependencies.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or training configurations.