bibkey: “saxe2013exact” authors: “Andrew M. Saxe; James L. McClelland; Surya Ganguli” year: 2013 title: “Exact solutions to the nonlinear dynamics of learning in deep linear neural networks” doi: null claim: “Deep linear networks admit analytically tractable learning dynamics under stated data and initialization assumptions.” strata_touched: [] license: “citation-only” triage: “anchor” url: “https://arxiv.org/abs/1312.6120”

Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

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arXiv:1312.6120v3, pages 3–6. The first submission is 20 December 2013; version 3 is 19 February 2014. The decoupled exact solutions impose whitened inputs, suitable orthogonal initial alignment, and balanced scalar modes. The contextual-spacetime ML volume cites this as the deep-linear framework and proves its own synchronous finite-step identities; those discrete identities are not attributed to this paper.