---
title: "From Approximation to Emergence: A Theory of Deep Learning — Stuff That Spins"
description: "arXiv:2607.01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation. From Approximation to Emergence develops a unified, proof-oriented account of modern deep learning theory, tracing a path from the classical foundations of approximation, optimization, an…"
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date: "2026-07-03T04:00:00+00:00"
modified: "2026-07-03T04:00:55.042387+00:00"
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# From Approximation to Emergence: A Theory of Deep Learning

**Source:** Unknown  
**Published:** July 3, 2026  
**Original:** https://arxiv.org/abs/2607.01311  

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