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Special Lagrangian cones in Deep Learning

arXiv 2609.20159 ↗First posted 17 Sep 2026math.DG cs.LG math.SGcited by 0

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Abstract (arXiv)

We introduce a matrix generalization of the cone of Harvey and Lawson and prove that it is an exact special Lagrangian manifold. We further show that it belongs to a family of exact special Lagrangian manifolds that foliate the balanced manifold arising in deep learning.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 4 of its 14 references that are in the map. First posted on arXiv 17 Sep 2026.

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References · 4

  1. 2018On the Optimization of Deep Networks: Implicit Acceleration by Overparameterizationcited by 284
  2. 2024The geometry of the deep linear networkcited by 11
  3. 2025An entropy formula for the Deep Linear Networkcited by 8
  4. 2025Regularization Implies balancedness in the deep linear networkcited by 4

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