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On the Entropy Formula for Real, Complex, and Quaternionic Deep Linear Networks

arXiv 2606.16579 ↗First posted 15 Jun 2026cs.LG math-ph math.DGcited by 0

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Abstract (arXiv)

We extend the entropy formula of Menon and Yu for the real Deep Linear Network (DLN) to its complex and quaternionic analogues, obtaining a unified formula for DLNs over ℝ, mathbbC, and mathbbH.

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References · 5

  1. 2019Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizerscited by 61
  2. 2024The geometry of the deep linear networkcited by 11
  3. 2022Deep Linear Networks for Matrix Completion -- An Infinite Depth Limitcited by 8
  4. 2025An entropy formula for the Deep Linear Networkcited by 8
  5. 2025Entropic Regularization in the Deep Linear Networkcited by 2

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