arXiv Artificial Intelligence

Beyond the Matrix Sign: Quadratic Spectral Descent

1 day ago 10.09.2026 07:00 👁 2 views
Beyond the Matrix Sign: Quadratic Spectral Descent

Quick summary

arXiv:2609.07597v1 Announce Type: cross Abstract: Muon can be interpreted as optimizing a linear local objective over a spectral-norm ball. This gives a matrix-sign update that preserves the singular directions of the gradient and assigns the same magnitude to all active singular modes. We ask whether these two properties remain optimal when local curvature is taken into account. To answer this question, we keep Muon's spectral-norm constraint unchanged and replace the linear local model with a quadratic one. We call the resulting method \emph{Quadratic Spectral Descent} (QSD). We show that cu

Key takeaways

  • arXiv:2609.07597v1 Announce Type: cross Abstract: Muon can be interpreted as optimizing a linear local objective over a spectral-norm ball.
  • This gives a matrix-sign update that preserves the singular directions of the gradient and assigns the same magnitude to all active singular modes.
  • We ask whether these two properties remain optimal when local curvature is taken into account.

Why it matters

“Beyond the Matrix Sign: Quadratic Spectral Descent” should be evaluated beyond branding and benchmark scores. Its practical importance will emerge in task accuracy, latency, unit cost, safety and integration with real workflows.

Kaynak sitede devamını oku: arXiv Artificial Intelligence ↗