Sven: Singular Value Descent as a Computationally Efficient Natural Gradient Method

arXiv:2604.01279 · cs.LG, cs.AI, hep-th, math.OC · Submitted 2026-04-01 · Read on arXiv

cs.LG, cs.AI, hep-th, math.OC

Submitted: 2026-04-01

Updated: 2026-10-05

Code: https://github.com/karpathy/nanoGPT

Terminology

• Loss Function — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes

Sources

• Descending into the Modular Bootstrap
• Efficient Per-Example Gradient Computations
• The Optimiser Hidden in Plain Sight: Training with the Loss Landscape's Induced Metric
• Revisiting the Polyak step size
• Gaussian Error Linear Units (GELUs)
• Deep Learning Scaling is Predictable, Empirically
• Scaling Laws for Neural Language Models
• Adam: A Method for Stochastic Optimization
• Muon is Scalable for LLM Training
• Jacobian Descent for Multi-Objective Optimization
• Natural Gradient Methods: Perspectives, Efficient-Scalable Approximations, and Analysis
• SOAP: Improving and Stabilizing Shampoo using Adam

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