Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail
Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance. While these laws guide the development of modern foundation models, the mechanisms underpinning them remain poorly understood, in part due to the absence of scalable analysis tools. To close this gap, we introduce "spectral position": a scalable measure of which eigenvalues of the empirical neural tangent kernel (eNTK) currently drive loss reduction. Applying this measure to scaling experiments, we find that spectral position decreases throughout training: learning shifts from dominant eigenmodes into the spectral tail. Larger models reach further into the tail than...
| Authors | Konstantin Nikolaou, Jonas Scheunemann, Sven Krippendorf et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 May 2026 |
| Last updated at source | 3 August 2026 |
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