Depth Improves Training-Time Scaling for Difficult Tasks in Deep Linear Networks
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arXiv:2607. 07884v1 Announce Type: new Abstract: In this short note we consider the gradient descent dynamics of deep scalar linear networks, $f(x) = \prod_{l=1}^L w_l x$, which enjoy exact time-course solutions for any integer depth.
The paper investigates how nonlinearity in attention mechanisms affects scaling laws in large language models. It finds that nonlinear attention leads to an inverse-depth decay of loss across various data spectra, enabling models to learn both strong and weak spectral directions simultaneously. This behavior contrasts with linear-attention models, which rely on a power-law data spectrum and learn directions sequentially.
arXiv:2509. 24882v2 Announce Type: replace Abstract: Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models.
arXiv:2606. 04409v1 Announce Type: cross Abstract: Modern deep neural networks usually have large parameter scales and nonlinear hierarchical structures, and they have achieved strong performance in computer vision.
arXiv:2602. 07697v3 Announce Type: replace-cross Abstract: Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights.
arXiv:2605. 29548v2 Announce Type: replace Abstract: Larger models learn tasks smaller models do not.