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.
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
arXiv:2606. 16112v1 Announce Type: cross Abstract: Residual architectures are ubiquitous in deep learning, but they suffer from a subtle structural limitation: the norm of the residual stream can grow rapidly with depth.
arXiv:2607. 14018v1 Announce Type: cross Abstract: We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization.
We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank.
arXiv:2606. 25008v1 Announce Type: new Abstract: Neural scaling laws describe how pre-training loss decays as power laws with training time, model size, and compute.