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.
By Tom\'as Figliolia, Beren Millidge
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: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.
By Katie Everett
arXiv:2606. 26538v1 Announce Type: cross Abstract: Deep Transformers are composed of uniformly stacked residual blocks, yet their deepest layers often add little value.
By Huzama Ahmad, Cao Viet Hai Nam, Se-Young Yun
The paper introduces the Drift Contract, a spectral update geometry for local learning that improves depth robustness and hyperparameter stability. By applying momentum orthogonalization with spectral step scaling to per‑layer updates, the authors achieve consistent performance across a wide range of widths and depths on CIFAR‑10 MLPs, outperforming local Adam and providing a per‑layer, input‑conditioned drift bound. The study also shows that the spectral geometry itself, rather than step‑size rules, drives the observed depth robustness, while a negative result indicates that the stability benefit is limited to non‑normalized layers.
By Fabien Polly
arXiv:2607. 13380v1 Announce Type: new Abstract: Predictive Coding (PC) offers a biologically motivated alternative to backpropagation via local weight updates, yet routing error between layers still relies on an autograd Jacobian-transpose ($J^\top$) product - the last non-local operation in PC.
By Junlong Shen, Xingyu Li