The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified.
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
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. 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
arXiv:2606. 11123v1 Announce Type: new Abstract: Backpropagation (BP) is widely viewed as biologically implausible, in part because it requires feedback weights to be the transpose of forward weights for error propagation.
By Gauthier Boeshertz, Razvan Pascanu, Claudia Clopath
arXiv:2608.30720v1 Announce Type: new
Abstract: Representational similarity is foundational to analyses of deep networks, yet distances between point-valued representations are not intrinsically tied...
By Kieran Murphy
arXiv:2608. 14664v1 Announce Type: new Abstract: How can we determine whether a trained neural network is already deep enough?
By Zeyu Liu, Jinhao Zhang, Yunquan Zhang, Guangming Tan, Xiang Gao, Fangming Liu, Daning Cheng
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
arXiv:2403.04545v4 Announce Type: replace
Abstract: Scaling factors in residual branches have emerged as a prevalent method for boosting neural network performance, especially in normalization-free a...
By Zixiong Yu, Guhan Chen, Jianfa Lai, Bohan Li, Songtao Tian
arXiv:2607. 15449v1 Announce Type: new Abstract: Using the language of Wilsonian renormalization group theory (RG), we treat the Transformer's attention mechanism as a perturbation of the trained MLP residual-stack fixed point and ask whether it constitutes a relevant, marginal, or irrelevant operator.
By Parviz Haggi-Mani, Irina Rish
The paper critiques the common practice of evaluating depth usage in depth‑recurrent language models by truncating depth during inference and measuring performance decline. It argues that this method conflates three distinct effects—fewer block applications, reduced computation, and an out‑of‑distribution readout—yet is usually interpreted as measuring only the second. To address this, the authors introduce the Depth Control Protocol (DCP), a suite of positive and negative controls that isolate each factor, along with a training intervention to confirm causality, specifically tailored for depth‑wise weight‑sharing architectures.
By Ha Van Dau, Thanh Tung Khuat, Nguyen Thanh Dung
arXiv:2607. 12438v1 Announce Type: new Abstract: Deep networks trained with label noise often learn clean structure before memorizing corrupted labels.
By Satwik Bathula, Anand A. Joshi