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:2606. 07559v1 Announce Type: cross Abstract: Fine-tuning a language model on contexts whose correct completion has a near-synonym competitor often fails silently.
By Vaibhav Prakash, Jayasri Dontabhaktuni
arXiv:2606. 10324v1 Announce Type: new Abstract: 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.
By Parviz Haggi-Mani, Irina Rish
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:2604. 00230v2 Announce Type: replace Abstract: Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised.
By Anamika Paul Rupa
arXiv:2607. 14466v1 Announce Type: new Abstract: Noise injection is a well-known technique in stochastic optimization.
By Matt L. Wiemann, Peter Melchior, Andrew K. Saydjari
The paper introduces a stability theory for Joint-Embedding Predictive Architectures (JEPAs), showing that training dynamics involve a driving force and a decay effect that determine representation collapse. By linearising the gradient flow, the authors derive a per‑mode stability ratio that separates data‑side and predictor‑side contributions, predicting a phase boundary confirmed across 800 configurations. Using this insight, they propose ResidualPred, a transformer predictor that biases attention toward the identity at initialization, improving representation rank and downstream accuracy on tabular and image benchmarks.
By Jos\'e Lucas De Melo Costa, Seong Woo Ahn, Fabrice Popineau, Arpad Rimmel, Bich-Li\^en Doan
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
The paper investigates how normalization makes neural networks scale‑invariant, creating a feedback loop between learning‑rate schedules and weight decay that controls the effective step size of the optimizer. It derives an exact discrete‑time law showing that a single scalar quantity captures all schedule and decay effects, with norm growth providing a self‑quenching counter‑force that defines a sharp boundary between contraction‑ and expansion‑dominated regimes. Through exact analysis of a normalized regression model and experiments on MLPs, CNNs, GPT‑2, and various datasets, the authors demonstrate that constant learning rates with weight decay are intrinsically unstable, leading to recurrent dynamics, and that adaptive optimizers exhibit weaker stabilization under normalization.
"whyItMatters":"The study provides a precise, actionable rule for controlling training dynamics and schedule design in modern deep learning by isolating a single governing quantity for scale‑invariant optimization."
arXiv:2610.35514v1 Announce Type: new
Abstract: Neural scaling laws describe the predictable power-law dependence of model performance on training time, dataset size, and model scale, with the expone...
By Taishi Watanabe, Ryo Karakida, Jun-nosuke Teramae
arXiv:2607. 13491v1 Announce Type: cross Abstract: Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters.
By Shuzhen Li, Yifan Zhang, Jiacheng Guo, Quanquan Gu, Mengdi Wang