arXiv:2506. 08764v3 Announce Type: replace Abstract: Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian.
arXiv:2602. 10949v2 Announce Type: replace-cross Abstract: Effective initialization in deep networks requires an understanding of random neural networks.
arXiv:2608. 08350v1 Announce Type: new Abstract: The initialisation of deep neural networks determines whether information and gradients can propagate across depth, yet a unified theory connecting these properties to learning dynamics remains elusive.
arXiv:2602. 05779v2 Announce Type: replace Abstract: The Edge-of-Chaos (EoC) theory developed for the random initialization of deep networks allows more efficient training by both preserving information in the initial outputs of the network and minimising exploding or vanishing gradients through characterisation of the intermediate layers as Gaussian processes.
arXiv:2605. 01288v3 Announce Type: replace Abstract: In deep networks with small initialization, training exhibits long plateaus separated by sharp feature-acquisition transitions.
arXiv:2607. 12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization.
We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class of two-layer diagonal linear networks (as defined in Definition 4.
arXiv:2606. 28464v1 Announce Type: new Abstract: In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture.
arXiv:2401. 04013v2 Announce Type: replace Abstract: Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom.
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
arXiv:2608. 14638v1 Announce Type: new Abstract: In this paper we study autoencoders, a special class of deep neural nets (DNNs) whose performance can be characterized via their fixed points.