arXiv:2605. 01288v3 Announce Type: replace Abstract: In deep networks with small initialization, training exhibits long plateaus separated by sharp feature-acquisition transitions.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
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:2607. 07845v1 Announce Type: new Abstract: The Hessian of the training loss governs the local geometry of the loss landscape, yet despite existing explanations for its largest eigenvalues, the origin of the vast multitude of vanishingly small eigenvalues remains elusive.
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
arXiv:2607. 12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization.
The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc. Prior works have focused on empirical results or pursued a theoretical treatment under overly simplified settings.