arXiv:2607. 17513v1 Announce Type: cross Abstract: Expert domains are trees; the Euclidean transformer is not, diluting parent-child structure exponentially at depth.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.
arXiv:2608. 14803v1 Announce Type: new Abstract: A recent line of work recasts the post-memorization phase of grokking as constrained optimization: once a network interpolates the training set, weight decay drives a slow drift along the zero-loss manifold toward lower norm.
arXiv:2607. 05268v1 Announce Type: cross Abstract: Whether a hyperbolic representation model uses its geometry cannot be read off its curvature parameter: what matters is the dimensionless operating point $\sqrt{c}\rho$ and whether the radial and cone machinery is active there.
arXiv:2608. 02668v1 Announce Type: cross Abstract: Residual connections are the de facto mechanism for training deep neural networks stably.
arXiv:2606. 02596v1 Announce Type: new Abstract: The curvature exponent $\alpha$ in $h_k \propto \sigma_k^\alpha$ -- governing how Hessian eigenvalues scale with gradient singular values -- varies systematically across layer types ($\alpha \approx 2$ for convolutions, $\approx 1$ for transformer attention, $< 1$ for MLP up-projections).
arXiv:2608. 05136v1 Announce Type: new Abstract: Gradient descent on a factored model $W = UV^\top$ is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not.
arXiv:2607. 03998v1 Announce Type: new Abstract: The local sharpness of the loss, the top Hessian eigenvalue $\lambda_1$, determines the largest stable gradient step, but measuring it normally requires Lanczos or Hessian-vector iterations.