arXiv:2607. 17513v1 Announce Type: cross Abstract: Expert domains are trees; the Euclidean transformer is not, diluting parent-child structure exponentially at depth.
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The paper introduces Hyper^2, a dual‑space consistency framework that applies hyperbolic geometry consistently to both the loss and the encoder in point‑cloud completion tasks. By reusing the same arcosh(1+αd²) function as a positional bias in refinement attention and as the Chamfer loss, Hyper^2 achieves significant Chamfer error reductions—up to 22.9% on ShapeNet‑55 and 37.5% on unseen ShapeNet‑34—while adding only ~1.6% FLOPs. The authors demonstrate that geometric consistency across encoder and loss, rather than either component alone, is key to effective hyperbolic supervision, supported by two model‑agnostic indicators that peak only when both are hyperbolic.
hyperbolix is an open‑source library for hyperbolic deep learning in JAX, built on Flax NNX. It provides six manifolds—including Euclidean, Poincaré ball, hyperboloid, κ‑stereographic, mixed‑curvature product, and proper velocity space—through a common interface, and implements a wide range of layer families (linear, convolution, attention, normalization, positional encoding, regression, vector quantization). The library also supplies Riemannian optimizers, wrapped distributions, dimensionality‑reduction techniques, and precision‑tested operations that replace numerically unstable formulas on the hyperboloid, ensuring accurate float32 computations at large distances.
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. 19584v1 Announce Type: new Abstract: We study landscapes for complex-parameterized networks.
arXiv:2608. 02668v1 Announce Type: cross Abstract: Residual connections are the de facto mechanism for training deep neural networks stably.