arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.
arXiv:2606. 20547v1 Announce Type: new Abstract: We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $\rho(g)$ carrying it.
arXiv:2609.21039v1 Announce Type: new Abstract: A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matri...
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...
arXiv:2602. 24264v2 Announce Type: replace-cross Abstract: Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems.
arXiv:2609.24209v1 Announce Type: new Abstract: The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent wor...
The study investigates how to automatically predict the build orientation for selective laser melting (SLM) of dental parts using supervised machine learning. Researchers trained two different neural network backbones—ResNet‑50 on multi‑view images and PointNeXt‑S on point clouds—on about 2,400 patient‑specific parts, evaluating 13 different ways to represent the up‑axis (six classical SO(3) parameterizations and seven unit‑sphere representations). They found that applying test‑time augmentation (TTA) over 21 known rotations consistently reduced angular error, with the octahedral map achieving the lowest mean error (10.6°) on ResNet‑50, while direct S² representations performed best overall but may be influenced by label noise.
The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent work finds only weak pointwise similarity between mo...
arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.