Jul 2026· 2026 6th International Conference on Electrical, Computer and Energy Technologies (ICECET)· pp. 1-7· 0 citations· 20 references
Abstract
Hyperbolic embedding methods for collaborative filtering constrain all representations to the hyperboloid manifold, imposing a single geometry regardless of data characteristics. We introduce LightConeFM, which removes this constraint and allows embeddings to freely occupy any causal region of Lorentz-Minkowski space-timelike, lightlike, or spacelike-using only standard gradient descent without Riemannian optimization. Experiments on four real-world datasets reveal two consistent findings: (1) unconstrained embeddings outperform their constrained counterparts on every dataset (up to +7.0% AUC), and (2) the learned causal zone distribution predicts where hyperbolic geometry provides benefit over Euclidean alternatives (Pearson $r=0.94$, Spearman $\rho=1.0)$ -datasets with predominantly timelike users exhibit the largest gains, while predominantly spacelike datasets are better served by Euclidean methods. On a job recommendation dataset, LightConeFM achieves +5.99% AUC improvement in cold-start settings, indicating particular value for sparse, hierarchical domains.
The results give an empirical separation, on a real hierarchical-classification problem, between two natural latent geometries for a class-structured regularizer.
A general system of ordinary differential equations describing geodesics in the DLN is derived and an investigation into using an entropic log-volume form related to the geometry on the full-rank manifold as an explicit regularizer for a simple class of energies is investigated.
This work introduces a Nested Inductive Bias framework that utilizes a two-stage diffeomorphic composition to formally pull back non-Euclidean target geometries onto the SPD manifold, and proposes the Rational Conformal Metric (RCM), designed to establish state-of-the-art geometric robustness against outliers by boundi...
This work introduces Riemannian Orthogonally Decoupled Regularization (RODR) to reformulate the optimization trajectory by disentangling the normal (fitting) and tangential (distribution) components and establishes a generic and interpretable framework for disentangled geometric optimization in point cloud processing.
Hyper^2 is proposed, a dual-space consistency framework that extends HyperbolicCD by reusing the identical arcosh(1+alpha d^2) functional form as a positional bias on the refinement attention (a hyperbolic distance encoding), paired with HyperbolicCD's hyperbolic Chamfer loss under a single shared curvature alpha.
This work establishes the first curvature-independent regret guarantees for decentralized online optimization on Hadamard manifolds, and studies Distributed Riemannian Online Gradient Descent, which combines local Riemannian h-subgradient updates with an implicit Fr\'echet-mean consensus.
