Hokkaido University

Hyperbolic space suits hierarchical embeddings, but earlier hyperbolic Gaussian-process latent variable models had to approximate every kernel entry numerically and optimize auxiliary variables jointly, which became impractical at scale. RHFF-LVM instead approximates hyperbolic kernels with explicit finite-dimensional random features derived from the Helgason–Fourier transform, modeling observations as feature projections of the latents and removing numerical quadrature, variational bounds and inducing points. On a synthetic binary tree, its embedded distances reach a Spearman correlation of 84.3 with true path lengths, versus 74.9 for the Euclidean counterpart RFF-LVM and 82.4 for the strongest hyperbolic baseline, Poincaré Map.

Hyperbolic space suits hierarchical embeddings, but earlier hyperbolic Gaussian-process latent variable models had to approximate every kernel entry numerically and optimize auxiliary variables jointly, which became impractical at scale. RHFF-LVM instead approximates hyperbolic kernels with explicit finite-dimensional random features derived from the Helgason–Fourier transform, modeling observations as feature projections of the latents and removing numerical quadrature, variational bounds and inducing points. On a synthetic binary tree, its embedded distances reach a Spearman correlation of 84.3 with true path lengths, versus 74.9 for the Euclidean counterpart RFF-LVM and 82.4 for the strongest hyperbolic baseline, Poincaré Map.

Medical imaging foundation models have traded generality against pixel-level precision, and most return a label without evidence. EVLF-FM feeds both disease-level and pixel-level visual features into a language model, first with supervised fine-tuning and then with reinforcement learning on verifiable rewards, spanning six specialties and 10 imaging modalities. On internal diagnostic validation it reached the highest mean accuracy among evaluated models, 0.895, and averaged 0.842 Acc@0.5 for medical visual grounding across nine modalities.

Medical imaging foundation models have traded generality against pixel-level precision, and most return a label without evidence. EVLF-FM feeds both disease-level and pixel-level visual features into a language model, first with supervised fine-tuning and then with reinforcement learning on verifiable rewards, spanning six specialties and 10 imaging modalities. On internal diagnostic validation it reached the highest mean accuracy among evaluated models, 0.895, and averaged 0.842 Acc@0.5 for medical visual grounding across nine modalities.

The work proposes Dirac-interconnected neural elements (DINEs), a neural network model that represents a physical system as a differential-algebraic equation (DAE) whose algebraic constraints are given by a Dirac structure in kernel representation, thereby simultaneously identifying from data the interconnection among components as a Dirac structure and learning the characteristics of the components as neural networks, which keeps learned subsystems in unreduced form so they can be isolated or composed into a new system without retraining, and which can handle partially observable systems.

The work proposes Dirac-interconnected neural elements (DINEs), a neural network model that represents a physical system as a differential-algebraic equation (DAE) whose algebraic constraints are given by a Dirac structure in kernel representation, thereby simultaneously identifying from data the interconnection among components as a Dirac structure and learning the characteristics of the components as neural networks, which keeps learned subsystems in unreduced form so they can be isolated or composed into a new system without retraining, and which can handle partially observable systems.