Pseudo-Hyperbolic Neural Networks

Standard hyperbolic neural networks typically rely on a single timelike dimension, providing a strong inductive bias for hierarchical data but limiting their flexibility in modeling heterogeneous data with mixed structural patterns. In this work, we investigate representation learning on pseudo-hyperbolic manifolds with multiple timelike dimensions. Our main contribution is the proposal of Pseudo-Hyperbolic Multinomial Logistic Regression (QMLR), which, to our knowledge, is the first MLR classifier formulated directly on pseudo-hyperbolic manifolds. Specifically, QMLR derives an exact spacelike point-to-hyperplane decision function and constructs a timelike surrogate for cases where the corresponding global minimum-distance formulation is not well-defined. Class-dependent offsets are encoded through generalized Lorentz boosts, while a learnable gate adaptively combines the two causal branches. To enhance the representations supplied to QMLR, we further develop a pseudo-hyperbolic attention module that integrates geometry-aware aggregation, radial projection, and learnable residual interpolation while preserving the manifold constraint. Extensive experiments on graph node classification, electroencephalography (EEG) decoding, image classification, and genomic sequence learning demonstrate that our proposed framework outperforms the compared baselines in most settings, supporting pseudo-hyperbolic geometry as a flexible alternative for heterogeneous representation learning.