Neural Fiber Operators: Learning on Antipodally Symmetric Spherical Fiber Functions

Diffusion MRI (dMRI) is a critical non-invasive technique for characterizing white matter integrity. Predicting high angular resolution fiber orientation distribution (FOD) is crucial in clinical practice. Existing learning-based methods enable such FOD angular super resolution task but ignore the spherical-native geometry of FOD. To address this, we first reformulate FOD angular super resolution as a spherical operator learning problem, rather than conventional FOD regression. Based on this, we propose Neural Fiber Operator (NFO), a novel antipodal-symmetry-based neural operator, which efficiently learns the solution operator from FOD while preserving the antipodal symmetry of FOD. To exploit NFO, we design NFONet, a patch-based neural operator model for whole-brain or partial-brain FOD modeling. Extensive experiments are conducted on three complementary diffusion MRI datasets covering in-domain reconstruction, zero-shot generalization to independent cohorts and acquisition protocols, and ex-vivo biological validation. NFO consistently achieves state-of-the-art performance while using substantially fewer parameters. More importantly, NFO demonstrates robust generalization across progressively increasing distribution shifts, suggesting that the learned operator captures intrinsic properties of FOD angular super resolution. These results establish NFO as a principled framework for dMRI reconstruction and FOD modeling, and suggest that learning physically consistent solution operators provides a natural formulation for brain structure.