Learnable Persistent Topology for Multi-View Radar Semantic Segmentation

Objects in automotive radar produce sparse, fragmented echoes, making structural organisation central to interpreting Range--Doppler (RD), Range--Angle (RA), and Angle--Doppler (AD) views. Existing multi-view models capture which features group together, but not how connectivity and loop structure persist across scales. We introduce the first framework to learn cubical multifiltrations over a joint RD--RA--AD latent representation and integrate persistent $H_0$ and $H_1$ structure end-to-end into radar segmentation. Rather than relying on a fixed intensity-based construction, the filtration is learned, letting topology adapt to the fused representation; the resulting diagrams are vectorised, projected, and fused before RD and RA decoding. On CARRADA, the proposed method matches the strongest published methods in aggregate accuracy (63.85\% RD, 44.70\% RA mIoU) while achieving the highest car IoU in both views. Crucially, the gain is class-dependent: global persistence descriptors benefit spatially extended responses but not small, localised targets, a limitation of global conditioning rather than of persistence itself.