How Much Source Geometry to Trust? Adaptive Spiked Supports for Open-Set Domain Generalization

Open-set domain generalization (OSDG) requires acceptance regions to be loose enough to accommodate domain-shifted known samples yet compact enough to reject unknowns. Relying more on source-domain class geometry makes these regions more compact but less tolerant of domain shift, and since the reliability of that geometry varies across classes and source-domain configurations, no fixed degree of reliance suits all cases. This raises a central question: how much source geometry should we trust? We propose Adaptive Spiked Support (AdaSpike), which adapts this trust through cross-domain geometric consistency. Our key insight, which our robust OSDG analysis formalizes, is that greater source consistency suggests more stable target geometry and warrants greater trust, while greater discrepancy suggests more uncertainty and warrants less. Specifically, we show that the optimal acceptance region under a robust risk bound has a closed-form spiked structure, which preserves anisotropic scales along the $k$ leading source directions and assigns a shared isotropic scale to the rest, interpolating between isotropic and fully anisotropic supports. AdaSpike determines $k$ from its cross-domain discrepancy, having no need of target data or manual tuning. The supports are learned with objectives formulated from an OSDG risk bound, and a single support score serves both classification and rejection. Across three OSDG benchmarks and two backbones, AdaSpike outperforms existing methods in all six settings, improving average OSCR by 2.16 points over state-of-the-art methods.