Image feature extractors are rendered substantially more useful if different views of the same 3D location yield similar features while still being distinct from other locations. A feature extractor that achieves this goal even under significant viewpoint changes must recognise not just semantic categories in a scene, but also understand how different objects relate to each other in three dimensions. Existing work addresses this task by posing it as a patch retrieval problem, training the extracted features to facilitate retrieval of all image patches that project from the same 3D location. However, this approach uses a loss formulation that requires substantial memory and computation resources, limiting its applicability for large-scale training. We present a method for memory-efficient learning of location-consistent features that reformulates and approximates the smooth average precision objective. This novel loss function enables improvements in memory efficiency by three orders of magnitude, mitigating a key bottleneck of previous methods and allowing much larger models to be trained with the same computational resources. We showcase the improved location consistency of our trained feature extractor directly on a multi-view consistency task, as well as the downstream task of scene-stable panoptic segmentation, significantly outperforming previous state-of-the-art.