Learning reliable correspondences between images and point clouds is fundamental for 2D-3D matching. Despite recent progress in detection-free methods, existing approaches primarily optimize matching within a single model and often struggle to maintain reliable correspondences under challenging conditions such as noisy inputs, low overlap, and ambiguous structures. In this work, we propose TeaMatch, a novel framework that introduces teachability as a criterion for cross-modal representation learning. We define teachability as the ability of a representation to be effectively recovered by weak learners under degraded inputs, reflecting its structural consistency and robustness. To this end, we construct a set of task-specific weak students that simulate common failure modes and train them to imitate the teacher on a training split while evaluating their recoverability on a disjoint meta split. The teacher is then optimized to improve the students' ability to recover reliable correspondences, guided by correspondence-level and geometry-aware constraints. Our framework can be seamlessly integrated into existing coarse-to-fine matching pipelines without additional inference cost. Extensive experiments demonstrate that TeaMatch improves matching robustness and achieves state-of-the-art performance on challenging 2D-3D matching benchmarks.
Descriptor-free visual localization eliminates high-dimensional descriptor storage, preserves scene privacy, and simplifies map maintenance, yet its accuracy still lags far behind descriptor-based pipelines. We identify this gap to insufficient geometric discriminability in geometry-only matching. Without visual appearance, current methods underutilize local geometry cues, lack the global context among keypoints, and overfit to a single keypoint detector. We further observe that descriptor-free matching naturally enables multi-detector training, as heterogeneous keypoints can be optimized in a shared geometry-only space without aligning descriptor spaces. Building on these insights, we propose GeoMix, a descriptor-free 2D-3D matching framework that strengthens geometric discriminability at three levels. Locally, directional and distance-aware embeddings enrich neighborhood aggregation with fine-grained spatial structure. Globally, learnable context nodes aggregate and redistribute scene-wide information via cross-attention to resolve ambiguities beyond local receptive fields. At the training level, Mix-Training exploits this detector-agnostic geometry space to learn representations across multiple keypoint detectors. Extensive experiments on MegaDepth, Cambridge Landmarks, 7Scenes, and Aachen Day-Night show that GeoMix sets a new state of the art among descriptor-free methods, reducing 75th-percentile rotation error by 89\% and translation error by up to 90\% over the previous best, while generalizing zero-shot to unseen detectors and narrowing the gap to descriptor-based pipelines. Code is available at $\href{https://github.com/YejunZhang/Geomix}{\text{this links}}$.