Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration. Recent works increasingly leverage optimal transport (OT) for distributional alignment, whose effectiveness largely depends on sparse supervision that is hard or costly to obtain in practice. Existing works, however, largely overlook how to actively acquire high-quality supervision to improve their alignment performance under OT frameworks. In this paper, we propose a principled active alignment framework for optimal transport alignment called AvAtar. We quantify the informativeness of a candidate by measuring its gradient-based impact on the global alignment result, computed as the gradient propagation from the global alignment result to all possible supervisions of the candidate through the entropy-regularized OT formulation. While differentiating through OT is challenging given its constrained nature, we leverage the adjoint-state method to reformulate the computation to a linear system solvable by the conjugate gradient method with linear complexity and guaranteed convergence. By encoding the global alignment result via effective utility functions, AvAtar is applicable to general alignment problems under the OT framework. Extensive experiments on three representative alignment tasks demonstrate the effectiveness, scalability, and generalizability of the proposed AvAtar.

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