{"ID":2873174,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.08104","arxiv_id":"2509.08104","title":"APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction","abstract":"Training deep learning models for point cloud prediction tasks such as shape completion and generation depends critically on loss functions that measure discrepancies between predicted and ground-truth point sets. Commonly used functions such as Chamfer Distance (CD), HyperCD, and InfoCD rely on nearest-neighbor assignments, which often induce many-to-one correspondences, leading to point congestion in dense regions and poor coverage in sparse regions. These losses also involve non-differentiable operations due to index selection, which may affect gradient-based optimization. Earth Mover Distance (EMD) enforces one-to-one correspondences and captures structural similarity more effectively, but its cubic computational complexity limits its practical use. We propose the Adaptive Probabilistic Matching Loss (APML), a fully differentiable approximation of one-to-one matching that leverages Sinkhorn iterations on a temperature-scaled similarity matrix derived from pairwise distances. We analytically compute the temperature to guarantee a minimum assignment probability, eliminating manual tuning. APML achieves near-quadratic runtime, comparable to Chamfer-based losses, and avoids non-differentiable operations. When integrated into state-of-the-art architectures (PoinTr, PCN, FoldingNet) on ShapeNet benchmarks and on a spatiotemporal Transformer (CSI2PC) that generates 3D human point clouds from WiFi CSI measurements, APM loss yields faster convergence, superior spatial distribution, especially in low-density regions, and improved or on-par quantitative performance without additional hyperparameter search. The code is available at: https://github.com/apm-loss/apml.","short_abstract":"Training deep learning models for point cloud prediction tasks such as shape completion and generation depends critically on loss functions that measure discrepancies between predicted and ground-truth point sets. Commonly used functions such as Chamfer Distance (CD), HyperCD, and InfoCD rely on nearest-neighbor assign...","url_abs":"https://arxiv.org/abs/2509.08104","url_pdf":"https://arxiv.org/pdf/2509.08104v1","authors":"[\"Sasan Sharifipour\",\"Constantino Álvarez Casado\",\"Mohammad Sabokrou\",\"Miguel Bordallo López\"]","published":"2025-09-09T19:31:06Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cs.AI\"]","methods":"[\"Transformer\"]","has_code":false,"code_links":[{"ID":610027,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2873174,"paper_url":"https://arxiv.org/abs/2509.08104","paper_title":"APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction","repo_url":"https://github.com/apm-loss/apml","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}