Title: APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction
Venue: NeurIPS 2025
Accepted: yes
Keywords: point cloud loss

deep learning

one-to-one matching

optimal transport

Sinkhorn algorithm

adaptive temperature

spatio-temporal point cloud

WiFi CSI

point cloud completion

point cloud generation

shape prediction

differentiable loss

low-density regions

probabilistic assignment
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, InfoCD and Density-aware CD 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 spatio‑temporal Transformer (CSI2PC) that generates 3‑D 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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose a loss function for 3D point cloud shape completion and generation. This loss function is based on the Sinkhorn Distance, where it uses a temperature-scaled and data-driven parameter T to replace the control parameter $\\lambda$ for the entropy value in the Sinkhorn Distance.\n\nThis loss function achieves near-quadratic runtime, comparable to Chamfer-based losses, and approximates the matching quality of losses based on the Earth Mover's Distance.\n\nThe paper performs quantitative and qualitative evaluations on point cloud completion (ShapeNet and PCN) and generation (MM-Fi) benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. This paper proposes an Adaptive Probabilistic Matching Loss, which mitigates common shortcomings of losses based on Chamfer Distance, such as point clumping and density bias.\n2. The qualitative evaluation of APML is nearly identical to losses based on Earth Mover's Distance, while APML runtime is lower than EMD. APML combines the advantages of CD and EMD while avoiding their disadvantages in 3D point cloud tasks.\n\nWeaknesses:\n\n1. This paper lacks a comparison with EMD-based losses, which are among the most closely related losses to the proposed one, and serve as the primary motivation.\n2. This paper lacks an ablation experiment on the parameter T, which the authors propose to replace the control parameter $\\lambda$ of the entropy value in the Sinkhorn Distance.\n3. This paper lacks a detailed explanation about how to choose the value of parameter T and how the parameter T influences 3D point cloud tasks.\n\nQUESTIONS:\n1. Add an ablation experiment for parameter T that the authors propose.\n\n2. Add experiments based on EMD loss to directly compare the performance between the loss the authors propose and EMD loss.\n\n3. Add experiments that show results when choosing different $p_{min}$ values and explain why to choose them and how they influence the 3D point cloud tasks.\n\n4. How to choose the value of the data-driven parameter T that the authors propose? There are no experiments about it.\n\n5. The loss that the authors propose is based on the Sinkhorn loss and modifies its control parameter $\\lambda$. This paper should add experiments showing what will happen if there are different $\\lambda$ values when they are used in 3D point cloud tasks to verify the necessity of the change.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes using Adaptive Probabilistic Matching Loss (APML) as a loss function for point-cloud comparison. APML combines temperature-controlled point correspondences with the Sinkhorn algorithm to produce a matrix that is doubly stochastic. The temperature parameter introduced by the method is analytically determined, eliminating the need for manual tuning.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Designing a loss function for point-cloud correspondence is inherently challenging. APML achieves high-quality matching and learning with only a slight increase in computational cost compared to the widely used Chamfer Distance (CD) method.\n- The method was evaluated using the challenging cross-domain task CSI2PointCloud, demonstrating its practical performance in an application scenario.\n- The algorithm and its single additional hyperparameter are highly interpretable, suggesting that tuning should be straightforward in practice.\n\nWeaknesses:\n- The override used in \"Numerical Stability for Multiple Minima\" seems ad hoc and driven more by numerical convenience than the underlying design philosophy.\n- The comparisons use CD, InfoCD, and HyperCD. However, Earth Mover's Distance (EMD) is also a common form of supervision. Ideally, a direct comparison would be conducted using EMD. I acknowledge that existing EMD implementations often rely on unclear approximations. However, it would be valuable to explain why EMD supervision was omitted.\n- The large memory footprint is a practical drawback. Experiments supporting the claim that \"Leveraging this sparsity could dramatically reduce actual memory requirements.\" are needed.\n\nQUESTIONS:\n- L.73: \"introducing only one interpretable hyperparameter\" Does this refer to p_min?\n- A sensitivity analysis for p_min would be helpful. Since the experimental cost is not prohibitive and the hyperparameter is integral to the method, one would expect a more in-depth discussion of this topic within the paper, despite its brief mention.\n- Is applying the Sinkhorn algorithm solely to the distance matrix insufficient? Using Sinkhorn for assignment and introducing the temperature parameter are independent techniques. An ablation study testing each technique separately would clarify their novelty. As the paper notes, applying Sinkhorn after feature extraction is a well-known technique in non-rigid point-cloud matching.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this work, the authors propose an improved variant of Chamfer Distance (CD) for evaluating shape differences between predicted point clouds and ground truths in point cloud completion tasks. Unlike the traditional CD loss, which uses one-to-one nearest neighbor matching, the proposed method introduces a weighting algorithm that operates on the many-to-many dense matching cost matrix between predictions and ground truths. Experimental comparisons show that the proposed method outperforms existing CD variants, including CD, HCD, and InfoCD.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The proposed method can approach heavy Earth Mover Distance (EMD) with lower time complexity;\n\n2. According to the comparisons on baselines PoinTr, PCN, and FoldingNet, the proposed loss can help converge to better performances than CD, HCD, and InfoCD.\n\nWeaknesses:\n\n1. My major concern about this work is that the reducing of time complexity of the proposed method actually comes from the increasing of space complexity, where $O(N^2)$ memory may be required for the saving of cost matrix. Although further code-level optimization may be introduced to accelerate the proposed algorithm, it is still hard to reduce the $O(N^2)$ space complexity, making it hard to apply in practical usage. The results in Table 2 also show that the proposed method requires 5 times larger memory. \n\n2. Some related works are not sufficiently compared. Since the proposed method is some kind of a improved implementation of Chamfer Distance (CD), It may be necessary to discuss about other variants of CD, such as LCD in [1], or DCD in [2]. \n\n[1] Learnable Chamfer Distance for point cloud reconstruction\n\n[2] Balanced chamfer distance as a comprehensive metric for point cloud completion\n\nQUESTIONS:\nExcept the weaknesses mentioned in former section, I also have some other questions:\n\n1. From another perspective, the proposed method is also similar to a efficient variant of the Earth Mover Distance (EMD) by approaching the optimal one-to-one matching with the estimated probability. Therefore, I think some comparisons with efficient EMD such as [3, 4] is also necessary.\n\n[3] Morphing and Sampling Network for Dense Point Cloud Completion\n\n[4] Point-set Distances for Learning Representations of 3D Point Clouds\n\n2. Could you present more qualitative comparisons on the PCN or PoinTr baselines? The presented visualized results are all from the FoldingNet baseline, which may be too smoothed to clearly observe the shape improvements.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes AMPL, adaptive probabilistic matching loss, for 3D point cloud reconstruction. The key insight is to turn deterministic design into a data-driven one. By analytically computing hyper-parameters for Sink-horn iterations, the proposed loss can alleviate many-to-one correspondences introduced by CD-like losses, therefore achieving better EMD metric, yet with reduced computational burden. The experimental results to some extent show the advantage of the proposed loss in a set of reconstruction tasks.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n\n1. The idea and design are intuitive and simple, yet achieving considerable improvement on both quantitative and qualitative evaluations. \n\n2. I like the experiments on MM-FI, which shows to some extent the general utility of the proposed loss. \n\nWeaknesses:\n\nMy main concerns lie on three perspectives: \n\n1) Lack of EMD-like baseline, as well as comparisons on computational cost and effectiveness; \n\n2) Lack of stability analysis; \n\n3) Lack of ablation/analysis on the critical hyper-parameters such as $p_{\\min}$. \n\nPlease refer to the *Question* part for details.\n\nQUESTIONS:\n- The current baselines are all from the perspective of Chamfer-like formulation. Comparison to EMD loss should be provided, even only on small scale experiments, to validate that the proposed loss actually achieves balance between Chamfer-like and EMD-like approaches. \n\n- The adaptive nature of the proposed loss inevitably brings concern on stability. Can the randomness from batch sampling affect the final results? Some toy experiments with respect to, say, density control, would be helpful: For instance, one can consider point clouds with two level of densities, and then construct batches in different manners: 1) PCDs within the same batch are always of the same density; 2) PCDs within the same batch are always half-half from each density group; 3) Random batches. \n\nP.S. I indeed noticed the theoretical comparison in Tab.3 of the appendix, yet I would still suggest a more quantitative analysis. \n\n- As mentioned in Line 343, the behavior analysis of $p_{\\min}$ is left for future work, which I would strongly suggest against. This is indeed a critical parameter for the framework, simply demonstrating improvements on down-stream tasks does not fully justify the choice. Understanding the behavior of the method regarding the hyper-parameters like $p_{\\min}$ is necessary for confirming the contribution of this work.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}