Pith. sign in

REVIEW 4 major objections 5 minor 34 references

APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read APML loss approximates EMD's one-to-one matching at Chamfer-like cost

desk verdict A promising Sinkhorn-based loss with real EMD gains, but the cardinality claim and the adaptive-temperature novelty need work before it's a drop-in Chamfer replacement. read the letter →

arxiv 2509.08104 v1 pith:JIVNDKYI submitted 2025-09-09 cs.CV cs.AI

Sasan Sharifipour , Constantino Álvarez Casado , Mohammad Sabokrou , Miguel Bordallo López This is my paper · ORCID
classification cs.CVcs.AI
keywords pointcloudcompletionlossfunctionoptimaltransportSinkhorniterationsEarthmover'sdistanceChamfer3Dreconstructionwirelesssensing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes APML, a loss function for training point-cloud reconstruction models. It replaces the nearest-neighbor lookups of Chamfer Distance with a soft, differentiable transport plan: a temperature-scaled similarity matrix is refined by Sinkhorn iterations, and the loss is the expected distance under that plan. The temperature is set analytically so every point keeps a minimum assignment probability, removing the usual manual tuning of the Sinkhorn regularizer. The paper argues this gives EMD-like one-to-one supervision at near-quadratic cost, and reports 15–81% lower EMD with comparable F1 across FoldingNet, PCN, and PoinTr on ShapeNet/PCN, plus on WiFi-CSI human point cloud generation. A reader should care because it offers a practical middle ground between cheap but clumping Chamfer losses and expensive exact EMD.

What carries the argument

The load-bearing object is the symmetrized, Sinkhorn-normalized soft assignment matrix P built from the pairwise cost matrix C. Each row of the predicted-to-ground-truth softmax and each column of the ground-truth-to-predicted softmax is computed with an adaptive temperature T = -log((1-pmin)/((K-1)pmin))/g, where g is the local gap to the second-smallest cost; this guarantees a minimum assignment probability pmin and applies a uniform override when tied minima make the gap tiny. Iterated column and row normalization makes P an approximately doubly stochastic transport plan, and the loss L = <P, C> is fully differentiable. The mechanism's work is to convert many-to-one nearest-neighbor match

What would settle it

Compute the row and column sums after the Sinkhorn step for a pair with N != M: if they do not all approach 1 (or the specified marginals), the transport plan is not doubly stochastic and the loss is not a valid matching cost. A second test: train the same backbone with APML and with exact EMD on equal-sized subsampled clouds and compare per-class F1 and EMD; if APML's gains over CD disappear when exact EMD is available, the claim that it captures one-to-one structure is weakened.

Watch

Extended reading notes

Core claim

The central claim is that APML reproduces the geometric supervision of Earth Mover's Distance without solving an assignment problem. For predicted and ground-truth sets, it computes the pairwise Euclidean cost matrix, applies an adaptive softmax row-wise and column-wise to obtain directional assignment probabilities, averages them, then runs Sinkhorn-Knopp normalization to approximate a doubly stochastic transport plan. The loss is the inner product of that plan with the cost matrix (Eq. 9). The adaptive temperature is derived in closed form from pmin, the minimum probability guaranteed to the nearest match, using the second-smallest cost in each row or column as the representative gap. On t

Load-bearing premise

The load-bearing premise is that the Sinkhorn normalization always has a meaningful fixed point: when the predicted and ground-truth sets have different numbers of points, no matrix can have all rows and columns sum to one, and the paper provides no modified marginal constraints, despite claiming to handle varying cardinalities.

Editorial extensions

If this is right

  • Models trained with APML should produce fewer clumped points and better coverage in sparse regions than CD-trained models, because the transport plan spreads assignment mass rather than defaulting to many-to-one nearest neighbors.
  • APML can serve as a drop-in replacement for Chamfer losses in existing pipelines: it changes only the loss term and adds one interpretable hyperparameter (pmin).
  • The closed-form temperature schedule removes Sinkhorn-regularizer tuning; the same hyperparameters transfer from ShapeNet completion to WiFi-CSI point cloud generation in the paper's experiments.
  • The near-quadratic cost and differentiable plan make EMD-like supervision feasible at point counts where exact EMD's cubic solver would be prohibitive.
  • Because APML lowers EMD while sometimes increasing CD, evaluations that rely solely on Chamfer distance may understate its geometric fidelity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An inference beyond the paper: the Sinkhorn normalization described only converges to a doubly stochastic matrix when row and column counts are equal; extending APML to unequal cardinalities requires a principled modification, such as slack variables or unequal marginal targets, which the paper does not supply.
  • The reported empirical sparsity (more than 90% near-zero entries before Sinkhorn) suggests a sparse or low-rank implementation could push memory from quadratic toward log-linear, making APML practical for 16k-plus point clouds.
  • Because APML's adaptive temperature is computed per row and column, it may behave differently under extreme density imbalances than global-temperature Sinkhorn losses; a controlled study varying sampling density would clarify where it helps versus hurts.
  • The divergence between lower EMD and higher CD-L1/L2 on PoinTr suggests that APML changes the optimization geometry; combining it with a small CD term might recover point-wise accuracy without sacrificing structural alignment.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes APML, a differentiable loss for comparing unordered point sets. For each batch element it builds an N×M pairwise Euclidean cost matrix, applies row-wise and column-wise adaptive softmax with a temperature derived from a user-set pmin, averages the two directional probability matrices, refines the result by L_iter alternating Sinkhorn normalizations, and uses the Frobenius inner product of the refined matrix with the cost matrix as the loss. The method is evaluated as a training loss for FoldingNet, PCN, and PoinTr on PCN/ShapeNet completion and for CSI2PC on MM-Fi WiFi-to-point-cloud generation, reporting EMD, CD, F1, runtime, and memory. The main claims are near-quadratic EMD-like matching, no manual Sinkhorn tuning, reduced EMD by 15–81%, and comparable F1.

Significance. If the method worked as stated, APML would be a practical and broadly applicable replacement for CD-style losses in point-cloud prediction. The empirical scope is a strength: standard completion benchmarks with three backbones plus a real-world WiFi-CSI generation task, and the code is released. The limitations section is candid about pmin and memory. However, the theoretical formulation has correctness gaps that affect the scope of the contribution, and the experiments lack the ablations needed to isolate the adaptive-temperature mechanism. The core idea is salvageable, but the current manuscript overstates its guarantees.

major comments (4)
  1. [§3.2, Eqs. (7)–(8); Algorithm 1] The alternating column/row normalization to sums of 1 is only consistent when N=M. For N≠M, a nonnegative N×M matrix cannot have both every row sum and every column sum equal to 1, since the total mass would have to equal both M and N. The Sinkhorn iteration therefore has no fixed point; after column normalization the total mass is M and after row normalization it is N, so the output depends on the parity of L_iter. This contradicts the claim in Section 3 (first paragraph) that APML avoids 'set cardinality constraints' and the Introduction's 'may vary in cardinality'. All experiments use N=M, so the empirical numbers are not invalidated, but the method as defined is not a drop-in replacement for unequal-sized sets. Please redefine the Sinkhorn targets as a_i=1/N and b_j=1/M and adjust Eq. (9), which also lacks a 1/N normalization when rows are normalized to 1.
  2. [§3.1, Eqs. (2)–(5); §3.2] The pmin guarantee is not valid for the final transport plan, and it is not even guaranteed for the initial softmax in all cases. The derivation in Eqs. (2)–(3) bounds the softmax denominator using g = c~(2)+δ as a representative for all non-minimal costs. If several non-minimal entries share the value c~(2) with c~(2) > ε_g, the true denominator is larger than the bound, so the resulting probability can fall below pmin; e.g., K=100, pmin=0.8, c~(2)=1e-4 yields P_min ≈ 0.79. Step 4's uniform override also gives 1/K < pmin under ties. Moreover, the averaging in Eq. (6) and Sinkhorn in Eqs. (7)–(8) do not preserve the per-row/column softmax property. The abstract's 'guarantee a minimum assignment probability' and the contribution stating that each row and column of the transport plan assigns at least pmin are therefore unsupported.
  3. [§4, Table 1; §5] The claim of 'comparable F1' is not fully supported by Table 1. For PoinTr on PCN, APML achieves F1=0.67 versus HyperCD's 0.77; for PoinTr on SN34/SN55/Unseen-21, APML is 0.49–0.51 versus 0.52–0.56 for HyperCD. Since EMD is the metric that APML is explicitly designed to approximate, the large EMD reductions are partly by construction, and no baseline with a fixed-temperature Sinkhorn loss is reported. Please add an ablation that isolates the adaptive temperature (e.g., fixed T or fixed ε Sinkhorn) and report sensitivity to pmin, which is currently a hand-set hyperparameter.
  4. [Appendix C.1, Figure 3] The reported Wilcoxon p=0.008 is not reproducible from the tables as a two-sided test on F1. With n=8 categories, the minimum two-sided exact p is 0.0078 only when all eight differences have the same sign. Table 5 shows that for FoldingNet APML vs HyperCD, airplane is a loss for APML (0.773 vs 0.787), yielding a two-sided p of at least 0.0156. If the tests are one-sided, or are computed on EMD rather than F1, the text must say so. As written, the significance statement is ambiguous.
minor comments (5)
  1. [§4, Table 2] Table 2's caption says FoldingNet trained on ShapeNet-55, but the text in Section 4 refers to the PCN dataset for the same table. Please harmonize.
  2. [§4–§5, Table 2] Runtime and memory numbers are inconsistent: Section 4 says '~30% increase' but Table 2 gives 76h vs 55h ≈ 38%; Section 5 says 15–30%. Section 5 also says '4–5x RAM' while Table 2 reports <320GB vs <64GB for CD. Please make the reported values consistent.
  3. [Table 1] InfoCD + PoinTr on PCN reports F1=0.43, far below its own CD baseline (0.75) and inconsistent with the other InfoCD rows. Please check or explain this outlier.
  4. [§2] The description of CD's 'non-differentiable operations due to index selection' is overstated: a nearest-neighbor distance is differentiable almost everywhere, and standard implementations backpropagate through it. Consider rephrasing to 'piecewise differentiable'.
  5. [Algorithm 1] The pseudocode's per-row and per-column Python loops suggest a non-vectorized implementation. Clarify that this is conceptual pseudocode, while the actual implementation uses batched tensor operations.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: APML's transport-based loss is independent of the EMD metric; EMD gains are empirical, and the sole self-citation (CSI2PC) is not load-bearing.

full rationale

APML's derivation is self-contained. Equation (9) defines the loss as the Frobenius inner product of a Sinkhorn-refined soft assignment matrix and the pairwise cost matrix—an entropy-regularized optimal-transport cost with an adaptive temperature (Eqs. 3–5)—not the exact EMD objective in Eq. (12). The paper does not fit pmin or the temperature to EMD; pmin = 0.8 is fixed a priori and the temperature is computed per instance from the cost vector. The reported EMD reductions are empirical outcomes of training with a transport-based surrogate and are evaluated with an external exact EMD solver, so they are a design consequence, not a circular prediction. The only self-citation in the argument, ref. [16] (CSI2PC), is used as an experimental backbone and not as justification for APML's theoretical claims; no uniqueness theorem or ansatz is imported from prior author work. The reader-flagged N≠M Sinkhorn normalization issue (Eqs. 7–8 cannot both hold when N≠M) is a correctness/scope concern for unequal-sized sets, not a circularity, and all reported benchmarks use equal cardinality, so it does not change the circularity score. The acknowledged pmin hyperparameter limitation also concerns tuning, not derivation. Score 1 reflects only the minor, non-load-bearing self-citation.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central claim depends on the Sinkhorn scaling being a valid transport plan (requires N=M), on the hand-chosen pmin, and on the heuristic that a soft one-to-one objective improves geometric fidelity.

free parameters (5)
  • pmin = 0.8
    Minimum assignment probability in adaptive softmax; set by hand, held constant across all experiments, no sensitivity analysis.
  • delta (gap margin) = 1e-6
    Additive margin to second-smallest distance to compute temperature; numerical stability constant.
  • epsilon_g (uniform override threshold) = 1e-5
    Threshold on second-smallest distance below which uniform assignment is used; chosen by hand.
  • Liter (Sinkhorn iterations) = 10 (main) / 20 (appendix)
    Fixed number of Sinkhorn normalization iterations; controls approximation quality.
  • epsilon_stab (Sinkhorn stability) = 1e-8
    Denominator stabilization in normalization steps.
assumptions (3)
  • standard math Sinkhorn-Knopp alternating normalization converges to a doubly stochastic matrix for positive matrices
    Invoked in Section 3.2 to justify refining P into an approximate transport plan.
  • domain assumption The loss is used with N = M in all experiments, so row and column sums can both equal 1
    The paper defines the loss for arbitrary N,M but the Sinkhorn normalization to row/col sum 1 is infeasible for N != M; this assumption is unstated.
  • ad hoc to paper Soft probabilistic assignments with minimum top-match probability pmin provide useful training signal for point cloud geometry
    The core design choice of APML; no theoretical guarantee is provided for why this improves reconstruction.

how reviews work

0 comments
Cite this review

Pith. "Pith review of APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction." pith.science (2026). https://pith.science/paper/JIVNDKYI

@misc{pith2026250908104,
  author       = {Pith},
  title        = {Pith review of: APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JIVNDKYI}},
  note         = {Machine review of arXiv:2509.08104}
}
read the original 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.

Figures

Figures reproduced from arXiv: 2509.08104 by the authors.

Figure 1
Figure 1. Impact of loss functions on point cloud completion (using FoldingNet), and generation [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. F1 score on SN55 validation set across 150 epochs with FoldingNet. APML converges faster and achieves higher final performance. that Chamfer-based objectives often miss. A comparative assessment of visual perception against metrics point clouds can be seen in the Appendix D.1. Next, we analyze the convergence behavior and runtime characteristics [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Pair-wise Wilcoxon signed-rank p-values (8 object categories) comparing class-wise F1 scores for FoldingNet on the PCN dataset. Darker cells denote higher p; values below the 0.05 diagonal line indicate statistically significant differences. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Qualitative comparison of chair reconstructions across different loss functions. All models [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: F1 score on the validation set (Top: PCN. Middle: SN34 Bottom: SN55) over 150 epochs for four loss functions: Chamfer Distance (CD), InfoCD, HyperCD, and our proposed APML. The backbone is FoldingNet trained on the PCN dataset. 20 [PITH_FULL_IMAGE:figures/full_fig_p02…
Figure 6
Figure 6. Figure 6: Examples of the sparsity of the transport matrix [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 28 canonical work pages

  1. [1]

    In: International conference on machine learning

    Achlioptas, P., Diamanti, O., Mitliagkas, I., Guibas, L.J.: Learning representations and genera- tive models for 3d point clouds. In: International conference on machine learning. pp. 40–49. PMLR (2018)

    work page 2018

  2. [2]

    https://github

    Arritmic: Csi2pointcloud: Human point cloud generation from wifi csi. https://github. com/Arritmic/csi2pointcloud(2024), accessed: 2025-05-15

    work page 2024

  3. [3]

    In: International conference on artificial intelligence and statistics

    Blondel, M., Seguy, V ., Rolet, A.: Smooth and sparse optimal transport. In: International conference on artificial intelligence and statistics. pp. 880–889. PMLR (2018)

    work page 2018

  4. [4]

    arXiv preprint arXiv:2403.04356 (2024)

    Bringmann, K., Staals, F., van Wordragen, G., et al.: Fine-grained complexity of earth mover’s distance under translation. arXiv preprint arXiv:2403.04356 (2024)

    work page arXiv 2024

  5. [5]

    arXiv preprint arXiv:1512.03012 (2015)

    Chang, A.X., Funkhouser, T., Guibas, L., Hanrahan, P., Huang, Q., Li, Z., Savarese, S., Savva, M., Song, S., Su, H., et al.: Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012 (2015)

    arXiv 2015

  6. [6]

    Advances in neural information processing systems26(2013)

    Cuturi, M.: Sinkhorn distances: Lightspeed computation of optimal transport. Advances in neural information processing systems26(2013)

    work page 2013

  7. [7]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Dai, A., Chang, A.X., Savva, M., Halber, M., Funkhouser, T., Nießner, M.: Scannet: Richly- annotated 3d reconstructions of indoor scenes. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 5828–5839 (2017)

    work page 2017

  8. [8]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Dai, A., Ruizhongtai Qi, C., Nießner, M.: Shape completion using 3d-encoder-predictor cnns and shape synthesis. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 5868–5877 (2017)

    work page 2017

Show all 34 references
  1. [9]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Fan, H., Su, H., Guibas, L.J.: A point set generation network for 3d object reconstruction from a single image. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 605–613 (2017)

    2017

  2. [10]

    The international journal of robotics research32(11), 1231–1237 (2013)

    Geiger, A., Lenz, P., Stiller, C., Urtasun, R.: Vision meets robotics: The kitti dataset. The international journal of robotics research32(11), 1231–1237 (2013)

    2013

  3. [11]

    In: Storkey, A., Perez-Cruz, F

    Genevay, A., Peyre, G., Cuturi, M.: Learning generative models with sinkhorn divergences. In: Storkey, A., Perez-Cruz, F. (eds.) Proceedings of the Twenty-First International Confer- ence on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research, vol....

    2018

  4. [12]

    IEEE transactions on pattern analysis and machine intelligence43(12), 4338–4364 (2020)

    Guo, Y ., Wang, H., Hu, Q., Liu, H., Liu, L., Bennamoun, M.: Deep learning for 3d point clouds: A survey. IEEE transactions on pattern analysis and machine intelligence43(12), 4338–4364 (2020)

    2020

  5. [13]

    Journal of Machine Learning Research24(247), 1–44 (2023) 10

    Li, M., Yu, J., Li, T., Meng, C.: Importance sparsification for sinkhorn algorithm. Journal of Machine Learning Research24(247), 1–44 (2023) 10

    2023

  6. [14]

    Advances in Neural Information Processing Systems36, 76960–76973 (2023)

    Lin, F., Yue, Y ., Zhang, Z., Hou, S., Yamada, K., Kolachalama, V ., Saligrama, V .: Infocd: a contrastive chamfer distance loss for point cloud completion. Advances in Neural Information Processing Systems36, 76960–76973 (2023)

    2023

  7. [15]

    In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

    Lin, M., Xu, Y ., Wang, Z., Liu, Y .: Hyperbolic chamfer distance for point cloud completion. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 19176–19185 (2023)

    2023

  8. [16]

    In: 2025 IEEE 5th In- ternational Symposium on Joint Communications & Sensing (JC&S)

    Määttä, T., Sharifipour, S., Bordallo López, M., Álvarez Casado, C.: Spatio-temporal 3d point clouds from wi-fi-csi data via transformer networks. In: 2025 IEEE 5th In- ternational Symposium on Joint Communications & Sensing (JC&S). pp. 1–6 (2025). https://doi.org/10.1109/JCS6...

    2025

  9. [17]

    Foundations and Trends® in Machine Learning11(5-6), 355–607 (2019)

    Peyré, G., Cuturi, M., et al.: Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning11(5-6), 355–607 (2019)

    2019

  10. [18]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Qi, C.R., Su, H., Mo, K., Guibas, L.J.: Pointnet: Deep learning on point sets for 3d classification and segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 652–660 (2017)

    2017

  11. [19]

    International journal of computer vision40, 99–121 (2000)

    Rubner, Y ., Tomasi, C., Guibas, L.J.: The earth mover’s distance as a metric for image retrieval. International journal of computer vision40, 99–121 (2000)

    2000

  12. [20]

    In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

    Sarlin, P.E., DeTone, D., Malisiewicz, T., Rabinovich, A.: Superglue: Learning feature matching with graph neural networks. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 4938–4947 (2020)

    2020

  13. [21]

    Advances in Neural Information Processing Systems34, 5373–5389 (2021)

    Shen, Z., Feydy, J., Liu, P., Curiale, A.H., San Jose Estepar, R., San Jose Estepar, R., Nietham- mer, M.: Accurate point cloud registration with robust optimal transport. Advances in Neural Information Processing Systems34, 5373–5389 (2021)

    2021

  14. [22]

    Pacific Journal of Mathematics21(2), 343–348 (1967)

    Sinkhorn, R., Knopp, P.: Concerning nonnegative matrices and doubly stochastic matrices. Pacific Journal of Mathematics21(2), 343–348 (1967)

    1967

  15. [23]

    arXiv preprint arXiv:2401.12253 (2024)

    Tang, X., Shavlovsky, M., Rahmanian, H., Tardini, E., Thekumparampil, K.K., Xiao, T., Ying, L.: Accelerating sinkhorn algorithm with sparse newton iterations. arXiv preprint arXiv:2401.12253 (2024)

    2024 arXiv

  16. [24]

    Villani, C., et al.: Optimal transport: old and new, vol. 338. Springer (2008)

    2008

  17. [25]

    In: Proceedings of the IEEE/CVF International Conference on Computer Vision

    Wang, M., Luo, X., Li, Y .: Density-aware chamfer distance as a comprehensive metric for point cloud completion. In: Proceedings of the IEEE/CVF International Conference on Computer Vision. pp. 13014–13023 (2021)

    2021

  18. [26]

    In: Proceedings of the IEEE/CVF international conference on computer vision

    Xiang, P., Wen, X., Liu, Y .S., Cao, Y .P., Wan, P., Zheng, W., Han, Z.: Snowflakenet: Point cloud completion by snowflake point deconvolution with skip-transformer. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 5499–5509 (2021)

    2021

  19. [27]

    Advances in Neural Information Processing Systems36(2024)

    Yang, J., Huang, H., Zhou, Y ., Chen, X., Xu, Y ., Yuan, S., Zou, H., Lu, C.X., Xie, L.: Mm-fi: Multi-modal non-intrusive 4d human dataset for versatile wireless sensing. Advances in Neural Information Processing Systems36(2024)

    2024

  20. [28]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Yang, Y ., Feng, C., Shen, Y ., Tian, D.: Foldingnet: Point cloud auto-encoder via deep grid deformation. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 206–215 (2018)

    2018

  21. [29]

    In: Proceedings of the IEEE/CVF international conference on computer vision

    Yu, X., Rao, Y ., Wang, Z., Liu, Z., Lu, J., Zhou, J.: Pointr: Diverse point cloud completion with geometry-aware transformers. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 12498–12507 (2021)

    2021

  22. [30]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Yuan, X., Chamzas, D., Mitra, N.J.: Pcn: Point cloud completion network. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 774–783 (2018)

    2018

  23. [31]

    https://github.com/ yuxumin/PoinTr(2021), accessed: 2025-05-15 11

    Yuxumin: Pointr: Point cloud completion with transformers. https://github.com/ yuxumin/PoinTr(2021), accessed: 2025-05-15 11

    2021

  24. [32]

    In: European conference on computer vision

    Zhou, H., Cao, Y ., Chu, W., Zhu, J., Lu, T., Tai, Y ., Wang, C.: Seedformer: Patch seeds based point cloud completion with upsample transformer. In: European conference on computer vision. pp. 416–432. Springer (2022) 12 A Technical Appendix: Algorithm description and theoret...

    2022

  25. [33]

    Thresholded sparse format.Retaining only values ≥10 −3 yields a ∼5–6× reduction in practice, bringing the largest16k matrix below the 40 GB limit of a single A100

  26. [34]

    Both the histogram and heat-map example views confirm thateffectivememory usage is dominated by a tiny subset of matrix entries

    Mixed precision.Encoding the surviving non-zero blocks in FP16 would shave a further ∼30 % off the footprint. Both the histogram and heat-map example views confirm thateffectivememory usage is dominated by a tiny subset of matrix entries. This justifies storing P in a sparse C...

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.