{"id":"9caffa63-7dae-4ca7-8b1a-5b191bc383ac","arxiv_id":"2509.08104","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"APML is a differentiable Sinkhorn-based loss with an automatic temperature schedule that improves structure preservation in point cloud reconstruction, lowering EMD by 15-81% versus Chamfer-style losses.","lead":"This paper introduces APML, a new loss function for training 3D point cloud models that uses soft one-to-one matching instead of nearest-neighbor matching. It reports better spatial coverage, lower Earth Mover's Distance, and faster convergence on shape completion and WiFi-based human reconstruction.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"APML's Sinkhorn normalization is ill-defined when N≠M, despite claims of handling varying cardinality; experiments only cover N=M.","rationale":"The stress-test identifies the same load-bearing concern as the reader's weakest_assumption: the Sinkhorn normalization in Section 3.2 implicitly assumes N=M, while the paper claims to handle varying cardinality. This is a concrete mathematical flaw, not a stylistic disagreement. It does not invalidate the reported EMD improvements on benchmarks, which all use equal-sized point sets, but it does restrict the central claim of broad applicability and 'drop-in replacement' status. The reader's conditional verdict is therefore appropriate; the paper should either explicitly restrict APML to N=M or provide a principled extension for unequal cardinalities (e.g., Sinkhorn with separate row/column marginals summing to the same total mass). Other concerns, such as the absence of a fixed-temperature Sinkhorn baseline and the post-Sinkhorn breakdown of the pmin guarantee, are secondary and would also need attention, but the N≠M issue is the clearest and most load-bearing because it makes the algorithm ill-defined for a stated use case. A simple computational test can settle it immediately, and the analysis is straightforward from the total-mass contradiction.","tokens_in":16969,"tokens_out":8903,"duration_ms":96000,"concrete_test":"Run the released APML implementation on random point sets with N=1024 and M=2048, performing the Sinkhorn updates of Eqs. (7)–(8) for L_iter = 1, 2, 5, 10, 20, 50, 100. Record the maximum row-sum deviation from 1, the maximum column-sum deviation from 1, and the loss value Eq. (9) at each L_iter. If no iteration yields row sums and column sums simultaneously close to 1, and if the loss oscillates or systematically changes with L_iter, the procedure has no fixed point for N≠M, confirming that the method is only well-defined for N=M.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that APML is a drop-in replacement for Chamfer-style losses, and specifically that it 'avoid[s] the computational burden and set cardinality constraints associated with exact methods' (Section 3, first paragraph), is undermined by the Sinkhorn normalization in Section 3.2. Equations (7) and (8) alternately normalize columns and rows to sum to 1. For a nonnegative N×M matrix, if every row sums to 1 and every column sums to 1, the total sum of all entries must equal both N and M, which is impossible when N≠M. Consequently, the iterative process has no fixed point: after column normalization the total mass is M, after row normalization it is N, so the iterates oscillate and the loss (Eq. 9) depends sensitively on the arbitrary iteration count L_iter. The paper motivates the loss with point sets that 'may vary in cardinality' (Introduction) and claims to avoid cardinality constraints, yet it gives no modification (e.g., using uniform marginals 1/N and 1/M, or allowing unequal total mass) for the N≠M case. All reported experiments use N=M (e.g., PCN ground truth and predictions are both 16384 points), so the empirical EMD improvements are not invalidated, but the method as formally defined is not a general-purpose loss for unequal-sized point sets. This is a load-bearing scope/correctness issue: a user following the paper's algorithm on N≠M inputs would obtain an unstable or ill-defined training signal.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":17391,"tokens_out":13710,"duration_ms":164715,"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":[{"comment":"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.","section":"§3.2, Eqs. (7)–(8); Algorithm 1"},{"comment":"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.","section":"§3.1, Eqs. (2)–(5); §3.2"},{"comment":"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.","section":"§4, Table 1; §5"},{"comment":"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.","section":"Appendix C.1, Figure 3"}],"minor_comments":[{"comment":"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.","section":"§4, Table 2"},{"comment":"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.","section":"§4–§5, Table 2"},{"comment":"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.","section":"Table 1"},{"comment":"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'.","section":"§2"},{"comment":"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.","section":"Algorithm 1"}],"recommendation":"major_revision","confidential_remarks":"The main technical flaws are localized and fixable: replace the unit-margin Sinkhorn with 1/N and 1/M marginals, correct the pmin wording, and add an N≠M experiment or explicitly scope the contribution. I do not see grounds for rejection, but the paper should not be accepted until the Sinkhorn definition and the statistical reporting in Appendix C.1 are corrected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read on 2509.08104. It's a solid, well-engineered attempt at a Chamfer-distance replacement: Sinkhorn soft matching with an adaptive temperature derived from the local gap between the smallest and second-smallest distances. The authors ship code, use standard backbones and benchmarks, and show large EMD reductions (15–81%) with faster convergence and better-looking reconstructions. The WiFi-CSI application is a nice out-of-domain test.\n\nThe biggest issue is the cardinality gap. The paper explicitly motivates the loss as avoiding the set cardinality constraints of exact EMD, but the Sinkhorn normalization in Eqs. (7)–(8) alternates column and row normalization to sum to 1. For N≠M there is no doubly stochastic matrix with both row and column sums 1, so the iterates have no fixed point and the result depends on the iteration count. All experiments use N=M (16384 points), so the reported numbers are fine, but the method as defined does not do what the abstract says. The fix is easy (use uniform marginals 1/N and 1/M as Sinkhorn targets), but it needs to be stated and tested.\n\nSecond, the 'guaranteed minimum assignment probability' (pmin) is only guaranteed for the pre-Sinkhorn row/column softmax, not for the final transport plan. The abstract overstates it. This is more a wording issue than a mathematical one.\n\nThird, there's no ablation against a fixed-temperature Sinkhorn loss. That's the control that would isolate the adaptive temperature, which is the main claimed novelty. Without it, the EMD gains could come from the Sinkhorn structure itself. This is the experiment I'd most want to see before trusting the adaptive component.\n\nFourth, the statistical reporting is sloppy. They report a two-sided Wilcoxon p=0.008 for F1 over 8 categories, but the per-category F1 table shows at least one category where APML is worse; with 8 pairs and a negative difference, the two-sided p can't be 0.008. If they tested EMD, where all differences are positive, p=0.008 is the minimum possible, but then the caption is wrong. Either way, it needs correction.\n\nAlso, the EMD improvements are partly by construction since the loss approximates EMD; but they also report CD and F1, so it's not fully circular.\n\nOverall: the core idea is promising and the experiments are mostly convincing for the N=M setting. The paper deserves peer review, but it needs a proper cardinality fix and a fixed-temperature baseline before I'd use it as a drop-in replacement.","headline":"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.","tokens_in":17819,"tokens_out":5596,"would_cite":true,"duration_ms":63385,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"APML loss approximates EMD's one-to-one matching at Chamfer-like cost","keywords":["point cloud completion","loss function","optimal transport","Sinkhorn iterations","Earth mover's distance","Chamfer distance","3D reconstruction","wireless sensing"],"falsifier":"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.","tokens_in":16917,"feed_emoji":"📐","tokens_out":5008,"duration_ms":51963,"temperature":0.7,"pith_summary":"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.","feed_headline":"Soft one-to-one matching loss cuts EMD by up to 81%","feed_subtitle":"APML replaces Chamfer-style losses for point cloud completion and generation with smoother, faster-converging supervision.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Introduces EMD as a permutation-invariant loss for point-set generation, the baseline APML approximates.","marker":"[1]"},{"why":"Supplies entropy-regularized optimal transport and the differentiable Sinkhorn approximation APML builds on.","marker":"[6]"},{"why":"Defines Chamfer Distance, the primary baseline APML replaces.","marker":"[9]"},{"why":"InfoCD, a Chamfer-variant baseline, illustrates the density-coverage issues APML targets.","marker":"[14]"},{"why":"HyperCD, a Chamfer-variant baseline in hyperbolic space, is one of the losses APML is compared against.","marker":"[15]"},{"why":"CSI2PC, the WiFi-CSI transformer backbone used for cross-modal generation experiments.","marker":"[16]"},{"why":"Defines Earth Mover's Distance and its cubic-cost assignment formulation, the gold standard APML approximates.","marker":"[19]"},{"why":"Provides the alternating normalization algorithm used to make the assignment matrix approximately doubly stochastic.","marker":"[22]"},{"why":"PoinTr, a transformer backbone for point cloud completion used in evaluation.","marker":"[29]"},{"why":"PCN, both a completion backbone and the standard completion dataset and benchmark.","marker":"[30]"}],"fun_headline_variants":["APML: Differentiable one-to-one matching for 3D point clouds","Soft matching loss cuts EMD runtime without manual tuning","Adaptive Sinkhorn loss for robust 3D point cloud reconstruction","Near-quadratic EMD approximation for point cloud completion","Faster, differentiable one-to-one loss for 3D point clouds"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["APML: Differentiable one-to-one matching for 3D point clouds","Soft matching loss cuts EMD runtime without manual tuning","Adaptive Sinkhorn loss for robust 3D point cloud reconstruction","Near-quadratic EMD approximation for point cloud completion","Faster, differentiable one-to-one loss for 3D point clouds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000848,"raw_usage":{"total_tokens":3558,"prompt_tokens":805,"completion_tokens":2753,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":549,"completion_tokens_details":{"reasoning_tokens":2663}},"tokens_in":549,"tokens_out":2753,"duration_ms":27255,"temperature":1.0,"reasoning_tokens":2663,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T21:15:48.107679+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"In: International conference on machine learning","cited_arxiv_id":null,"evidence_quote":"Introduces EMD as a permutation-invariant loss for point-set generation, the baseline APML approximates."},{"cited_title":"Advances in neural information processing systems26(2013)","cited_arxiv_id":null,"evidence_quote":"Supplies entropy-regularized optimal transport and the differentiable Sinkhorn approximation APML builds on."},{"cited_title":"In: Proceedings of the IEEE conference on computer vision and pattern recognition","cited_arxiv_id":null,"evidence_quote":"Defines Chamfer Distance, the primary baseline APML replaces."},{"cited_title":"Advances in Neural Information Processing Systems36, 76960–76973 (2023)","cited_arxiv_id":null,"evidence_quote":"InfoCD, a Chamfer-variant baseline, illustrates the density-coverage issues APML targets."},{"cited_title":"In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition","cited_arxiv_id":null,"evidence_quote":"HyperCD, a Chamfer-variant baseline in hyperbolic space, is one of the losses APML is compared against."},{"cited_title":"In: 2025 IEEE 5th In- ternational Symposium on Joint Communications & Sensing (JC&S)","cited_arxiv_id":null,"evidence_quote":"CSI2PC, the WiFi-CSI transformer backbone used for cross-modal generation experiments."},{"cited_title":"International journal of computer vision40, 99–121 (2000)","cited_arxiv_id":null,"evidence_quote":"Defines Earth Mover's Distance and its cubic-cost assignment formulation, the gold standard APML approximates."},{"cited_title":"In: Proceedings of the IEEE/CVF international conference on computer vision","cited_arxiv_id":null,"evidence_quote":"PoinTr, a transformer backbone for point cloud completion used in evaluation."},{"cited_title":"In: Proceedings of the IEEE conference on computer vision and pattern recognition","cited_arxiv_id":null,"evidence_quote":"PCN, both a completion backbone and the standard completion dataset and benchmark."}],"review_version":1}