{"id":"1e6e14d1-04e6-4567-a4ea-c909fc6c048b","arxiv_id":"2411.16995","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"CFPS claims to improve task accuracy by swapping low-curvature points in an FPS set with high-curvature points using a learned exchange ratio, but the reported results are internally inconsistent.","lead":"This paper proposes CFPS, a point cloud downsampling method that merges furthest point sampling (FPS) ranks with deep-network curvature scores and uses a reinforcement learning policy to decide how many low-curvature points to swap out for high-curvature points. The authors report accuracy gains over FPS on classification, segmentation, and shape completion, but the preprint contains several internal inconsistencies that undermine the reported numbers.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"CFPS's swap rule is undefined: Section 3.2 defines J=C*S while Algorithm 2 line 7 defines J=C+S, and raw signed mean curvature is never normalized, so the reported downstream gains are not tied to a fixed algorithm.","rationale":"The reader's weakest_assumption is the joint-rank ordering, and my read agrees. The contribution of the paper is exactly the swap defined by J; if J is ambiguous or scale-dependent, there is no unique CFPS method to evaluate. I checked the manuscript: Section 3.2 gives J=C*S, Algorithm 2 line 7 gives J=C+S. These are not equivalent, and neither is a valid importance score for 'high-curvature' unless C is normalized or taken in absolute value. Signed mean curvature is negative on concave regions and positive on convex regions, so a raw signed ranking is not a sharpness ranking. The unboundedness of C also means the FPS soft rank can be irrelevant wherever curvature magnitudes are large. The missing clamp on nexchange is a separate defect: G is a fraction of total N, not of K, and Table 3 reports fixed ratios up to 0.9; with N=2048, K=256 this requests 1843 swaps. The empirical record is also shaky (Tables 2 and 6 disagree on FPS/CFPS ModelNet40 accuracy; Table 5's text contradicts its own F1 numbers), but those could in principle stem from different experimental settings. The J/nexchange problem cannot be explained by settings: the algorithm as written is not well defined. A corrected paper with a single normalized joint rank, a clamped swap count, and released code could change the verdict, but as submitted the central claim is unsupported.","tokens_in":13973,"tokens_out":7932,"duration_ms":75402,"concrete_test":"Re-implement CFPS on a fixed split with the two rank definitions (J=C*S and J=C+S), using both raw signed C and normalized |C|, and enforce nexchange = min(floor(G*N), K). For G=0.9, N=2048, K=256, record whether the unclamped rule produces invalid swaps. Then run VRCNet on MVP and PointNet++ on ModelNet40 under each variant. If the Table 1 values (CD 5.60, F1 0.52) and Table 2 ModelNet40 accuracy (0.983) are reproduced by only one variant, or by none, the reported mechanism is not a fixed, well-defined algorithm.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that swapping low-curvature FPS-selected points for high-curvature non-selected points improves classification, segmentation, and completion. The swap is the algorithm, and the algorithm is not well-defined. Section 3.2 defines the joint rank as J = C * S, where C is raw mean curvature and S is the FPS soft rank; Algorithm 2, line 7, instead computes J = C + S. These define different orderings. Moreover, C is signed and unbounded and is never normalized or converted to absolute value; for signed mean curvature, the lowest-C points are not flat points but strongly concave points, and where |C| is large the curvature term swamps S entirely, so the FPS-coverage component has no effect on the swap. Algorithm 2 also never clamps nexchange = floor(G*N) to the core size K: for the fixed ratio G=0.9 reported in Table 3, with N=2048 and a typical target K=256, nexchange=1843 > K, which is not a valid exchange. Since the reported gains in Tables 1, 2, 6, and 8 are produced by an unspecified or invalid variant of this swap, the central claim is not supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Curvature Informed Furthest Point Sampling (CFPS), a point-cloud downsampling method that replaces a fraction of the points chosen by furthest point sampling with high-curvature points from the unselected set, where the fraction is learned by a REINFORCE-based policy network. The authors claim state-of-the-art results on single-view partial point cloud completion (MVP), classification (ModelNet10/40), and part segmentation (ShapeNetPart), and they include ablations on the exchange ratio and on training strategies, plus a theoretical regret bound in the appendix.","tokens_in":14409,"tokens_out":4596,"duration_ms":42949,"significance":"If the empirical claims were reproducible, CFPS would be a practically valuable drop-in sampling module: it preserves FPS coverage while adding a learned geometric bias, and it is designed for end-to-end training. The paper also provides a useful comparison of FPS-based and learned sampling methods and reports computational overhead. However, the current manuscript does not establish the central claim because the algorithm is specified inconsistently (joint rank defined as both multiplication and addition, with unnormalized signed curvature), key quantitative results contradict each other, and the theoretical regret bound relies on invalid assumptions. The absence of released code and of error bars further prevents verification.","major_comments":[{"comment":"The core swap operation is not well-defined. Section 3.2 defines the joint rank as J = C * S, while Algorithm 2 line 7 computes J = C + S; these define different orderings. Moreover, C is a raw signed mean curvature with no normalization, so the relative weight of curvature and FPS rank depends on the scale and sign of C, and the lowest-C points are strongly concave points rather than flat points. Finally, Algorithm 2 does not clamp nexchange = floor(G * N) to the core-set size K; for the reported N=2048, K=256, and G=0.9, nexchange=1843 > K, which is not a valid exchange. Consequently, the results in Tables 1, 2, 6, and 8 cannot be attributed to a fixed, reproducible algorithm.","section":"Section 3.2, Algorithm 2"},{"comment":"The classification results are mutually inconsistent. Table 2 reports CFPS achieving 0.983 overall accuracy on ModelNet40, whereas Table 6 reports 96.2% for the same method and dataset, and the FPS baseline likewise differs (0.97 vs. 94.8%). At most one of these sets of numbers can be correct, and without code or a clarification the claimed improvement over FPS cannot be taken at face value.","section":"Tables 2 and 6"},{"comment":"The training-strategy ablation is internally contradictory. The text states that CFPS-only achieves an F1-Score of 0.52, 'slightly lower than FPS-only' (which is 0.50), and it describes the hybrid FPS+CFPS score of 0.507 as 'the best performance.' Numerically 0.52 > 0.50 and 0.507 < 0.52, so either the table values or the narrative are erroneous. This undermines the ablation conclusion about the benefit of the adaptive ratio.","section":"Appendix A.1, Table 5"},{"comment":"The theoretical regret bound is not valid. The quantity Xt = E_{pi*}[R] - E_{pi_phi}[R] is not zero-mean (it is nonnegative under an optimal policy) and is not i.i.d. because the policy parameters phi change over time. Additionally, the Hoeffding interval is misapplied: with |R| <= M, Xt lies in [-2M, 2M], not in [0, 2M] as implied by setting a = 2M and b = 0. Thus Eq. (9) does not follow and the claimed O(sqrt(T log(1/delta))) regret bound is unsupported.","section":"Appendix C, Eqs. (5)-(9)"},{"comment":"All reported metrics are single numbers without variance or repeated-run statistics. Given the small reported margins (e.g., F1 from 0.50 to 0.52, accuracy from 94.8% to 96.2%), statistical significance cannot be assessed, and the absence of released code prevents independent verification. This is a load-bearing gap for the paper's central claim of consistent improvement.","section":"Tables 1, 2, 3, 6, 8"}],"minor_comments":[{"comment":"The sentence 'In this paper, We introduce' has a capitalization error; 'we' should be lowercase. There are also typographical errors such as 'paramteres' (Table 4/7 caption) and 'establlishing' (Appendix C.3).","section":"Page 2, Introduction"},{"comment":"Tables 4 and 7 are identical and both present the same computational-complexity data; one should be removed or they should be differentiated.","section":"Tables 4 and 7"},{"comment":"Figure 2, the architecture diagram, is referenced but the text does not explain the legend for J, C, S, and G; adding a short description would improve readability.","section":"Figure 2"},{"comment":"The paper cites 'Supplymentary' for an architecture diagram; this should be corrected to 'Supplementary.'","section":"References"},{"comment":"The curvature definition states H = (k1 + k2)/2 but does not specify how mean curvature is estimated from the MSECNet normals on a point cloud; a citation to the exact estimation method would help reproducibility.","section":"Section 3.1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has several internal contradictions in the algorithm definition and in the reported numbers. I would require the authors to provide code, to disambiguate the joint-rank definition and normalization, and to reconcile Tables 2 and 6 and Appendix A.1 before resubmission. If the inconsistencies cannot be resolved, the paper should be rejected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper has a genuinely new idea: combine FPS soft ranks with learned curvature scores and use a REINFORCE-trained exchange ratio to swap low-curvature core points for high-curvature outsiders. That arrangement is not in the cited literature, and the authors are fair in noting that SampleNet and Learning to Sample operate in a different, two-step paradigm. The empirical setup covers three tasks and reports FLOPs/params, which is more than many sampling papers do.\n\nBut the write-up undermines its own central claim. The joint rank is defined as J = C*S in Section 3.2 and as J = C + S in Algorithm 2, line 7. Those are different orderings. And C is raw mean curvature, signed and unbounded; for a concave region the lowest C points are not flat but strongly curved. The ranking is scale-dependent, so the mechanism is not fixed. Algorithm 2 also never clamps nexchange to the core size K. With G = 0.9, N = 2048, and K = 256, nexchange = 1843, which is not a valid exchange. The reported gains in Tables 1, 2, 6, and 8 therefore come from an algorithm the text does not uniquely specify.\n\nThere are also straightforward internal contradictions. ModelNet40 accuracy is 0.983 in Table 2 and 96.2% in Table 6; one is wrong. Appendix A.1 says CFPS-only achieves 0.52, \"slightly lower\" than FPS-only's 0.50, then calls 0.507 best, which is self-contradictory. The regret bound in Appendix C assumes E[Xt] = 0 and i.i.d. samples; neither holds for a REINFORCE update on a single noisy trajectory. The theory appendix should be removed or redone.\n\nWhat survives is the seed of a plausible drop-in sampling method. The authors should fix the algorithm definition (pick one rank formula, normalize curvature, clamp the exchange), rerun the experiments, and release code and error bars. As written, the empirical claims are unverified.\n\nFor a reader: this is worth a skim for the idea alone, but not worth citing or building on yet. A serious editor could send it to review because the novelty is real and the flaws are correctable, but the paper needs major revision before it is trustworthy.","headline":"A promising sampling idea whose central algorithm is undefined in the write-up: the joint rank is C*S in one place and C+S in another, and the reported gains are not tied to a fixed procedure.","tokens_in":14780,"tokens_out":2074,"would_cite":false,"duration_ms":19799,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Curvature-informed furthest point sampling (CFPS) swaps low-curvature points out of the FPS core set and claims the swap lifts classification, segmentation, and shape completion without changing the downstream network.","keywords":["point cloud downsampling","furthest point sampling","curvature","reinforcement learning","REINFORCE","shape completion","point cloud classification","point cloud segmentation"],"falsifier":"Re-running the ModelNet40 classification with several seeds and fixed, pre-registered hyperparameters would settle whether the reported 96.2% versus 94.8% gap over FPS is stable, since the paper reports single runs without a voting strategy. Separately, computing the joint rank on one cloud with both the product definition (Section 3.2) and the sum definition (Algorithm 2) would show whether the swapped set - and hence the claimed mechanism - is even uniquely defined.","tokens_in":13803,"feed_emoji":"📐","tokens_out":18124,"duration_ms":145161,"temperature":0.7,"pith_summary":"Furthest point sampling (FPS) is the standard way to thin a point cloud while keeping coverage, but it ignores local geometry, so sharp or curved regions may be undersampled. The paper proposes curvature-informed FPS (CFPS), which keeps the FPS core set and then swaps out a learned fraction of its low-curvature points for high-curvature points from the discarded set, scoring points by a joint rank that combines the FPS soft rank and the estimated mean curvature. The swap fraction is produced by a small policy network trained with REINFORCE, which makes the sampling layer trainable end-to-end. The paper reports that this single change improves shape completion on MVP (F1-score from 0.50 to 0.52, Chamfer distance from 5.96 to 5.60), classification on ModelNet40 (96.2% versus 94.8%), and segmentation on ShapeNetPart, all without changing the downstream architectures. If the numbers hold, CFPS is a drop-in improvement over FPS in any architecture that already uses furthest point sampling.","feed_headline":"Curvature swap beats FPS on 3D point cloud tasks","feed_subtitle":"A learned swap ratio trades redundant flat points for sharp ones and beats FPS on completion and classification.","key_machinery":"The load-bearing object is the joint rank J = C * S (stated in Section 3.2) or J = C + S (stated in Algorithm 2), which fuses the normalized FPS soft rank S = F/(N-1) with a pointwise mean-curvature estimate C obtained from learned normal and curvature estimators. The other piece is the exchange-ratio policy πφ: a small temporal convolutional network that reads the curvature values and outputs a Beta distribution over the swap fraction G in [0,1], trained by the REINFORCE policy-gradient rule with an exponential-moving-average baseline. Together they convert a fixed, non-differentiable FPS step into a module with a learned swap count, n_exchange = floor(G·N), that is updated end-to-end through the reward signal of the downstream task while the FPS core set itself is recomputed deterministically.","core_discovery":"The central claim is that FPS's weakness is not its coverage heuristic but its blindness to local geometry, and that this blindness can be fixed without abandoning FPS. The algorithm runs FPS to obtain a soft rank S = F/(N-1) for each point, estimates pointwise mean curvature, forms a joint rank that combines the two, and swaps the lowest-ranked points inside the FPS set with the highest-ranked points outside it, where the number of swapped points is a learned fraction of the input size. The paper argues that points on flat regions are redundant, so trading them for high-curvature points preserves sharp features while FPS still supplies global coverage. On the MVP completion benchmark it reports that VRCNet+CFPS improves the F1-score from 0.50 to 0.52 and reduces the Chamfer distance from 5.96 to 5.60; on ModelNet40 classification it reports 96.2% overall accuracy against 94.8% for FPS; and on ShapeNetPart segmentation it reports higher mIoU than FPS and the APES baseline. The paper claims state-of-the-art results among end-to-end downsampling methods, noting that one-pass learned samplers such as SampleNet and Learning to Sample fall outside its comparison framework.","pith_inferences":["Because curvature is computed on the fly and the downstream network is left unchanged, CFPS could plausibly be retrofitted to already-trained FPS pipelines as a test-time sampling choice; the paper demonstrates only end-to-end training, so this use is an untested extrapolation.","A reader implementing from the text must pick between two different joint ranks (a product in Section 3.2 and a sum in Algorithm 2), and the paper does not say which definition produced the tables; checking both on one cloud would show whether the headline gains depend on that choice.","The paper's state-of-the-art claim is scoped: it sets aside one-pass learned samplers such as SampleNet and Learning to Sample on the grounds that they sample once before the network, so the comparison covers only methods that downsample repeatedly inside the network.","A reader of the appendix will find the training-strategy ablation hard to reconcile: CFPS-only is listed with F1-score 0.52 while the FPS+CFPS hybrid is listed at 0.507, yet the text describes the hybrid as the best configuration, leaving the configuration behind the headline numbers unclear."],"forward_implications":["Any FPS-based architecture can adopt CFPS without redesign: the reported gains on completion, classification, and segmentation come from swapping the sampling layer only.","On the MVP benchmark, the swap improves completion fidelity: F1-score at the 1% threshold rises from 0.50 to 0.52 and Chamfer distance falls from 5.96 to 5.60.","On ModelNet10 and ModelNet40, CFPS reports 0.996 and 0.983 accuracy versus 0.990 and 0.97 for FPS (Table 2), and 96.2% versus 94.8% in a separate comparison (Table 6).","On ShapeNetPart segmentation, CFPS reports 84.5% category mIoU and 86.7% instance mIoU, above FPS (83.0% for both) and above both APES variants.","The benefit concentrates on geometry with high curvature variation: for near-uniform objects such as sofas the ablation shows CFPS matches FPS, while beds, bookshelves, and tables gain most from larger exchange counts."],"supporting_citations":[{"why":"defines the furthest point sampling strategy that CFPS starts from and modifies.","marker":"[4]"},{"why":"PCPNet, the network that supplies the pointwise curvature scores used in the joint rank.","marker":"[8]"},{"why":"MSECNet, the normal estimator whose normals feed the curvature computation.","marker":"[48]"},{"why":"VRCNet, the completion backbone on which the CFPS gains in F1-score and Chamfer distance are reported.","marker":"[23]"},{"why":"PointNet++, the classification backbone used for the ModelNet10 and ModelNet40 comparisons.","marker":"[27]"},{"why":"APES, the learned edge-sampling baseline that CFPS is compared against on all three tasks.","marker":"[43]"},{"why":"the REINFORCE policy-gradient rule used to train the exchange-ratio estimator.","marker":"[42]"},{"why":"provides the ModelNet10 and ModelNet40 datasets used for the classification benchmarks.","marker":"[47]"}],"fun_headline_variants":["Curvature-aware swap outperforms FPS on point cloud tasks","Learned curvature swap beats FPS in classification and completion","Swap flat points for sharp ones: FPS upgraded with curvature","Reinforcement learning improves FPS using curvature scores"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method rests on the combined curvature-and-FPS score reliably ranking which points to keep, but the curvature values are used unnormalized, the score is defined as a product in one place and a sum in another, and the learned swap count is not clamped to the core-set size - so the exchanged set can change with the curvature scale or exceed the available points.","fun_headline_variants_meta":{"raw":{"variants":["Curvature-aware swap outperforms FPS on point cloud tasks","Learned curvature swap beats FPS in classification and completion","Swap flat points for sharp ones: FPS upgraded with curvature","Reinforcement learning improves FPS using curvature scores"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000592,"raw_usage":{"total_tokens":2809,"prompt_tokens":1010,"completion_tokens":1799,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":626,"completion_tokens_details":{"reasoning_tokens":1730}},"tokens_in":626,"tokens_out":1799,"duration_ms":12030,"temperature":1.0,"reasoning_tokens":1730,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:38:29.654798+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-running the ModelNet40 classification with several seeds and fixed, pre-registered hyperparameters would settle whether the reported 96.2% versus 94.8% gap over FPS is stable, since the paper reports single runs without a voting strategy. Separately, computing the joint rank on one cloud with both the product definition (Section 3.2) and the sum definition (Algorithm 2) would show whether the swapped set - and hence the claimed mechanism - is even uniquely defined.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"PCPNet, the network that supplies the pointwise curvature scores used in the joint rank."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the furthest point sampling strategy that CFPS starts from and modifies."},{"cited_title":"MSECNet: Accurate and Robust Normal Estimation for 3D Point Clouds by Multi-Scale Edge Conditioning","cited_arxiv_id":"2308.02237","evidence_quote":"MSECNet, the normal estimator whose normals feed the curvature computation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"VRCNet, the completion backbone on which the CFPS gains in F1-score and Chamfer distance are reported."},{"cited_title":"R., Yi, L., Su, H., and Guibas, L","cited_arxiv_id":null,"evidence_quote":"PointNet++, the classification backbone used for the ModelNet10 and ModelNet40 comparisons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"APES, the learned edge-sampling baseline that CFPS is compared against on all three tasks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the REINFORCE policy-gradient rule used to train the exchange-ratio estimator."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the ModelNet10 and ModelNet40 datasets used for the classification benchmarks."}],"review_version":1}