{"id":"0e996ea2-11a4-440f-a76e-60095e7f54e0","arxiv_id":"2502.05229","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A segmentation model that pools vector-quantized features via optimal transport to learnable references reports state-of-the-art Dice scores on Synapse (82.23) and ACDC (91.44) benchmarks.","lead":"L2GNet is a new medical image segmentation architecture that pools vector-quantized image codes using optimal transport against learnable references, instead of the self-attention used in transformer models. The authors report higher accuracy and lower boundary errors than several existing methods on two public benchmarks, but the experimental evidence lacks statistical rigor.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed superiority over SynergyNet and other baselines rests on unverified comparability: Tables 1 and 2 give no evidence that baselines were retrained under L2GNet's exact protocol and report no variance, so the margins could be setup artifacts.","rationale":"The paper's central claim is that L2GNet achieves state-of-the-art segmentation accuracy by replacing self-attention with an optimal-transport-based mapper. Everything else in the paper—the architectural description, the ablations on codebook size and number of references—supports this claim only if the comparison numbers in Tables 1 and 2 are trustworthy. The most load-bearing assumption is therefore that all baselines were evaluated under the same experimental protocol as L2GNet, including retraining with identical hyperparameters and data handling. The text asserts that the SynergyNet configuration was followed, but it neither specifies that configuration nor says that baseline scores were re-produced in it. Since SynergyNet is from the same research group and its code is available, this is not an impossible requirement; it is a missing piece of evidence. The internal inconsistencies in reported SynergyNet numbers (HD 23.59 vs 23.29, DSC 79.65 vs 79.61) make the concern concrete rather than hypothetical: different tables appear to draw from different runs or publications. The absence of error bars compounds the issue, especially for Hausdorff distance, which is sensitive to outliers and run-to-run variation. I am not raising a technical objection to the optimal-transport construction itself: the method is derived from Mialon et al. and may work as advertised. But the empirical superiority claim cannot be separated from the comparability issue. A controlled head-to-head retraining test would settle this directly. I therefore agree with the reader's weakest-assumption analysis and recommend the verdict remain conditional: the paper should be accepted only if the authors provide code, exact configurations, retrained baselines, and variance estimates.","tokens_in":8219,"tokens_out":3836,"duration_ms":42449,"concrete_test":"Obtain the code and exact configuration from the authors and retrain every baseline in Tables 1 and 2 under identical preprocessing, optimizer, learning rate, epochs, augmentation, and data splits, running at least five seeds per method. Then check whether L2GNet(4-ref) still beats SynergyNet by more than 1 DSC point on both Synapse and ACDC; if the margin shrinks or reverses, the headline superiority claim fails. Alternatively, as a minimal controlled check, rerun only SynergyNet and L2GNet(4-ref) with the same codebase and report per-seed means and standard deviations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 states that experiments followed \"the same preprocessing and training configuration described in SynergyNet[16],\" but it never lists that configuration (input size, optimizer, learning rate, epochs, loss, augmentation, data splits) and never states whether the CLS, DLS, and CDLS baselines were retrained in that setting or whether their numbers were cited from the original papers. Because SynergyNet [16] shares authors with this work and is therefore readily retrainable, the absence of a controlled re-run is a concrete gap. The reported margins on Synapse (DSC 82.23 vs 79.65, HD 14.17 vs 23.59) and ACDC (DSC 91.44 vs 89.78, HD 1.24 vs 1.86) are large enough to be meaningful only if protocol is matched. Internal inconsistencies in the paper's own tables reinforce this concern: SynergyNet's Synapse HD is 23.59 in Table 1 but 23.29 in Tables 4 and 5, and its DSC is 79.65 in Table 1 but 79.61 in Table 3, suggesting the baseline numbers were not produced by a single controlled run. With no error bars, run-to-run variance alone could erase the smaller ACDC DSC margin (1.66 points), and HD is notoriously noisy. Thus the central claim that L2GNet outperforms CLS, DLS, and CDLS methods is plausible but not rigorously established as presented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes L2GNet, a medical image segmentation architecture that combines vector-quantized discrete representations with a trainable optimal-transport (OT) embedding to replace dot-product self-attention. The authors argue that CLS, DLS, and CDLS methods either miss long-range dependencies or capture redundant ones, and that L2GNet's OT-based pooling onto learned references yields discriminative global representations at linear cost. The method is evaluated on the Synapse multi-organ and ACDC cardiac datasets, reporting improvements over several baselines including the authors' own SynergyNet. The central empirical claim is that L2GNet outperforms state-of-the-art CLS, DLS, and CDLS methods, but the experimental validation is incomplete and internally inconsistent.","tokens_in":8418,"tokens_out":3408,"duration_ms":35737,"significance":"If the central claim were rigorously established, L2GNet would be a useful contribution: it offers a concrete alternative to quadratic self-attention bottlenecks, is applicable to 2D medical image segmentation, and its integration of VQ with an OT embedding is a plausible way to encourage structured, anatomy-aware aggregation. The paper explicitly builds on the trainable OT embedding of Mialon et al. [22] and Sinkhorn's algorithm [21], and the novelty lies in adapting these tools for discrete-code aggregation in segmentation rather than inventing a new OT formalism. The complexity argument (reducing the attention matrix from O(n^2) to O(n)) is reasonable, and the use of multiple references resembles multi-head attention. However, the significance is currently limited by the lack of controlled experiments, missing error bars, and several presentation defects. No code or trained models are released, which further hampers verification of the empirical claims.","major_comments":[{"comment":"The experimental section never specifies the preprocessing and training configuration claimed to follow SynergyNet [16] (e.g., input resolution, optimizer, learning rate, batch size, number of epochs, loss terms, augmentation, and official train/validation splits), nor does it state whether the CLS/DLS/CDLS baselines in Tables 1 and 2 were retrained under L2GNet's protocol or their numbers were taken from the original publications. Because SynergyNet, SSNet, and TranSSNet are prior work by the same authors, a controlled re-run of all baselines in the same setting is feasible and is required to support the claimed superiority; otherwise the margins in Tables 1 and 2 may reflect protocol differences rather than architectural benefit.","section":"Section 4, Dataset and Experiment Settings"},{"comment":"No error bars, confidence intervals, or significance tests are reported for any metric. The ACDC DSC margin between L2GNet(4-ref) and TranSSNet is only 0.12 points (91.44 vs 91.32), and between L2GNet(4-ref) and SynergyNet is 1.66 points; with the run-to-run variance typical of medical image segmentation, these differences cannot be judged without multiple seeds. The HD metric is particularly sensitive to outliers and should be reported with variance.","section":"Tables 1 and 2"},{"comment":"The baseline numbers are internally inconsistent: SynergyNet's Synapse HD is 23.59 in Table 1 but 23.29 in Tables 4 and 5, and its Synapse DSC is 79.65 in Table 1 but 79.61 in Table 3. This suggests that baseline scores were not produced by a single controlled evaluation protocol, and it directly undermines the credibility of the comparisons in the main tables. The authors should rerun all baselines in exactly the L2GNet setting and report a single consistent set of numbers.","section":"Tables 1, 3, 4, and 5"},{"comment":"Equation (3), which defines the proposed embedding phi_{z_ref}(z_dis), is not readable as typeset: it mixes the indices 1i and tit, contains an unexplained '×S,...,' and the expression is not a well-formed vector. In addition, the preceding sentence defines the cost as M = -psi(z_dis), but M should be a pairwise cost matrix between codes and reference elements. Because this equation is the core of the proposed L2GMapper, it must be rewritten precisely and consistently.","section":"Section 3, Eq. (3)"}],"minor_comments":[{"comment":"The listed keywords ('Cirrhotic liver segmentation, Abdominal MRI dataset, liver segmentation, ...') do not match the paper's content, which concerns multi-organ and cardiac segmentation via optimal transport; these keywords should be corrected.","section":"Abstract and Keywords"},{"comment":"Tables 3 and 6 are identical (codebook embedding size analysis) and should be merged or one should be removed.","section":"Tables 3 and 6"},{"comment":"The phrase 'an novel approach' contains a grammatical error; it should be 'a novel approach.'","section":"Abstract"},{"comment":"The notation is inconsistent: the text introduces pairwise costs C, but Eq. (1) uses M_{ij}; the variable should be matched to avoid ambiguity.","section":"Section 2, Eq. (1)"},{"comment":"Reference [1] (Kawaguchi et al.) appears not to be cited in the body of the paper; either cite it or remove it.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is written in preprint style with several presentation issues (duplicated tables, keyword mismatch, typographical errors). The main scientific concern is the lack of a controlled baseline comparison; since the authors have access to their own prior baselines, a proper re-run should be feasible. I would also flag that no code is provided, which makes reproducibility harder; I suggest the editor require code release or detailed training configuration if the paper is resubmitted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a reasonable application of a known optimal-transport embedding to medical segmentation, but the experimental section is not rigorous enough to support the headline claim. The core mechanism is from Mialon et al. (2020); the new part is pairing it with vector-quantized codes in a U-Net bottleneck and testing it on Synapse/ACDC. That is a legitimate combination, and the efficiency logic (linear instead of quadratic memory) is sound.\n\nWhat the paper does well: the method description is clear about borrowing the OT embedding, and Figure 2 qualitatively shows the kind of inter-organ confusion the authors say they are fixing. The ablation over codebook size and number of references gives some sense of the design space, and the DSC/HD numbers on ACDC are strong if they hold up.\n\nThe soft spot is the baseline comparison. The paper says it follows SynergyNet's configuration but never lists that configuration, and never says whether CLS/DLS/CDLS baselines were retrained under identical conditions or whether the numbers are quoted from the original papers. The internal evidence matters here: SynergyNet's Synapse HD is 23.59 in Table 1 but 23.29 in Tables 4 and 5, and its DSC is 79.65 in Table 1 but 79.61 in Table 3. That suggests the baseline numbers were not produced by a single controlled run. With no error bars, the ACDC margin of 1.66 DSC points over SynergyNet could easily be run-to-run noise. So the central superiority claim is plausible but not established as presented.\n\nThere are also presentation issues that should have been caught before submission: the keyword list mentions 'cirrhotic liver segmentation' and 'T1-weighted MRI dataset,' which have nothing to do with this paper; Tables 3 and 6 are duplicated; Tables 4 and 5 are near-duplicates; and Equation 3 is garbled. These are fixable but they erode confidence.\n\nWho this is for: researchers working on efficient attention alternatives for medical segmentation. It deserves a serious referee — the idea is worth engaging with — but the authors need to provide code and configurations, retrain baselines in a controlled setting, report variance, and clean up the manuscript. I'd treat it as a major-revision candidate, not a rejection.","headline":"A plausible application of optimal-transport pooling to medical segmentation that is currently undermined by unverified baseline comparability and internal inconsistencies in the reported numbers.","tokens_in":9057,"tokens_out":2790,"would_cite":false,"duration_ms":27857,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T07","49Q22","92C55"],"pacs":[],"model":"deepseek-v4-flash","headline":"L2GNet replaces self-attention with optimal-transport pooling and reports higher segmentation accuracy on two medical benchmarks.","keywords":["medical image segmentation","optimal transport","vector quantization","discrete latent space","Sinkhorn distances","self-attention replacement","multi-organ segmentation","cardiac segmentation"],"falsifier":"Re-run SynergyNet, TransUNet, SSNet, TranSSNet, and VQUNet in the exact L2GNet training configuration across multiple random seeds with identical data splits. If the mean Dice gaps on Synapse and ACDC shrink below run-to-run variance, or L2GNet no longer leads, the paper's central superiority claim is refuted. A complementary check: compute the transport plans and test whether removing the position kernel $S$ or replacing Sinkhorn with random assignment eliminates the reported gains.","tokens_in":7930,"feed_emoji":"🫀","tokens_out":6377,"duration_ms":59385,"temperature":0.7,"pith_summary":"The paper introduces L2GNet, a segmentation model whose bottleneck aligns vector-quantized image codes to a small set of learnable references using optimal transport and Sinkhorn distances, instead of computing dot-product self-attention. The authors argue that this captures long-range dependencies among pertinent anatomical regions while avoiding attention between redundant regions, which they identify as a source of false negatives and poor generalization in CLS, DLS, and CDLS models. On the Synapse multi-organ and ACDC cardiac benchmarks, L2GNet with four references reports mean Dice scores of 82.23 and 91.44, respectively, exceeding the CDLS model SynergyNet and other Transformer-based baselines. The significance would be a computationally cheaper bottleneck that generalizes better across organs and cardiac structures.","feed_headline":"Optimal-transport pooling powers a sharper organ segmenter","feed_subtitle":"L2GNet lifts mean Dice to 82.23 on Synapse and 91.44 on ACDC by aligning codes to learnable references.","key_machinery":"The load-bearing component is the L2GMapper, a bottleneck that replaces the quadratic self-attention matrix with a linear-cost optimal-transport pooling step. It works by taking vector-quantized codes $z_{\\rm dis}$, mapping them through a kernel embedding $\\psi$ into an RKHS, computing the Sinkhorn transport plan $T(\\psi(z_{\\rm dis}), z_{\\rm ref})$ between codes and a trainable reference $z_{\\rm ref}$, and pooling the codes into $t$ bins with weights from the transport plan multiplied by a position kernel $S_{ij}=e^{-\\frac{1}{\\sigma^2_{\\rm pos}}(i/n-j/t)^2}$. Multiple references $z^1_{\\rm ref},\\dots,z^q_{\\rm ref}$ play the role of attention heads, and all Sinkhorn operations are differentiable, so the references are learned by backpropagation; the Nyström method is used as an approximation when code sets are large.","core_discovery":"The central claim is that global context for segmentation can be obtained by optimal-transport alignment of discrete codes to a trainable reference rather than by self-attention. After the encoder produces a continuous latent and vector quantization converts it to discrete codes, the L2GMapper embeds those codes in a reproducing kernel Hilbert space, computes a Sinkhorn transport plan between the codes and a learnable reference, and pools codes into buckets weighted by both transport mass and a position-dependent similarity. The authors report that this procedure yields state-of-the-art results on Synapse and ACDC, with L2GNet(4-ref) reaching 82.23 mean DSC and 14.17 HD on Synapse and 91.44 DSC and 1.24 HD on ACDC, outperforming CLS, DLS, and CDLS baselines including SynergyNet, TransUNet, and VQUNet. They interpret the gains as evidence that the model learns inter-class and intra-class anatomical dependencies and reduces false negatives.","pith_inferences":["Editorial inference: the comparison would be strongest if all baselines were re-trained under L2GNet's exact protocol with multiple seeds, since the paper's tables do not report variance and only state that SynergyNet's configuration was followed.","Editorial inference: the position-aware transport plan could be visualized as attention maps to test the claim that it focuses on pertinent regions and avoids redundant pairs; the paper does not provide such a quantitative analysis.","Editorial inference: the same optimal-transport bottleneck may extend to 3D volumes and semi-supervised settings, where the authors' claimed linear complexity and annotation efficiency would matter most.","Editorial inference: the method's benefit may depend on the entropy regularization $\\varepsilon$ in Sinkhorn and the position-kernel width $\\sigma_{\\rm pos}$; ablating those would clarify whether the gain comes from optimal transport or from the added positional prior."],"forward_implications":["Self-attention bottlenecks in segmentation networks can be replaced by a linear-complexity optimal-transport pooling module without sacrificing accuracy on multi-organ and cardiac tasks.","The reported margins over SynergyNet, TransUNet, and VQUNet imply that modeling dependencies between pertinent regions, rather than all pairwise patch interactions, is sufficient for strong segmentation performance.","Codebook size and the number of references are tunable and affect results: L2GNet peaks at $K=512$ and $q=4$ in the reported experiments, and performance degrades at smaller codebooks and at $q=2$.","Because the module is a drop-in bottleneck, the same design could be attached to other encoders and decoders, potentially improving generalization on additional anatomy segmentation tasks."],"supporting_citations":[{"why":"Supplies the Sinkhorn algorithm that computes the entropic optimal-transport plan efficiently and differentiably.","marker":"[21]"},{"why":"Introduces the trainable optimal-transport embedding for feature aggregation and the multi-reference construction that L2GMapper adapts.","marker":"[22]"},{"why":"Provides the entropic Kantorovich formulation of optimal transport used in the paper's objective.","marker":"[24]"},{"why":"Defines vector quantization and the codebook loss that produces the discrete codes.","marker":"[14]"},{"why":"Shows how kernel embeddings and reference parameters can be learned end-to-end by backpropagation.","marker":"[25]"},{"why":"Serves as the main CDLS baseline and supplies the training configuration the experiments follow.","marker":"[16]"},{"why":"Represents the Transformer-based CLS baseline that L2GNet must outperform on long-range dependencies.","marker":"[12]"},{"why":"Provides the DLS baseline (VQUNet) against which the discrete-code component is compared.","marker":"[13]"},{"why":"Gives the Nyström approximation used when the set of discrete codes is large.","marker":"[23]"},{"why":"Defines the dot-product self-attention mechanism that L2GMapper is proposed to replace.","marker":"[6]"}],"fun_headline_variants":["Optimal transport pooling beats attention for organ segmentation","L2GNet: Global anatomy via transport, no self-attention needed","Segmentation gains from transport-aligned discrete codes","Transport-based global context sharpens medical segmentation","L2GNet: Optimal transport for sharper, generalized segmentation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported superiority assumes every baseline was measured under the same preprocessing, optimizer, epochs, data splits, and augmentation as L2GNet; the paper only states that it follows SynergyNet's configuration and does not show that the baseline numbers come from that same protocol.","fun_headline_variants_meta":{"raw":{"variants":["Optimal transport pooling beats attention for organ segmentation","L2GNet: Global anatomy via transport, no self-attention needed","Segmentation gains from transport-aligned discrete codes","Transport-based global context sharpens medical segmentation","L2GNet: Optimal transport for sharper, generalized segmentation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000194,"raw_usage":{"total_tokens":1378,"prompt_tokens":997,"completion_tokens":381,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":613,"completion_tokens_details":{"reasoning_tokens":302}},"tokens_in":613,"tokens_out":381,"duration_ms":4463,"temperature":1.0,"reasoning_tokens":302,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T23:32:22.479931+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run SynergyNet, TransUNet, SSNet, TranSSNet, and VQUNet in the exact L2GNet training configuration across multiple random seeds with identical data splits. If the mean Dice gaps on Synapse and ACDC shrink below run-to-run variance, or L2GNet no longer leads, the paper's central superiority claim is refuted. A complementary check: compute the transport plans and test whether removing the position kernel $S$ or replacing Sinkhorn with random assignment eliminates the reported gains.","supporting_citations":[{"cited_title":"Sinkhorn distances: Lightspeed com- putation of optimal transport,","cited_arxiv_id":null,"evidence_quote":"Supplies the Sinkhorn algorithm that computes the entropic optimal-transport plan efficiently and differentiably."},{"cited_title":"A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention","cited_arxiv_id":"2006.12065","evidence_quote":"Introduces the trainable optimal-transport embedding for feature aggregation and the multi-reference construction that L2GMapper adapts."},{"cited_title":"Computational opti- mal transport,","cited_arxiv_id":null,"evidence_quote":"Provides the entropic Kantorovich formulation of optimal transport used in the paper's objective."},{"cited_title":"Neural discrete representation learning,","cited_arxiv_id":null,"evidence_quote":"Defines vector quantization and the codebook loss that produces the discrete codes."},{"cited_title":"End-to-end kernel learning with super- vised convolutional kernel networks,","cited_arxiv_id":null,"evidence_quote":"Shows how kernel embeddings and reference parameters can be learned end-to-end by backpropagation."},{"cited_title":"Synergy- Net: Bridging the gap between discrete and continuous representations for precise medical image segmenta- tion,","cited_arxiv_id":null,"evidence_quote":"Serves as the main CDLS baseline and supplies the training configuration the experiments follow."},{"cited_title":"Vector quantisation for robust segmentation,","cited_arxiv_id":null,"evidence_quote":"Provides the DLS baseline (VQUNet) against which the discrete-code component is compared."},{"cited_title":"Using the Nystr ¨om method to speed up kernel machines,","cited_arxiv_id":null,"evidence_quote":"Gives the Nyström approximation used when the set of discrete codes is large."},{"cited_title":"Attention is all you need,","cited_arxiv_id":null,"evidence_quote":"Defines the dot-product self-attention mechanism that L2GMapper is proposed to replace."}],"review_version":1}