{"id":"b76dae9f-84bc-46be-9b48-b028a0261ca3","arxiv_id":"2607.07077","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":7,"one_line_summary":"A hyperbolic-space framework with geometric entailment constraints and a graph-aware Mamba module improves brain-network classification of ASD and MDD by explicitly modeling ROI-to-community-to-whole-brain hierarchy.","lead":"The paper proposes a brain-network analysis framework that maps regions, functional communities, and whole-brain graphs into hyperbolic space to model their hierarchy, combined with a graph-aware Mamba module for long-range dependencies. It could improve diagnosis of autism and depression from fMRI scans and highlight which brain circuits are disrupted.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"The hyperbolic entailment module (HBRL) — the paper's central contribution — shows marginal or negative ablation effects, and headline gains over SOTA lack statistical significance testing despite large standard deviations.","rationale":"The reader correctly identified the marginal HBRL contribution in the rationale but elevated the theoretical concern about strict tree-like hierarchy as the primary weakest assumption. I find the empirical insufficiency more directly load-bearing: the ablation results show HBRL can *hurt* performance (REST-MDD: 69.24→68.66 when added to GaMamba alone), and the headline gains over SOTA (1.4–1.9%) are smaller than the reported standard deviations (±2.3–3.3%). Without paired significance testing, the central claim rests on differences that are statistically indistinguishable from noise. The verdict remains CONDITIONAL — the method is architecturally sound and the GaMamba contribution is real, but the paper has not demonstrated that its titular contribution (hyperbolic hierarchical learning) provides statistically reliable benefit. A simple paired test on existing fold-level results would settle this immediately. If the authors can show p < 0.05 for both the SOTA comparison and the HBRL ablation, the claim strengthens considerably; if not, the hyperbolic component's value is in serious doubt.","tokens_in":21841,"tokens_out":2218,"duration_ms":60637,"concrete_test":"Perform paired statistical tests (paired t-test or Wilcoxon signed-rank) on the per-fold accuracies of: (a) HLBG (full) vs. CAGT, and (b) GaMamba+SA vs. GaMamba+SA+HBRL, on both ABIDE-I and REST-MDD. If p > 0.05 in comparison (b) on either dataset, the HBRL module's contribution is not statistically significant, weakening the central claim. If p > 0.05 in comparison (a), the headline SOTA improvement is indistinguishable from noise.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central claim is that explicitly modeling ROI→community→whole-brain hierarchy in hyperbolic space yields more discriminative representations. However, the ablation results (Table 3) undermine this claim empirically. On REST-MDD, adding HBRL to GaMamba alone *decreases* ACC from 69.24% to 68.66% (and AUC from 73.35 to 72.60). On ABIDE-I, HBRL adds only 0.49% ACC over GaMamba alone (73.91→74.40). The full model's gains over the second-best baseline (CAGT) are 1.44% (ABIDE-I) and 1.90% (REST-MDD), but the reported standard deviations are ±3.32 and ±2.27 respectively — these differences are well within the noise envelope of 10-fold cross-validation. No paired statistical test (paired t-test, Wilcoxon signed-rank, etc.) is reported across folds. The GaMamba module, not the hyperbolic component, accounts for the majority of the improvement (2.22% on ABIDE-I, 1.51% on REST-MDD over baseline). If the HBRL module does not consistently improve performance and the headline gains are not statistically distinguishable from noise, the central claim that hyperbolic hierarchical modeling is the key driver of improved diagnosis is not adequately supported. The reader's theoretical concern about strict tree-like assumptions is valid but secondary — the more immediate problem is that the empirical evidence does not clearly establish that the hyperbolic component helps at all.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"The manuscript proposes HLBG, a framework for brain disorder diagnosis from fMRI functional connectivity graphs. The method has two main contributions: (1) a Graph-aware Mamba (GaMamba) module that injects GAT-derived structural prompts into the selective state-space model's readout matrix, and (2) a Hierarchical Brain Representation Learning (HBRL) module that projects ROI-, community-, and whole-brain-level embeddings into Lorentzian hyperbolic space and enforces ROI→community→whole-brain entailment via two geometric cone losses. Experiments on ABIDE-I (ASD) and REST-MDD (MDD) show improvements over GNN, Graph Transformer, and Mamba baselines. The mathematical formulations follow standard hyperbolic geometry and SSM definitions. The core concern is that the central contribution—hyperbolic hierarchical modeling—is not clearly supported by the ablation evidence, and headline gains lack statistical testing.","tokens_in":22720,"tokens_out":1493,"duration_ms":108880,"significance":"The paper addresses a genuine gap: most brain-graph methods model either flat node-level or community-level structure without an explicit geometric hierarchy. The idea of using Lorentzian entailment cones to enforce ROI⊂community⊂brain relationships is novel for this application. The GaMamba design—injecting topology into the SSM readout rather than relying solely on node ordering—is a reasonable architectural choice. However, the significance is tempered by the fact that the hyperbolic component shows inconsistent ablation benefits, and the empirical gains over the strongest baseline fall within the reported standard-deviation envelope without statistical testing.","major_comments":[{"comment":"Table 3 (ablation): The HBRL module—the paper's central contribution—shows inconsistent or marginal ablation effects. On REST-MDD, adding HBRL to GaMamba alone *decreases* ACC from 69.24% to 68.66% and AUC from 73.35% to 72.60%. On ABIDE-I, HBRL adds only 0.49% ACC over GaMamba alone (73.91→74.40). The full model's gains over the second-best baseline (CAGT) are 1.44% ACC on ABIDE-I and 1.90% on REST-MDD, but the reported standard deviations are ±3.32 and ±2.27 respectively. No paired statistical test (paired t-test, Wilcoxon signed-rank, etc.) is reported across the 10 folds. The authors should either (a) provide paired statistical tests across folds to demonstrate that the improvements are significant, or (b) acknowledge that the hyperbolic component's contribution is marginal and reframe the central claim accordingly. As it stands, the empirical evidence does not clearly establish that","section":null},{"comment":"Table 2 (comparison with SOTA): The headline improvements over the second-best method (CAGT) are 1.44% ACC on ABIDE-I and 1.90% on REST-MDD. Given the standard deviations (±3.32 and ±2.27), these differences are within the noise envelope of 10-fold cross-validation. Without a paired statistical test comparing HLBG against CAGT fold-by-fold, it is not possible to determine whether the reported gains are real or artifacts of variance. The authors should report per-fold results for at least the top two methods and apply an appropriate paired test.","section":null},{"comment":"§3.3, Eqs. (9)–(11): The entailment-cone loss enforces a strict tree-like hierarchy where each ROI falls within the entailment cone of exactly one community, and each community within the whole-brain cone. However, brain regions such as the precuneus participate in multiple functional networks simultaneously. The manuscript does not discuss how this strict tree assumption interacts with the overlapping, non-hierarchical structure of functional brain organization. The authors should either (a) discuss this limitation explicitly and justify why the tree approximation is reasonable, or (b) consider a softer entailment that allows partial membership. The concern is not that the tree assumption is wrong by definition, but that without any discussion or sensitivity analysis, it is unclear whether the constraint could distort representations for hub regions.","section":null},{"comment":"§3.3, Eq. (5)–(6): The aggregation function φ(·) that produces community-level (Z_c) and whole-brain (Z_b) representations from ROI features is an attention-based weighted summation. This aggregation is performed in Euclidean space *before* the exponential map into hyperbolic space. The entailment losses then operate on the hyperbolic projections of these pre-aggregated vectors. The authors should clarify whether Euclidean aggregation followed by hyperbolic projection is geometrically consistent—i.e., whether the resulting hyperbolic points meaningfully represent the 'parent' of their children in the Lorentz model, or whether the aggregation should be performed using Fréchet means or other hyperbolic-native operations to ensure that the entailment losses.","section":null}],"minor_comments":[{"comment":"Figure 3 contains garbled characters (e.g., '/uni00000024/uni00000026...') instead of readable axis labels. This should be replaced with legible labels.","section":null},{"comment":"§3.1: The top-k parameter for adjacency construction is mentioned (k=30 in §4.2) but the sensitivity to this choice is not analyzed. A brief note on robustness would improve readability.","section":null},{"comment":"§4.2: The curvature parameter κ is set to 1.3 for ABIDE-I and 0.39 for REST-MDD, but no justification is given for these different values or how they were selected. A brief explanation would help readers understand whether this is dataset-specific tuning or principled selection.","section":null},{"comment":"Several references have future dates (e.g., Wang et al. 2026, Jia et al. 2026). If these are accepted/in-press works, this should be noted; if they are arXiv preprints, the citation format should reflect this.","section":null},{"comment":"§3.4: The OCRead module is referenced as following prior work (Kan et al. 2022; Pei et al. 2025) but its role in the overall pipeline is described only briefly. A one-sentence explanation of why structured graph-level readout is preferred over simple pooling would help readers.","section":null},{"comment":"Table 2: The 'vanillaTF' baseline (Vaswani et al. 2017) is a generic Transformer applied to brain graphs. It would be useful to clarify how it is adapted for graph input (e.g., using node sequences).","section":null}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about HBRL's marginal ablation effects is well-founded and is the primary reason for the major revision recommendation. The GaMamba module appears to carry most of the empirical improvement, while the hyperbolic component—the paper's claimed novelty—does not consistently help. If the authors can provide statistical tests showing significance, or reframe the contribution to emphasize GaMamba with HBRL as a complementary regularizer rather than the central driver, the paper could be acceptable. The tree-like hierarchy assumption is a secondary concern that deserves discussion but is not necessarily fatal."},"author_rebuttal":null,"desk_editor":{"model":"glm-5.2","letter":"The paper you sent combines hyperbolic entailment constraints with a graph-aware Mamba variant for brain-network classification. Here's what matters: the GaMamba module is a solid engineering contribution, and the hyperbolic component — the paper's headline — doesn't clearly justify itself empirically. That tension is the thing to focus on if you referee this. What's genuinely new: injecting GAT-derived structural prompts into Mamba's readout matrix (Eq. 1) is a clean, sensible way to preserve graph topology in a state-space model. The multi-branch architecture with community-specific local branches plus a global branch is well-motivated. The Lorentzian exponential map and entailment cone formulations (Eqs. 7–11) are mathematically standard but correctly applied. The biomarker analysis identifies reasonable regions (precuneus, MFG, olfactory cortex) that align with prior ASD/MDD literature. Credit where due: the engineering is competent and the writing is clear. Now the soft spots, and one of them is load-bearing. The ablation in Table 3 shows HBRL — the hyperbolic module that gives the paper its name — adds only 0.49% ACC on ABIDE-I over GaMamba alone, and actually *decreases* ACC on REST-MDD (69.24 → 68.66). GaMamba accounts for the bulk of the improvement (2.22% and 1.51% over baseline). So the central claim that hyperbolic hierarchical modeling drives the gains is not supported by the paper's own ablation. The headline improvements over the second-best baseline (1.44% on ABIDE-I, 1.90% on REST-MDD) come with standard deviations of ±3.32 and ±2.27 — no paired statistical test is reported, so we can't distinguish signal from noise. The hierarchy is also imposed a priori via the Yeo atlas rather than discovered, which weakens the framing somewhat, though I'd call that a minor issue compared to the empirical gap. Several hyperparameters (κ, λ₁, λ₂, w, N_b) are tuned per dataset without principled justification, and no code is released. The biomarker analysis is restricted to correctly classified subjects, which introduces selection bias. My take: the GaMamba contribution is real and worth publishing. The hyperbolic component needs either stronger empirical evidence or a reframing as a regularizer rather than the central novelty. The paper deserves a serious referee who can push the authors to either justify HBRL's value or reposition the contribution honestly.","headline":"GaMamba is the real contribution; the hyperbolic module doesn't clearly earn its keep","tokens_in":22650,"tokens_out":1274,"would_cite":false,"duration_ms":42709,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Hyperbolic geometry maps brain hierarchy, boosting disorder diagnosis","keywords":[],"falsifier":"If one were to take brain regions known to participate in multiple communities (e.g., the precuneus or medial prefrontal cortex) and measure their angular distance to each candidate parent community in the learned hyperbolic embedding, a strict entailment model would predict that they fall within exactly one cone. If instead these regions are systematically pushed to the boundaries or outside of all community cones, or if the model's classification accuracy degrades specifically for subjects whose functional architecture is most non-tree-like, that would indicate the strict hierarchy is distal","tokens_in":22057,"feed_emoji":"🧠","tokens_out":785,"duration_ms":171849,"temperature":0.7,"pith_summary":"The paper argues that brain networks have a natural three-tier hierarchy—individual regions, functional communities, and the whole brain—and that this hierarchy is best captured not in flat Euclidean space but in hyperbolic space, a geometry with constant negative curvature that naturally accommodates tree-like, nested structures. The authors propose a framework called HLBG that projects region, community, and whole-brain representations into Lorentzian hyperbolic space and then enforces two geometric entailment constraints: one requiring each region to fall within the entailment cone of its parent community, and another requiring each community to fall within the cone of the whole brain. This forces the learned representations to respect the part-to-whole containment structure of functional brain organization. The paper also introduces a Graph-aware Mamba module that injects graph topological structure into the Mamba state-space model, allowing it to capture long-range dependencies across brain regions while preserving local connectivity patterns. The combined system is tested on autism (ABIDE-I) and depression (REST-MDD) classification, yielding modest but consistent accuracy improvements over Euclidean graph neural networks and graph Transformers, and producing attention-based biomarker maps that align with known neuroscience findings.","feed_headline":"Hyperbolic geometry maps brain hierarchy, boosting disorder diagnosis","feed_subtitle":"By forcing brain regions, communities, and whole-brain networks into nested entailment cones in curved space, the method captures hierarchy ","key_machinery":"The two entailment losses are the novel geometric machinery. Each parent node (community or whole-brain) defines an entailment cone in hyperbolic space—a region of the manifold whose aperture depends on the parent's distance from the origin. The loss function penalizes any child whose angular position relative to the parent exceeds the cone's half-aperture angle. This converts the abstract notion of hierarchy into a concrete geometric constraint: children must lie within their parent's cone, which in hyperbolic space is exponentially cheaper to satisfy at deeper tree levels than in Euclidean space. The second mechanism is GaMamba, which modifies Mamba's output readout matrix by adding a GAT-","core_discovery":"The central claim is that explicitly imposing ROI-to-community-to-whole-brain hierarchical containment constraints in Lorentzian hyperbolic space produces more discriminative brain-network representations than flat-space methods, because the negative-curvature geometry naturally mirrors the nested, tree-like organization of functional brain architecture. The entailment-cone loss is the load-bearing mechanism: it penalizes region representations that fall outside their community's cone and community representations that fall outside the whole-brain cone, thereby enforcing a geometric hierarchy that Euclidean aggregation cannot express.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Hyperbolic entailment cones enforce brain network hierarchy for diagnosis","Curved-space containment constraints capture brain hierarchy for disorder detection","Lorentzian geometry models ROI-to-whole-brain hierarchy, improving diagnosis","Geometric entailment in hyperbolic space maps nested brain structure for diagnosis","Hyperbolic space encodes brain hierarchy across regions, communities, networks"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The entailment-cone constraint assumes that the functional brain hierarchy is strict enough that each region belongs unambiguously within a single community's cone and each community within the whole-brain cone. In reality, many brain regions—hub regions like the precuneus—participate in multiple overlapping functional networks simultaneously, so the true structure may be a graph with cross-links rather than a clean tree.","fun_headline_variants_meta":{"raw":{"variants":["Hyperbolic entailment cones enforce brain network hierarchy for diagnosis","Curved-space containment constraints capture brain hierarchy for disorder detection","Lorentzian geometry models ROI-to-whole-brain hierarchy, improving diagnosis","Geometric entailment in hyperbolic space maps nested brain structure for diagnosis","Hyperbolic space encodes brain hierarchy across regions, communities, networks"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":693,"prompt_tokens":600,"completion_tokens":93,"prompt_tokens_details":null},"tokens_in":600,"tokens_out":93,"duration_ms":22898,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T20:29:33.434448+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If one were to take brain regions known to participate in multiple communities (e.g., the precuneus or medial prefrontal cortex) and measure their angular distance to each candidate parent community in the learned hyperbolic embedding, a strict entailment model would predict that they fall within exactly one cone. If instead these regions are systematically pushed to the boundaries or outside of all community cones, or if the model's classification accuracy degrades specifically for subjects whose functional architecture is most non-tree-like, that would indicate the strict hierarchy is distal","supporting_citations":[],"review_version":1}