{"id":"05be0b97-83f5-43ba-9b98-6bdccbd42a48","arxiv_id":"2501.14197","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A bi-directional curriculum module that trains two copies of any graph anomaly detector on opposite difficulty orderings and fuses their scores improves detection on seven benchmarks.","lead":"This paper proposes BCL, a curriculum learning schedule for graph anomaly detection that ranks nodes by how far they sit from the average node and trains two copies of any detector, one on typical nodes first and one on unusual nodes first. It reports that the schedule improves ten existing detectors on seven public graph datasets, including perfect scores on the small Facebook dataset.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim that the BDS-based ordering drives the reported gains is not yet established: no random-ordering control is run, and the 'none' column in Table 3 is undefined, so the improvements could come from the two-model fusion or from BDS itself as an anomaly score.","rationale":"I read the paper as proposing a plug-and-play curriculum module, and the central claim is that the ordering of training nodes by BDS is what produces large gains over ten detectors. The weakest point is that the difficulty measure is never validated as a measure of learnability. The paper's Figure 3 only shows that BDS separates normal from anomalous nodes, which is exactly what an unsupervised anomaly score would do, not that low/high BDS nodes are easier to learn in the claimed directions. I agree with the reader that this is load-bearing. The missing random-ordering control is the decisive experiment. The paper does provide some useful evidence: it compares against CLNode and RCL, and it ablates HomoCL versus HeteCL, showing both directions matter. That suggests the two directions have complementary value, but it does not distinguish the ordering from the fusion. Also, the paper's Eq. 3 uses ||.||_1 but calls it the Euclidean norm, a small internal inconsistency that should be fixed. No code is released, and the perfect scores on Facebook (AUC=1.0 and F1=1.0 for four methods) are extreme and would benefit from a leakage check; the random-order control is the cheapest way to test whether the schedule is responsible or whether the BDS computation itself is the active ingredient. Therefore the verdict should remain conditional: the method is plausible, but the central mechanism is not conclusively demonstrated until the random-order ablation is run. This matches the reader's conditional verdict, so no change is needed.","tokens_in":14297,"tokens_out":5936,"duration_ms":53389,"concrete_test":"Implement BCL exactly as in Algorithm 1 on Amazon and Facebook, but replace Q_homo and Q_hete with two independently random permutations of the training nodes (or with the reverse of the BDS order), keeping the two-model fusion, pacing functions, and hyperparameters identical. If the random-order version reaches AUC within 1% of the reported BCL numbers, the BDS ordering is not causal and the central curriculum claim fails; if it drops substantially (e.g., more than 5%), the ordering is load-bearing. Also run the 'none' control from Table 3 as a full configuration and report explicitly whether it uses one or two models.","verdict_should_be":"UNCHANGED","load_bearing_attack":"BCL's novelty rests on the assertion that the bi-directional difficulty score BDS (Eq. 3), the L1 distance between a GAE node embedding and the global mean embedding, orders nodes by learnability: low-BDS nodes are easy for the homogeneity direction and high-BDS nodes easy for the heterogeneity direction. This is the load-bearing premise. But BDS is, by construction, an unsupervised deviation score: rare anomaly nodes naturally lie far from the centroid, and the paper's own Figure 3 confirms that anomalous nodes concentrate at high BDS. Thus the 'heterogeneity' curriculum is simply training first on nodes that are already likely anomalies, and the 'homogeneity' curriculum on nodes likely normal. That might help, but it does not establish that the curriculum order is the causal mechanism. The reported gains could come (a) from the two-model fusion in Eq. 10, which is an ensemble of two independently trained detectors and would improve performance even with random order, or (b) from BDS acting as an unsupervised anomaly prior that upweights likely anomalies in the supervised loss. Table 3 includes a 'none' column that ought to be the control for the pacing function, but the paper never defines what 'none' is; if it is the original single-model detector, the comparison conflates curriculum with fusion, and if it is a two-model no-curriculum version, the paper should say so. No ablation with random or reversed ordering is reported, and no significance tests or error bars are given. This missing control matters most for the perfect AUC=1.0/F1=1.0 claims on Facebook, which would be expected if BDS leaks anomaly information into the training schedule, but a random-order control would reveal whether the exact ordering is needed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Bi-directional Curriculum Learning (BCL), a plug-and-play training module for graph anomaly detection (GAD). BCL first trains a graph autoencoder and computes a Bi-directional Difficulty Score (BDS) for each node as the L1 distance between the node's embedding and the global mean embedding. Nodes are then sorted in ascending BDS order to form a homogeneity-focused curriculum and in descending order to form a heterogeneity-focused curriculum. Two copies of the base GAD detector are trained with these curricula using a paced subset selection, and their anomaly scores are combined via a weighted fusion. The authors report that BCL improves ten GAD models across seven datasets, including perfect AUC and F1 scores on the Facebook dataset for several detectors, and they perform ablations over pacing functions, the fusion weight, and the curriculum hyperparameters.","tokens_in":14599,"tokens_out":4743,"duration_ms":43589,"significance":"If the empirical claims are correct, BCL would be a simple, model-agnostic way to improve many graph anomaly detectors, which is potentially impactful given the plug-and-play framing. The breadth of the evaluation (ten detectors and seven datasets) is a strength, and the paper addresses an interesting and under-explored question: how to design curricula for GAD when both homogeneous and heterogeneous nodes can be informative. The complexity analysis is reasonable. However, the causal role of the BDS ordering is not established: the paper lacks random-ordering controls, the 'none' column in Table 3 is undefined, and no variance or significance measures are reported. Because the central claim is that the curriculum ordering itself drives the gains, these omissions are load-bearing. The paper currently reads as a promising but unverified empirical proposal rather than a fully supported contribution.","major_comments":[{"comment":"The linear pacing function is written as g(t) = min(1, λ0 + (1 - λ0 * t / T)). As written, at t = 0 this gives 1 + λ0, so the function does not start at λ0; the intended formula is presumably λ0 + (1 - λ0) * t / T. Since the paper recommends the linear pacing function in RQ4, this formula error affects the reproducibility of the main recommended configuration.","section":"Section 4.2, Eq. (7)"},{"comment":"The 'none' column is never defined. If 'none' denotes the original single-model detector without BCL, then the comparison conflates the curriculum effect with the effect of training two models and fusing their scores; if 'none' denotes a two-model version without pacing, that must be stated explicitly. The gap between the 'none' values and the base detectors in Table 2 (e.g., MLP AUC 0.6705 vs. MLP+BCL 'none' AUC 0.8512 on Amazon) suggests that much of the gain may come from the two-model fusion rather than from the curriculum ordering. Please define this condition and add the appropriate controls.","section":"Table 3"},{"comment":"The central claim that BDS-based ordering drives the improvements is not supported by any random-ordering or reversed-ordering ablation. BDS is, by construction, an unsupervised deviation score: Figure 3 itself shows that anomalous nodes cluster at high BDS, so the heterogeneity curriculum is essentially training on likely anomalies first. The observed gains could therefore come from (a) the two-model fusion in Eq. (10), (b) BDS acting as an unsupervised anomaly prior, or (c) the specific ascending/descending order. Please report random-order and reversed-order baselines with the same two-model fusion to isolate the effect of the curriculum ordering.","section":"Section 4.1 and Algorithm 1"},{"comment":"No variance, error bars, or significance tests are reported. Many of the claimed improvements are very small (for example, several F1 changes are below 0.001), and some BCL results are worse than the corresponding single-direction baselines. Without repeated runs or paired tests, the statement that BCL 'significantly improves' ten detectors is not statistically supported. Please report standard deviations over at least five seeds or provide permutation/paired tests.","section":"Section 5, Tables 2 and 3"},{"comment":"The claim that 'GraphSAGE, BWGNN, AMNET, and GHRN combined with BCL achieve AUC and F1 scores of 1 on the Facebook dataset' and that 'no previous study has been able to achieve' this is overstated. The Facebook dataset has only 1,081 nodes, and Table 2 shows that the HomoCL baseline alone already achieves 1.0000 AUC and 1.0000 F1 for GraphSAGE, so BCL is not necessary for this perfect result. The statement should be tempered and supported by comparison with previously reported results under identical protocols.","section":"Section 5.2, Facebook results"}],"minor_comments":[{"comment":"The text says '||·||1 denotes the Euclidean norm,' but the subscript 1 denotes the L1 (Manhattan) norm. Please correct the wording.","section":"Eq. (3)"},{"comment":"The expression Vhomo ← {Vtrain[i] | i ∈ Qhomo[1 : λt × |V|]} is ambiguous because Qhomo contains node identifiers, not positions in Vtrain. Please clarify the indexing.","section":"Algorithm 1, line 13"},{"comment":"The figure references are inconsistent: Section 5.5 refers to 'Figure 3' when discussing α, and Section 5.6 refers to 'Figure 4' when discussing λ0 and T. These should be Figure 4 and Figure 5, respectively.","section":"Sections 5.5 and 5.6"},{"comment":"There is a stray word 'Avatar' in the Experimental Details paragraph; it appears to be an editing artifact and should be removed.","section":"Section 5.1"},{"comment":"The text uses 'rootedness pacing function' and the table header uses 'geomo'; these should be 'root' and 'geometric' for consistency.","section":"Section 5.4 and Table 3"},{"comment":"No code or detailed reproducibility instructions are provided. Given that the contribution is a plug-and-play training module, releasing code would substantially strengthen the paper.","section":"Overall"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a useful problem and the experimental scope is broad, but the missing controls and undefined 'none' condition are central to the paper's causal claim. The perfect-score claim on Facebook is risky because it is achieved by one of the two directional models alone. I would encourage the authors to add random-ordering ablations, define and analyze the 'none' condition, and report variance. If these are added convincingly, the paper could become a solid empirical contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, here's my read on the BCL paper. The genuinely new thing is applying curriculum learning to graph anomaly detection with a two-direction ordering: low BDS (distance to the centroid of a graph-autoencoder embedding) first for the homogeneity-focused model, high BDS first for the heterogeneity-focused one. That is a real twist on CLNode and RCL, and the writing is clear enough that I could re-implement it from the text.\n\nThe paper does several things well. The experiment matrix is wide: ten detectors across seven datasets, with per-direction ablations (HomoCL/HeteCL) and a comparison of three pacing functions. The BDS itself is cheap to compute and works as an unsupervised deviation score, which is a sensible signal for anomaly detection. The authors are also candid about some failure cases, e.g., CLNode hurting performance on some datasets.\n\nBut the central claim—that the ordering, not the machinery, drives the gains—is not established. The Table 3 'none' column is never defined. If it is the original single-model detector, the comparison conflates curriculum with two-model fusion. If it is a no-curriculum two-model version, the paper should say so, because that would isolate the pacing effect. There is no random- or reversed-ordering ablation, and no variance or significance reporting. That matters because BDS is, by construction, an anomaly score: high-BDS nodes are likely anomalous. Training on them first may simply upweight anomalies in the loss, and the AUC=1.0/F1=1.0 on Facebook looks exactly like what you'd expect if the score leaks the label. I can't tell from the current evidence whether the curriculum order or the BDS prior is doing the work.\n\nAlso, Eq. (7) has a typo (missing parenthesis; should read (1-λ0)*t/T), and the complexity analysis glosses over the two-model training cost. These are minor.\n\nOverall, this is a solid, interesting idea with an incomplete evaluation. It is worth a serious referee. I would tell the authors to add a random-ordering control, define the 'none' baseline, report standard deviations across seeds, and include a comparison against simply training on the BDS-based anomaly weighting. If the ordering still matters after that, the paper becomes much stronger.","headline":"A plausible new curriculum-learning recipe for GAD that deserves a serious referee, but the paper needs a random-ordering control and a defined 'none' baseline before the central mechanism claim holds.","tokens_in":15183,"tokens_out":3294,"would_cite":false,"duration_ms":29622,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that a bi-directional curriculum—training one detector copy from the most typical nodes and another from the most atypical—plugged into ten existing graph anomaly detectors improves them on seven datasets, with four…","keywords":["graph anomaly detection","curriculum learning","graph neural networks","homogeneity","heterogeneity","training scheduler","bi-directional difficulty score","node classification"],"falsifier":"A concrete test would be to hold everything in BCL fixed—the two-model split, the pacing schedule, and the fusion—but replace the BDS ordering with a random permutation of nodes, and compare against the BDS ordering on the same seven datasets. If the random-order control matches BCL's AUC improvements under multiple seeds, the claim that the score-based difficulty measure drives the gain is falsified. A second check would rerun the reported perfect AUC/F1 of 1 on Facebook across many random seeds and fixed hyperparameter grids, since a perfect score on a 1081-node benchmark with only 2.3% anomalies can be brittle.","tokens_in":14077,"feed_emoji":"📈","tokens_out":10727,"duration_ms":81174,"temperature":0.7,"pith_summary":"The paper argues that graph anomaly detection (GAD) models are currently trained without regard for which nodes are easy or hard, and that existing graph curriculum learning methods only exploit homogeneity, which leaves gains on the table. It introduces Bi-directional Curriculum Learning (BCL), which assigns each node a score equal to the L1 distance between its graph-autoencoder representation and the global mean representation, then trains two copies of any GAD model on opposite orderings of that score—one starting with the most typical nodes and the other with the most atypical—and fuses their outputs. The authors report that this plug-and-play module significantly improves ten existing GAD detectors across seven widely used datasets, with GraphSAGE, BWGNN, AMNET, and GHRN reaching AUC and F1 scores of 1 on the Facebook dataset. A reader should care because the contribution is a training schedule, not a new architecture, so if the claim holds it is a cheap and general upgrade for existing anomaly detectors.","feed_headline":"A single training-order change lifts ten graph anomaly detectors","feed_subtitle":"Starting one model with typical nodes and the other with atypical ones pushes AUC and F1 up on seven benchmarks.","key_machinery":"The central object is the Bi-directional Difficulty Score (BDS), defined in Eq. (3) as $BDS(v_i) = \\|h_i - \\bar{h}\\|_1$, the distance from a node's learned representation to the global mean representation of all nodes. This one scalar produces two curricula: ascending order feeds the homogeneity-focused model, which learns typical patterns first, and descending order feeds the heterogeneity-focused model, which learns atypical patterns first. Around BDS, BCL wraps a continuous training scheduler with three pacing functions—linear, root, and geometric—that control how quickly harder nodes are admitted, and a convex fusion step $\\alpha \\text{Score}_{\\text{homo}} + (1-\\alpha)\\text{Score}_{\\text{hete}}$ that combines the two models' outputs. The machinery's role is to translate the familiar idea of easy-to-hard training into the two complementary signals that a GAD model can exploit.","core_discovery":"The central claim is that a graph anomaly detector can learn better when its training set is ordered along both directions of a single difficulty spectrum: nodes closest to the global mean representation are easiest for a homogeneity-focused model, and nodes farthest from the mean are easiest for a heterogeneity-focused model. The paper constructs this ordering with the Bi-directional Difficulty Score $BDS(v_i) = \\|h_i - \\bar{h}\\|_1$, where $h_i$ comes from a two-layer GCN graph autoencoder and $\\bar{h}$ is the average of all node representations. BCL sorts nodes by BDS ascending and descending, feeds each sorted sequence to an identical copy of the detector through a continuous pacing function that gradually admits harder nodes, and computes the final anomaly score as $\\alpha \\cdot \\text{Score}_{\\text{homo}} + (1-\\alpha) \\cdot \\text{Score}_{\\text{hete}}$. The paper's experiments, run on seven datasets and ten detectors, are offered as evidence that this dual-direction curriculum consistently outperforms both the unmodified detectors and prior homogeneity-only curriculum methods.","pith_inferences":["Because BDS is computed with an unsupervised graph autoencoder before any label is used, the same node ordering could in principle be applied to unlabeled or semi-supervised anomaly detection tasks, although the paper only evaluates supervised detectors.","The Facebook dataset's small size (1081 nodes, 2.3% anomalies) makes perfect scores plausible even without a curriculum, so the strongest test of the claim would be a stress-run on a large, low-anomaly-rate benchmark where small differences in ranking matter.","The two-model fusion doubles the detector's forward pass cost; an alternative single-model design with two output heads or epoch-switched ordering might recover most of the gain at half the inference cost, but that is an extension, not a claim in the paper."],"forward_implications":["Any existing graph anomaly detector can be upgraded without changing its architecture; the paper demonstrates this for MLP, GCN, GAT, GraphSAGE, and six state-of-the-art detectors.","Detectors built to handle heterophily, such as CARE-GNN and Split-GNN, still gain from the heterogeneity-first curriculum, suggesting the two directions capture complementary information rather than duplicating model strengths.","The gain is sensitive to the fusion weight $\\alpha$; the paper shows different detectors prefer different balances between homogeneity and heterogeneity, so tuning this single parameter is part of the reported improvement.","Among the three pacing functions, the linear scheduler gives the most consistent improvements on the Amazon dataset, which the paper recommends as the default choice."],"supporting_citations":[{"why":"Supplies the CLNode homogeneity-only curriculum and difficulty measure that BCL is designed to outperform; Figure 3 compares BDS with CLNode's score.","marker":"[Wei et al., 2022]"},{"why":"Provides RCL, an edge-level graph curriculum baseline that BCL is compared against in the experiments.","marker":"[Zhang et al., 2023]"},{"why":"The two-layer GCN used as the autoencoder encoder whose representations $h_i$ define BDS in Eq. (3).","marker":"[Kipf and Welling, 2016]"},{"why":"Defines BWGNN, a spectral GAD detector that BCL improves and that is used in the scheduler and hyperparameter analyses.","marker":"[Tang et al., 2022]"},{"why":"Provides PC-GNN, a GAD detector with imbalanced-learning components that BCL is applied to and improves.","marker":"[Liu et al., 2021]"},{"why":"Provides CARE-GNN, a fraud-detection GNN designed against camouflaged fraudsters, one of the ten detectors in the BCL evaluation.","marker":"[Dou et al., 2020]"},{"why":"Provides AMNet, a GNN anomaly detector that BCL improves; AMNet is named among detectors reaching perfect scores on Facebook.","marker":"[Chai et al., 2022]"},{"why":"Provides GHRN, a heterophily-aware spectral detector used as a baseline that BCL improves.","marker":"[Gao et al., 2023]"},{"why":"Provides Split-GNN, a heterophily-oriented fraud detector used as a baseline that BCL improves.","marker":"[Wu et al., 2023]"},{"why":"Source of the Yelp dataset, one of the seven benchmarks used in the evaluation.","marker":"[Rayana and Akoglu, 2015]"}],"fun_headline_variants":["Training-order flip lifts ten graph detectors","Dual-direction curriculum sharpens graph anomaly detection","Simple reorder boosts ten graph anomaly models","Both homogeneity and heterogeneity guide training for better GAD","Reorder nodes, boost graph anomaly detectors"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the distance between a node's learned representation and the global mean representation genuinely orders nodes by learning difficulty for every GAD method—that low-BDS nodes really are the easy ones for the homogeneity direction and high-BDS nodes really are the easy ones for the heterogeneity direction—so the curriculum is not just a fixed arbitrary ordering.","fun_headline_variants_meta":{"raw":{"variants":["Training-order flip lifts ten graph detectors","Dual-direction curriculum sharpens graph anomaly detection","Simple reorder boosts ten graph anomaly models","Both homogeneity and heterogeneity guide training for better GAD","Reorder nodes, boost graph anomaly detectors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000147,"raw_usage":{"total_tokens":1193,"prompt_tokens":960,"completion_tokens":233,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":166}},"tokens_in":576,"tokens_out":233,"duration_ms":2941,"temperature":1.0,"reasoning_tokens":166,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:14:51.534969+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete test would be to hold everything in BCL fixed—the two-model split, the pacing schedule, and the fusion—but replace the BDS ordering with a random permutation of nodes, and compare against the BDS ordering on the same seven datasets. If the random-order control matches BCL's AUC improvements under multiple seeds, the claim that the score-based difficulty measure drives the gain is falsified. A second check would rerun the reported perfect AUC/F1 of 1 on Facebook across many random seeds and fixed hyperparameter grids, since a perfect score on a 1081-node benchmark with only 2.3% anomalies can be brittle.","supporting_citations":[{"cited_title":"Clnode: Cur- riculum learning for node classification","cited_arxiv_id":null,"evidence_quote":"Supplies the CLNode homogeneity-only curriculum and difficulty measure that BCL is designed to outperform; Figure 3 compares BDS with CLNode's score."},{"cited_title":"Curriculum Learning for Graph Neural Networks: Which Edges Should We Learn First","cited_arxiv_id":"2310.18735","evidence_quote":"Provides RCL, an edge-level graph curriculum baseline that BCL is compared against in the experiments."},{"cited_title":"Rethinking graph neural networks for anomaly de- tection","cited_arxiv_id":null,"evidence_quote":"Defines BWGNN, a spectral GAD detector that BCL improves and that is used in the scheduler and hyperparameter analyses."},{"cited_title":"Pick and choose: A gnn-based imbalanced learning approach for fraud detection","cited_arxiv_id":null,"evidence_quote":"Provides PC-GNN, a GAD detector with imbalanced-learning components that BCL is applied to and improves."},{"cited_title":"Enhancing graph neural network-based fraud detectors against camouflaged fraudsters","cited_arxiv_id":null,"evidence_quote":"Provides CARE-GNN, a fraud-detection GNN designed against camouflaged fraudsters, one of the ten detectors in the BCL evaluation."},{"cited_title":"Can abnormality be detected by graph neural networks? In Proceedings of the 31st International Joint Conference on Artificial Intelligence (IJCAI),","cited_arxiv_id":null,"evidence_quote":"Provides AMNet, a GNN anomaly detector that BCL improves; AMNet is named among detectors reaching perfect scores on Facebook."},{"cited_title":"Ad- dressing heterophily in graph anomaly detection: A per- spective of graph spectrum","cited_arxiv_id":null,"evidence_quote":"Provides GHRN, a heterophily-aware spectral detector used as a baseline that BCL improves."},{"cited_title":"Collective opinion spam detection: Bridging re- view networks and metadata","cited_arxiv_id":null,"evidence_quote":"Source of the Yelp dataset, one of the seven benchmarks used in the evaluation."}],"review_version":1}