{"id":"0952bc21-ef2a-42c2-8eb8-e53ca2adc90b","arxiv_id":"2412.17355","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A bidirectional, information-bottleneck-guided graph condensation method selects a meso-scale graph and condenses in both directions, outperforming prior one-directional multi-scale approaches on several benchmarks, though with inconsistent gains at larger scales.","lead":"This paper proposes a graph condensation method that first builds a medium-sized summary graph, then shrinks and grows it to produce smaller and larger versions for devices with different computing power. The method aims to preserve useful information across all sizes better than existing one-directional compression approaches.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The IB objective is never concretely instantiated: Eq. (3) references a condensed graph before it exists, and Algorithm 1 does not specify how Eq. (7) is computed or combined with Eq. (10), leaving the central mechanism unverified.","rationale":"The reader's weakest assumption—that the implementation faithfully optimizes the SCIB objective—is well placed, and my concern overlaps with it. I add two sharper technical observations: Eq. (3) is circular as written because it selects a subgraph of a condensed graph that has not yet been constructed, and the Appendix derivation of Eq. (7) contains a conditional-direction error and a dropped entropy term, so the claimed variational bound is not formally established. These are not merely presentation issues: if the actual code does not compute Eq. (7), the paper's central mechanism is untested and the empirical margins could be attributable to the GDEM backbone or training schedule. I do not see grounds to reject the work outright; the idea is plausible and the empirical tables are extensive, with a public code link that could settle the question. The appropriate disposition remains conditional: the paper should be accepted only after the loss is specified precisely and verified in code, or after an ablation shows the IB term is genuinely load-bearing. The reader already reached CONDITIONAL, so my verdict is UNCHANGED rather than a move to a different disposition.","tokens_in":26407,"tokens_out":9713,"duration_ms":97616,"concrete_test":"Inspect the released code at https://github.com/RingBDStack/BiMSGC: locate the training loss in Algorithm 1's second loop and verify whether LSCIB (Eq. 7) is actually computed, with explicit implementations of Q, R, and the f term, and a stated weighting against Eq. (10). Then rerun the code with the IB term's weight set to zero; if Table 1's reported accuracies do not change by more than the reported standard deviations, the information bottleneck objective is not responsible for the results and the central claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the information-bottleneck-guided meso-scale selection and the SCIB objective. Eq. (3) selects G'_m from Sub(G'), but G' is the condensed graph being learned; at Step 1 no condensed graph exists, so the objective is circular unless G' is a typo for the original graph G, in which case the notation and derivation do not match the method. Step 3 gives no functional form for Q or R—\"importance score\" and \"Bernoulli distribution with parameter θ\" are not enough to define Eq. (7)—and Algorithm 1 says to train using \"Eq. (10) and Eq. (7)\" without specifying the total loss, the weighting, or the optimization procedure. The Appendix derivation is also not rigorous: Eq. (13) reverses the conditional direction, and Eq. (14) drops -E[log P(∇θ)] while claiming a lower bound, so the bound holds only up to an ignored constant (or not at all). If LSCIB is not actually present in the training loss, the empirical gains could come from the GDEM backbone, the meso-scale training schedule, or hyperparameter choices rather than the IB mechanism, and the Fig. 4 ablation does not define how the \"without IB\" condition is implemented. The paper needs a precise, code-consistent specification of the actual loss before the claimed theoretical and empirical superiority can be evaluated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes BiMSGC, a multi-scale graph dataset condensation framework that selects an intermediate 'meso-scale' condensed graph via an information-bottleneck criterion and then trains condensed graphs at both smaller and larger scales bidirectionally, combining eigenbasis matching with a subgraph condensation information bottleneck (SCIB) objective. The authors report large improvements over existing graph condensation baselines on Cora, Citeseer, Ogbn-Arxiv, Flickr, and Reddit, together with cross-architecture generalization experiments and an ablation study. The central claim is that the IB-guided meso-scale starting point and the SCIB objective preserve useful information across scales and thereby avoid the scaling-down degradation and scaling-up collapse observed in large-to-small and small-to-large paradigms.","tokens_in":26714,"tokens_out":2972,"duration_ms":30327,"significance":"The proposed direction—using information-bottleneck reasoning to choose a meso-scale and then condensing bidirectionally—is conceptually appealing and, if implemented as described, would be a useful contribution to multi-scale graph condensation. The empirical results are consistently strong across five datasets, and the paper improves reproducibility by providing a code repository and following the GC-Bench protocol. However, the manuscript currently does not specify the concrete optimization of the SCIB objective: the variational distributions Q and R, the total training loss, and the combination of Eq. (7) with Eq. (10) are left abstract, and the appendix derivation contains algebraic errors. Because the claimed theoretical motivation rests on this unspecified mechanism, the significance of the work cannot be fully assessed from the current text.","major_comments":[{"comment":"Equation (3) defines the meso-scale as argmax over G'_sub in Sub(G'), but at Step 1 no condensed graph G' exists yet; G' is the object being learned in the subsequent bi-directional phase. If G' is intended to be the original graph G, the notation is inconsistent with the rest of the derivation. The text states that the step 'is only a preliminary estimation' and can be approximated with MINE or GIB, but no concrete procedure is given for how the candidate meso-scale sizes are compared or how MINE/GIB are used in practice. This circularity and lack of detail make the meso-scale selection step unverifiable as specified.","section":"Section 4.1, Step 1, Eq. (3)"},{"comment":"The SCIB objective in Eq. (7) is never instantiated. Step 3 describes Q only as 'assigning importance score to each node's impact on the training loss' and R as 'a Bernoulli distribution with parameter theta', without functional forms, parameterization, or how the expectation in Eq. (7) is estimated. Algorithm 1 says to train Gs and Gl 'using Eq. (10) and Eq. (7)' but does not specify the total loss (e.g., whether the two terms are summed, weighted, or optimized alternately), the optimization procedure, or how the gradient with respect to theta is computed. In addition, Eq. (10) contains an Ld term that is never defined; the surrounding text defines only Le and Lo. Without a precise, code-consistent specification of the actual loss, the claimed central mechanism cannot be evaluated, and the empirical gains could be attributed to the GDEM backbone or the meso-scale training schedule rather than to the information-bottleneck objective.","section":"Section 4.1, Step 3 and Algorithm 1"},{"comment":"The derivation of the lower bound for I(Gsub; nabla_theta) is not correct as written. Equation (13) writes the mutual information as E[log P(Gsub | nabla'_theta) / P(nabla'_theta)], which reverses the conditional direction of the true joint likelihood; the correct factorization uses P(nabla_theta | Gsub). Equation (14) then drops the -E[log P(nabla_theta)] term while claiming a lower bound, and the introduction of Q(nabla_theta | Gsub) in both numerator and denominator changes the quantity being bounded. As written, the claimed inequality I(Gsub; nabla_theta) >= E[log Q(nabla_theta | Gsub)] does not follow from the preceding line. Since this derivation is the theoretical basis for the SCIB objective, the bound must be corrected and stated precisely.","section":"Appendix A, Eqs. (13)-(14)"},{"comment":"The complexity analysis is not rigorous enough to support the claimed order-of-magnitude improvement. The text first gives O(2(KN'd + Kd^2 + KN'^2)), then immediately says the actual time complexity is O(KN'd + Kd^2 + KN'^2) because 'the first stage training already contains some of the optimization objectives for the second stage', but this reduction is not quantified. The comparison with re-condensation O(N'(KN'd + Kd^2 + KN'^2)) assumes that the meso-scale selection step (which involves MINE or GIB estimation) and the bi-directional phase have negligible or overlapping cost, which is not shown. The analysis also says 'the original image' where it should say 'the original graph'. Please provide a step-by-step cost accounting for meso-scale selection, meso-scale training, and the two bi-directional training branches.","section":"Section 4.3, Complexity Analysis"},{"comment":"The ablation for the information bottleneck is not defined. The caption of Figure 4 says results are shown 'with and without IB', but the text never states what 'without IB' means operationally: is Eq. (7) omitted entirely, is the compression term beta*E[f(...)] removed, or is a different objective substituted? The meso-scale sensitivity analysis also only considers pre-set candidates 0.2, 0.5, 0.8 and reports average accuracy; this does not directly test the claim that the IB-based adaptive selection identifies an optimal meso-scale. Please specify the exact configuration of the ablation and, if possible, compare against random or fixed meso-scale choices to isolate the effect of the selection criterion.","section":"Section 5.4, Ablation Study"}],"minor_comments":[{"comment":"The phrase 'when consenting to the primary sub-scale' appears to be a typo for 'when condensing to the primary sub-scale'.","section":"Abstract"},{"comment":"The sentence 'Following the approach of GMI (Peng et al. 2020)., we estimate...' has an extra period before the comma.","section":"Section 3.3"},{"comment":"The regularization loss in Eq. (9) is denoted Lo, but Eq. (10) uses Ld; please clarify whether Ld is a typo for Lo or an additional term.","section":"Section 4.2, Eq. (10)"},{"comment":"In the first sentence, 'the K largest eigenvalues of the original image' should read 'of the original graph'.","section":"Section 4.3"},{"comment":"The phrase 'under the guidance of Informational Bottleneck principles' should be 'Information Bottleneck principles' for consistency.","section":"Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The paper has a coherent empirical contribution and a plausible mechanism, but the current manuscript does not specify the actual training loss corresponding to the information-bottleneck objective. Before further review, the authors should provide a precise, code-consistent description of Eqs. (7) and (10), how they are combined, and the exact definition of the 'without IB' ablation. If the implementation deviates from the IB objective as written, the theoretical motivation in Section 4 needs to be revised accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things up front. The core idea is genuinely new: instead of going large-to-small or small-to-large, condense a middle-scale graph first and work outward in both directions. The experiments are broad and the gains are real, especially on Reddit. The second thing is less pleasant: the loss the method actually optimizes is never specified precisely enough to implement from the paper. That gap sits at the center of the contribution.\n\nWhat is new: the meso-scale-first bidirectional schedule and the use of an information bottleneck objective to select that scale. That is a real step beyond He et al. and Fang et al. The ablation gives some evidence the IB component helps, and the cross-architecture generalization tables are thorough and cleanly reported.\n\nNow the soft spots. Eq. (3) selects G'_m from Sub(G') when G' is the condensed graph being learned; at Step 1 no condensed graph exists. Either this is a typo for the original graph G or the derivation does not match the method. Eq. (7) is the heart of the method, but Q and R are described only as an 'importance score' and a 'Bernoulli distribution with parameter θ'; Algorithm 1 says to train with Eq. (10) and Eq. (7) but never gives the combined loss or the weighting. Eq. (10) itself uses an Ld term that is never defined. The appendix derivation of the IB bounds has genuine errors: Eq. (13) reverses the conditioning direction, and Eq. (14) drops a KL term while still writing '≥'. The complexity analysis is hand-wavy. There is a GitHub link, which helps, but the text should stand alone. None of these are fatal to the underlying idea, but they block reproduction.\n\nThe evaluation protocol — condense one largest graph, then sample subgraphs at test time — is standard for this subfield, so I would not call it a flaw. But it means the 'multi-scale' claim is really single-scale condensation plus subgraph sampling. And 'large margin' is true at small scales; at larger scales GEOM matches or beats BiMSGC on some settings (Cora 2.0%, Ogbn-Arxiv 0.5%).\n\nWho this is for: people working on graph condensation and dataset distillation. The paradigm deserves a serious referee. I would send it to review but ask for a precise, code-consistent specification of the actual loss before judging the central claim.","headline":"Genuinely new meso-scale-first paradigm for multi-scale graph condensation with strong empirical results, but the IB objective is so under-specified that the paper's central claim cannot be checked from the text alone.","tokens_in":27259,"tokens_out":3704,"would_cite":false,"duration_ms":35308,"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":"A middle-scale start beats shrink-then-grow graph condensation.","keywords":["multi-scale graph dataset condensation","graph neural networks","information bottleneck","mutual information","graph eigenbasis matching","node classification","dataset condensation","bi-directional condensation"],"falsifier":"Remove the information-bottleneck term from the loss while keeping the meso-scale and bidirectional training; if accuracy at small scales does not drop, the bottleneck term is not responsible for the reported gains. Alternatively, pick a random middle scale instead of the mutual-information-selected one and rerun the full pipeline; if all middle scales perform the same, the meso-scale selection procedure is not doing the claimed work.","tokens_in":26202,"feed_emoji":"🕸️","tokens_out":9257,"duration_ms":79153,"temperature":0.7,"pith_summary":"Graph dataset condensation produces a small synthetic graph that trains a model almost as well as the full graph; multi-scale condensation aims to produce such graphs at several sizes for devices with different memory. The paper claims that the usual shortcuts—condensing from a large graph down to smaller ones, or from a small graph up to larger ones—lose information, respectively as \"scaling down degradation\" and \"scaling up collapse.\" BiMSGC instead first condenses to an estimated \"meso-scale,\" the smallest graph that still holds the most useful information about the original, then condenses both downward and upward from that hub. The paper argues that this bidirectional route, guided by an information-bottleneck loss and eigenbasis matching, preserves mutual information across all target scales and beats both unidirectional paradigms in accuracy and speed.","feed_headline":"A middle-scale start beats shrink-then-grow graph condensation","feed_subtitle":"Pick the meso-scale first, then condense up and down; accuracy holds at every size for a fraction of the cost.","key_machinery":"The load-bearing object is the meso-scale subgraph $G'_m$, found by a subgraph information bottleneck objective that balances informativeness against compression. The second piece is the Subgraph Condensation Information Bottleneck (SCIB) loss, a variational bound that replaces the two mutual-information terms in the bottleneck with an expectation over an importance-scoring distribution $Q$ and a Bernoulli mask distribution $R$, and is used as the training signal for both the downward (meso-to-small) and upward (meso-to-large) stages. The third piece is eigenbasis matching: the Laplacian eigenbasis of the original graph is matched by the condensed graph's eigenbasis, with a low-frequency basis (first $M$ eigenvectors) for the meso and smaller scales and a wider basis (first $N'$ eigenvectors) for the large scale, so that structural information is carried through the scale changes.","core_discovery":"The central claim is that an optimal middle scale exists for any multi-scale graph condensation task, and that anchoring the whole condensation process there avoids the two failure modes of unidirectional scaling. Concretely, the paper proposes to choose the meso-scale graph $G'_m$ by maximizing $I(G'_{\\mathrm{sub}}; Y') - \\beta I(G'; G'_{\\mathrm{sub}})$ (the subgraph information bottleneck), then train it with eigenbasis matching to capture the low-frequency structure of the original graph. From that hub, smaller scales are obtained by pruning nodes from $G'_m$ and larger scales by expanding it, with every step trained under the Subgraph Condensation Information Bottleneck objective $\\mathcal{L}_{\\mathrm{SCIB}} = \\mathbb{E}[\\log Q(H(G,Y)|G'_{\\mathrm{sub}})] - \\beta \\mathbb{E}[f(G'_{\\mathrm{sub}},G')]$. The paper reports that on Cora, Citeseer, Ogbn-Arxiv, Flickr, and Reddit, BiMSGC improves node-classification accuracy at nearly every tested scale, keeps accuracy nearly lossless even at very small subgraph ratios, generalizes across five GNN architectures, and on Citeseer achieves a $20.85\\times$ speedup over re-condensation baselines.","pith_inferences":["The paper leaves the meso-scale estimator unspecified in practice (it suggests a neural mutual-information estimator or a graph information bottleneck but does not detail the training), so a natural test is whether a cheap surrogate—for instance, spectral energy of the Laplacian—locates the same meso-scale.","The claimed plug-and-play compatibility with any graph condensation method is not demonstrated; only eigenbasis matching is tested, so whether SCIB behaves as advertised with gradient-matching or trajectory-matching backbones is an open empirical question.","If the information-bottleneck regularizer is what drives the near-lossless small-scale results, then the same objective could be applied to single-scale condensation as a regularizer, not just to multi-scale pipelines."],"forward_implications":["Multi-scale condensation can be run in one pass from a single meso-scale graph instead of re-condensing at every target scale, reducing the time complexity by roughly a factor of the number of scales.","Very small condensed graphs, useful for low-memory edge devices, should no longer show the sharp accuracy drop that appears when they are sampled from a large condensed graph.","The condensed graphs should transfer across GNN architectures with low variance, because the eigenbasis matching preserves low-frequency structural information rather than overfitting one model class.","The information-bottleneck term can act as a denoiser: on some datasets the condensed graphs match or exceed whole-dataset accuracy, suggesting that removing redundant information helps generalization."],"supporting_citations":[{"why":"Introduces multi-size dataset condensation and the large-to-small degradation problem that motivates the paper's meso-scale idea.","marker":"(He et al. 2024)"},{"why":"Named alongside He et al. as the source of the three multi-scale condensation paradigms (re-condensation, large-to-small, small-to-large) that BiMSGC unifies.","marker":"(Fang et al. 2024)"},{"why":"Provides the mutual-information estimator used to diagnose scaling down degradation and scaling up collapse in the empirical analysis.","marker":"(Peng et al. 2020)"},{"why":"Supplies the neural mutual-information estimator suggested for approximating the meso-scale selection objective.","marker":"(Belghazi et al. 2018)"},{"why":"Defines the graph information bottleneck that the subgraph condensation information bottleneck extends to the condensation setting.","marker":"(Wu et al. 2020)"},{"why":"Provides the variational information-bottleneck derivation used to obtain the SCIB upper and lower bounds.","marker":"(Abdelaleem, Nemenman, and Martini 2023)"},{"why":"The eigenbasis matching condensation method that BiMSGC adopts as its concrete implementation backbone.","marker":"(Liu, Bo, and Shi 2024)"}],"fun_headline_variants":["Optimal middle graph anchors robust graph condensation","Meso-scale first: bi-directional graph condensation","Start at the meso-scale for stable graph condensation","Meso-scale hub avoids one-way condensation pitfalls"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the implemented training loop actually optimizes the Subgraph Condensation Information Bottleneck objective; the paper describes the importance scores and Bernoulli mask only in words, without giving their concrete functional forms, the loss weight, or the training procedure that connects equation (7) to Algorithm 1.","fun_headline_variants_meta":{"raw":{"variants":["Optimal middle graph anchors robust graph condensation","Meso-scale first: bi-directional graph condensation","Start at the meso-scale for stable graph condensation","Meso-scale hub avoids one-way condensation pitfalls"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000905,"raw_usage":{"total_tokens":3959,"prompt_tokens":1075,"completion_tokens":2884,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":2824}},"tokens_in":691,"tokens_out":2884,"duration_ms":22133,"temperature":1.0,"reasoning_tokens":2824,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:33:08.078599+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Remove the information-bottleneck term from the loss while keeping the meso-scale and bidirectional training; if accuracy at small scales does not drop, the bottleneck term is not responsible for the reported gains. Alternatively, pick a random middle scale instead of the mutual-information-selected one and rerun the full pipeline; if all middle scales perform the same, the meso-scale selection procedure is not doing the claimed work.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Named alongside He et al. as the source of the three multi-scale condensation paradigms (re-condensation, large-to-small, small-to-large) that BiMSGC unifies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the mutual-information estimator used to diagnose scaling down degradation and scaling up collapse in the empirical analysis."},{"cited_title":"I.; Baratin, A.; Rajeshwar, S.; Ozair, S.; Bengio, Y.; Courville, A.; and Hjelm, D","cited_arxiv_id":null,"evidence_quote":"Supplies the neural mutual-information estimator suggested for approximating the meso-scale selection objective."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The eigenbasis matching condensation method that BiMSGC adopts as its concrete implementation backbone."}],"review_version":1}