{"id":"ac54995e-fc53-4460-b6c6-9229be95ab54","arxiv_id":"2504.20421","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In dynamic node classification, GCN discriminative power is characterized by the probability that a node's future label matches its neighbors' current labels, which the authors formalize as dynamic homophily.","lead":"The authors show that on dynamic graphs, a graph neural network's ability to predict future node labels depends on whether a node's future label matches its neighbors' current labels, and they define a new measure, dynamic homophily, that captures this. The measure tracks GNN accuracy across time on real and synthetic graphs better than the standard static homophily measure.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3.2 is false for l >= 2: the induction conflates current-label and future-label conditioning and ignores degree/neighbor heterogeneity; a 4-node path counterexample violates the claimed equality.","rationale":"After checking the central claim, I find a decisive counterexample to Theorem 3.2 for l = 2, and the same flaw propagates to all l >= 2. The proof in Appendix B.2 has two intertwined errors. First, the induction step (Appendix Eqs. 29-30) expresses the l+1-layer separation of future-label classes in terms of the l-layer separation of current-label classes, E_{V_t^+} h^{(l)} - E_{V_t^-} h^{(l)}, but then applies the inductive hypothesis (which concerns V_{t+1}) to that current-label quantity. These two separations differ unless static and dynamic homophily coincide. Second, the proof replaces each node's neighbor-weighted average by a mixture with a single global h+, ignoring that the expectation of h^{(l)}(j) over neighbors conditional on y_t(j) is degree-weighted and can be correlated with local structure. The 4-node path example makes the failure concrete and exact. The theorem's assumptions are satisfied (binary labels, Gaussian features; sigma can be taken arbitrarily small), and the computed separation disagrees with the claimed formula in both magnitude and sign. This is not a subtle edge case: Eq. 5 is the paper's central equation. I credit the paper for a plausible l = 1 statement with node-averaged h and for useful empirical correlations between the proposed measure and GNN performance. Those empirical results may still stand. However, the advertised theoretical characterization of GCN separation across layers, the oversmoothing-rate interpretation, and the layer-dependent design insights all rest on the false induction. The variance lower-bound issue in Theorem 3.4 (Appendix B.4) flagged by the reader is also real, but secondary: if the numerator is wrong, the AUROC bound is unreliable regardless of the variance terms. Because the central theorem is demonstrably false, I recommend REJECT, or at least a major revision restricting all theoretical claims to l = 1 and providing a corrected proof for deeper layers if one exists. I did not find manuscript text acknowledging this limitation; the closest self-criticism (Section 5.2) concerns correlation weakness for SAGE on Math, not the correctness of Theorem 3.2.","tokens_in":32676,"tokens_out":19033,"duration_ms":178780,"concrete_test":"Run the deterministic 4-node path with self-loops, y0 = [+, +, -, -], y1 = [-, -, +, +], x_t(i) = y_t(i), mu = 1, sigma = 0 (or arbitrarily small). Compute h+ and h- as node-averaged local agreement per Appendix D.4: h+ = (1/3 + 0)/2 = 1/6, h- = (0 + 1/3)/2 = 1/6. Theorem 3.2 for l = 2 predicts E_{V^+_1} h^{(2)} - E_{V^-_1} h^{(2)} = 2 * (1/6 + 1/6 - 1)^2 = 8/9. Apply two GCN layers with self-loop mean aggregation: h^{(1)} = [1, 1/3, -1/3, -1], h^{(2)} = [2/3, 1/3, -1/3, -2/3]; the future-positive mean (nodes 3,4) is -1/2 and the future-negative mean (nodes 1,2) is +1/2, giving an actual separation of -1. The claimed equality fails. Additionally, independently re-derive the induction step in Appendix Eq. (30) without assuming E_{V_t^+} h^{(l)} - E_{V_t^-} h^{(l)} = 2 mu (h+ + h- - 1)^l; the counterexample shows this assumption is false.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim is Theorem 3.2, an exact equality for the l-layer separation of future positive and negative nodes. The proof in Appendix B.2 is invalid for l >= 2. In the induction step (Eqs. 29-30), the authors partition each future-positive node's neighbors by the neighbor's current label and then replace E_{j in V_t^+} h^{(l)}_t(j) and E_{j in V_t^-} h^{(l)}_t(j) with the inductive hypothesis, which concerns expectations over future labels V_{t+1}. These quantities are not equal in general: the l-layer separation of current-label classes is governed by static homophily, not by dynamic homophily. The proof also uses a single global h+ for every node, ignoring that local neighbor composition and degree normalization affect the expectation of the aggregated representation. A concrete deterministic counterexample refutes the theorem. On a 4-node path with self-loops, set y0 = [+, +, -, -], y1 = [-, -, +, +], and x_t(i) = y_t(i) (mu = 1, sigma -> 0). With the node-averaged definition used in Appendix D.4, h+ = (1/3 + 0)/2 = 1/6 and h- = (0 + 1/3)/2 = 1/6, so h+ + h- - 1 = -2/3. Theorem 3.2 for l = 2 predicts a separation of 2 * (-2/3)^2 = 8/9. Direct computation gives h^{(1)} = [1, 1/3, -1/3, -1] and h^{(2)} = [2/3, 1/3, -1/3, -2/3]. The future-positive mean (nodes 3,4) is -1/2, the future-negative mean (nodes 1,2) is +1/2, so the true separation is -1, not +8/9. The equality fails in both magnitude and sign. Since Theorem 3.2 is the foundation for the proposed dynamic homophily measure and for the AUROC bound in Theorem 3.4, the central theoretical contribution does not hold as stated.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies GNN performance in dynamic node classification and proposes dynamic homophily, defined as the probability that a node's future label equals its neighbor's current label. It derives theoretical claims for linear GCNs: Theorem 3.2 states that after l layers the expected representation difference between future positive and negative nodes equals 2*mu_t*(h_t^+ + h_t^- - 1)^l; Theorem 3.3 gives a concentration bound for this difference; and Theorem 3.4 bounds expected AUROC via recursively defined variance lower bounds. It also defines multiclass and continuous-time extensions. Empirically, it compares dynamic homophily with static homophily as correlates of AUROC for seven GNN architectures on SI-model synthetic graphs, Higgs Twitter networks, and DPPIN protein interaction networks, reporting that dynamic homophily has substantially higher Spearman correlations with GNN AUROC than static homophily.","tokens_in":2388,"tokens_out":5894,"duration_ms":135425,"significance":"If the theoretical results were correct, the paper would provide a clean first characterization of GNN discriminative power in dynamic graphs and a practically useful metric. The empirical study is extensive and the core observation that static homophily can stay high while GNN performance collapses, whereas dynamic homophily tracks performance, is interesting and potentially valuable. However, the central theoretical claim, Theorem 3.2, is false for l >= 2, and the variance argument behind Theorem 3.4 is not a valid lower bound. Because the paper's main message is theory-driven, the empirical correlations do not repair the theoretical foundation. The dynamic homophily measure itself and the empirical findings may be salvageable as a standalone descriptive contribution, but the paper as submitted does not establish its central claims.","major_comments":[{"comment":"The induction step in the proof of Theorem 3.2 is invalid for l >= 2. In Eqs. (29)-(30), the proof writes the expected future-positive representation at layer l+1 in terms of expectations over current-labeled classes V_t^+ and V_t^-, and then applies the inductive hypothesis to E_{i in V_t^+}[h_t^(l)(i)] - E_{i in V_t^-}[h_t^(l)(i)]. But the inductive hypothesis is a statement about expectations over future-labeled nodes V_{t+1}^+ and V_{t+1}^-; the two quantities are not equal in general, since the l-layer separation of current-label classes is governed by static homophily rather than by the dynamic quantities h_t^+ and h_t^-. The proof also uses a single global factor h_t^+ for every node, although the expectation of a degree-normalized neighborhood average depends on the local neighbor composition and on the degree of each center. The theorem is false for l = 2. Consider the 4-node path with self-loops, y_0 = [+, +, -, -], y_1 = [-, -, +, +], x_t(i) = y_t(i), mu = 1, sigma -> 0. Using the node-averaged definition in Appendix D.4, h_t^+ = h_t^- = 1/6, so (h_t^+ + h_t^- - 1)^2 = 4/9 and Theorem 3.2 predicts a separation of 8/9. Direct computation gives h_t^(1) = [1, 1/3, -1/3, -1] and h_t^(2) = [2/3, 1/3, -1/3, -2/3]; the mean of the future-positive nodes {3,4} is -1/2 and the mean of the future-negative nodes {1,2} is +1/2, so the true separation is -1, not +8/9. The equality fails in both sign and magnitude, so the central theoretical claim is not established.","section":"Section 3.2, Theorem 3.2 and Appendix B.2"},{"comment":"The variance lower bounds in Eq. (12) are not valid for GCN mean aggregation. The proof treats each node's aggregated representation as a two-term weighted sum h_t^+ Z_+ + (1 - h_t^+) Z_- rather than as an average over the actual neighborhood. For a node with d neighbors and a same-class neighbor count S ~ Bin(d, h), the variance of the aggregation (1/d) sum_{j=1}^d Z_j is sigma^2/d + 4 mu^2 h(1-h)/d, which can be much smaller than h^2 sigma^2 + (1-h)^2 sigma^2 when d is large. Thus the recursively defined quantities v_{t+1}^+(l) and v_{t+1}^-(l) are not lower bounds on the true variances; in common high-degree settings they are larger than the true variance. Consequently the claimed upper bound on expected AUROC in Eq. (11) has the wrong direction and is not guaranteed. Since Theorem 3.4 underlies the layer-wise AUROC predictions in Figure 2 and the design recommendations, this is a load-bearing gap, not a minor technicality.","section":"Section 3.2, Theorem 3.4 and Appendix B.4"},{"comment":"The AUROC characterization in Eq. (4) is not correct as written. The denominator should be the standard deviation of the difference h_t^(l)(i) - h_t^(l)(j) for a random positive-negative pair, but the displayed formula uses V_{i,j}[h_t^(l)(i) + h_t^(l)(j)] and omits the covariance between the two representations. The two nodes in a random positive-negative pair have correlated representations because they share neighbors after multiple GCN layers, and the expression also assumes that the difference is Gaussian with a single variance. No independence or homoscedasticity assumption is stated in the lemma. Theorem 3.4 substitutes its variance recursion into this formula, so the error propagates to the main AUROC bound.","section":"Section 3.1, Lemma 3.1, Eq. (4)"},{"comment":"The concentration bound in Theorem 3.3 is not proven for general graphs. In Eq. (41), the proof claims that x_t(i) appears in the positive-class mean 'precisely d_t(i)*l times' and uses this to derive the Lipschitz norm L_{t,+}^(l) in Eq. (9). This count is not correct for arbitrary graph topologies: the coefficient of x_t(i) in h_t^(l)(j) is a sum over length-l walks from j to i of products of inverse degrees, and it cannot be reduced to a fixed factor d_t(i)^l independent of the walk structure. The explicit bounds in Eqs. (9)-(10) are therefore unsupported. The concentration statement may be repairable by a more careful Lipschitz analysis, but as submitted the proof does not establish the theorem as stated.","section":"Section 3.2, Theorem 3.3 and Appendix B.3"}],"minor_comments":[{"comment":"The expectation subscripts in Eqs. (27) and (28) are garbled: both lines use E_{j|V_t^+}[x_t(j)] where the negative-case derivation requires one term over V_t^- and one over V_t^+, and the sign algebra leading to (2h_t^+ - 1)*mu is written incorrectly (the second term should be -(1-h_t^+)*mu rather than +(h_t^+ - 1)*mu).","section":"Appendix B.2, Eqs. (27)-(28)"},{"comment":"Dynamic homophily is computed in the experiments as a node-averaged quantity, while Theorem 3.2 defines h_t^+ and h_t^- as probabilities over neighbor draws. These two notions agree only when every future node is weighted equally and neighbors are sampled uniformly; the paper should state this equivalence explicitly and confirm that the implementation matches Definition 3.5.","section":"Appendix D.4, Eq. (83)"},{"comment":"The propagation rule in Eq. (2) uses the degree d(i)+1 after adding a self-loop, but the proof recursions in Eqs. (24), (39), and (41) switch between d_t(i)+1 and d_t(i)^l without explanation, and the notation hat{N}_t(i)^l is never defined.","section":"Appendix B.2-B.3"},{"comment":"The checklist states 'No' for code, data, and instructions needed to reproduce the main experimental results, although the footnote in Section 4.3 provides a GitHub URL. This discrepancy should be resolved.","section":"Checklist item 3(a)"},{"comment":"The caption and text should make clear that Figure 2 visualizes the upper bound from Eq. (11) rather than measured AUROC, especially because the bound itself is based on the variance recursion whose validity is questioned above.","section":"Figure 2 and surrounding text"}],"recommendation":"reject","confidential_remarks":"The empirical finding that dynamic homophily correlates more strongly than static homophily with GNN AUROC is interesting and might support a more modest descriptive paper. However, the theoretical centerpiece is false: Theorem 3.2 fails already at l = 2 on a simple deterministic graph, and the variance bounds in Theorem 3.4 are not lower bounds under degree-normalized mean aggregation. These are not local fixable issues within the current scope because the proposed measure is explicitly derived from the erroneous separation formula. I would advise the editor that the paper should be rejected in its current form, while noting that the dataset construction and empirical protocol could be reused in a revised submission that does not claim the multilayer theoretical characterization."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper has a good empirical instinct—cross-time label agreement, not same-time agreement, tracks GNN performance on temporal node classification. The l=1 separation result is clean, and the proposed measure is a natural dynamic analog of static homophily. But Theorem 3.2 as stated is false for l>=2. The induction in Appendix B.2 replaces expectations over current-label classes with the inductive hypothesis about future-label classes; those are different quantities. The 4-node path counterexample checks out: y0=[+,+,-,-], y1=[-,-,+,+], mu=1, l=2 gives true separation -1 while the formula predicts +8/9 (using their node-averaged h). So the polynomial-in-dynamic-homophily separation story does not survive past one layer.\n\nThe empirical work is the stronger part. Across pseudo-synthetic SI-type graphs and real dynamic graphs, dynamic homophily correlates with AUROC notably better than static homophily for most GNN/dataset combinations. That is a useful finding even without the multi-layer theorem, because many deployed GNNs use 2-3 layers. The paper is also honest about when the correlation fails (SAGE on Math). What I would not take away is the layer-combination design recommendation: it rests on Figure 2 and Theorem 3.4, which inherit the false theorem and also have a variance derivation that drops degree normalization and assumes a two-draw mixture; that direction is doubtful.\n\nOne more small thing: the checklist says no for code release, but footnote 1 gives a GitHub URL. The empirical results are not fully reproducible as submitted, which matters because the theory is shaky.\n\nWho should read this: people designing dynamic GNNs and working on heterophily. The dynamic homophily definition and the correlation evidence are worth engaging with; the theory needs a rewrite, probably restricting to l=1 or deriving the correct multi-layer recursion with static and dynamic homophily both in play.\n\nRecommendation: send to review, but expect major revision. The central claim is false as stated, so acceptance would be premature. A referee could salvage a useful empirical paper.","headline":"The dynamic homophily idea is worth engaging with, but the central theorem only holds for one layer; the multi-layer generalization is invalid, and that breaks the theoretical story.","tokens_in":33648,"tokens_out":4624,"would_cite":false,"duration_ms":45254,"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":"In dynamic graphs, GCN accuracy is governed by future-label agreement with current neighbors, not static homophily.","keywords":["graph neural networks","homophily","dynamic graphs","node classification","GCN","temporal graphs","AUROC","message passing"],"falsifier":"On a dynamic stochastic block model with controlled $h^+_t$ and $h^-_t$ and large node degrees, compute the empirical AUROC and true variance of a one-layer GCN; the central claim fails if AUROC does not move monotonically with $h^+_t + h^-_t - 1$, or if the true variance is smaller than the recursive lower bound $v^+_{t+1}(1)+v^-_{t+1}(1)$ used in Theorem 3.4.","tokens_in":32465,"feed_emoji":"📈","tokens_out":13456,"duration_ms":118931,"temperature":0.7,"pith_summary":"Dynamic node classification asks a GNN to predict next-step labels from the current graph. The paper's central claim is that a GCN's discriminative power at time $t$ is governed by the probability that a node's future label matches its neighbors' current labels, encoded as class-wise probabilities $h^+_t$ and $h^-_t$. Formally, the expected representation gap between future positive and negative nodes after $l$ GCN layers is $2\\mu_t(h^+_t + h^-_t - 1)^l$, and the expected AUROC is bounded above by a function of the same probabilities. The paper names this quantity dynamic homophily and shows empirically that it tracks GNN AUROC across epidemiological, social, and protein-interaction graphs, while static homophily stays high and does not track performance. If the claim is right, static homophily is the wrong diagnostic for evolving graphs, and low dynamic homophily, not low static homophily, is what breaks GNNs.","feed_headline":"One probability governs GCN accuracy on evolving graphs","feed_subtitle":"Future-label agreement with current neighbors predicts GNN performance; static homophily does not.","key_machinery":"The machinery is the single-layer mean-aggregation calculation that partitions a node's neighbors by whether their current label equals the node's future label. For one GCN layer, a future positive node's expected representation becomes $(2h^+_t - 1)\\mu_t$ and a future negative node's becomes $(1 - 2h^-_t)\\mu_t$, so the class gap is $2\\mu_t(h^+_t + h^-_t - 1)$; induction over layers raises the factor to the $l$-th power, yielding Theorem 3.2. The same partition trick feeds Theorem 3.4, which bounds expected AUROC by $1 - \\Phi\\left(-2\\mu_t(h^+_t+h^-_t-1)^l / (v^+_{t+1}(l)+v^-_{t+1}(l))\\right)$ with recursive variance lower bounds $v^+_{t+1}(l)=h^{+2}_t v^+_{t+1}(l-1)+(1-h^+_t)^2 v^-_{t+1}(l-1)$ and symmetrically for $v^-$. Gaussian Lipschitz concentration (Theorem 3.3) then guarantees the empirical class gap tracks the expected gap with high probability when class sizes are large. The named object that carries the argument is dynamic homophily, $h^D_t = \\frac{1}{|C|}\\sum_{c\\in C} h^c_t$, the average probability that a node's label at $t+1$ equals its neighbor's label at $t$.","core_discovery":"The discovery is stated exactly in Theorem 3.2: after $l$ layers of a GCN with mean aggregation, the expected representation gap between nodes that will be positive at $t+1$ and nodes that will be negative at $t+1$ is $2\\mu_t(h^+_t + h^-_t - 1)^l$, where $h^+_t$ and $h^-_t$ are the probabilities that a future positive (resp. negative) node's label at $t+1$ equals its neighbor's label at $t$. This quantity interpolates between high dynamic homophily, where the gap grows with depth, and low dynamic homophily, where the gap shrinks or changes sign. Theorem 3.4 converts the gap into an upper bound on expected AUROC using recursively defined variance lower bounds that depend only on the same probabilities, which predicts that odd-layer GCNs improve monotonically in dynamic homophily while even layers can recover when both homophily levels are low. The empirical counterpart is that dynamic homophily achieves median Spearman correlations around 0.75 with homophilous GNN AUROC and 0.78 with heterophilous GNN AUROC across the tested dynamic graphs, while static homophily's medians are 0.26 and 0.38, respectively.","pith_inferences":["Beyond the paper, one can test whether the same separation formula holds for other mean-aggregation message-passing architectures by replacing the linear-GCN induction with their propagation rules; the paper only analyzes linear GCNs, so this is an extension.","The variance bound in Theorem 3.4 ignores the actual count of neighbors and degree normalization by modeling each aggregate as two Gaussian draws; a tighter analysis would keep the full neighbor sum in the variance recursion.","Dynamic homophily could serve as a dataset-level diagnostic for temporal graph benchmarks: graphs with high static homophily but low dynamic homophily should be exactly where standard GNNs underperform, which can be checked on existing temporal benchmark suites.","In multiclass settings, the appendix's dynamic compatibility matrix, rather than the scalar average, is the natural correlate of per-class AUROC; testing whether row distances of that matrix predict class-wise performance would extend the binary result."],"forward_implications":["If Theorem 3.2 is correct, oversmoothing in dynamic GCNs is not a fixed depth effect: the class gap shrinks by the factor $h^+_t + h^-_t - 1$ per layer, so low dynamic homophily accelerates the loss of discriminative signal with depth.","Even-layer GCNs become a partial remedy in low dynamic homophily regimes: when both class probabilities are below 0.5, the squared factor makes the expected gap positive again, so depth can restore some separability.","Dynamic homophily, not static homophily, is the quantity to measure in next-step node classification; the experiments show static homophily remains high while dynamic homophily and AUROC move together across time.","Heterophilous GNN designs (ego-neighbor separation, residual connections) improve absolute performance under low dynamic homophily but still degrade as dynamic homophily falls, so the limitation is not specific to plain GCNs.","Combining intermediate GCN layer representations is a concrete design direction for dynamic GNNs that must perform well across changing dynamic homophily levels."],"supporting_citations":[{"why":"Defines static homophily and identifies GNN limitations on heterophilous graphs, the baseline that dynamic homophily extends.","marker":"Zhu et al., 2020"},{"why":"Introduces the GCN with mean aggregation whose representations Theorem 3.2 and Theorem 3.4 analyze.","marker":"Kipf and Welling, 2017"},{"why":"Justifies the linear GCN analysis and provides the SGC model used as a homophilous baseline.","marker":"Wu et al., 2019"},{"why":"Establishes GCN oversmoothing in deep layers, which Theorem 3.2 refines through dynamic homophily, and supplies GCNII as a heterophilous baseline.","marker":"Li et al., 2018"},{"why":"Gives the Gaussian concentration inequality used to prove Theorem 3.3's bound on empirical class-gap distance.","marker":"Wainwright, 2019"},{"why":"Provides the Lipschitz-gradient norm bound used to compute the concentration rate for GCN layer outputs.","marker":"Vershynin, 2018"},{"why":"Supplies the AUROC concentration bound in Theorem 3.4 that ties empirical to expected AUROC.","marker":"Agarwal et al., 2005"},{"why":"Constructs the Higgs dynamic social network datasets used to evaluate dynamic homophily's correlation with GNN AUROC.","marker":"De Domenico et al., 2013"},{"why":"Provides the DPPIN dynamic protein-protein interaction datasets used in the real-world evaluation.","marker":"Fu and He, 2022"}],"fun_headline_variants":["Dynamic homophily predicts GNN performance, static doesn't","New homophily measure explains GCNs on evolving graphs","GCN accuracy on dynamic graphs: one probability rules","Future labels, not current, determine GCN success","Redefining homophily for time-varying networks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on replacing each node's neighbor aggregation with a weighted mixture of two Gaussian draws, one per class, weighted by $h^+_t$ and $1-h^+_t$ (and symmetrically for negatives), ignoring how many neighbors the node actually averages over and how degree normalization changes the sum.","fun_headline_variants_meta":{"raw":{"variants":["Dynamic homophily predicts GNN performance, static doesn't","New homophily measure explains GCNs on evolving graphs","GCN accuracy on dynamic graphs: one probability rules","Future labels, not current, determine GCN success","Redefining homophily for time-varying networks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000487,"raw_usage":{"total_tokens":2421,"prompt_tokens":985,"completion_tokens":1436,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":1356}},"tokens_in":601,"tokens_out":1436,"duration_ms":10813,"temperature":1.0,"reasoning_tokens":1356,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:30:19.003891+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a dynamic stochastic block model with controlled $h^+_t$ and $h^-_t$ and large node degrees, compute the empirical AUROC and true variance of a one-layer GCN; the central claim fails if AUROC does not move monotonically with $h^+_t + h^-_t - 1$, or if the true variance is smaller than the recursive lower bound $v^+_{t+1}(1)+v^-_{t+1}(1)$ used in Theorem 3.4.","supporting_citations":[{"cited_title":"Beyond homophily in graph neural networks: Current limitations and effective designs","cited_arxiv_id":null,"evidence_quote":"Defines static homophily and identifies GNN limitations on heterophilous graphs, the baseline that dynamic homophily extends."},{"cited_title":"Generalization bounds for the area under the roc curve","cited_arxiv_id":null,"evidence_quote":"Supplies the AUROC concentration bound in Theorem 3.4 that ties empirical to expected AUROC."},{"cited_title":"The anatomy of a scientific rumor","cited_arxiv_id":null,"evidence_quote":"Constructs the Higgs dynamic social network datasets used to evaluate dynamic homophily's correlation with GNN AUROC."}],"review_version":1}