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REVIEW 3 major objections 6 minor 106 references

Effects of Dropout on Performance in Long-range Graph Learning Tasks

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Random edge-dropping methods make deep graph networks less sensitive to distant nodes and hurt their performance on long-range tasks; the paper introduces DropSens to restore that sensitivity.

desk verdict Solid theory on DropEdge-variants shrinking L-hop sensitivity, but the paper overclaims the causal story—DropNode is the tell. read the letter →

arxiv 2502.07364 v2 pith:W4U3BKXE submitted 2025-02-11 cs.LG

Jasraj Singh , Keyue Jiang , Brooks Paige , Laura Toni This is my paper · ORCID
classification cs.LG
keywords graphneuralnetworksover-squashingDropEdgelong-rangelearningsensitivityanalysisdropoutrewiringmessagepassing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Deep graph networks that pass messages locally suffer from over-squashing: information from far-away nodes gets crushed before it can influence a node's representation. This paper argues that the popular random-dropping techniques used to make deep networks trainable, such as DropEdge, DropAgg, DropGNN, and dropout-style variants, make over-squashing worse because on average they weaken every edge that carries information across long distances. In a linear graph convolutional network the paper proves this precisely: with asymmetric normalization, any of these methods lowers the expected sensitivity of a node to features of nodes $L$ hops away, and the sensitivity falls further as the dropping probability rises. The same conclusion is extended to nonlinear networks through existing sensitivity bounds and Monte Carlo influence estimates, and confirmed on synthetic and real-world long-range benchmarks, where the best dropout configurations usually underperform the no-drop baseline. To fix the problem the paper introduces DropSens, which chooses per-edge dropping probabilities so that the fraction of information preserved along each incoming edge stays fixed; on GCNs, DropSens beats graph-rewiring methods designed to reduce over-squashing on node-classification tasks.

What carries the argument

The engine of the argument is the expected propagation matrix $\dot P := \mathbb{E}[\hat A]$ under the random edge masks, together with the identity that expected sensitivity in a linear GCN equals $\bigl(\mathbb{E}[\hat A]^L\bigr)_{ij}\lVert W\rVert_1$. Because masks are independent across layers, expectation passes through the product, so the $L$-step transition probability of this random walk controls how much node $i$'s output depends on node $j$'s input. For DropEdge, Lemma 3.1 gives $\dot P_{ii} = (1-q^{d_i+1})/((1-q)(d_i+1))$ and $\dot P_{ij} = (1-\dot P_{ii})/d_i$, with analogous entries for DropAgg and DropGNN that have even larger self-loop weights. The proof of Theorem 3.1 exploits that a path from $j$ to $i$ with $d_G(j,i)=L$ contains no self-loop, so every factor on the path is strictly smaller than in the no-drop case. DropSens inverts this by fixing the fraction $c$ of information preserved over a cross-edge through $1-c = (q_i - q_i^{d_i+1})/(d_i(1-q_i))$, producing per-target-degree dropping probabilities that keep distant edges stronger.

What would settle it

On the SyntheticZINC benchmark at a high commute-time percentile, train 11-layer GCNs with DropEdge at $q=0.2$ and $q=0.5$, and compute the mean expected sensitivity $\bigl(\mathbb{E}[\hat A]^L\bigr)_{ij}$ for the selected distant pairs together with test MAE; the paper's claim implies sensitivity falls and MAE rises as $q$ increases, so observing higher sensitivity with better MAE, or lower sensitivity with worse MAE, would show that expected sensitivity is not the controlling factor.

Watch

Extended reading notes

Core claim

The central discovery is stated as Theorem 3.1: in an $L$-layer linear GCN with $\hat A = \hat A_{\mathrm{asym}}$, using DropEdge, DropAgg, or DropGNN decreases the sensitivity of a node $i$ to a node $j$ in $S^{(L)}(i)$, thereby reducing the effective receptive field, and the sensitivity decreases monotonically as the dropping probability increases. The reason is that the expected propagation matrix $\mathbb{E}[\hat A]$ under these masks behaves like a non-uniform random walk: its self-loop entries become larger and its cross-edge entries become smaller than in a no-drop model. Every path connecting nodes exactly $L$ hops apart contains no self-loops, so each factor in the expansion of $(\mathbb{E}[\hat A]^L)_{ij}$ shrinks, and with it the expected Jacobian norm that measures over-squashing. The paper derives exact expected matrix entries for DropEdge (Lemma 3.1), gives analogous entries for DropAgg and DropGNN, extends existing nonlinear MPNN sensitivity upper bounds to random masks, and empirically verifies exponential decay of expected sensitivity with distance on the Cora graph. On long-range benchmarks, the best-performing dropout configurations typically fail to beat NoDrop, while DropSens—which keeps a fixed information fraction $c$ on each incoming edge—raises distant sensitivity and outperforms rewiring baselines on GCN node classification while remaining competitive on graph classification.

Load-bearing premise

The load-bearing premise is that the expected sensitivity of random-mask message passing, computed while ignoring the optimization trajectory, is what determines whether a dropout-trained GNN will generalize well on a long-range task; if training dynamics override this signal, the predicted connection to test accuracy weakens.

Editorial extensions

If this is right

  • On homophilic, short-range datasets, dropout-style methods improve test accuracy in the majority of configurations, but on heterophilic, long-range datasets they usually underperform the no-drop baseline; evaluations that only use short-range tasks therefore overstate the general usefulness of these methods.
  • Increasing the dropping probability monotonically reduces expected sensitivity between nodes $L$ hops apart, so the same knob that relieves over-smoothing also worsens over-squashing.
  • DropSens, which holds the per-edge information fraction fixed, improves distant sensitivity and outperforms graph-rewiring baselines on GCN node-classification tasks while using the same number of dropped edges and fewer propagated messages.
  • Graph-level long-range tasks are less affected by dropping methods, since the readout mixes information from distant nodes; this suggests over-squashing has limited impact on graph-level performance.
  • The theoretical guarantees cover degree-normalized GCN-like message passing; GAT, ResGCN, and graph transformers fall outside the analysis, and DropSens itself does not transfer to GIN's message-passing scheme.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • We infer that the expected-sensitivity diagnostic could be computed before training on any fixed graph, providing a cheap way to predict whether a given dropout probability is safe for a long-range task without running the training loop.
  • We infer that the per-edge information-preservation principle behind DropSens could be applied to feature dropout or attention dropout by using the actual induced edge weights under the mask; the paper does not test this extension.
  • We infer that benchmark suites for methods intended to train deep GNNs should routinely include heterophilic and synthetic commute-time tasks, because homophilic-only evaluations cannot separate local fitting from long-range capacity.
  • We infer that architectures with global propagation, such as graph transformers, may need no DropSens-like correction, whereas attention-based local message passing could benefit from a sensitivity-aware masking analog.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper studies the effect of random-dropping methods (DropEdge, DropNode, DropAgg, DropGNN, Dropout, DropMessage) on long-range graph learning. In a linear GCN with asymmetric normalization, the authors compute the expected propagation matrix under each edge-dropping variant (Lemma 3.1 and Appendix B.1) and prove Theorem 3.1 that DropEdge, DropAgg, and DropGNN reduce expected sensitivity between nodes at distance exactly L, with sensitivity decreasing in the dropping probability. They also extend nonlinear sensitivity bounds to the random-dropping setting (Appendix C.1). Based on this analysis, they propose DropSens, which sets per-node dropping probabilities to preserve a target fraction c of information across edges. Experiments on SyntheticZINC, homophilic/heterophilic node classification, and graph classification show that dropping methods generally improve homophilic and harm heterophilic performance, and DropSens improves over DropEdge on heterophilic tasks and is competitive with graph-rewiring baselines on several datasets.

Significance. The paper addresses a real gap: dropout-style methods for deep GNNs have mostly been evaluated on short-range tasks, and their effect on over-squashing is underexplored. The theoretical analysis is clean and, within its stated scope (linear GCN, asymmetric normalization, exact L-hop pairs), the Lemma and Theorem appear correct. The paper also provides reproducible experiments and a practical algorithm, DropSens, with implementations in the appendix. However, the central causal claim, that the proved sensitivity decay explains observed long-range performance degradation, is undermined by the paper's own DropNode results and by the explicit decision to ignore optimization effects, which the experiments show are necessary to explain DropNode's behavior. The manuscript is valuable but requires substantial revision to align its claims with what is actually proven.

major comments (3)
  1. [Section 3, Eq. (B.15), Table 1a, Appendix F.2] The abstract and conclusion state that 'DropEdge-variants reduce sensitivity between distant nodes, limiting their suitability for long-range tasks,' and that these variants 'exacerbate the over-squashing problem.' However, Eq. (B.15) shows that DropNode's expected propagation matrix is exactly the NoDrop matrix, so Theorem 3.1 does not predict any sensitivity loss for DropNode. Table 1a nevertheless shows DropNode consistently degrading heterophilic accuracy (e.g., GCN on Chameleon -0.674, on Squirrel -0.656; GAT on Chameleon -6.090), and Appendix F.2 explicitly attributes this degradation to 'the effects on the learning trajectory,' an effect the theory brackets in Section 3. Thus, for one member of the named family, the observed long-range degradation is not caused by the theoretical mechanism the paper proves; the causal story requires the optimization trajectory to do decisive work. This is an internal inconsistency in the central claim and should be resolved by either excluding DropNode from the theoretical statements or by providing a separate, testable mechanism for its behavior.
  2. [Section 3, Appendix E.2] The theory computes the expected sensitivity of the stochastic network under random masks while explicitly ignoring the optimization trajectory. At test time, the dropping methods are turned off (q=0), as stated in Appendix E.2: 'isolating the effects on optimization and generalization, which our theory does not address.' Nevertheless, the paper uses the sensitivity decay to explain test-time performance differences; for example, Section 5.2 concludes that the dropping methods 'harm generalization in long-range tasks by forcing models to overfit to short-range signals.' This is a causal leap: Theorem 3.1 characterizes the training-time expected sensitivity at initialization, not the generalization behavior of the learned parameters. The DropNode case is a concrete counterexample in which the empirical degradation has no sensitivity-based explanation. To support the central claim, the paper should either directly measure sensitivity of the trained models (e.g., on test-time graphs) and correlate it with performance, or substantially weaken the causal language connecting Theorem 3.1 to the experimental results.
  3. [Section 3, Theorem 3.1, Abstract] The theorem is proved only for node pairs at distance exactly L in an L-layer GCN, and the text explicitly states that no general conclusion follows for nodes separated by fewer than L hops or for arbitrary distances. The abstract, however, states without qualification that 'theoretical results showing that DropEdge-variants reduce sensitivity between distant nodes' and the conclusion repeats this broader claim. The empirical Figure 1a does support a broader decay for DropEdge on Cora, but the theoretical contribution is narrower. The claims should be aligned with the proven scope, or the theory should be extended to all distances.
minor comments (6)
  1. [Section 2.2, Abstract] The paper uses 'DropEdge-variants' to include DropNode, DropAgg, and DropGNN, while Dropout and DropMessage are called 'Dropout-variants'; however, the theoretical results in Section 3 only cover edge-dropping methods, and the abstract's phrase 'DropEdge- and Dropout-variants exacerbate the over-squashing problem' goes beyond the theory for Dropout and DropMessage.
  2. [Section 4, Eq. (4.1)] The statement in the abstract that DropSens increases sensitivity to distant nodes 'despite dropping the same number of edges' is ambiguous; DropSens drops edges according to a target-node degree distribution, so the expected number of dropped edges differs from DropEdge for a given q. Please clarify whether 'same number' refers to the expected total.
  3. [Section 5.2] The best-performing dropping probability is selected from up to nine values per dataset-model-dropout combination after 20 runs, and then a t-test is performed on 50 new samples; no correction for multiple comparisons is applied, which can inflate the reported significance.
  4. [Figure 1b] 'relatively insignificant' should be 'relatively small' to avoid the statistical meaning of 'insignificant.'
  5. [Table 2b, Abstract] DropSens does not consistently outperform the rewiring baselines on graph classification (e.g., Mutag 70.20 vs. FoSR 80.00 and DIGL 79.70; Proteins 70.61 vs. FoSR 73.42), so the abstract's claim of consistently outperforming graph rewiring techniques is too strong; Section 5.3's qualified 'performs competitively' should be used in the abstract as well.
  6. [Appendix E.3, Listing 1] The expression sympy.real_roots(...)[-2] is fragile; please document the ordering of the roots and add a comment explaining why the second-to-last root is the desired solution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Theorem 3.1 follows from a first-principles expectation calculation, DropSens is a construction rather than a prediction, and no self-citation chain or fitted-input-as-prediction step appears.

full rationale

The paper's central theoretical claim is derived self-containedly rather than assumed. Equation 3.2 expresses expected sensitivity as (E[Â])^L_{ij} ||W||_1 under i.i.d. layer-wise edge masks; Lemma 3.1 and Appendix B.1 compute E[Â] directly from the Bernoulli mask distributions for each DropEdge variant; Appendix B.2 proves Theorem 3.1 by comparing the product of expected transition probabilities along loop-free L-hop paths with the corresponding NoDrop entries. No fitted parameter is later renamed as a prediction, and the theorem is stated for fixed weights and graph topology. The DropSens construction in Equation 4.1 is also not circular: it sets a per-edge dropping probability so that a user-chosen fraction c of cross-edge information is preserved, so the resulting increase in expected sensitivity is a design guarantee, not a fitted explanation of the experimental results. The paper does not use the DropSens benchmark outcomes to tune c or to retrofit the theory. There is no load-bearing self-citation: the cited sensitivity and rewiring results [8, 33, 44, 79] are by other authors, and the paper invokes no uniqueness theorem from its own prior work. The manuscript does contain an acknowledged internal limitation, flagged explicitly in Appendix F.2: DropNode has no expected sensitivity loss (Equation B.15), yet its test performance degrades on heterophilic datasets, and the paper attributes this to learning-trajectory effects that Section 3 says it is ignoring. This weakens the abstract's blanket statement that DropEdge-variants reduce sensitivity between distant nodes, but it is a correctness and scope concern, not a circular reduction of an output to an input.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical or mathematical entities are postulated; DropSens is an algorithm, not an entity. The main free parameters are the dropout probabilities and DropSens's c and q_max, which are chosen per dataset in the experiments. The axioms reflect the theory's restriction to linear networks, layer-wise independent masks, and the decision to ignore optimization effects.

free parameters (3)
  • DropSens information-preservation fraction c = chosen from {0.5, 0.8, 0.9, 0.95} per dataset
    Controls the target fraction of information preserved over cross-edges in Eq. 4.1; selected per task using validation performance, so it is a fitted/choice parameter for the empirical DropSens results.
  • DropSens maximum dropping probability q_max = chosen from {0.2, 0.3, 0.5, 0.8} per dataset
    Caps the per-edge dropping probabilities and filters configurations that would reduce to plain DropEdge; selected via validation as part of the 11-configuration search.
  • Dropout probability q per method = grid {0.1, ..., 0.9}, best per dataset
    For each dropping method, the best q is selected on validation from nine values before reporting test accuracy, so reported comparative results depend on this per-dataset selection.
assumptions (4)
  • domain assumption Asymmetric normalization A_hat = D_tilde^{-1} A_tilde for the theoretical sensitivity analysis
    Invoked in Section 3 before Lemma 3.1 to make the expected propagation matrix tractable; the paper handles symmetric normalization only through Monte Carlo approximation in Appendix D.1.
  • standard math Edge masks are independent across layers, giving E[product of A_hat^(l)] = (E[A_hat])^L
    Used in Eq. 3.2 and Theorem 3.1; this follows from the standard layer-wise independent sampling of DropEdge variants, though within a layer the mask entries are correlated through degree normalization.
  • ad hoc to paper Expected sensitivity under random masks, ignoring optimization effects, predicts test-time generalization on long-range tasks
    Stated explicitly in Section 3: 'we will ignore the effect of DropEdge-variants on the optimization trajectory'; the paper's main empirical conclusions map the sensitivity result onto test performance, making this the load-bearing bridge.
  • domain assumption The Jacobian-norm sensitivity definition of [79] is the operative measure of over-squashing
    Adopted from prior work and used as the central object of the theoretical analysis, so the validity of the over-squashing statements is tied to that definition.

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Cite this review

Pith. "Pith review of Effects of Dropout on Performance in Long-range Graph Learning Tasks." pith.science (2026). https://pith.science/paper/W4U3BKXE

@misc{pith2026250207364,
  author       = {Pith},
  title        = {Pith review of: Effects of Dropout on Performance in Long-range Graph Learning Tasks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W4U3BKXE}},
  note         = {Machine review of arXiv:2502.07364}
}
read the original abstract

Message Passing Neural Networks (MPNNs) are a class of Graph Neural Networks (GNNs) that propagate information across the graph via local neighborhoods. The scheme gives rise to two key challenges: over-smoothing and over-squashing. While several Dropout-style algorithms, such as DropEdge and DropMessage, have successfully addressed over-smoothing, their impact on over-squashing remains largely unexplored. This represents a critical gap in the literature, as failure to mitigate over-squashing would make these methods unsuitable for long-range tasks -- the intended use case of deep MPNNs. In this work, we study the aforementioned algorithms, and closely related edge-dropping algorithms -- DropNode, DropAgg and DropGNN -- in the context of over-squashing. We present theoretical results showing that DropEdge-variants reduce sensitivity between distant nodes, limiting their suitability for long-range tasks. To address this, we introduce DropSens, a sensitivity-aware variant of DropEdge that explicitly controls the proportion of information lost due to edge-dropping, thereby increasing sensitivity to distant nodes despite dropping the same number of edges. Our experiments on long-range synthetic and real-world datasets confirm the predicted limitations of existing edge-dropping and feature-dropping methods. Moreover, DropSens consistently outperforms graph rewiring techniques designed to mitigate over-squashing, suggesting that simple, targeted modifications can substantially improve a model's ability to capture long-range interactions. Our conclusions highlight the need to re-evaluate and re-design existing methods for training deep GNNs, with a renewed focus on modelling long-range interactions.

Figures

Figures reproduced from arXiv: 2502.07364 by the authors.

Figure 1
Figure 1. Empirical sensitivity analysis using the Cora dataset. 1. increases the sensitivity of a node’s representations to its own input features, and 2. decreases the sensitivity to its neighbors’ features. L-layer Linear GCNs. Unfortunately, we cannot draw similar conclusions in L-layer networks, for nodes at arbitrary distances. To see this, view P˙ as the transition matrix of a non-uniform random walk. This walk has hig… view at source ↗
Figure 2
Figure 2. Train and test MAE of 11-layer GCNs on the SyntheticZINC dataset, averaged over 10 initializations. 4 Sensitivity-Aware DropEdge Lemma 3.1 tells us that DropEdge decreases the weight of cross-edges, (j → i), in the expected propagation matrix, i.e. the strength of message passing over these edges decreases. The fraction of information preserved over a cross-edge is dependent only on the dropping probability and the … view at source ↗
Figure 3
Figure 3. Relative change in test-time performance of a GCN using DropSens, compared to the baseline DropEdge, on real-world datasets from Section 5.2. In this work, we use Cora [57], CiteSeer [31] and PubMed [62] as representatives of homophilic datasets [52, 98], and Squirrel, Chameleon and TwitchDE [69] to represent heterophilic datasets [52]. The networks’ statistics are presented in [PITH_FULL_IMAGE:figures/full_fig_p00… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Entries of P¨6 , averaged after binning node-pairs by their shortest distance [PITH_FULL_IMAGE:figures/full_fig_p025_4.png]
Figure 5
Figure 5. Figure 5: Entries of P6 ℓ=0 P˙ ℓ , averaged after binning node-pairs by their shortest distance. D.1 Symmetrically Normalized Propagation Matrix The results in Section 3 correspond to the use of Aˆ = Aˆasym for aggregating messages – in each message passing step, only the in-deg…
Figure 6
Figure 6. Figure 6: Edge-wise dropping probabilities under DropSens for varying values of c, along with corresponding approximations as in Equation E.1. mapper [ d_i ] = q_i in_degrees = degrees [ edge_index [1]] # Edge index -> in - degree of target node qs = mapper [ in_degrees ] # Edge…
Figure 7
Figure 7. Figure 7: Dropping probability versus test accuracy of DropEdge-GCN. The theory the explains the contrasting trends as follows: random edge-dropping pushes models to fit to local information during training, which is suitable for short-range tasks, but harms test-time performanc…
Figure 8
Figure 8. Figure 8: Dropping probability versus test accuracy of DropNode-GCN. F.2 Remark on DropNode In Equation B.15, we noted that DropNode does not suffer from loss in sensitivity. However, those results were in expectation. Moreover, our analysis did not account for the effects on th…
Figure 9
Figure 9. Figure 9: DropEdge probability versus training accuracy of GCNs. The training performance improves with q, suggesting that the models are not underfitting. Instead, the reason for poor test-time performance ( [PITH_FULL_IMAGE:figures/full_fig_p031_9.png]

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