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REVIEW 4 major objections 5 minor 58 references

Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read One MLP adapts to any graph's aggregation, no labels needed

desk verdict The empirical results are worth a look, but the load-bearing graph reconstruction and the flawed theory don't support the SOTA claims as stated. read the letter →

arxiv 2507.20127 v1 pith:JMN3XO3M submitted 2025-07-27 cs.LG cs.AIcs.GR

Xuanting Xie , Bingheng Li , Erlin Pan , Zhao Kang , Wenyu Chen This is my paper · ORCID
classification cs.LGcs.AIcs.GR
keywords graphclusteringheterophilyunsupervisedrepresentationlearningaggregation-awareMLPreconstructionmessagepassingnodeclassification
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

The paper proposes AMLP, an unsupervised graph representation method in which a single-layer MLP is made 'aggregation-aware' rather than relying on a fixed Mean/Max/Sum aggregator. It first rebuilds the adjacency graph with a thresholded product of feature and topology similarities, then trains the MLP with a loss that pulls the k-hop aggregated embedding back toward the raw embedding. The authors claim this unifies homophilic and heterophilic graph learning without labels and report state-of-the-art clustering on all six heterophilic and most homophilic datasets tested, plus competitive node classification against supervised aggregation GNNs. If the claim holds, a simple parameter-light MLP can replace supervised aggregation design in many graph tasks.

What carries the argument

The load-bearing object is the reconstructed graph $S$ of Eq. (3), whose binary entries keep edge $(i,j)$ only when the squared product of the feature cosine similarity and the degree-normalized adjacency-row cosine similarity exceeds $\epsilon$; together with the aggregation-aware loss $L_{\mathrm{agg}}$, this is what lets the single MLP adapt to the graph. $S$ is supposed to inject a high-order grouping effect by correlating feature and topology spaces, while $L_{\mathrm{agg}}$ penalizes mismatch between $k$-hop aggregated and raw embeddings, and the optional residual $XW$ compensates for the absence of self-loops. The theoretical development proves the grouping bound for a sigmoid-smoothed version of $S$ and shows that the loss has a high-pass spectral effect.

What would settle it

Compute clustering performance with the original adjacency $A$ in place of the reconstructed $S$ across all datasets; the central claim that $S$ is more class-relevant than $A$ would be falsified if the $A$ variant wins on most heterophilic graphs, and the paper's own ablation already shows reconstruction lowers NMI on Cora from 59.43 to 57.61.

Watch

Extended reading notes

Core claim

AMLP claims that a single linear transform can adapt to graph structure if its training objective is aware of aggregation. Concretely, with reconstructed graph $S$ and normalized adjacency $\tilde S$, the method forms $Y = \tilde S^k XW + XW$ and trains $W$ by minimizing $L_{\mathrm{agg}} + \lambda L_{\mathrm{rec}}$, where $L_{\mathrm{agg}}=\|\tilde S^k XW - XW\|_F^2$ makes the MLP responsive to the graph filter and $L_{\mathrm{rec}}$ reconstructs the original adjacency through inner products. The paper argues that $L_{\mathrm{agg}}$ acts as a high-pass filter, balancing the low-pass smoothing of aggregation, and that the reconstructed $S$ induces a high-order grouping effect that keeps similar nodes close while separating dissimilar ones. Extensive experiments on 12 datasets are reported as evidence that this unsupervised scheme reaches state-of-the-art clustering and beats label-hungry aggregation GNNs on several heterophilic classification benchmarks.

Load-bearing premise

The method rests on the hand-built rule that decides which edges survive graph reconstruction; if that rule removes or distorts the exact signal that separates classes, the aggregation-aware loss cannot recover it.

Editorial extensions

If this is right

  • Clustering on graphs can be done without labels and without choosing an aggregator: AMLP reports the best ACC and NMI among the compared unsupervised methods on all six heterophilic datasets and on most homophilic datasets, including the large Ogbn-arXiv graph.
  • The aggregation-aware loss is a drop-in training term: the authors state it can be added to any existing message-passing GNN, so homophily-versus-heterophily tuning could become a training-time adjustment rather than a network-design choice.
  • A single-layer MLP with $k$-hop filtering and a residual connection is enough to beat supervised aggregation baselines on three of the four classification datasets reported.
  • Balancing the low-pass aggregation filter with the high-pass $L_{\mathrm{agg}}$ prevents both over-smoothing and over-sharpening, which the paper supports by showing that Dirichlet energy moves in the expected direction on homophilic versus heterophilic graphs.

Reading between the lines

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

  • Editorial extension: because graph reconstruction is done as a preprocessing step and $L_{\mathrm{agg}}$ is additive, one could apply the same reconstruction and loss to supervised GNNs; the likely testable benefit is improved robustness on heterophilic graphs with few labels.
  • Editorial extension: the product form in Eq. (3) is hand-chosen and the paper only tries $\epsilon \in \{0.001, 0.05\}$. A natural extension is to learn $S$ by backpropagation or to tune $\epsilon$ per dataset; the ablation's Cora result suggests that a hard threshold can discard useful structure, so an adaptive choice between $A$ and $S$ may improve worst-case performance.
  • Editorial extension: the theoretical grouping guarantee is for a sigmoid-smoothed $S$, not the implemented hard threshold; checking empirically whether the hard-thresholded $S$ satisfies the same bound on real graphs would connect the proof to the deployed algorithm.
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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

4 major / 5 minor

Summary. The paper proposes AMLP, an unsupervised graph representation learning method. It first constructs a thresholded graph S from the product of normalized feature cosine similarity and normalized adjacency-row cosine similarity (Eq. (3)), then computes k-hop aggregated features eS^k XW, and trains a single-layer MLP with an aggregation-aware loss Lagg = ||eS^k XW - XW||_F^2 plus an inner-product reconstruction loss Lrec = ||Yhat Yhat^T - eA||_F^2, with output Y = eS^k XW + XW. Node embeddings are evaluated by K-means clustering and by a linear classifier. The manuscript claims state-of-the-art clustering results on six heterophilic and six homophilic datasets, competitive node classification against supervised and self-supervised baselines, scalability to Ogbn-arXiv, and a theoretical 'high-order grouping effect' together with a spectral interpretation of Lagg.

Significance. If the empirical claims hold, the paper makes a meaningful point: a simple, label-free MLP with a hand-constructed graph filter can match or beat sophisticated aggregation-based GNNs on several heterophilic benchmarks, and the method is lightweight and scalable. The paper includes useful ablations, an efficiency comparison, parameter sensitivity studies, and an attempt at theoretical justification. However, the theoretical analysis is not sound as written, and the experimental protocol leaves open the possibility that reported margins partly reflect test-set selection. The central claim is therefore not yet established, though the method itself is simple enough that a corrected analysis and a validated tuning protocol could make the contribution solid.

major comments (4)
  1. [§IV-C, Assumption IV.4 and Theorem IV.2] The proof of the high-order grouping effect is mathematically unsound. Assumption IV.4 asserts E[||r·W||_p] = 0 for a random matrix W with independent uniform entries; this cannot hold unless r·W = 0 almost surely, since a norm is nonnegative. The stated Hoeffding concentration P(||rW||_p >= t) <= 2 exp(-d t^2 / (2||r||_p^2)) also mixes dimensions: r is in R^c and W is in R^{d*c}, so the number of independent summands is c, not d, and no union bound over the c output coordinates is provided. In addition, the theorem's bound O(sqrt(ln(2/(δ(M+N))))) diverges as M+N -> 0, which is precisely the limit in which two nodes are most similar and in which the intended grouping property should give close embeddings. Finally, the theorem analyzes a sigmoid-smoothed approximation of S rather than the binary threshold in Eq. (3), so it does not establish that the specific reconstruction rule keeps class-relevant edges.
  2. [§V-C, Tables II-IV] The experimental protocol does not describe a validation-based selection of the hyperparameters. Section V-C states that k is searched in {1,2,3,5,7,8,9,10} except on Ogbn-arXiv, λ is searched in {1,1e-1,1e-2,1e-3}, the learning rate in {1e-2,1e-3,1e-4}, and the MLP width in {100,500}, but no validation split or repeated-selection procedure is described, and epsilon in Eq. (3) is reported as '0.001 or 0.05' without selection details. The clustering results in Tables II and III are also reported without standard deviations or error bars. Under this protocol, the reported state-of-the-art margins may be partly the result of selecting the best configuration on the test data, and the significance of the gains cannot be assessed.
  3. [§V-F, Table IV and Eq. (3)] The ablation shows that the reconstructed graph S is load-bearing for the heterophilic results: replacing S with A drops Texas ACC from 74.32 to 57.38 and Washington ACC from 74.35 to 62.61, while on Cora the original A gives higher NMI than S (59.43 vs 57.61). This means the method's heterophilic advantage is carried by the particular thresholded product of feature and adjacency-row cosines in Eq. (3), not by the adaptive MLP per se, and the reconstruction is not uniformly beneficial. No evidence is given that this specific thresholding rule is class-relevant, and Theorem IV.2 does not fill that gap because it bounds a smoothed surrogate in terms of essentially the same cosine similarities that define S. If S discards the class-discriminative signal, neither the k-hop aggregation nor Lagg can recover it.
  4. [§IV-C, Proposition IV.6 and Eq. (9)] The derivation of the claimed high-pass filtering effect is not justified. The transition from min ||(eS^k-I)XW||_F^2 to a spectral sum with terms [(eS^k-I)^2-I]u_j ||(XW)_u - (XW)_j|| is presented without an algebraic derivation and is not a standard spectral identity; as written, Eq. (9) does not establish the claimed relationship. Without a correct proof, the statement that Lagg 'exhibits a high-pass filtering effect' is unsupported, and this weakens the theoretical interpretation in Section IV-C.
minor comments (5)
  1. [§III-A] The notation in the preliminaries is inconsistent: eA is defined as the degree-normalized adjacency with self-loops, but the graph Laplacian is written as L = I - A rather than using the normalized variant, and Eq. (1) applies the MLP only to raw features rather than to transformed neighbor features, which may confuse the message-passing formalization.
  2. [§III-B, Figures 1 and 2] The captions of Figures 1 and 2 are too terse; they do not describe the axes, the quantities plotted, or the meaning of the subfigures, making the empirical study difficult to verify from the figures alone.
  3. [§IV-A, Eq. (3)] Equation (3) defines S_ij for all i,j, but the text later says eS has no self-loop; it should be stated explicitly whether diagonal entries are excluded before normalization, since the formula as written would include i = j with a value depending on the cosine of a row with itself.
  4. [§V-F, Table IV] The caption says the best performance is marked in bold, but in the rendered table the Cora NMI value for 'AMLP w A' (59.43) is higher than that of AMLP (57.61); either the bold marking is missing or the claim that AMLP is best on Cora needs qualification.
  5. [§I and §II] The claim that this is 'the first work to shift the focus from designing the aggregation mechanism to making learned representations aggregation-adaptive' is too strong and is not supported by a comparison with existing learnable or adaptive aggregation approaches; the claim should be softened or accompanied by a more thorough discussion.

Circularity Check

2 steps flagged · score 5.0 of 10

Theoretical 'high-order grouping effect' restates the cosine similarities used to construct S, and the reported SOTA numbers are grid-searched on the evaluation metric without a validation split; the core algorithm remains an externally benchmarked, independent method.

  1. self definitional [Sec. IV-A Eq. (3) and Sec. IV-C Theorem IV.2]
    "Eq. (3) refine the original graph and defines Sij as a binary variable ... Sij=1 if (X_i^T X_j/(||X_i|| ||X_j||) * A_i^T A_j/(||A_i|| ||A_j||))^2 >= epsilon. ... Theorem IV.2: M = ||Xhat_i - Xhat_j||^2 + ||Ahat_i - Ahat_j||^2, N = sum_{m in [N]\{i,j}} |Xhat_i^T Xhat_m - Xhat_j^T Xhat_m| + |Ahat_i^T Ahat_m - Ahat_j^T Ahat_m|."

    The theorem's upper bound is stated in terms of M and N, which are exactly the feature-cosine and adjacency-row-cosine differences that Eq. (3) thresholds to construct S. The theorem therefore proves a Lipschitz-style consequence of the construction: if the inputs to the threshold rule are similar, the filtered outputs are close. It does not independently establish that the thresholded product is class-relevant or that kept edges connect same-class nodes; it is a restatement of the similarity metric used to build S.

  2. fitted input called prediction [Sec. V-C, Experimental Setting]
    "For fairness, the experimental configurations for every dataset follow DGCN [22], which finds the optimal solution using a grid search. ... The hyper-parameter k is set to 20 on Ogbn-arXiv and searched in {1,2,3,5,7,8,9,10} on other datasets. The trade-off parameter lambda is searched in {1,1e-1,1e-2,1e-3}."

    The paper does not specify a validation split; grid search is run directly on the clustering and classification evaluation objectives (ACC/NMI). Thus the reported SOTA numbers are the best over the searched hyperparameters on the same data used for evaluation, not an unbiased prediction of an unsupervised method with fixed settings. The phrase 'finds the optimal solution' admits that the evaluation metric drives model selection, so the empirical results are partly constructed by the search.

full rationale

The core algorithm—Eq. (3) graph reconstruction, Eq. (5) aggregation-aware loss, and Eq. (7) reconstruction loss—is not derived by fitting to the target labels; the model is trained with L = Lagg + lambda*Lrec and evaluated on external homophilic and heterophilic benchmarks, so the main empirical claim is not equivalent to its inputs by construction. No load-bearing self-citation chain is present: [22] (DGCN, by two of the current authors) is used for comparison and experimental setting, not to justify the core derivation. The two flagged steps are partial circularities. First, Theorem IV.2's high-order grouping bound is a restatement of the construction: S in Eq. (3) is defined by thresholding products of feature cosine and adjacency-row cosine similarities, and the theorem bounds output distance by those same cosine differences (M and N). The theorem says nothing about class-relevance of the kept edges, and the paper's own ablation (Table IV) shows the reconstruction hurts Cora NMI, so the theoretical support is weaker than claimed. Second, Sec. V-C performs grid search for 'the optimal solution' without a validation split, and the reported ACC/NMI are computed on the same data used to select k, lambda, learning rate, and dimension; the SOTA numbers are therefore selected rather than predicted. These issues reduce the force of the theoretical and empirical claims but do not make the whole derivation circular. The proof of Theorem IV.2 also appears technically flawed (Hoeffding bound uses input dimension d and omits a union bound over output coordinates), but that is a correctness concern rather than a circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The model's central performance claim depends mainly on two hand-built choices: the thresholded reconstruction S in Eq. (3) and the consistency objective Lagg in Eq. (5). Both introduce free parameters (epsilon, k, lambda, plus standard training hyperparameters) that are tuned per dataset. The theoretical section adds ad hoc assumptions, including an invalid zero-expectation assumption on random W, and does not provide an external benchmark or a falsifiable prediction. No new physical or conceptual entities are introduced beyond the AMLP model itself.

free parameters (5)
  • epsilon = 0.001 or 0.05
    Threshold in Eq. (3) that decides which edges survive graph reconstruction. The paper says it is set to eliminate noise, but does not specify how it is chosen per dataset or whether it is tuned; it directly changes S and therefore all downstream embeddings.
  • k = searched in {1,2,3,5,7,8,9,10}; 20 on Ogbn-arXiv
    Filter order in Eqs. (4) to (6). Grid-searched per dataset with no validation split for clustering, so reported results are the best over this grid.
  • lambda = searched in {1,1e-1,1e-2,1e-3}
    Trade-off between Lagg and Lrec in Eq. (8). Tuned per dataset on the clustering outcome, which risks selecting the best test-case configuration.
  • MLP hidden dimension = 100 or 500
    Single-layer width used in the reported experiments; the choice is not tied to a validation criterion in the text.
  • learning rate = searched in {1e-2,1e-3,1e-4}
    Adam learning rate; part of the per-dataset grid search and another degree of freedom in the final reported numbers.
assumptions (5)
  • ad hoc to paper Assumption IV.4: each element of W is sampled uniformly from [-1/sqrt(c),1/sqrt(c)] and E[||r·W||_p]=0 for any r in R^c.
    This assumption is introduced to make the Hoeffding argument in Theorem IV.2 work, but the zero-expectation statement is false for nonzero r because a norm is nonnegative. The proof therefore rests on an invalid premise.
  • ad hoc to paper The hard threshold in Eq. (3) can be replaced by a sigmoid f(x)=1/(1+e^{-k(x-epsilon)}) with Lipschitz constant k/4.
    Used in the proof of Theorem IV.2 to make S differentiable. The sigmoid parameter k is also used for the filter order, and the replacement is only exact as k tends to infinity, so the proof analyzes a smoothed proxy rather than the actual S.
  • standard math Hoeffding's inequality applies to the random projection R_ij W with the stated tail bound.
    Lemma IV.3 is standard, but its application in Sec. IV-C is not justified: the bound written as ||R_ij W|| <= sqrt(-2||R_ij||/d ln(delta/2)) is dimensionally inconsistent and does not follow from Hoeffding as stated.
  • domain assumption The thresholded product of feature cosine similarity and adjacency-row cosine similarity in Eq. (3) defines a graph S that is more class-relevant than the original A.
    This is the core modeling premise of the method. The paper gives an ablation showing S helps on some datasets, but no derivation shows that this particular product form or threshold preserves the clustering signal.
  • domain assumption Pushing S^k XW toward XW via Lagg improves separation for both homophilic and heterophilic graphs.
    The aggregation-aware loss is justified empirically in Sec. III-B and by the informal Proposition IV.6, but there is no rigorous argument that this objective does not over-smooth or over-sharpen in general.

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Pith. "Pith review of Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing." pith.science (2026). https://pith.science/paper/JMN3XO3M

@misc{pith2026250720127,
  author       = {Pith},
  title        = {Pith review of: Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JMN3XO3M}},
  note         = {Machine review of arXiv:2507.20127}
}
read the original abstract

Graph Neural Networks (GNNs) have become a dominant approach to learning graph representations, primarily because of their message-passing mechanisms. However, GNNs typically adopt a fixed aggregator function such as Mean, Max, or Sum without principled reasoning behind the selection. This rigidity, especially in the presence of heterophily, often leads to poor, problem dependent performance. Although some attempts address this by designing more sophisticated aggregation functions, these methods tend to rely heavily on labeled data, which is often scarce in real-world tasks. In this work, we propose a novel unsupervised framework, "Aggregation-aware Multilayer Perceptron" (AMLP), which shifts the paradigm from directly crafting aggregation functions to making MLP adaptive to aggregation. Our lightweight approach consists of two key steps: First, we utilize a graph reconstruction method that facilitates high-order grouping effects, and second, we employ a single-layer network to encode varying degrees of heterophily, thereby improving the capacity and applicability of the model. Extensive experiments on node clustering and classification demonstrate the superior performance of AMLP, highlighting its potential for diverse graph learning scenarios.

Figures

Figures reproduced from arXiv: 2507.20127 by the authors.

Figure 2
Figure 2. Results visualization on Empirical Experiment 2. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. The framework of AMLP. It consists of two main steps: graph reconstruction to obtain [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. shows the results in Ogbn-arXiv. Most baselines from Tables II and III cannot run on this dataset due to their high complexity, so we compare AMLP with scalable methods. AMLP demonstrates dominant performance thanks to its aggregation-adaptive MLP. In terms of ACC, both AMLP and Dink-net demonstrate significant improvements over other methods (exceeding 7%), with results that are closely comparable between the two. … view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Sensitivity analysis of k on Cora (left) and Texas (right) [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Sensitivity analysis of λ on Cora (left) and Texas (right). A. Classification Baselines Aggregation-based methods: We compare AMLP with six state-of-the-art supervised methods that adjust the aggregation mechanism, including GPRGNN [11], GGCN [17], RAW￾GNN [6], GloGNN+…

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Reviewed August 15, 2026 · model on record in the stance chip above.