On the Effectiveness of Random Weights in Graph Neural Networks

Beatrice Bevilacqua; Bruno Ribeiro; Carola-Bibiane Sch\"onlieb; Moshe Eliasof; Thu Bui

REVIEW 4 major objections 6 minor 44 references

On the Effectiveness of Random Weights in Graph Neural Networks

T0 review · 4 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper claims that replacing learned message-passing weights in graph neural networks with on-the-fly random diagonal matrices yields accuracy comparable to end-to-end training while cutting training time by up to 6x and GPU memory by…

desk verdict A genuinely useful empirical paper on random-weight GNNs whose headline claims outrun what is measured: the rank-collapse theory is wrong, and the 6x speedup excludes pretraining, but the construction is new and the benchmark study is extensive. read the letter →

arxiv 2502.00190 v1 pith:E7X4ITFA submitted 2025-01-31 cs.LG stat.ML

Thu Bui , Carola-Bibiane Schönlieb , Bruno Ribeiro , Beatrice Bevilacqua , Moshe Eliasof This is my paper · ORCID

classification cs.LGstat.ML MSC 68T07

keywords randomweightsgraphneuralnetworksmessagepassingfeaturecollapserankpreservationtrainingefficiencypropagationRAP-GNN

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 argues that the learned weight matrices inside a GNN's message-passing layers are not the main source of its predictive power. It proposes RAP-GNN (Random Propagation GNN), which replaces those weights with diagonal matrices sampled uniformly at random on every forward pass, keeps a pretrained frozen embedding, and trains only the final classifier. Across node and graph classification benchmarks, RAP-GNN matches or slightly exceeds end-to-end trained GNNs while cutting per-epoch training time by up to 6x and GPU memory by up to 3x. The authors also give a rank-based explanation: random diagonal weights preserve feature rank across layers, whereas random full matrices collapse it, so the method avoids the feature-collapse problem that limits deep GNNs. If correct, this challenges the assumption that end-to-end training of message passing is necessary.

What carries the argument

The load-bearing object is the on-the-fly random diagonal weight matrix $w^{(l)} = \operatorname{diag}(\alpha^{(l)})$ with $\alpha^{(l)} \sim \mathrm{Uniform}([0,1])^d$, plugged into standard GNN layers such as GCN or GIN. Because $\mathbb{E}[w^{(l)}] = 0.5 I_d$, the channel-mixing update $h^{(l)} w^{(l)}$ preserves the rank of the embedding matrix in expectation (Observation 2), whereas a full random matrix satisfies $\mathbb{E}[w^{(l)}] = 0.5 \mathbf{1}_{d \times d}$, making all output columns linearly dependent and collapsing the expected rank to 1 (Observation 1). The diagonal form also replaces matrix multiplication with element-wise scaling, which is the main source of the reported speed and memory gains. The other load-bearing component is the separately pretrained, frozen embedding $f^{\mathrm{pre}}_\phi$, which maps raw features into the hidden space before random propagation begins.

What would settle it

Run RAP-GNN on a standard benchmark such as ogbn-proteins with the frozen embedding replaced by a randomly initialized, untrained embedding while keeping all other settings fixed; if accuracy remains close to the end-to-end baseline, the random-weight claim stands without pretraining, whereas a large drop, as the paper's own appendix suggests, would show that the pretrained embedding is carrying the task information.

Watch

Extended reading notes

Core claim

In the paper's own terms, the central discovery is that random weights can be surprisingly effective in GNNs. Concretely, RAP-GNN uses $w^{(l)} = \operatorname{diag}(\alpha^{(l)})$ in each message-passing layer, with $\alpha^{(l)}$ sampled from a uniform distribution on $[0,1]^d$ at every forward pass; a node embedding $f^{\mathrm{pre}}_\phi$ is pretrained on the downstream task and then frozen; and only a classifier $c_\theta$ is learned. The paper reports accuracy comparable to end-to-end training on Cora, CiteSeer, PubMed, TUDatasets, OGB molecular benchmarks, ogbn-proteins, and ogbn-products, with up to 6x lower training time and 3x lower GPU memory. It further claims that the random diagonal structure produces random graph propagation operators that mitigate feature rank collapse, while full random matrices collapse the expected feature rank to 1.

Load-bearing premise

The method's accuracy rests on the pretrained embedding layer: it is trained on the downstream task before being frozen, so if pretraining is counted as learned signal, the headline claim that random weights alone are effective is weaker.

Editorial extensions

If this is right

Deep GNNs become much cheaper: RAP-GNN cuts per-epoch training time by up to 6x and GPU memory by up to 3x, so deeper architectures are more affordable.
The method is backbone-agnostic: the paper shows it working with GCN, GIN, and GraphSage layers, so it can be dropped into existing GNN architectures.
Feature diversity is preserved: random diagonal propagation keeps embedding rank high across many layers, which directly addresses oversmoothing and rank-collapse problems in deep GNNs.
On-the-fly sampling beats fixed random weights: resampling diagonal weights every forward pass gives consistently better accuracy than sampling once at initialization.
Training reduces to learning the classifier on top of a frozen pretrained embedding, so the computational burden moves away from message passing.

Reading between the lines

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

Editorial inference: if the claim holds, message-passing weights in GNNs may be acting closer to a smoothing operator than to a learned feature extractor, shifting design effort toward pretrained embeddings and classifiers.
Editorial inference: the same random-propagation scheme could be tested on settings the paper does not cover, such as heterophilic graphs or temporal graphs, where learned weights are commonly believed to be essential.
Editorial inference: the rank-preservation argument is stated in expectation; a natural extension is to prove concentration or finite-width bounds on the embedding rank, since small graphs may show substantial variance.
Editorial inference: because new weights are sampled each batch, RAP-GNN injects stochasticity during training; separating that regularization effect from the efficiency effect would clarify why it generalizes.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The thing to know: RAP-GNN is a real, specific construction not in the reservoir or ELM literature, and the empirical study backing it is the best part of the paper. On-the-fly diagonal random sampling in message-passing layers, a frozen task-pretrained embedding, and classifier-only training — that combination is new, and they acknowledge the RC/ELM/untrained-ticket lineage honestly. The benchmarks are broad (Planetoid, TU, OGB, ogbn-proteins/products; GCN, GIN, GINE, GraphSage) and the accuracy numbers are believable: RAP-GNN lands at parity with end-to-end, sometimes a hair better, across almost every dataset. Credit where due: they run the ablation that hurts them most. Table 6 in D.2 shows that with a random or identity embedding, the method collapses (near-chance with random embedding, OOM or degradation with identity). They disclose that the pretrained embedding is task-supervised and carries real information. That is more honest than most papers. Now the soft spots, in order of severity. Observation 1 is simply wrong. It swaps E[rank(·)] with rank(E[·]). A full random matrix with continuous entries is almost surely full rank, so rank(hw) = rank(h) with probability one for fixed h; E[rank] is d', not 1. The 0.5·1 expectation argument does not imply linearly dependent columns in any realized sample. The empirical contrast between diagonal and full random weights is real, and Figure 4 shows the collapse, but the explanation needs to be rewritten. Observation 2 reaches a true conclusion (diagonal scalings preserve rank a.s.) for the same confused reason. The efficiency claim is overstated. The 6x speedup is per-epoch for the classifier phase only. Algorithm 1 pretrains the embedding on the downstream task until convergence, and that cost is never reported. The stress-test guess that total wall-clock might be worse than end-to-end is speculation — the honest statement is that total time is simply unreported, and on large datasets the pretraining phase is not obviously cheap. A total-wall-clock table would settle it. Framing: 'random weights are surprisingly effective' is confounded. Full random weights on-the-fly are near chance; Random Embedding plus random diagonal is near chance. What works is a task-pretrained embedding plus diagonal random propagation. That is a legitimate and interesting finding, but the abstract sells it as random weights doing the work. Minor: inference samples weights per forward pass, so predictions are stochastic, and they never average multiple draws — a cheap Monte Carlo ensemble that could only help. Also, on-the-fly beats fixed diagonal by margins that are within noise on several datasets (82.42 vs 81.32 on Cora), so the 'importance of on-the-fly sampling' section is weaker than it claims; the diagonal structure and the pretrained embedding are the load-bearing parts. Who should read this: anyone working on efficient or single-pass GNN training, and the reservoir/ELM crowd. It deserves a serious referee — the empirical content is substantial, the flaws are addressable, and a revised version with corrected theory and honest cost accounting would be a solid NeurIPS/ICML paper. Send it out, but tell the authors to fix Observation 1 and report pretraining cost before acceptance.

Referee Report

4 major / 6 minor

Summary. The paper studies whether the learned weight matrices in GNN message-passing layers can be replaced by random weights. The proposed method, RAP-GNN, uses per-layer diagonal weight matrices sampled uniformly on [0,1] at every forward pass; a node embedding layer f_pre^phi is pretrained on the downstream task and then frozen, and only a classifier c_theta is trained. The paper claims competitive accuracy with end-to-end trained GNNs across node and graph classification benchmarks, with per-epoch training time reduced by up to 6x and GPU memory by up to 3x, and presents two theoretical observations (Observations 1 and 2) claiming that full random weight matrices collapse the rank of node embeddings while diagonal random matrices preserve it. Experiments cover Planetoid, TUDatasets, OGB, and the large-scale ogbn-proteins and ogbn-products datasets with GCN, GIN, and GraphSage backbones, including comparison with reservoir-computing and extreme-learning-machine baselines.

Significance. The empirical study is the paper's main asset: results are reported on a wide range of datasets and backbones with 5 seeds, the hyperparameter search spaces are fully specified (Tables 12-14), and the comparison includes RC-based methods and a range of ablations over random-weight structure and embedding strategies. The ablations are genuinely informative: full random weights (on-the-fly or fixed) collapse on ogbn-products (Table 4), whereas diagonal random weights remain competitive, and RAP-GNN substantially improves over the frozen pretrained embedding alone (Table 1: Cora 82.42 vs 56.55), showing that the random propagation layers contribute real computation. If the central claims can be made accurate, the paper offers a useful, resource-efficient GNN variant and a set of well-documented negative results. However, the theoretical justification for the diagonal design is currently invalid, the efficiency numbers exclude the supervised pretraining phase, and the role of the pretrained embedding is under-reported; each of these must be corrected before the contribution is as strong as the abstract claims.

major comments (4)

[§3.2, Observation 1] The derivation in Observation 1 exchanges expectation and rank without justification, and its conclusion is false under the stated assumptions. The paper asserts E[rank(tilde_h)] = rank(E[tilde_h]) = 1 for tilde_h = h^{(l)} w^{(l)} with w^{(l)} an iid U[0,1] full matrix. This is invalid: for continuous iid entries, w^{(l)} has full rank with probability one, so if h^{(l)} has rank d', h^{(l)} w^{(l)} has rank d' almost surely and E[rank] = d'. The rank-1 quantity is the rank of the mean matrix, which is not the rank of a realized feature matrix. Observation 1 therefore cannot support the claimed theoretical motivation for diagonal over full random weights, and the empirical rank collapse of the full-random baselines in Figure 4 must instead be attributed to the propagation operator and nonlinearities rather than to w^{(l)}. Observation 2's conclusion (rank preservation) is true almost surely for nonzero diagonal scaling, but its stated justification through E[w^{(l)}] = 0.5 I_d is also not the correct argument. Both observations, and the abstract's claim of 'random graph propagation operators ... reduce the problem of feature rank collapse', need to be reworked.
[§4.3 / Algorithm 1] The efficiency claims exclude the pretraining phase. Figure 2, Figure 3, and Table 7 measure only the classifier-training phase of RAP-GNN; Algorithm 1 trains f_pre^phi itself on the downstream task until convergence before freezing it, and none of the hyperparameter tables (Tables 12-14) report MaxPreEpochs or the wall-clock time and memory of the pretraining phase. The abstract's 'up to 6x training time' and 'up to 3x memory' claims therefore hold only per-epoch within the second phase, and the total end-to-end training cost of RAP-GNN (pretraining included) is never established; it could be comparable to, or larger than, end-to-end GNN training. The claims must be restated as phase-local savings with the pretraining cost reported.
[§3.1 / Appendix D.2 (Table 6)] The 'random weights are surprisingly effective' claim is confounded by the downstream-supervised pretraining of f_pre^phi. Section 3.1(i) trains the embedding on the downstream task, and Table 6 shows this supervision carries substantial task information: Random Embedding is near chance (Cora 26.30 vs RAP-GNN 82.42) and Identity Embedding drops accuracy (Cora 78.44, PubMed 73.46). However, the same Table 6 shows that Fixed Random Embedding, which requires no pretraining at all, achieves 82.82/71.48/78.76 on Cora/CiteSeer/PubMed, statistically indistinguishable from RAP-GNN on all three datasets. The paper's own evidence thus contradicts the claim that pretraining the embedding is necessary; the text in Appendix D.2 says only that some embedding is needed to map input features to dimension d. The authors should either adopt the fixed-random-embedding variant (eliminating the uncounted pretraining cost) or report the pretraining cost and make the comparison to the random embedding explicit. As written, the abstract overstates the role of randomness.
[§3.1(iii), inference] The stochastic inference protocol is not ensembled and its variance is unreported. Section 3.1(iii) samples one set of random weights per forward pass at inference, making the model a random estimator; the reported +/- std across 5 seeds mixes seed-level variability with weight-sampling variability. Since forward passes through the random layers require no gradients, averaging several weight draws at inference is essentially free and likely reduces variance. The paper should at minimum report the test-metric distribution over weight draws and, ideally, evaluate ensembled inference against the single-draw protocol.

minor comments (6)

[Appendix C, Figure 4] The figure caption describes the plotted quantity as 'the mean of Var(h^{(l)}) (in log scale)' while the text and the axis label say 'Rank (log scale)'; these are different quantities and the caption should be corrected.
[§3.2] In Observation 1, the step E[h^{(l)} w^{(l)}] = h^{(l)} E[w^{(l)}] treats h^{(l)} as fixed; the conditioning on h^{(l)} (or an independence assumption) should be stated explicitly.
[Appendix E, Tables 12-14] The hyperparameter notation mixes ranges in square brackets with sets in braces (e.g., HIDDEN DIM. '[256, 300]' on ogbn-products); state the convention once in the text and apply it consistently.
[Tables 1-4 and Introduction] Dataset names are rendered inconsistently ('CITE SEER', 'CORA' in table headers) and the Introduction contains the typo 'consistence performance'; please correct these.
[§3.3] The permutation-equivariance discussion could clarify that it applies per graph in the node-classification setting (a single graph) and per batch in graph classification; the phrase 'not across different graphs' is only meaningful under batching.
[Table 2] The RC baselines are reported with several N/A entries; state the source of the reported numbers and the backbone/configuration used for those baselines so that the comparison is reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the empirical claims rest on independent baselines and public benchmarks, and the disclosed pretrained-embedding dependence is an ablation, not a definitional reduction.

full rationale

I walked the paper's claimed derivation chain. RAP-GNN is explicitly defined as random diagonal message-passing weights combined with a frozen pretrained embedding (Section 3.1, Algorithms 1 and 2). The central empirical claim, that random weights can match end-to-end training, is tested against independent baselines (End-to-End, Fixed Random Diagonal, Fixed Random Weights, Random Weights, and Reservoir Computing methods) on public datasets, so the accuracy numbers are not derived from any fitted constant that is then relabeled as a prediction. The paper does disclose and ablate the pretrained embedding in Appendix D.2 (Table 6), where Identity and Random embeddings cause large accuracy drops; this weakens the strength of the headline 'random weights alone' narrative, but it is an omitted-cost and scope-of-claim concern, not circularity: the abstract and method explicitly state that RAP-GNN includes the pretrained embedding, and the ablation is an honest sensitivity test rather than a parameter being fit and then 'predicted.' The 6x/3x efficiency figures are direct per-phase runtime and memory measurements, not quantities implied by the method's own assumptions; the unmeasured pretraining phase is an excluded-cost concern, not a definitional equivalence. The theoretical Observations 1 and 2 are elementary calculations about feature rank under diagonal versus full random matrices; Observation 2 is a rank-preservation fact that does not assume the downstream accuracy it is used to explain. Self-citations (e.g., Eliasof et al. 2023a, 2023b, 2024; Murphy et al. 2019) appear as related work and motivation, not as load-bearing justification or imported uniqueness theorems. No quoted step reduces an equation to its own input by construction, and no fitted parameter is renamed as a prediction. Therefore, no significant circularity is present.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

Central claim rests on empirical benchmarks plus a mathematical observation. No new physical entities are introduced. The main unstated dependency is the supervised pretrained embedding and the invalid expectation/rank commute.

free parameters (2)

Per-dataset hyperparameters (hidden dimension, number of GNN layers L, learning rate, dropout, number of embedding… = varies per dataset, see Tables 12-14
The reported performance is obtained after validation-based hyperparameter search per dataset for every method; the central accuracy claim depends on these choices.
Pretraining epochs for f_pre^phi = not reported
Algorithm 1 defines MaxPreEpochs but the paper does not state its value or its compute cost, which is required to evaluate the total training time claim.

assumptions (4)

ad hoc to paper E[rank(h w)] = rank(E[h w]) for random weight matrices.
Observation 1 in Section 3.2 relies on this invalid step to conclude full random weights collapse feature rank to 1. Rank and expectation do not commute.
domain assumption Labels are available for supervised pretraining of the embedding and the final classifier.
The training protocol (Algorithm 1) pretrains f_pre^phi on the downstream task; the method would not be label-free.
domain assumption Benchmark datasets and standard splits are representative and correctly used.
Empirical conclusions depend on standard Planetoid, TUDataset, and OGB benchmarks with 5 random seeds.
domain assumption Graph propagation with diagonal random weights preserves feature diversity across layers.
Observation 2 is true for pure channel-wise scaling, but the full GNN update also applies adjacency mixing and nonlinearities; the paper asserts the effect persists in practice.

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Pith. "Pith review of On the Effectiveness of Random Weights in Graph Neural Networks." pith.science (2026). https://pith.science/paper/E7X4ITFA

@misc{pith2026250200190,
  author       = {Pith},
  title        = {Pith review of: On the Effectiveness of Random Weights in Graph Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E7X4ITFA}},
  note         = {Machine review of arXiv:2502.00190}
}

abstract

Graph Neural Networks (GNNs) have achieved remarkable success across diverse tasks on graph-structured data, primarily through the use of learned weights in message passing layers. In this paper, we demonstrate that random weights can be surprisingly effective, achieving performance comparable to end-to-end training counterparts, across various tasks and datasets. Specifically, we show that by replacing learnable weights with random weights, GNNs can retain strong predictive power, while significantly reducing training time by up to 6$\times$ and memory usage by up to 3$\times$. Moreover, the random weights combined with our construction yield random graph propagation operators, which we show to reduce the problem of feature rank collapse in GNNs. These understandings and empirical results highlight random weights as a lightweight and efficient alternative, offering a compelling perspective on the design and training of GNN architectures.

Figures

Figures reproduced from arXiv: 2502.00190 by the authors.

**Figure 2.** Training time (a), inference time (b), and accuracy (c) for node classification on PubMed with GCN backbone. The runtimes [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** GPU memory usage comparison on on the PubMed [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Comparison of the mean of Var h (l) (in log scale) across layers for End-to-End and RAP-GNN on the PubMed dataset using the same GCN architecture with residual connections with L = 64 and d = 256. RAP-GNN increases embedding variance with higher rate compared to End-…

**Figure 5.** Figure 5: Weight matrices learned in an end-to-end trained GCN with residual connections are shown for layer 1 (a) and layer 64 (b), each [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Comparison of GPU memory consumption on the ogbn [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

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write newline

" write newline "" before.all 'output.state := FUNCTION fin.entry add.period write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence '...

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

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