Active Few-Shot Learning for Vertex Classification Starting from an Unlabeled Dataset

Ansgar Scherp; Felix Burr; Marcel Hoffmann

REVIEW 5 major objections 6 minor 44 references

Active Few-Shot Learning for Vertex Classification Starting from an Unlabeled Dataset

T0 review · 5 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Cold-start graph classification with tiny label budgets favors prototypical networks over GCNs, and the gap widens when the class oracle is replaced by clustering: prototypes lose 1% average accuracy while GCNs lose 9%.

desk verdict Useful empirical comparison of cold-start pipelines, but the headline robustness gap between GPN and GCN is confounded by clustering different representation spaces. read the letter →

arxiv 2504.18696 v1 pith:JCSP6IHF submitted 2025-04-25 cs.LG

Felix Burr , Marcel Hoffmann , Ansgar Scherp This is my paper · ORCID

classification cs.LG

keywords activelearningfew-shotvertexclassificationgraphneuralnetworksprototypicalcoldstartk-medoidsclusteringlabelpropagation

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

Given a graph with no labels at all and a small budget for a human annotator, which model should you train? The paper argues for prototypical networks: models that assign each vertex the class of the nearest prototype (a representative embedding per class) rather than learning a decision boundary like a GCN. Its headline evidence is robustness under realism: when the idealized class oracle, which guarantees balanced per-class sampling, is replaced by $k$-medoids clustering of the model's embeddings, the GCN loses 9% average accuracy while the prototypical network loses only 1%. The same pattern holds when the number of classes is unknown and must be estimated, costing both models about another 1%. For any pipeline that must annotate an unlabeled graph from scratch with fewer than 20 labels per class, this makes prototype-based models the safer default.

What carries the argument

The central mechanism is replacing the class oracle with $k$-medoids clustering: at each round, the current model's vertex embeddings are clustered into $k$ pseudo-classes and the active learning strategy draws vertices from these clusters, so that sampling a cluster medoid approximates sampling a representative vertex per class without knowing any labels. The prototypical model represents each class $c$ by a PageRank-weighted prototype $r_c = \sum_{v \in V_{l,c}} h_v \, e_{s_v}$ over the labeled embeddings, and classifies a vertex by the closest prototype under Euclidean distance, with logits $p(c|v) = e^{-d(h_v,r_c)} / \sum_{c' \in C} e^{-d(h_v,r_{c'})}$. Training uses a three-part loss, an intra-class prototype distance term plus Euclidean and cosine regularizers that push prototypes apart. Label propagation, $Y' = \alpha D^{-1/2} A D^{-1/2} Y + (1-\alpha) Y$ with uncertain pseudo-labels filtered out by a normalized-entropy threshold of 0.2, exploits homophily to multiply the effective labeled set. For the third experiment, the class count is estimated by $k$-means over $k \in [2,100]$ with the elbow rule on Deep Graph Infomax embeddings.

What would settle it

Run the "Unbalanced Sampling" procedure on a heterophilic graph (homophily below roughly 0.3) and compare the prototypical model's accuracy loss against the balanced-oracle setting; or, once a few labels exist, compute the adjusted Rand index between the $k$-medoids pseudo-labels and the true labels after the first sampling round. If the prototype model loses as much as or more than the GCN's 9%, or the first-round pseudo-labels are near chance, the central robustness claim is limited to graphs whose embeddings cluster by class.

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Extended reading notes

Core claim

The paper claims that in the cold-start regime, a transductive, fully unlabeled graph annotated round by round by a human-in-the-loop, prototypical models outperform discriminative models (GCNs) whenever fewer than 20 labeled samples per class are available. This is established through three experiments that successively relax assumptions: "Balanced Sampling" keeps a class oracle that supplies one labeled vertex per class per round; "Unbalanced Sampling" drops the oracle and instead partitions the embedding space with $k$-medoids clustering into pseudo-classes from which vertices are drawn; "Unknown Number of Classes" additionally estimates the class count by $k$-means with the elbow rule on Deep Graph Infomax embeddings. The central quantitative claim is that dropping the oracle costs the GCN 9% average accuracy on the Planetoid datasets but costs the prototypical network only 1%, with a further 1% for both when the class count is estimated. The paper also claims that label propagation on the homophilic graphs artificially extends the training set and helps most in early rounds, that medoid sampling is the best of the four active learning strategies tested, and that the prototypical model tolerates up to roughly 20% annotation noise.

Load-bearing premise

The load-bearing premise is that $k$-medoids clustering of the model's current embeddings produces pseudo-classes that align with the true classes well enough that sampling one medoid per pseudo-class approximates balanced per-class sampling; the paper only tests homophilic graphs (homophily 0.44–0.77), and if the embeddings do not cluster by true class, the reported 1% robustness to dropping the class oracle fails.

Editorial extensions

If this is right

When annotating a graph from scratch with fewer than 20 labeled samples per class, use a prototypical network rather than a GCN; the prototype model wins across all three experimental settings.
A class oracle is replaceable: $k$-medoids pseudo-label clustering costs the prototypical model only 1% average accuracy, so few-shot vertex classification does not require balanced per-class sampling.
The medoid active learning strategy outperforms random, entropy, and PageRank sampling on average, making it the default choice among the four tested.
Label propagation on homophilic graphs increases accuracy by effectively enlarging the training set, with the largest gains in the early annotation rounds.
Estimating the number of classes rather than assuming it costs about 1% more on average, so the method remains viable when the class count is unknown.

Reading between the lines

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

I would expect the 1% versus 9% robustness gap to shrink or invert on heterophilic graphs (outside the tested homophily range of 0.44–0.77), because $k$-medoids pseudo-clusters will no longer track true classes; this is a direct, testable extension.
A cheap operational check follows from the paper's mechanism: once a handful of labels exist, compute the adjusted Rand index between $k$-medoids pseudo-labels and true labels; if it is near chance early on, the class-oracle-free advantage of prototypical models is unlikely to appear on that graph.
The results imply a reusable default recipe for cold-start graph annotation pipelines, prototype backbone, medoid sampler, label propagation with entropy filtering, that would be worth adopting as a standard baseline in future graph active learning studies.

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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

Quick take: this is a useful empirical comparison of prototypical versus discriminative models for cold-start vertex classification, with a real confound that the authors half-acknowledge. The headline number—GCN loses 9% when you drop the class oracle, GPN loses 1%—is backed by 10-seed runs on five datasets, and they ship code. That is more than most papers in this area.

What is new is the systematic setup: start without labels, add active learning and label propagation, and relax assumptions in three stages. Prior work combines active learning with GPN or does open-world graph AL, but I do not see the direct comparison under these three oracle assumptions anywhere. The paper is also honest about its limits: homophily-only, transductive, and no held-out validation for two key hyperparameters.

The main soft spot is the confound in the robustness comparison. In the unbalanced sampling experiment, k-medoids clustering runs on GPN's Euclidean-trained embeddings but on GCN's logits. The authors say in Section VI that clustering logits is 'sub-optimal, as these do not represent a metric space.' So the 9% versus 1% gap conflates the learning paradigm with how cluster-friendly the representation is. A controlled experiment that clusters the same representation type (for instance, GCN's penultimate embeddings) would tell you whether prototypical models are inherently more robust or just have a better space for k-medoids. Without that, the causal claim stays open. To be fair, in the balanced-sampling experiment GPN also beats GCN on the small datasets, so model type matters independently; it is the specific robustness gap that is not cleanly attributed.

Minor issues: alpha and the entropy threshold are chosen on the same datasets they are evaluated on; the unknown-classes experiment covers only three small datasets; and the class estimates are far off (Cora 11 vs 7, CiteSeer 13 vs 6) yet accuracy does not collapse, which is interesting but under-tested. The citation pattern is fine; they cite the earlier active-learning-plus-GPN work, so there is no narrative overclaim.

I would bring this to a reading group and would cite the pipeline comparison with a caveat about the confound. It deserves a serious referee: the experiments are reproducible and the confound is addressable. I would not desk reject it.

Referee Report

5 major / 6 minor

Summary. The paper addresses cold-start active learning for vertex classification on a fully unlabeled graph. It compares a prototypical model (GPN) with a discriminative model (GCN) under three decreasingly realistic assumptions: a balanced class oracle, k-medoids pseudo-labeling without an oracle, and an estimated number of classes. Label propagation is optionally used to expand the labeled set. The authors report 10-seed experiments on Cora, CiteSeer, PubMed, Reddit2, and ogb-arXiv, concluding that prototypical models outperform discriminative models with small label budgets and that dropping the class oracle costs GCN about 9% accuracy on Planetoid while GPN loses only about 1%. Source code is provided.

Significance. The setting is timely and practical: few-shot node classification usually assumes a class oracle or pre-labeled auxiliary classes, and the paper attacks the harder cold-start scenario. The study is reasonably broad in datasets and assumption levels, uses 10 seeds with standard deviations, includes an imperfect-annotator robustness check, and releases code. If the central comparison survives scrutiny, the recommendation of a prototypical model for cold-start active learning on homophilic graphs would be a useful, actionable result. However, as detailed below, the headline robustness gap is currently confounded, selective in its averaging, and the experimental bookkeeping needs clarification before the claims are fully supported.

major comments (5)

[Abstract and Table V] The abstract states that 'the average performance of discriminative models decreases by 9%' while 'prototypical models only lose 1%' when the class oracle is dropped, but Table V shows that these are the Planetoid-only numbers in parentheses, not the all-dataset averages. Across all five datasets, the GPN average rises from 53.3 (balanced) to 55.0 (k-medoids), while the GCN average falls from 41.5 to 38.3; the Planetoid-only changes are 61.6 to 60.4 for GPN and 56.9 to 47.9 for GCN. Please either qualify the abstract to say 'on the Planetoid datasets' or use the all-dataset averages, because the current wording overstates a result that changes sign in aggregate for the prototypical model.
[Section IV.B and Section VI] The oracle-robustness comparison is confounded. In the Unbalanced Sampling experiment, pseudo-labels used for sampling come from k-medoids clustering of GPN Euclidean-trained embeddings, but for the GCN the same step is applied to logits, and Section VI explicitly concedes that logits 'do not represent a metric space' and calls this sub-optimal. The 9% versus 1% gap therefore combines two changes at once: the learning paradigm and the geometric suitability of the representation being clustered. To attribute the gap to prototypical versus discriminative learning, run a controlled condition with the clustering representation held fixed across both models (for example, cluster both on the same DGI or raw-feature representation, or augment the GCN with a metric-compatible embedding objective) and show that the robustness difference persists.
[Section IV.B, Appendix D, Algorithm 1] The budget and per-class sample accounting are internally inconsistent. Section IV.B fixes the budget at B = |C| * 5 over five sampling rounds and Algorithm 1 stops when |Vl| exceeds B, but Appendix D says that for Reddit2 and ogb-arXiv the model trains on 10 samples per class in each iteration. Five such rounds would give 50 samples per class, exceeding both the stated budget and the abstract's 'fewer than 20 samples per class' scope. In the Unknown Number of Classes experiment the estimated k differs from |C| (11 versus 7 on Cora, 13 versus 6 on CiteSeer), yet the text says the sampler draws k vertices per round while keeping B = |C| * 5; these statements cannot both hold. Please report the exact per-round sample count, the number of rounds actually executed, and the total budget for each dataset and experiment.
[Section III] The label-propagation hyperparameters alpha = 0.9 and the entropy threshold 0.2 were chosen from pre-experiments, but the manuscript does not report whether those pre-experiments used a held-out split. Because all reported accuracies are on the same five datasets, selecting these values on the same test data would make the label-propagation and absolute-accuracy results optimistic. Please add a sensitivity analysis over alpha and the entropy threshold, or describe a validation procedure that does not use test labels.
[Section IV.B, Appendix E, Table IV] The Unknown Number of Classes experiment is run only on Cora, CiteSeer, and PubMed; Appendix E states that the DGI-based class estimation failed on Reddit2 and ogb-arXiv after 48 hours. The contribution claim that 'estimating the number of classes does not decrease performance' is therefore not supported for large graphs, and the abstract's 'across all experiments' phrasing overreaches. In addition, the elbow estimates are far from the true class counts (11 versus 7 on Cora, 13 versus 6 on CiteSeer), so a single point estimate is thin evidence for the claim; a sensitivity analysis over k would be more convincing.

minor comments (6)

[Section III] The total loss is written as L = Lr + lambda(Le + Lc), but the intra-class term was defined as Lp; please rename one of them for consistency.
[Section IV.B] The procedure says every experiment starts by assigning pseudo-labels via k-medoids clustering, but the Balanced Sampling experiment uses the ground-truth partition; please clarify that the k-medoids step only applies to the Unbalanced and Unknown settings.
[Section IV.B and Appendix I] The legend labels 'LP-own' in Figures 6-8 are never defined in the text; please define this strategy or rename it.
[Tables II-IV] FeatProp reports identical values in all three experiments; please state explicitly whether it is rerun under each setting or is a static baseline, and explain how a static baseline is comparable across experiments.
[Tables II and III] The LP+Random and LP+Entropy rows are identical in several columns (e.g., Cora in Table II); please explain why entropy sampling degenerates to random sampling for the LP baseline.
[Various] Please correct the many typos and stray fragments, including 'Appendix E.y having' and 'se an estimation' in Section IV.B, 'Appendix HDeviations' in Section V, and 'Pubmed' in Section VI, and fix 'Sogli et al.' to 'Solgi et al.' in Section II.B.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; empirical comparisons are self-contained, and the flagged issues are tuning and confound risks, not circular reductions.

full rationale

After walking the derivation chain, I find no step in which an output is equivalent to an input by definition, no fitted parameter is renamed as a prediction, and no load-bearing claim rests on a self-citation. The central claims are empirical measurements: accuracy differences in Tables II-IV, the averages in Table V, and the robustness gap (9% vs 1%) are computed from those tables, not derived from the model equations. The k-medoids pseudo-labeling procedure is not defined in terms of the reported accuracy; it uses model embeddings and is applied symmetrically to both model families. The label-propagation hyperparameters (alpha=0.9, entropy threshold=0.2) are selected in pre-experiments and disclosed, which is a tuning/leakage risk rather than circularity, because the reported accuracies are not forced by these choices by construction. The acknowledged asymmetry that GPN clusters Euclidean-trained embeddings while GCN clusters logits ('which is sub-optimal, as these do not represent a metric space') is a confound in the comparison, not a circular reduction; it leaves open the possibility of a controlled experiment. No self-citations by the authors are present or load-bearing, and the paper's own stated limitations (hyperparameter fixation, homophily reliance, transductive setting) are experimental scope limitations rather than admissions of circular reasoning.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard GNN machinery, the homophily assumption for label propagation, and the assumption that k-medoids clustering on learned embeddings approximates true classes well enough to replace a class oracle. The free parameters are mostly standard hyperparameters, but alpha and the entropy threshold are tuned on the same datasets via pre-experiments, which is the main circularity burden. No new theoretical entities are introduced.

free parameters (9)

alpha (label propagation) = 0.9
Chosen 'from pre-experiments' in Section III to balance own label versus neighbor logits; no held-out validation set, so this is tuned on the same datasets.
pseudo-label entropy threshold = 0.2
Chosen 'from pre-experiments' in Section III to discard uncertain propagated labels; directly affects the label propagation contribution.
lambda (prototype regularization weight) = 1
Taken from Xu et al. [30] without tuning; controls the strength of prototype separation terms in the GPN loss.
learning rate = 0.005
Listed in Table VI, taken from literature; fixed across all datasets and models.
hidden size = 64
Listed in Table VI, same for all models and datasets.
dropout = 0.5
Listed in Table VI, fixed across experiments.
estimated number of classes k (Cora, CiteSeer, PubMed) = 11, 13, 7
From k-means with elbow rule on Deep Graph Infomax embeddings (Appendix E); differs from true class counts 7, 6, 3.
number of sampling rounds = 5
Chosen 'to balance computation time with the number of results' (Section IV.B).
early stopping patience = 4 iterations
Algorithm 1 stops when the model has not improved for 4 validation checks; chosen by hand.

assumptions (5)

domain assumption The graph is homophilic, so label propagation produces useful pseudo-labels.
Section III states 'The dataset is assumed to be homophilic, which is the foundation of being able to apply label propagation.' All five test datasets have homophily between 0.44 and 0.77.
domain assumption Transductive setting: all vertices and edges are available during training.
Section III: 'we assume a transductive learning setting, i.e., all vertices and edges on the graph are present during training.' Standard for Planetoid datasets.
domain assumption The human annotator labels queried vertices perfectly in the main experiments.
Section III: 'We assume that the human annotator perfectly labels given vertices.' This is later relaxed in Appendix F.
domain assumption k-medoids clustering on current model embeddings yields pseudo-classes aligned with true classes.
Section IV.B replaces the class oracle with k-medoids pseudo-label assignment; the robustness result depends on clusters matching classes. This is not validated beyond the homophilic benchmark datasets.
standard math Standard GNN and linear algebra machinery (GCN message passing, normalized adjacency, Euclidean distances) is taken as given.
Background assumptions from Kipf and Welling [8] and Snell et al. [7]; not proven in this paper.

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Cite this review

Pith. "Pith review of Active Few-Shot Learning for Vertex Classification Starting from an Unlabeled Dataset." pith.science (2026). https://pith.science/paper/JCSP6IHF

@misc{pith2026250418696,
  author       = {Pith},
  title        = {Pith review of: Active Few-Shot Learning for Vertex Classification Starting from an Unlabeled Dataset},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JCSP6IHF}},
  note         = {Machine review of arXiv:2504.18696}
}

abstract

Despite the ample availability of graph data, obtaining vertex labels is a tedious and expensive task. Therefore, it is desirable to learn from a few labeled vertices only. Existing few-shot learners assume a class oracle, which provides labeled vertices for a desired class. However, such an oracle is not available in a real-world setting, i.e., when drawing a vertex for labeling it is unknown to which class the vertex belongs. Few-shot learners are often combined with prototypical networks, while classical semi-supervised vertex classification uses discriminative models, e.g., Graph Convolutional Networks (GCN). In this paper, we train our models by iteratively prompting a human annotator with vertices to annotate. We perform three experiments where we continually relax our assumptions. First, we assume a class oracle, i.e., the human annotator is provided with an equal number of vertices to label for each class. We denote this as "Balanced Sampling''. In the subsequent experiment, "Unbalanced Sampling,'' we replace the class oracle with $k$-medoids clustering and draw vertices to label from the clusters. In the last experiment, the "Unknown Number of Classes,'' we no longer assumed we knew the number and distribution of classes. Our results show that prototypical models outperform discriminative models in all experiments when fewer than $20$ samples per class are available. While dropping the assumption of the class oracle for the "Unbalanced Sampling'' experiment reduces the performance of the GCN by $9\%$, the prototypical network loses only $1\%$ on average. For the "Unknown Number of Classes'' experiment, the average performance for both models decreased further by $1\%$. Source code: https://github.com/Ximsa/2023-felix-ma

Figures

Figures reproduced from arXiv: 2504.18696 by the authors.

**Figure 2.** Imperfect human Annotator experiment on the Cora [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 4.** Overview of test accuracy deviations on Cora with 10 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: shows the effectiveness of k-medoids clustering, using the model embeddings during the “Unbalanced Sampling” experiment. Replacing k-medoids clustering with a perfect clustering, as in the “Balanced Sampling” experiment, results in sampling the same number of vertices…

**Figure 6.** Figure 6: Test accuracy on Cora, assuming perfect clustering [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 8.** Figure 8: Test accuracy on Cora, using k-medoids clustering and estimating classes [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 7.** Figure 7: Test accuracy on Cora, using k-medoids clustering 0 0.2 0.4 0.6 0.8 1 0 22 Test accuracy Budget used LP-entropy LP-medoids LP-own LP-pagerank LP-random 0 0.2 0.4 0.6 0.8 1 0 22 Test accuracy Budget used LP-entropy-LP LP-medoids-LP LP-own-LP LP-pagerank-LP LP-random-LP …

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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