IceBerg: Debiased Self-Training for Class-Imbalanced Node Classification

Daixin Wang; Dingshuo Chen; Hongrui Liu; Jeffrey Xu Yu; Jun Zhou; Tong Zhao; Zhiqiang Zhang; Zhixun Li

REVIEW 4 major objections 6 minor 55 references

IceBerg: Debiased Self-Training for Class-Imbalanced Node Classification

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

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Pith's one-line read Rebalancing pseudo-labels by their per-class counts lets GNNs turn unlabeled nodes into a cure for both class imbalance and extreme label scarcity.

desk verdict A practical pseudo-label rebalancing module that shows consistent empirical gains, but the debiasing story is unverified and the added propagation component does not consistently beat the simpler module. read the letter →

arxiv 2502.06280 v1 pith:Y65VI26F submitted 2025-02-10 cs.LG

Zhixun Li , Dingshuo Chen , Tong Zhao , Daixin Wang , Hongrui Liu , Zhiqiang Zhang , Jun Zhou , Jeffrey Xu Yu This is my paper · ORCID

classification cs.LG

keywords class-imbalancednodeclassificationself-trainingpseudo-labelinggraphneuralnetworksfew-shotlearninglabeldistributionshiftbalancedsoftmaxpropagationandtransformationdecoupling

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 labeled nodes are only the visible surface of what graph models can learn from, and that the large unlabeled pool can fix two weaknesses at once: skewed class proportions and extremely scarce labels. Its central claim is that a small module, Double Balancing, which counts the model's own pseudo-labels on unlabeled nodes and rebalances the unsupervised loss against those counts, substantially improves existing class-imbalanced node classification methods with almost no extra training cost. A second component separates graph propagation from feature transformation so that supervision signals travel further without triggering over-smoothing, which the paper identifies as the real bottleneck when minority classes have only one or two labels. Together these pieces form IceBerg, reported to reach the best balanced accuracy and macro-F1 among the compared methods across homophily and heterophily benchmarks, and also to set the best few-shot accuracy on citation graphs. The practical promise is that strong gains come from a surgical change to an existing pipeline rather than from a new architecture.

What carries the argument

The load-bearing object is Double Balancing, a plug-in that computes a dynamic confidence threshold as the mean model confidence on unlabeled nodes, counts pseudo-labels per class to obtain $\pi_c$, and adds to the unsupervised loss a balanced-softmax term on adjusted logits $q[c] = f_\theta(v)[c] + \mu \log \pi_c$, with an optional symmetric cross-entropy term for noise tolerance. The supporting machinery is the propagation-then-transformation (PPTT) architecture: node features are diffused over many hops by a personalised-PageRank-style update before a simple MLP classifier is trained, so supervision propagates farther and the propagation itself can be precomputed once. The two pieces work together because pseudo-labels enlarge the set of propagation sources while decoupling enlarges the distance each source can reach.

What would settle it

On a graph with known full labels, compute the true per-class distribution of the unlabeled set and compare it with the pseudo-label counts $\pi_c$ from a majority-biased model; if the discrepancy is large and rebalancing against the true counts no longer improves, or hurts, balanced accuracy relative to using the model's counts, then the claimed debiasing mechanism is not what carries the gain.

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Extended reading notes

Core claim

The discovery is that the class distribution of unlabeled nodes, though unknown, can be usefully estimated by the pseudo-labels the model itself produces, and that this estimate is enough to debias self-training. In Double Balancing, a dynamic confidence threshold selects pseudo-labels, their per-class counts form an estimated distribution, and the unsupervised loss is reweighted by adjusting logits with the log of those counts and applying balanced softmax. Because the model is majority-biased, majority classes generate both more pseudo-labels and higher-confidence ones; rebalancing the unsupervised term against the estimated counts counteracts the Matthew effect, in which the rich classes get richer. The paper further claims that heavily imbalanced minority classes face a hidden few-shot problem, and that disentangling propagation from transformation, then increasing propagation hops with a precomputed diffusion process, lets weak supervision reach distant nodes without over-smoothing. On this reading, IceBerg is not a new GNN but a debiased self-training wrapper plus an architectural decoupling, and the paper reports consistent gains across nine datasets and imbalance ratios of 10 and 20.

Load-bearing premise

The load-bearing premise is that the per-class counts of pseudo-labels on unlabeled nodes accurately estimate the true class distribution of the unlabeled set, so that rebalancing the loss against those counts corrects rather than amplifies the model's bias.

Editorial extensions

If this is right

Adding Double Balancing on top of any of the seven base balancing methods improves average balanced accuracy on Cora, CiteSeer, PubMed, and CS; on Cora at imbalance ratio 10 the average gain over the base model is about +6.85 points for DB and +8.35 for the full IceBerg.
In few-shot node classification with 1, 2, 3, and 5 labels per class, IceBerg reports the best accuracy on Cora, CiteSeer, and PubMed, with the largest margin appearing at one label per class.
The dynamic threshold lets the model use a large fraction of unlabeled nodes early in training while keeping pseudo-label accuracy high; on Cora at imbalance ratio 20 it reaches roughly 60% utilization and 90% pseudo-label accuracy around epoch 100.
Because propagation is precomputed and decoupled from the trained MLP, IceBerg can match or beat the base model's training time despite using pseudo-labels.
The gains persist on large graphs such as Physics, ogbn-arxiv, and CoraFull and on heterophilic graphs such as Penn94 and Roman-Empire.

Reading between the lines

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

If the pseudo-label counts inherit strong majority bias, the estimated distribution $\pi_c$ will under-count minority classes; the paper's noise-tolerant term smooths the loss but does not fix a biased count itself, so the mechanism's ceiling is set by pseudo-label accuracy.
The same recipe, count pseudo-labels per class and rebalance the unsupervised loss with a balanced objective, applies to any self-training pipeline; a direct test would be to plug Double Balancing into a non-graph semi-supervised classifier with a class-imbalanced unlabeled pool.
The 'tip of the iceberg' framing implies that class imbalance and label scarcity are partly the same failure: supervision does not reach enough nodes. If so, the value of the unlabeled loss should grow as labels become rarer, which the paper's few-shot results support and which is testable by ablating the weight $\lambda$ on the unsupervised term.

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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

Short version: this is a useful empirical paper with a weak theoretical hinge. The core idea—apply balanced softmax to the pseudo-label counts during self-training, so the unsupervised loss penalizes majority overconfidence—consistently improves imbalanced node classification across a lot of settings. The paper does that carefully, with nine datasets, a wide set of baselines, and both class-imbalanced and few-shot evaluations. The DB module really is a few lines of code, and the efficiency measurements are honest about overhead. That part deserves credit.

But the paper claims more than it shows. The load-bearing step is that pi_c, the count of model-generated pseudo-labels above a dynamic threshold, estimates the true unlabeled class distribution. There is no evidence for that, and the paper's own Matthew-effect analysis argues against it: a majority-biased model will threshold in more majority-class examples, so pi_c inherits the bias. Section 3.2 explicitly concedes p_l(x|y) != p_u(x|y) under heavy imbalance, which is exactly the regime of the main tables. The noise-tolerant term addresses label noise, not class-frequency bias. So the debiasing story is not proven; the empirical success may be due to a heuristic that still works.

Second, the decoupled propagation component (IceBerg over DB) does not consistently help. On PubMed and CS, in both IR=10 and IR=20 tables, DB alone is equal to or better than IceBerg on balanced accuracy. The 'state-of-the-art' framing leans on the combined framework, but the incremental contribution of the architecture is at best mixed.

Third, the reporting is incomplete: Tables 2 and 4 don't include standard deviations, so we can't tell if the gains are significant; key hyperparameters (mu, beta, lambda, alpha, T) are not reported. And there's a factual error: the paper says ogbn-arxiv has no public split, but OGB provides an official one. That needs fixing for reproducibility.

All that said, the empirical evidence is extensive and mostly consistent, and the DB module is likely to be genuinely useful to practitioners. It deserves a serious referee, but the referee should push for the missing artifacts, a direct check of pi_c against true class counts, and a more honest separation of DB's contribution from the propagation component.

I'd bring this to a reading group for the empirical design, but I wouldn't cite it yet without seeing the missing numbers.

Referee Report

4 major / 6 minor

Summary. The paper proposes IceBerg, a framework for class-imbalanced and few-shot semi-supervised node classification on graphs. The method consists of two components: (i) Double Balancing (DB), a plug-in module that computes confidence-thresholded pseudo-labels on unlabeled nodes, estimates the per-class pseudo-label distribution (Eqs. 5-6), and reweights the unsupervised cross-entropy loss with a balanced-softmax logit adjustment (Eqs. 7-8), optionally augmented by a symmetric cross-entropy noise-tolerance term (Eq. 9); and (ii) a decoupled propagation-then-transformation backbone (Eqs. 10-11) that performs many steps of graph diffusion before an MLP classifier, intended to propagate weak supervision to distant nodes. The paper reports experiments on nine datasets across homogeneous, heterogeneous, large, and few-shot settings, comparing DB and IceBerg as plug-ins over seven base balancing methods and against several CIGL and FSGL baselines, together with efficiency studies and visualizations.

Significance. If the reported gains are reproducible, the contribution is practically significant: DB is a genuinely simple plug-in that appears to improve balanced accuracy and macro-F1 consistently over base methods (e.g., Table 2 average improvements of +5.80 to +13.96 for DB, and larger gains in the heavy-imbalance Table 4). The release of code, the integration of many baselines into one framework, and the evaluation across nine datasets are notable strengths. However, the central 'debiased' claim rests on an unverified estimate of the unlabeled class distribution formed from the model's own pseudo-labels, and the main comparative tables report only means over ten runs without standard deviations or significance tests. The significance of the contribution is therefore conditional on resolving those two concerns.

major comments (4)

[Section 3.1, Eqs. (5)-(8)] The debiasing mechanism is self-referential: the class-frequency estimate pi_c is computed from the model's own pseudo-labels after confidence thresholding, and Section 3.2 and Appendix A.1 document that the labeled and unlabeled distributions differ and that selection bias is severe in the heavy-imbalance/few-shot regime. The paper asserts (Section 3.1) that 'pseudo labels can serve as a good estimate' of the class distribution, but it never compares pi_c to the true class counts of the unlabeled set. Because the model is majority-biased (the Matthew effect) and because thresholding preferentially admits high-confidence, majority-class nodes, pi_c is a biased statistic and the pseudo-labeled set is not a random draw from V_U. The noise-tolerant term in Eq. (9) mitigates label noise but does not correct a biased class-frequency estimate. Please provide empirical validation of pi_c on datasets with known unlabeled labels, or an oracle-pi_c ablation, or a theoretical argument that the bias cancels under the logit adjustment in Eq. (8).
[Tables 2 and 4] All main results are reported only as means over ten runs, with no standard deviations or significance tests. Several comparisons that are load-bearing for the paper's claims are numerically small or inconsistent: in Table 2, DB and IceBerg are nearly tied on PubMed (77.17 vs. 77.48 average balanced accuracy) and on CS (88.71 vs. 88.47); in Table 4, IceBerg is slightly below DB on PubMed (76.30 vs. 76.38) and on CS (84.41 vs. 84.52). Without variance information, the claims that IceBerg 'further boosts' DB and achieves state-of-the-art performance are not supported. Please report standard deviations or paired significance tests for the core comparisons.
[Section 3.2, Tables 1-4] The contribution of the decoupled propagation component is not isolated in the main experiments. Table 1 shows that increasing propagation hops improves balanced accuracy on Cora and CiteSeer for one unspecified model, and Table 3 compares IceBerg with DB in the few-shot setting, but IceBerg always combines DB with the decoupled architecture. There is no ablation that adds the decoupled propagation alone to the same base model. Given that several IceBerg-vs-DB differences are small or negative on PubMed and CS, the paper should report BASE, BASE+propagation, BASE+DB, and IceBerg under the same protocol across datasets and imbalance ratios to support the claimed benefit of propagation.
[Section 4.4 and implementation details] The method introduces several free parameters -- mu (Eq. 8), beta (Eq. 9), lambda, alpha, and T (Eqs. 10-11) -- but the 'parameter study' in Section 4.4 only examines the dynamic threshold (Figure 3) and does not report sensitivity to any of these parameters. Since the paper emphasizes that DB is a simple plug-and-play module with 'almost no additional training overhead', the robustness of the reported gains to mu, beta, and T should be demonstrated, at least on one or two representative datasets.

minor comments (6)

[Eq. (6)] Equation (6) omits the class index: pi_c should be defined as the count of pseudo-labels assigned to class c that also pass the threshold, for example pi_c = sum_j 1(pred_j = c and max(f_theta(v_j)) >= tau'), since the quantity is used per class in Eq. (8).
[Section 2] The sentence 'According to the ording the model arrages theP and T operations' is garbled and should be rewritten.
[Section 3.2 heading] The heading 'Propagation then Tramsformation' contains a typo; it should read 'Transformation'.
[Table 2] The CiteSeer IceBerg macro-F1 entry '62.83±18.22' appears to be a formatting error carried over from another column; the reported average should be checked and corrected.
[Tables 2 and 6] The appendices use both 'OOT' (out-of-time) and 'OOM' (out-of-memory) for missing experimental entries; the notation should be standardized, as Table 6 uses OOM where Table 2 uses OOT.
[Section 3.2, Figure 2] The two-moon toy experiment is described only qualitatively; a quantitative description of the setup, the plotted quantities, and the observed effect would make the selection-bias argument easier to evaluate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the pseudo-label-based balancing is a self-training design, and the central performance claim is validated on held-out labels.

full rationale

The derivation chain has two components: Double Balancing, which counts model-generated pseudo-labels (Eqs. 5-6) and uses those counts in a balanced-softmax logit adjustment (Eqs. 7-8), and decoupled propagation with diffused features (Eqs. 10-11). The only self-referential element is that the balancing weights pi_c are computed from the model's own pseudo-labels. However, this is an explicit design feature of self-training rather than a circular derivation: the paper does not define its target quantity in terms of pi_c, and it does not relabel a fitted parameter as a prediction. The central empirical claim, that IceBerg improves balanced accuracy and macro-F1, is evaluated against held-out ground-truth labels in Tables 2-4 and 6-7, so it has independent content. The paper explicitly states the load-bearing assumption that pseudo labels estimate the class distribution ('Surprisingly, we found that the pseudo labels generated by the model can serve as a good estimation of unlabeled set class distribution', Section 1) and also acknowledges the risk of confirmation bias (Section 3.1) and the failure of p_l(x|y) = p_u(x|y) = p_t(x|y) in heavy-imbalance and few-shot regimes (Section 3.2). These are stated limitations and risk factors, not hidden circularity: no equation reduces to its own input by construction. The self-citations, including DR-GST [22] with overlapping authors, are used as baselines or general motivation and are not load-bearing for the framework's derivation. I therefore find no significant circularity.

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

The paper introduces no new physical or conceptual entities. Its free parameters are mostly unreported hyperparameters, which is a reproducibility concern. The main load-bearing assumption is that model-generated pseudo-labels provide a reliable estimate of the unlabeled class distribution; this is stated but not proven.

free parameters (5)

mu (logit adjustment strength) = not reported
Scaling parameter in Eq. 8 controlling intensity of balanced softmax adjustment; no value or tuning range given in the paper.
beta (noise-tolerant trade-off) = not reported
Trade-off hyperparameter in Eq. 9 for the symmetric cross-entropy term; no value reported.
lambda (unsupervised loss weight) = not reported
Trade-off between supervised and unsupervised loss in Eq. 3; no value reported.
alpha (restart probability) = not reported
Restart probability in the diffusion-based propagation Eq. 10; no value reported.
T (number of propagation steps) = not reported, Table 1 suggests 10-14
Number of propagation hops in Eq. 10 is treated as a tunable hyperparameter; Table 1 shows performance varying with hops, but the final choice is not stated.

assumptions (5)

ad hoc to paper Pseudo labels generated by the model accurately estimate the unlabeled class distribution (pi_c).
Stated in Section 3.1: 'due to the high accuracy of pseudo labels, they can serve as a good estimate of pseudo class distribution.' This is load-bearing for Double Balancing but not proven; if false, balancing is miscalibrated.
domain assumption Class conditional distributions of labeled, unlabeled, and test sets are consistent (p_l(x|y) = p_u(x|y) = p_t(x|y)).
Assumed in the domain-adaptation analysis of Eq. 4 in Section 3.1; the paper later notes this does not always hold under selection bias, but the derivation of Double Balancing depends on it.
domain assumption The target test class distribution is balanced (p_t(y) uniform).
Used in Eq. 4 to frame CIGL as label distribution shift; this matches balanced accuracy and macro-F1 evaluation but may not hold in real applications.
domain assumption Model degradation in deep GNNs is primarily caused by transformations, not propagation.
Imported from cited prior work [48] and used to justify the PPTT architecture in Section 3.2; not verified in this paper.
ad hoc to paper The dynamic threshold tau' = mean confidence selects pseudo labels with sufficiently high accuracy.
Implicit in Eqs. 5-6; the paper shows empirically (Figure 3) that the dynamic threshold yields about 90% pseudo accuracy on Cora, but provides no general guarantee.

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Cite this review

Pith. "Pith review of IceBerg: Debiased Self-Training for Class-Imbalanced Node Classification." pith.science (2026). https://pith.science/paper/Y65VI26F

@misc{pith2026250206280,
  author       = {Pith},
  title        = {Pith review of: IceBerg: Debiased Self-Training for Class-Imbalanced Node Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y65VI26F}},
  note         = {Machine review of arXiv:2502.06280}
}

read the original abstract

Graph Neural Networks (GNNs) have achieved great success in dealing with non-Euclidean graph-structured data and have been widely deployed in many real-world applications. However, their effectiveness is often jeopardized under class-imbalanced training sets. Most existing studies have analyzed class-imbalanced node classification from a supervised learning perspective, but they do not fully utilize the large number of unlabeled nodes in semi-supervised scenarios. We claim that the supervised signal is just the tip of the iceberg and a large number of unlabeled nodes have not yet been effectively utilized. In this work, we propose IceBerg, a debiased self-training framework to address the class-imbalanced and few-shot challenges for GNNs at the same time. Specifically, to figure out the Matthew effect and label distribution shift in self-training, we propose Double Balancing, which can largely improve the performance of existing baselines with just a few lines of code as a simple plug-and-play module. Secondly, to enhance the long-range propagation capability of GNNs, we disentangle the propagation and transformation operations of GNNs. Therefore, the weak supervision signals can propagate more effectively to address the few-shot issue. In summary, we find that leveraging unlabeled nodes can significantly enhance the performance of GNNs in class-imbalanced and few-shot scenarios, and even small, surgical modifications can lead to substantial performance improvements. Systematic experiments on benchmark datasets show that our method can deliver considerable performance gain over existing class-imbalanced node classification baselines. Additionally, due to IceBerg's outstanding ability to leverage unsupervised signals, it also achieves state-of-the-art results in few-shot node classification scenarios. The code of IceBerg is available at: https://github.com/ZhixunLEE/IceBerg.

Figures

Figures reproduced from arXiv: 2502.06280 by the authors.

**Figure 1.** Left: Confidence of pseudo labels in the long-tailed node classification task. The first four classes are majority classes, and the latter three are minority classes. Right: Matthew Effect of standard multi-stage self-training on longtailed graph datasets. 2 Preliminary Notations. To maintain consistency of notations, we use bold uppercase and lowercase letters to represent matrices and vectors, and calligraphic f… view at source ↗

**Figure 2.** Toy example on the two-moon dataset. We utilize a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** On the Cora dataset, when the imbalance ratio (IR) is [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Visualization of node representations. applications of CIGL, its techniques have been applied to many other tasks as well, e.g., graph anomaly detection [27, 53], graph fairness learning [19], and graph data pruning [43]. 5.2 Few-Shot Graph Learning Besides, modern art…

**Figure 5.** Figure 5: The first row is the class distribution of the unla [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: The time it takes to run 1000 epochs across datasets. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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