Cluster-Aware Noise Estimation (CANE)

• CANE is a label-free learning framework for node classification on text-attributed graphs that models noise as cluster-conditional, capturing local reliability differences.
• It estimates cluster-specific self-trust terms by aggregating agreement scores from annotated graph and feature-space neighbors to guide pseudo-label expansion and iterative correction.
• Experimental results demonstrate that CANE outperforms global and class-conditional noise models, offering significant gains on datasets with pronounced cluster heterogeneity.

Cluster-Aware Noise Estimation (CANE) is a label-free learning framework for node classification on text-attributed graphs in which a LLM supplies noisy pseudo-labels for a budgeted subset of nodes, and the noise is modeled as cluster-conditional rather than merely global or class-conditional. In its canonical formulation, nodes are partitioned in self-supervised feature space, a cluster-conditional transition tensor $T_c[k,i,j]=P(\hat y=j\mid y=i,\mathrm{cluster}=k)$ is estimated without access to ground-truth labels, and the resulting local reliability estimates are used both to gate pseudo-label expansion and to control iterative label correction (Thapaliya et al., 27 May 2026). The acronym is ambiguous in the literature: an earlier method uses CANE to mean Candidates vs. Noises Estimation for large multi-class classification, which is a different method and a different problem setting (Han et al., 2017).

1. Problem setting and empirical motivation

CANE was introduced for label-free node classification on text-attributed graphs (TAGs) under the deliberately restrictive assumption that no ground-truth node labels are available during training. The graph is written as $G=(V,E)$, each node $v\in V$ has a semantic text attribute $t_v$, and the unknown true label is $y_v\in\{1,\ldots,C\}$. Rather than collecting manual labels, the pipeline queries an LLM on a subset $S\subseteq V$, $|S|\le B$, and obtains noisy pseudo-labels $\hat y_v\in\{1,\dots,C\}$ for $v\in S$. These pseudo-labeled nodes then seed a downstream GNN.

The motivation for CANE is the observation that LLM annotation errors are not adequately described by a single global noise rate or even by a class-conditional confusion matrix. The central empirical claim is that LLM errors are not only class-dependent but also region-dependent in feature space. Within one nominal class, different feature-space clusters can have sharply different annotation reliability. The paper’s DBLP example makes this concrete: within the true class “Database,” average LLM accuracy is $64.7\%$, but cluster-level accuracy ranges from $G=(V,E)$0 in one cluster to $G=(V,E)$1 in another (Thapaliya et al., 27 May 2026).

Appendix diagnostics formalize this claim by clustering nodes with $G=(V,E)$2 clusters and testing within-class variation in per-cluster LLM accuracy. The class-conditional null is strongly rejected on all reported benchmarks, with $G=(V,E)$3 on CiteSeer, $G=(V,E)$4 on Cora, $G=(V,E)$5 on PubMed together with small effect size $G=(V,E)$6, $G=(V,E)$7 on WikiCS, and $G=(V,E)$8 on DBLP. These results motivate a learning system that trusts LLM labels more in locally reliable regions, is more conservative in unreliable regions, and is more willing to overwrite labels where the annotator is known to fail.

2. Cluster-conditional noise model

The defining object in CANE is the cluster-conditional transition matrix

$G=(V,E)$9

Here $v\in V$0 indexes feature-space clusters, $v\in V$1 indexes the unknown true class, and $v\in V$2 indexes the observed LLM label. The diagonal entry $v\in V$3 is the probability that the LLM correctly labels a class-$v\in V$4 node in cluster $v\in V$5. The paper also introduces the coarser class-conditional matrix

$v\in V$6

and uses this contrast to argue that class-level averaging destroys local structure that is essential for robust pseudo-labeling (Thapaliya et al., 27 May 2026).

Operationally, CANE obtains cluster assignments $v\in V$7 by embedding nodes with a self-supervised GraphMAE2 encoder and grouping them into $v\in V$8 regions by subspace clustering or $v\in V$9-means on GraphMAE2 embeddings. The paper does not provide an explicit clustering objective, but it does fix $t_v$0 as the default pipeline setting.

The method is positioned as a structured middle ground between class-conditional and fully instance-dependent noise modeling. A class-conditional approach uses $t_v$1, independent of region; a fully instance-dependent model would allow noise rates to vary per node. CANE instead assumes that instance dependence is organized by feature-space clusters, which the paper describes as “a structural special case” of instance-dependent noise. A plausible implication is that CANE trades some flexibility for estimability: it preserves locality absent from class-conditional models while avoiding a free per-instance transition model.

3. Label-free estimation of local reliability

Because true labels are unavailable, CANE does not estimate the full tensor $t_v$2 directly. Its main estimator targets the diagonal self-trust terms $t_v$3 through a cross-modality agreement signal computed on a probe subset. The pipeline first allocates a fraction

$t_v$4

of the annotation budget to a probe set $t_v$5, where the full budget is

$t_v$6

For a probe node $t_v$7, CANE defines a mixed neighborhood $t_v$8 containing annotated graph neighbors and nearest neighbors in feature space, then computes agreement

$t_v$9

These per-node scores are aggregated into a cluster/class-specific reliability estimate

$y_v\in\{1,\ldots,C\}$0

and the diagonal of the transition tensor is set by

$y_v\in\{1,\ldots,C\}$1

The remaining probability mass is distributed uniformly across off-diagonal entries; the paper does not provide an explicit formula. If a $y_v\in\{1,\ldots,C\}$2 cell has too few probe nodes, the estimate backs off first to the cluster level and then to the global mean agreement (Thapaliya et al., 27 May 2026).

The rationale is that graph-local and feature-local corroboration provide a label-free proxy for correctness. The paper explicitly rejects a simpler concentration-based estimator because a broad within-cluster label distribution can arise either from clean class mixing or from noisy labeling in an otherwise single-class cluster. Agreement is intended to separate those cases more effectively.

Several reported diagnostics support the estimator’s usefulness. On PubMed, agreement recovers the true $y_v\in\{1,\ldots,C\}$3 LLM accuracy while concentration underestimates it by $y_v\in\{1,\ldots,C\}$4 percentage points. Ablations using an oracle $y_v\in\{1,\ldots,C\}$5 built from ground-truth labels perform nearly identically to the label-free estimate, which the authors interpret as leaving little oracle headroom. Clusterability diagnostics further report that GraphMAE2 clusters have $y_v\in\{1,\ldots,C\}$6–$y_v\in\{1,\ldots,C\}$7 single-class purity and that the LLM mode matches the dominant true class in $y_v\in\{1,\ldots,C\}$8–$y_v\in\{1,\ldots,C\}$9 of clusters (Thapaliya et al., 27 May 2026).

4. Pipeline, training objective, and decision rules

CANE’s end-to-end workflow begins with GraphMAE2 embeddings of the unlabeled graph, followed by clustering with $S\subseteq V$0. Under the total query budget $S\subseteq V$1, representative seed nodes are selected from each cluster, favoring central, dense nodes. A fraction $S\subseteq V$2 is annotated first to estimate $S\subseteq V$3, after which the remaining $S\subseteq V$4 seeds are queried and the full seed set is used for GNN training.

The downstream GNN is trained on LLM-labeled seeds with ELR, written in the paper as

$S\subseteq V$5

The expanded ELR formula is not given. CANE then performs pseudo-label expansion with a cluster-aware admission threshold. For an unlabeled node $S\subseteq V$6 whose GNN-predicted class is $S\subseteq V$7, the threshold is

$S\subseteq V$8

and the pseudo-label is admitted only if model confidence exceeds this value. When local reliability is high, the threshold stays near the baseline $S\subseteq V$9; when reliability is low, the threshold rises and expansion becomes stricter (Thapaliya et al., 27 May 2026).

Iterative label correction uses a complementary rule. If the GNN prediction disagrees with a node’s current label $|S|\le B$0, the label is changed only when neighbor support exceeds

$|S|\le B$1

This makes correction conservative in trustworthy regions and more permissive in locally noisy ones. The alternating part of the method concerns retraining and correction only: the paper explicitly states that $|S|\le B$2 is estimated once from the probe set and is not re-estimated by EM or by repeated noise-model updates.

The reported correction dynamics are fast. Convergence typically occurs in 2 to 4 rounds, and the first round accounts for 83–98\% of all corrections. Relative to LoCLE, CANE also avoids graph rewiring, and the paper reports approximate GNN training times of $|S|\le B$3 s for LLM-GNN, $|S|\le B$4 s for LoCLE, and $|S|\le B$5 s for CANE, while holding annotation budget and annotator fixed (Thapaliya et al., 27 May 2026).

5. Experimental regime and reported performance

CANE is evaluated on five text-attributed graph benchmarks: CiteSeer, Cora, PubMed, WikiCS, and DBLP. Appendix dataset statistics report 3,186 nodes and 6 classes for CiteSeer, 2,708 nodes and 7 classes for Cora, 19,717 nodes and 3 classes for PubMed, 11,701 nodes and 10 classes for WikiCS, and 14,376 nodes and 4 classes for DBLP. The main annotator is gpt-3.5-turbo, with gpt-4o-mini used for annotator-robustness experiments. The prompting protocol matches LoCLE and LLM-GNN: zero-shot prompting, category list provided, target node text inserted, chain-of-thought prompting, $|S|\le B$6 self-consistency samples, and majority-voted answer retained as the LLM label. The appendix states $|S|\le B$7 tokens per query, whereas the compute table summarizes $|S|\le B$8 tokens per node; the paper does not reconcile this discrepancy (Thapaliya et al., 27 May 2026).

The downstream GNN backbones are GCN and GAT, both with 2 layers, 64 hidden units, 300 epochs, Adam with learning rate $|S|\le B$9, weight decay $\hat y_v\in\{1,\dots,C\}$0, and dropout 0.7. Baselines are LLM-GNN (FP), LLM-GNN (GP), LLM-GNN (RIM), DMA, and LoCLE. The most conceptually relevant baseline is DMA because it estimates a class-conditional confusion matrix; the strongest practical baseline is LoCLE.

Across 10 dataset-backbone combinations, CANE beats LoCLE on 8/10 settings and beats matched-budget LLM-GNN and DMA on all 10. The largest gain is on WikiCS-GAT, where the reported result is about +6.05 points over LoCLE. The per-setting results reported against LoCLE are as follows.

Setting	CANE	LoCLE
CiteSeer-GAT	75.11	72.16
Cora-GAT	75.60	75.23
PubMed-GAT	81.82	81.08
WikiCS-GAT	74.91	68.86
DBLP-GAT	77.28	76.36
CiteSeer-GCN	75.92	73.62
Cora-GCN	75.04	79.81
PubMed-GCN	81.85	81.69
WikiCS-GCN	72.70	72.73
DBLP-GCN	75.66	72.89

The gains are largest on DBLP, WikiCS, and CiteSeer, which the paper links to stronger cluster-conditional noise heterogeneity. CANE helps less on PubMed, where LLM labels are already accurate and nearly class-conditional, and it underperforms LoCLE on Cora-GCN. The paper attributes the Cora-GCN deficit to small graph size, sparse local evidence per cluster, LoCLE’s rewiring being especially effective on that dense homophilous graph, and possible over-reading of reliability under spatially coherent mislabeling (Thapaliya et al., 27 May 2026).

The ablation results are structurally important. Removing $\hat y_v\in\{1,\dots,C\}$1 lowers accuracy, especially on high-heterogeneity GAT settings. Collapsing $\hat y_v\in\{1,\dots,C\}$2 to a class-conditional matrix removes most of the benefit, which supports the claim that locality rather than generic noise modeling drives the gains. Sweeping $\hat y_v\in\{1,\dots,C\}$3 shows that most datasets plateau by $\hat y_v\in\{1,\dots,C\}$4. Sweeping the number of clusters over $\hat y_v\in\{1,\dots,C\}$5 changes average accuracy by less than $\hat y_v\in\{1,\dots,C\}$6 percentage points. Replacing GraphMAE2 $\hat y_v\in\{1,\dots,C\}$7-means with raw-feature $\hat y_v\in\{1,\dots,C\}$8-means or spectral clustering changes results only slightly, by up to about $\hat y_v\in\{1,\dots,C\}$9 percentage points. Under reduced annotation budgets, CANE degrades more gracefully than LoCLE on most datasets, and with gpt-4o-mini it still beats LoCLE on 7/10 settings (Thapaliya et al., 27 May 2026).

6. Relation to prior models and to other “cluster-aware” noise methods

Within label-free graph learning, CANE is best understood as a response to the limitations of global and class-conditional noise models. A global-noise model assigns one reliability level to the entire annotator. A class-conditional model uses $v\in S$0 but ignores region. CANE’s argument is that the average matrix $v\in S$1 can over-trust hard clusters, under-use easy clusters, and blur locally distinct failure modes. The paper states that simply plugging a global matrix into forward correction does not help; the gains arise from keeping the noise model local (Thapaliya et al., 27 May 2026).

The acronym collision with Candidates vs. Noises Estimation is a recurrent source of confusion. The 2017 CANE method addresses very large multi-class softmax learning by comparing a small candidate set against sampled noise classes; its theory concerns consistency, asymptotic variance, and candidate recall in large-class classification, not cluster-conditional LLM reliability on graphs (Han et al., 2017). The two methods share only an acronym.

A broader methodological motif of “cluster-aware” or structure-aware noise handling appears in several adjacent areas, but these are analogous rather than identical methods. In cluster weak-lensing mass estimation, Wiener filtering on cluster-relevant angular scales is used to suppress large-scale modes that induce covariance between radial bins (Murray et al., 19 May 2025). In weighted edge clustering, WECAN introduces a global noise component and judges whether an edge is noisy relative to cluster-specific structural explanations of its topology and weight (Li et al., 10 Mar 2025). In SZ cluster detection, an iterative matched-filter procedure re-estimates noise covariance after masking detected clusters, thereby preventing signal contamination of the noise model (Zubeldia et al., 2022). In quantum error mitigation, Q-Cluster clusters noisy bit-strings in Hamming space, estimates an effective global bit-flip rate, and reshapes the distribution in a cluster-aware fashion (Patil et al., 15 Apr 2025). In distributed sensor networks, D-ALS enlarges innovation sets with neighboring information and uses batch covariance intersection to reduce variance in covariance estimation, which suggests a possible building block for cluster-level covariance estimation even though the method is not explicitly cluster-aware (Li et al., 2020).

These comparisons suggest a common pattern: noise estimation becomes materially more useful when it is conditioned on structure that is already relevant to the downstream task, whether that structure is feature-space locality, cluster morphology, edge-cluster geometry, or detected-source support. CANE’s distinct contribution is to instantiate that principle for LLM supervision on text-attributed graphs.

7. Assumptions, limitations, and scope

CANE assumes that the graph admits meaningful feature-space clusters and that those clusters are coherent enough for local agreement to be informative. The appendix validates this empirically, but the assumption remains central: the method is explicitly less compelling on weakly clustered graphs, and the paper notes that on graphs such as ogbn-arxiv, a coverage-oriented selector like LLM-GNN may be more effective (Thapaliya et al., 27 May 2026).

A second assumption is partial independence of graph and feature neighborhoods. The agreement estimator relies on annotated graph neighbors and nearest neighbors in feature space providing partially independent corroboration. If errors are spatially coherent, so that entire neighborhoods share the same LLM mistake, agreement can overestimate reliability. The paper presents this as a likely explanation for the Cora-GCN deficit, including an extreme example in which a Cora cluster that is $v\in S$2 true class-1 is annotated $v\in S$3 correctly while nodes still agree with one another almost unanimously.

A third limitation is support sparsity. CANE needs enough probe examples per cluster/class cell. When support is inadequate, the estimator backs off to cluster-level and then global means, reducing locality. Cora is again identified as difficult: 28.6\% of cells have too little support. More generally, the method is sensitive to small graphs with many cluster-class cells relative to budget, to LLM bias patterns, and to settings in which graph homophily and feature similarity reinforce the same wrong label.

The paper is explicit about what it does not claim. It does not recover a richly estimated off-diagonal local confusion model from unlabeled data; in practice it estimates the diagonal self-trust terms and fills off-diagonals uniformly. It does not use EM or iterative re-estimation of $v\in S$4. It does not include graph rewiring, which leaves room for LoCLE to outperform in some structural regimes. Its main success case is therefore specific: large enough text-attributed graphs, meaningful cluster structure, limited label budget, and LLM annotation errors that vary sharply across local regions rather than only across classes. Under those conditions, CANE’s central claim is that where the annotator fails matters as much as which class it fails on (Thapaliya et al., 27 May 2026).