cs.LGOct 30, 2026
SaveWhen Links Mislead: Label-Free Structural Polarity for Zero-Shot Classification of Web Pages
Organizations: School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China · Institute of Artificial Intelligence and Future Networks, Beijing Normal University, Zhuhai 519087, China · College of Computing and Data Science, Nanyang Technological University, Singapore
Abstract
Web platforms such as digital libraries, online stores and university sites must classify new pages before anyone labels them. Large language models (LLMs) can label each page from its text, but these labels are noisy, and links could correct them only where linked pages share classes. Existing zero-shot methods ignore the links, or pull a page toward its neighbours as label propagation and graph neural networks (GNNs) do, which hurts where linked pages differ in class. Others weight propagation by an LLM-estimated homophily that costs extra calls and drifts across LLMs. We find that the sign with which links should enter a prediction, which we call structural polarity, is readable without true labels. It is the excess agreement of LLM labels and text-prototype predictions along links. We thus propose ZeroPolar, which gates one signed propagation step by this statistic. Training-free ZeroPolar mixes prototype scores with any number of LLM labels, and ZeroPolar-T denoises the labels with a text classifier once half of the pages carry one. With one GPT-4o label per page, ZeroPolar-T reaches the highest mean accuracy on eleven graphs (73.99%), 6.01 points above LLM-BP and significantly above all eighteen baselines we compare. With LLM labels on only 5% of the pages, training-free ZeroPolar leads a GNN trained on these labels by 10.80 points.
Figures & tables
Figure 1. ZeroPolar measures links instead of trusting them. A professor’s page has four course in-links, so a step toward them gives course, while ZeroPolar finds that labels barely agree along the graph’s links and pushes away. On the left, a professor's home page from the Wisconsin graph, whose true class is faculty, has four in-links from course pages, with a key for solid same-class and dashed different-class links. On the right, two stacked lanes. The upper lane, Trust links, assumes that linked pages share a class, pulls the page toward its neighbours and labels it course, marked wrong. The lower lane, \sys{}, reads that zero-shot labels along the graph's links agree barely above chance, sets the marker on the minus side of a minus and plus scale, pushes the page away from its neighbours and keeps faculty, marked correct.
Figure 2. Reading polarity on eleven graphs. (a, c) LLM estimates of the homophily (§ 3.1 ) cost 500 calls and drift from the truth. (b, d) Excess agreement along edges (§ 4.2 ) splits the graphs at . Four panels in a two-by-two grid, two schematics in the top row and two scatter plots in the bottom row. First, a small graph whose sampled edges go to two LLMs that answer whether the endpoints share a class, giving one homophily estimate below a dashed true value and one above it by a drift. Second, the excess agreement, the share of edges whose endpoints carry the same label minus the chance agreement, which sets the sign to plus when it reaches delta. Third, homophily estimated by GPT-4o-mini and DeepSeek-V4-Flash against the true homophily on eleven graphs, with the two estimates on Children on either side of the diagonal and DeepSeek-V4-Flash well above it. Fourth, the excess agreement of LLM labels and of prototype predictions against the true excess agreement, with all homophilous graphs above the threshold line and all WebKB graphs below it.
Figure 3. Overview of ZeroPolar. The gate (b) reads (§ 4.2 ) from the signals in (a), and the budget routes it to ZeroPolar (c) or ZeroPolar-T (d). The bottom row shows two measured cases, on Cora and Texas. Framework diagram in four panels and a bottom row. Panel a shows a graph of web pages and an LLM that reads each page with the class names and labels it with a class, some of them wrong, and a text encoder whose embeddings meet class prototypes built from twenty LLM labels per class, giving the prototype prediction of each node. Panel b draws the prototype predictions and the LLM labels on two small graphs with solid same-label and dashed different-label edges, computes the excess agreement of each, takes their maximum and compares it with delta, which sets the sign sigma, plus to pull toward the neighbours and minus to push away. A bus carries sigma to panel c, \sys{}, if fewer than half of the test nodes carry an LLM label, and to panel d, \sysT{}, otherwise. \sys{} mixes softmax scores with the one-hot LLM label, while \sysT{} trains an MLP on the LLM labels. Both apply the same signed step, whose formula sits in panel d, and predict the class with the highest score. The bottom row shows a Cora paper whose MLP label Rule Learning becomes Probabilistic Methods after a plus step, since the MLP gives most of its in-neighbours Probabilistic Methods, and a Texas page whose MLP label faculty becomes student after a minus step that pushes it away from the faculty label of most of its in-neighbours.
Figure 4. Accuracy change from one step of Eq. ( 1 ) on prototype scores, toward or away from the neighbours. The better sign flips where the statistic crosses (§ 4.2 ), and the gate picks it on every graph. A scatter over eleven graphs of the accuracy change from one propagation step toward the neighbours, blue dots, or away from them, brown triangles, against the label-free statistic s, with a vertical dashed line at delta. Left of the line lie the four WebKB graphs, where the step toward the neighbours loses about ten points and the step away loses little or gains. Right of it lie the seven homophilous graphs, where the step toward the neighbours gains a little and the step away loses much more. Orange rings mark the sign that the gate picks, which is the better sign on every graph.
| Design graphs | Other graphs | Mean | ||||||||||||||
| Method | Calls | Cora | Cite | Pub | Wiki | Corn | Hist | Child | Sport | Tex | Wisc | Wash | Design | Other | All | |
| Vanilla ( Li et al., 2025 ) | 0 | 68.610 | 67.099 | 76.363 | 63.171 | 85.288 | 58.335 | 28.940 | 59.372 | 78.342 | 75.572 | 66.783 | 72.106 | 61.224 | 66.171 | |
| LLM direct ( OpenAI, 2024b ) | 70.295 | 64.770 | 89.858 | 66.102 | 45.550 | 53.303 | 30.764 | 66.358 | 63.102 | 56.604 | 48.908 | 67.315 | 53.173 | 59.601 | ||
| Training-free | LLM labels + LP ( Zhou et al., 2003 ) | 75.092 | 68.355 | 91.202 | 72.738 | 48.168 | 61.858 | 32.800 | 71.596 | 67.914 | 58.491 | 51.092 | 71.111 | 57.292 | 63.573 | |
| LLM-BP ( Wang et al., 2025b ) | 72.589 | 69.508 | 75.547 | 67.746 | 83.264 | 59.860 | 24.807 | 61.920 | 81.658 | 77.748 | 73.144 | 73.731 | 63.190 | 67.981 | ||
| LLM-BP (appr.) ( Wang et al., 2025b ) | 71.415 | 68.658 | 76.813 | 67.964 | 84.921 | 59.490 | 29.402 | 61.512 | 79.394 | 75.648 | 70.044 | 73.954 | 62.582 | 67.751 | ||
Table 1. Zero-shot accuracy (%) with GPT-4o labels on eleven graphs.
| Method | Computer | arXiv | Mean | |
|---|---|---|---|---|
| Vanilla ( Li et al., 2025 ) | 36.41 | 67.43 | 51.92 | |
| LLM direct | 62.10 | 75.46 | 68.78 | |
| Training-free | LLM labels + LP ( Zhou et al., 2003 ) | 63.92 | 75.46 | 69.69 |
| LLM-BP ( Wang et al., 2025b ) | 51.99 | 66.37 | 59.18 | |
| LLM-BP (appr.) ( Wang et al., 2025b ) | 46.85 | 67.70 | 57.27 | |
| Gated switch | 63.92 | 75.46 | 69.69 |
Table 2. Accuracy (%) with Qwen3.8-27B labels on two additional graphs, Computer and arXiv.
Figure 5. Mean accuracy on the homophilous against the WebKB graphs, where the dashed line joins the baselines that no other beats on both (a), and the lead of ZeroPolar-T by in-degree with 95% CIs (b), with GPT-4o labels. Two panels. Left, a scatter of the homophilous-graph mean against the WebKB mean, with baselines marked by family and a dashed line through LLM-BP, LLM-BP (appr.), ACM-GCN h64 and SAGE h256, which no other baseline beats on both axes. \sysT{}, a star near 71 and 79 percent, lies above and to the right of every baseline, \sys{} is close to it, and GOFA-T lies left of the frame. Right, bars for the lead of \sysT{} in four in-degree buckets over SAGE h64, MLP h256, LLM-BP and \sys{} with interval bars, about 5 to 8 points over LLM-BP in every bucket and near zero over SAGE h64 at six or more in-edges.
| Variant | Design | Other | All | |
|---|---|---|---|---|
| ZeroPolar-T | No step (MLP only) | 76.69 | 69.44 | 72.74 |
| Step always | 74.39 | 64.11 | 68.78 | |
| Step always | 42.47 | 55.28 | 49.45 | |
| ZeroPolar-T | 78.68 | 70.08 | 73.99 | |
| ZeroPolar | No gate (always ) | 74.47 | 60.18 | 66.68 |
| No step | 77.95 | 65.20 | 71.00 |
Table 3. Controls that remove or flip one part of each implementation, GPT-4o labels.
| GPT-4o | Qwen3-8B | ||||
|---|---|---|---|---|---|
| Method | All | Other | All | Other | Addl. |
| LLM direct | 48.98 | 43.79 | 50.10 | 43.19 | 27.41 |
| LLM-BP ( Wang et al., 2025b ) | 58.54 | 49.27 | 49.15 | 42.63 | 26.89 |
| Gated switch | 62.75 | 53.09 | 52.75 | 42.73 | 30.52 |
| ZeroPolar | 63.38 | 53.56 | 55.52 | 46.27 | 29.65 |
| SAGE h64 ( Hamilton et al., 2017 ) | 62.71 | 53.74 | 54.75 | 45.10 | 30.35 |
Table 4. Macro-F1 averaged over seeds and then over graphs.
Figure 6. Eleven-graph mean accuracy against LLM calls, for ZeroPolar against SAGE h64 and Locle at few labels (a) and for the budget switch of § 4.1 against the best baseline (b), shaded where ours leads. Two line panels on logarithmic axes of LLM calls over the eleven graphs. Left, at few labels, \sys{} starts near 63 percent at about 800 calls with 5 prototype labels per class, reaches about 67 percent at about 1.3 thousand calls with 10, and stays near 67 to 69 percent up to about 49 thousand calls, while SAGE h64 rises from about 42 percent at about 800 calls to about 64 percent and Locle with the zero-shot cache rises from about 54 to about 62 percent over its four budgets between about 1.8 thousand and 14 thousand calls, both below \sys{} throughout. Right, from about 64 thousand to about 257 thousand calls around the full budget of one LLM label per test node, our line, which follows the budget switch between the two implementations, rises from about 70 percent to about 74 percent at the full budget and stays flat beyond it. The best baseline, the per-budget maximum of all \nNbaseWbaselines, stays near 69 percent up to about 90 thousand calls and rises to about 73 percent at the full budget. Our line is above it across the whole axis, and the gap is shaded.
| Qwen3.8-27B | Qwen3-8B | Llama-3.1-8B | Mistral-7B | |||||||||
| Method | Other | All | Addl. | Other | All | Addl. | Other | All | Addl. | Other | All | |
| Vanilla | 61.87 | 66.31 | 51.92 | 50.79 | 58.40 | 38.55 | 53.69 | 60.01 | 38.16 | 52.28 | 58.49 | |
| LLM direct | 68.91 | 72.15 | 68.78 | 53.70 | 59.34 | 44.37 | 54.12 | 58.73 | 47.27 | 53.66 | 56.69 | |
| Training-free | LLM labels + LP | 68.91 | 72.15 | 69.69 | 53.65 | 59.33 | 44.64 | 54.07 | 58.74 | 47.31 | 53.92 | 57.04 |
| LLM-BP | 63.66 | 66.36 | 59.18 | 51.85 | 55.60 | 43.22 | 57.87 | 59.31 | 41.20 | 49.10 | 45.23 | |
| LLM-BP (appr.) | 62.75 | 67.54 | 57.27 | 52.15 | 60.08 | 43.98 | 56.19 | 62.33 | 42.88 | 54.05 | 60.47 | |
Table 5. Mean accuracy (%) with open LLM annotators. A dash marks a setting not run.
Figure 7. Eleven-graph mean accuracy with GPT-4o labels when one setting of ZeroPolar or ZeroPolar-T changes. Six small line panels, one per setting, beta plus, beta minus, delta, tau, w and the number of steps, on a shared accuracy axis from 66 to 76 percent. ZeroPolar stays near 72 percent across beta plus, beta minus, delta and tau and drops with more steps. ZeroPolar-T, drawn for w, delta and steps, stays near 74 percent and drops with two steps.
| Method | ||||
|---|---|---|---|---|
| Vanilla | 46.51 | 64.12 | 68.88 | 73.61 |
| Vanilla + NA | 41.78 | 57.66 | 63.30 | 68.64 |
| LLM-BP | 47.88 | 65.13 | 69.10 | 73.34 |
| LLM-BP (appr.) | 47.70 | 65.45 | 69.64 | 74.03 |
| ZeroPolar, no LLM labels | 47.32 | 64.76 | 69.02 | 73.82 |
| ZeroPolar | 67.63 | 73.66 | 74.91 | 76.16 |
Table 6. Eleven-graph mean accuracy in the few-shot setting of LLM-BP with true labels per class and GPT-4o labels.
| Qwen3-8B | Llama-3.1-8B | |||||||
|---|---|---|---|---|---|---|---|---|
| Method | Inst. | Photo | Mean | Inst. | Photo | Mean | ||
| LLM-BP ( Wang et al., 2025b ) | 62.75 | 50.50 | 44.33 | 52.53 | 61.67 | 52.02 | 24.80 | 46.16 |
| ZeroPolar | 61.05 | 54.52 | 44.82 | 53.46 | 60.53 | 55.42 | 48.30 | 54.75 |
| MLP h256 ( Chen et al., 2024d ) | 42.28 | 46.57 | 42.79 | 43.88 | 44.65 | 47.23 | 48.52 | 46.80 |
| SAGE h256 ( Hamilton et al., 2017 ) | 41.99 | 46.72 | 43.04 | 43.92 | 44.80 | 47.12 | 48.93 | 46.95 |
| SAGE h64 ( Hamilton et al., 2017 ) | 41.59 | 46.11 | 42.96 | 43.56 | 45.09 | 46.76 | 49.67 | 47.17 |
Table 7. Accuracy on three further Web platforms with Qwen3-8B or Llama-3.1-8B as the annotator.
Figure 8. Eleven-graph mean accuracy as injected noise replaces GPT-4o labels by random classes, for ZeroPolar-T and baselines (a) and for two gates of ZeroPolar (b). Two line panels against the injected noise rate from zero to forty percent. Left, \sysT{} has the highest mean at every rate, above SAGE h256, SAGE h64, MLP h256, the gated switch and a flat LLM-BP line near 68 percent. Right, \sys{} with the larger of the two statistics declines slowly, while the gate that reads only the LLM labels falls steeply at high noise, with solid lines for clean prototype labels and dashed lines for noisy ones.
Figure 9. Two nodes repaired by the signed step of ZeroPolar-T , with the gate at on Cora and on Texas. Frames mark correct and wrong classes. Two cases stacked. Above, a Cora paper on a non-axiomatic reasoning system whose GPT-4o label is correct, whose MLP prediction is Rule Learning and whose seven in-neighbours all belong to Probabilistic Methods, and the plus step returns it to Probabilistic Methods. Below, a Texas home page that GPT-4o and the MLP label faculty, whose three in-neighbours are a course, a faculty and a project page, and the minus step moves it to student.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 10. Eleven-graph mean accuracy against LLM calls for both implementations and every baseline. Line plot on a logarithmic axis of LLM calls with a three-column legend below it. LLM-BP (appr.) and LLM-BP appear as short curves over their prototype budgets near 63 to 69 percent with dashed flat lines beyond their last point, and Vanilla, which makes no call, is a dashed horizontal line near 66 percent. SAGE h64 and \sysT{} climb from about 40 percent at the smallest budgets to about 72 and 74 percent at the full budget, while \sys{} stays near 68 percent and rises to about 72 percent. Locle with the zero-shot cache is a short curve over its four budgets from about 54 to 62 percent at a few thousand calls. The other baselines, including four heterophily GNNs, appear as single points at one label per test node between about 60 and 73 percent.
| Design graphs | Other graphs | Mean | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Method | Calls | Cora | Cite | Pub | Wiki | Corn | Hist | Child | Sport | Tex | Wisc | Wash | Design | Other | All | |
| Trained | MLP h64 ( Chen et al., 2024d ) | 75.461 | 69.512 | 90.112 | 74.055 | 66.318 | 69.137 | 35.137 | 75.227 | 84.848 | 71.195 | 65.211 | 75.091 | 66.793 | 70.565 | |
| MLP h256 ( Chen et al., 2024d ) | 75.154 | 69.486 | 90.281 | 72.630 | 75.742 | 68.824 | 34.333 | 75.263 | 87.522 | 75.094 | 70.742 | 76.658 | 68.630 | 72.279 | ||
| GCN h64 ( Kipf and Welling, 2017 ) | 77.245 | 71.720 | 86.934 | 74.426 | 42.932 | 68.840 | 34.723 | 78.153 | 65.241 | 58.994 | 37.991 | 70.651 | 57.324 | 63.382 | ||
| GCN h256 ( Kipf and Welling, 2017 ) | 76.507 | 71.447 | 86.629 | 74.038 | 41.361 | 68.002 | 33.925 | 77.656 | 67.558 | 59.119 | 59.825 | 69.997 | 61.014 | 65.097 | ||
| SAGE h256 ( Hamilton et al., 2017 ) | 77.122 | 71.551 | 89.579 | 74.420 | 72.775 | 68.371 | 35.493 | 77.896 | 82.175 | 75.220 | 72.926 | 77.089 | 68.680 | 72.502 | ||
Table 8. Zero-shot accuracy (%) of every trained baseline with GPT-4o labels on eleven graphs.
| Design graphs | Other graphs | Mean | ||||||||||||
| Method | Cora | Cite | Pub | Wiki | Corn | Hist | Child | Sport | Tex | Wisc | Wash | Design | Other | All |
| GraphGPT ( Tang et al., 2024 ) | 17.48 | 13.93 | 42.94 | 33.59 | 10.18 | 12.31 | 9.94 | 4.53 | 18.48 | 12.35 | 20.64 | 23.62 | 13.04 | 17.85 |
| LLaGA ( Chen et al., 2024a ) | 11.62 | 19.52 | 7.56 | 10.98 | 12.57 | 7.95 | 10.09 | 1.84 | 15.51 | 15.09 | 10.48 | 12.45 | 10.16 | 11.20 |
| OFA ( Liu et al., 2024 ) | 20.36 | 41.31 | 28.18 | 30.77 | 29.84 | 8.25 | 3.05 | 15.18 | 11.77 | 4.80 | 6.04 | 30.09 | 8.18 | 18.14 |
| ZeroG ( Li et al., 2024 ) | 60.40 | 50.35 | 74.68 | 46.74 | 10.47 | 36.55 | 12.72 | 14.27 | 53.48 | 12.66 | 8.30 | 48.53 | 23.00 | 34.60 |
| UniGLM ( Fang et al., 2025 ) | 45.57 | 52.26 | 70.33 | 55.05 | 23.03 | 44.24 | 21.48 | 33.46 | 21.39 | 27.16 | 24.01 | 49.25 | 28.62 | 38.00 |
Table 9. Zero-shot accuracy (%) of six published graph models reported by LLM-BP, next to ours with GPT-4o labels.
| Method | Computer | arXiv | Mean | |
|---|---|---|---|---|
| Vanilla ( Li et al., 2025 ) | 33.16 | 43.93 | 38.55 | |
| LLM direct | 45.30 | 43.44 | 44.37 | |
| Training-free | LLM labels + LP ( Zhou et al., 2003 ) | 45.84 | 43.44 | 44.64 |
| LLM-BP ( Wang et al., 2025b ) | 42.92 | 43.52 | 43.22 | |
| LLM-BP (appr.) ( Wang et al., 2025b ) | 43.79 | 44.17 | 43.98 | |
| Gated switch | 45.84 | 43.93 | 44.89 |
Table 10. Accuracy (%) with Qwen3-8B labels on the two additional graphs, Computer and arXiv.
| Qwen3-8B | Llama-3.1-8B | Mistral-7B | ||||||
|---|---|---|---|---|---|---|---|---|
| Method | Other | All | Addl. | Other | All | Addl. | Other | All |
| SAGE h64 ( Hamilton et al., 2017 ) | 57.86 | 63.44 | 54.54 | 54.26 | 59.23 | 51.01 | 57.03 | 60.63 |
| GPR-GNN h256 ( Chien et al., 2021 ) | 57.53 | 62.70 | 55.16 | 55.23 | 58.96 | 51.45 | 56.46 | 58.91 |
| H2GCN h64 ( Zhu et al., 2020 ) | 59.11 | 64.40 | 53.09 | 55.15 | 59.86 | 50.41 | 57.47 | 60.44 |
| FAGCN h256 ( Bo et al., 2021 ) | 58.40 | 64.19 | 54.31 | 53.98 | 58.79 | 49.62 | 57.93 | 58.83 |
| ACM-GCN h64 ( Luan et al., 2022 ) | 58.00 | 63.70 | 52.46 | 54.95 | 59.00 | 49.44 | 57.17 | 60.17 |
Table 11. Mean accuracy (%) of SAGE h64, the four heterophily GNNs and ZeroPolar-T with three open LLM annotators.
| Baseline | Setting | Difference [95% CI] | Ahead |
|---|---|---|---|
| MLP h64 ( Chen et al., 2024d ) | Patience 50 | ||
| MLP h256 ( Chen et al., 2024d ) | Patience 50 | ||
| GCN h64 ( Kipf and Welling, 2017 ) | Patience 50 | ||
| GCN h256 ( Kipf and Welling, 2017 ) | Patience 50 | ||
| SAGE h256 ( Hamilton et al., 2017 ) | Patience 50 | ||
| SAGE h64 ( Hamilton et al., 2017 ) | Patience 50 |
Table 12. ZeroPolar-T minus each trained baseline with a patience of 50 on the eleven graphs with GPT-4o labels, and over ten training seeds per setting.
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