BLADE: Distilled LLM Regularization for Calibrated Knowledge Graph Completion
Organizations: Department of Computer Science, Iowa State University · Brac University · Department of Civil, Construction & Environmental Engineering, Iowa State University
Abstract
Knowledge graph completion models optimize ranking, although many downstream applications require calibrated probabilities. We present BLADE, a variational model that separates latent truth from graph recording and distills offline language-model judgments into a frozen teacher regularizer. The LLM is absent during inference. Posterior samples provide predictive probabilities and epistemic uncertainty, while the compact teacher remains available only as an optional triage factor. Across five benchmarks, BLADE remains competitive under a common ranking protocol and reduces adaptive ECE by a macro-average of 60.1% relative to deep ensembles and 78.1% relative to temperature-scaled RotatE. On identical FB15k-237 candidate sets, BLADE also improves ECE, Brier score, and NLL over validation-selected histogram binning and a matched generative ComplEx2 model, with these improvements persisting on a prespecified near-miss pool. Under controlled injected missingness, the full triage score achieves a mean AUC-PR of 0.863, compared with 0.805 for its strongest non-teacher variant. Leakage stress tests show that aligned semantics matter, but they cannot exclude knowledge acquired during LLM pretraining. We therefore claim calibration only for the declared candidate distributions, not for all unobserved triples.
Figures & tables
| Method | FB15k-237 | WN18RR | CoDEx-M | NELL-995 | Hetionet |
|---|---|---|---|---|---|
| RotatE | .338 | .476 | .310 | .492 | .210 |
| SimKGC | .368 | .524 | .354 | .521 | .230 |
| KG2E | .291 | .410 | .265 | .415 | .180 |
| Deep ensemble | .349 | .488 | .321 | .504 | .219 |
| BLADE | .365 .002 | .518 .003 | .348 .002 | .522 .004 | .243 .002 |
| Method | FB15k-237 | WN18RR | CoDEx-M | NELL-995 | Hetionet |
|---|---|---|---|---|---|
| RotatE + temperature | .082 / .142 | .071 / .120 | .089 / .151 | .091 / .155 | .065 / .118 |
| MC-dropout RotatE | .074 / .131 | .065 / .114 | .081 / .142 | .079 / .139 | .058 / .109 |
| Deep ensemble | .045 / .102 | .038 / .091 | .050 / .112 | .052 / .118 | .034 / .082 |
| KG2E | .112 / .185 | .104 / .171 | .121 / .198 | .118 / .192 | .098 / .161 |
| BLADE without teacher | .049 / .110 | .044 / .098 | .055 / .119 | .058 / .122 | .041 / .089 |
| BLADE | .018 / .061 | .014 / .048 | .021 / .068 | .025 / .072 | .011 / .039 |
| Exact candidate pool | Hard near-miss pool | |||||
|---|---|---|---|---|---|---|
| Method | ECE | Brier | NLL | ECE | Brier | NLL |
| RotatE + histogram binning | .023 | .071 | .244 | .052 | .105 | .349 |
| ComplEx 2 + relation-wise Platt | .022 | .068 | .232 | .047 | .099 | .331 |
| BLADE–ComplEx | .021 | .065 | .226 | .041 | .091 | .309 |
| BLADE–RotatE | .018 | .061 | .214 | .036 | .085 | .289 |
Appendix figures & tables43 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset | Entities | Relations | Train | Valid | Test |
|---|---|---|---|---|---|
| FB15k-237 | 14,541 | 237 | 272,115 | 17,535 | 20,466 |
| WN18RR | 40,943 | 11 | 86,835 | 3,034 | 3,134 |
| CoDEx-M | 17,050 | 51 | 185,584 | 10,310 | 10,617 |
| NELL-995 | 75,492 | 200 | 154,213 | 5,000 | 9,693 |
| Hetionet | 45,119 | 24 | 2,250,197 | 45,000 | 45,000 |
| Family | Representative systems | Primary object | Role in this paper |
|---|---|---|---|
| Classical KGE | TransE, ComplEx, RotatE | Transductive ranking score | Core ranking baselines and decoder context |
| Additional KGE | ConvE | Neural ranking score | Ranking reference under matched protocols |
| Path/GNN KGC | NBFNet, RED-GNN, A*Net | Path- or subgraph-based rank | Strong ranking references, not direct calibration baselines |
| Score calibration | Platt, temperature, isotonic, beta, histogram | Candidate-conditional scalar probability | Same-pool direct comparison |
| Generative KGE | ComplEx 2 | Normalized triple distribution | Same-pool direct comparison |
| Distributional KGE | KG2E, TransG, variational KGE | Embedding uncertainty | Structural predecessors and reruns |
| Dataset | Method | H@1 | H@3 | H@10 |
|---|---|---|---|---|
| FB15k-237 | RotatE | .241 | .374 | .535 |
| SimKGC | .281 | .402 | .551 | |
| Deep ensemble | .252 | .384 | .539 | |
| BLADE | .277 .003 | .399 .003 | .548 .004 | |
| WN18RR | RotatE | .428 | .493 | .571 |
| SimKGC | .472 | .548 | .626 |
| Source | Dataset | Published result | Protocol distinction |
|---|---|---|---|
| NBFNet ( Zhu et al., 2021 ) | FB15k-237 / WN18RR | MRR .415 / .551 | Published standard filtered results; no supported CoDEx-M, NELL-995, or Hetionet cells are imported. |
| Generative ComplEx 2 reference | FB15k-237 | ComplEx MRR .342 .005 | PLL with dimension 1000; published ECE uses a balanced single-corruption pool and different probability maps. |
| XG4Repo | Hetionet | MRR .61 | Relation-specific compound–treats–disease task, not all-relation transductive completion. |
| FtG | NELL-995 | MRR .53 | Different split and filter-then-generate inference; retained as context rather than a matched baseline. |
| Calibrator | OOF NLL | SD |
|---|---|---|
| Global Platt | .309 | .009 |
| Relation-wise Platt | .271 | .008 |
| Beta calibration | .280 | .009 |
| Isotonic regression | .255 | .008 |
| Histogram binning | .247 | .007 |
| Method | Adaptive ECE | Brier | NLL |
|---|---|---|---|
| RotatE + temperature scaling | .082 .004 | .142 .004 | .449 .011 |
| RotatE + global Platt | .038 .003 | .089 .003 | .302 .008 |
| RotatE + relation-wise Platt | .030 .003 | .079 .002 | .265 .007 |
| RotatE + beta calibration | .033 .003 | .082 .003 | .274 .008 |
| RotatE + isotonic regression | .026 .003 | .074 .002 | .251 .007 |
| RotatE + histogram binning | .023 .003 | .071 .002 | .244 .007 |
| Method | Adaptive ECE | Brier | NLL |
|---|---|---|---|
| RotatE + histogram binning | .052 .004 | .105 .004 | .349 .010 |
| ComplEx + relation-wise Platt | .064 .005 | .117 .004 | .379 .011 |
| ComplEx 2 + min–max | .059 .004 | .112 .004 | .366 .010 |
| ComplEx 2 + relation-wise Platt | .047 .004 | .099 .003 | .331 .009 |
| BLADE–ComplEx | .041 .003 | .091 .003 | .309 .009 |
| BLADE–RotatE | .036 .003 | .085 .003 | .289 .008 |
| Detector | FB15k-237 | WN18RR | CoDEx-M | NELL-995 | Hetionet |
|---|---|---|---|---|---|
| Posterior mean only | .712 / .685 | .745 / .721 | .692 / .670 | .704 / .681 | .758 / .734 |
| Teacher only | .681 / .640 | .612 / .584 | .674 / .635 | .690 / .652 | .710 / .682 |
| Mean + uncertainty | .754 / .731 | .780 / .754 | .731 / .710 | .748 / .724 | .801 / .784 |
| Mean + observation model | .798 / .772 | .821 / .795 | .780 / .759 | .792 / .768 | .834 / .815 |
| Full BLADE score | .852 / .831 | .881 / .862 | .840 / .819 | .849 / .824 | .892 / .875 |
| FB15k-237 | Hetionet | |||||
|---|---|---|---|---|---|---|
| Variant | MRR | FN AUC | MRR | FN AUC | ||
| Full BLADE | .365 | .018 | .852 | .243 | .011 | .892 |
| No teacher | .342 | .049 | .758 | .214 | .039 | .805 |
| No observation model | .361 | .034 | .764 | .238 | .027 | .810 |
| Point embeddings | .340 | .078 | .710 | .211 | .062 | .748 |
| Anonymized entities | .349 | .021 | .812 | .220 | .014 | .854 |
| Model | MRR | ECE | Brier | FN AUC-PR |
|---|---|---|---|---|
| ComplEx + rel.-wise Platt | .346 .003 | .034 .003 | .083 .003 | .768 .007 |
| BLADE–ComplEx | .359 .003 | .021 .002 | .065 .002 | .844 .006 |
| BLADE–RotatE | .365 .002 | .018 .002 | .061 .002 | .852 .005 |
| Dataset | LLM Backbone | Queries | Pos. Frac. | Type-Neg. | Random-Neg. |
|---|---|---|---|---|---|
| FB15k-237 | LLaMA-3-70B | 50,000 | 0.20 | 0.40 | 0.40 |
| WN18RR | LLaMA-3-70B | 20,000 | 0.20 | 0.40 | 0.40 |
| CoDEx-M | LLaMA-3-70B | 30,000 | 0.20 | 0.40 | 0.40 |
| NELL-995 | LLaMA-3-70B | 40,000 | 0.20 | 0.40 | 0.40 |
| Hetionet | LLaMA-3-70B | 60,000 | 0.20 | 0.40 | 0.40 |
| Dataset | Distill MSE | Teacher AUC | Teacher ECE | Reject rate | Strict split overlap |
|---|---|---|---|---|---|
| FB15k-237 | .018 .001 | .842 .006 | .061 .004 | 0.7% | 0.0% |
| WN18RR | .021 .002 | .816 .008 | .074 .005 | 0.4% | 0.0% |
| CoDEx-M | .020 .001 | .831 .007 | .068 .004 | 0.8% | 0.0% |
| NELL-995 | .024 .002 | .805 .010 | .081 .006 | 1.2% | 0.0% |
| Hetionet | .026 .002 | .823 .009 | .077 .005 | 1.5% | 0.0% |
| Dataset | Calibration candidates | Bins | Min bin count | Max bin count | Max gap |
|---|---|---|---|---|---|
| FB15k-237 | 122,796 | 20 | 6,139 | 6,140 | .044 |
| WN18RR | 18,804 | 20 | 940 | 941 | .038 |
| CoDEx-M | 63,702 | 20 | 3,185 | 3,186 | .049 |
| NELL-995 | 58,158 | 20 | 2,907 | 2,908 | .052 |
| Hetionet | 270,000 | 20 | 13,500 | 13,500 | .031 |
| Dataset | Dim. | GNN | Neg. | Samples | Teacher | KGC train/valid | Eval. | Total | |
|---|---|---|---|---|---|---|---|---|---|
| FB15k-237 | 500 | 2 | 64 | 64 | .10 | 1.1 | 34.5 | 1.8 | 37.4 |
| WN18RR | 500 | 2 | 64 | 64 | .08 | 0.8 | 21.9 | 1.4 | 24.1 |
| CoDEx-M | 500 | 2 | 64 | 64 | .10 | 1.0 | 28.9 | 1.7 | 31.6 |
| NELL-995 | 500 | 2 | 128 | 64 | .06 | 1.4 | 39.4 | 2.1 | 42.9 |
| Hetionet | 500 | 3 | 128 | 96 | .06 | 2.0 | 53.8 | 2.9 | 58.7 |
| Pool | Comparator | ECE [95% CI] | Brier [95% CI] | NLL [95% CI] |
|---|---|---|---|---|
| Exact | Histogram binning | (.003) | (.002) | (.002) |
| Exact | ComplEx 2 + rel.-wise Platt | (.009) | (.006) | (.007) |
| Hard | Histogram binning | (.002) | (.002) | (.002) |
| Hard | ComplEx 2 + rel.-wise Platt | (.002) | (.002) | (.002) |
| Teacher condition | FB15k-237 | WN18RR | CoDEx-M | NELL-995 | Hetionet |
|---|---|---|---|---|---|
| Full teacher | .018 / .852 | .014 / .881 | .021 / .840 | .025 / .849 | .011 / .892 |
| Description-free | .020 / .838 | .016 / .868 | .023 / .825 | .028 / .833 | .013 / .879 |
| No-test-exposure strict | .020 / .844 | .016 / .872 | .023 / .831 | .028 / .838 | .013 / .884 |
| Anonymized entities | .021 / .812 | .019 / .840 | .026 / .798 | .031 / .806 | .014 / .854 |
| Relation-only | .037 / .774 | .031 / .802 | .042 / .760 | .045 / .771 | .027 / .820 |
| Permuted within relation | .145 / .520 | .132 / .541 | .150 / .508 | .156 / .516 | .124 / .508 |
| Split | Positive | Verified neg. | Total | Prevalence |
|---|---|---|---|---|
| Validation | 10,310 | 10,310 | 20,620 | 0.500 |
| Test | 10,311 | 10,311 | 20,622 | 0.500 |
| Method | ECE | Brier | NLL | AUC-PR | AUROC | Bal. acc. |
|---|---|---|---|---|---|---|
| RotatE + sel. post-hoc | ||||||
| Five-model ensemble | ||||||
| ComplEx 2 + rel. Platt | ||||||
| BLADE–ComplEx | ||||||
| BLADE–RotatE |
| Metric | Paired diff. | 95% paired interval | Holm |
|---|---|---|---|
| Adaptive ECE | |||
| Brier | |||
| NLL | |||
| AUC-PR | |||
| AUROC | |||
| Bal. accuracy |
| Bin | Cand. | Pos. | Mean conf. | Emp. rate | Abs. gap |
|---|---|---|---|---|---|
| 1 | 1,032 | 15 | |||
| 2 | 1,031 | 31 | |||
| 3 | 1,031 | 52 | |||
| 4 | 1,031 | 77 | |||
| 5 | 1,031 | 113 | |||
| 6 | 1,031 | 155 |
| Dataset | Pipeline | MRR | H@1 | H@3 | H@10 | ECE | ACE | NLL |
|---|---|---|---|---|---|---|---|---|
| FB15k-237 | RotatE + KGE Cal. | |||||||
| FB15k-237 | BLADE, query-norm. | |||||||
| FB15k-237 | BLADE + KGE Cal. | |||||||
| CoDEx-M | RotatE + KGE Cal. | |||||||
| CoDEx-M | BLADE, query-norm. | |||||||
| CoDEx-M | BLADE + KGE Cal. |
| Field | Frozen value |
|---|---|
| Repository | github.com/Yang233666/KGE-Calibrator |
| Branch | master |
| Commit | cd08ec4ef023756fe2bbe62390dd1e4d13c08944 |
| Freeze date | 2026-08-01 |
| Entry point | Main-RotatE.py |
| Core method | KGEC_method.py |
| Dataset | Metric | Diff. | 95% interval | Adj. |
|---|---|---|---|---|
| FB15k-237 | MRR | |||
| FB15k-237 | ECE | |||
| FB15k-237 | ACE | |||
| FB15k-237 | NLL | |||
| CoDEx-M | MRR | |||
| CoDEx-M | ECE |
| Dataset | Metric | Diff. | 95% interval | Adj. |
|---|---|---|---|---|
| FB15k-237 | ECE | |||
| FB15k-237 | ACE | |||
| FB15k-237 | NLL | |||
| CoDEx-M | ECE | |||
| CoDEx-M | ACE | |||
| CoDEx-M | NLL |
| Negative source | Ratio | Interpretation |
|---|---|---|
| Random/type-compat. | Easy, low prevalence | |
| Random/type-compat. | Easy, balanced | |
| Model-mined near miss | Hard, low prevalence | |
| Model-mined near miss | Hard, balanced |
| Method | Source | Ratio | ECE | Brier | NLL | Evidence |
|---|---|---|---|---|---|---|
| RotatE+hist. | Rand. | Existing | ||||
| RotatE+hist. | Rand. | New | ||||
| RotatE+hist. | Near | New | ||||
| RotatE+hist. | Near | Existing | ||||
| BLADE–RotatE | Rand. | Existing | ||||
| BLADE–RotatE | Rand. | New |
| Method | Metric | Diff. eff. | 95% CI | Prev. eff. | 95% CI | Interact. | 95% CI | |||
|---|---|---|---|---|---|---|---|---|---|---|
| RotatE+HB | ECE | |||||||||
| RotatE+HB | Brier | |||||||||
| RotatE+HB | NLL | |||||||||
| BLADE–RotatE | ECE | |||||||||
| BLADE–RotatE | Brier | |||||||||
| BLADE–RotatE | NLL |
| Teacher | Distill | Parser | MRR | ECE | Inj. FN |
|---|---|---|---|---|---|
| repeat | MSE | reject | AUC-PR | ||
| Pool A | |||||
| Pool B | |||||
| Pool C | |||||
| Mean SD |
| Metric | Btwn. SD | Seed SD | Btwn. var. | Seed var. | Teacher share |
|---|---|---|---|---|---|
| MRR | |||||
| ECE | |||||
| Inj.-FN AUC-PR |
| Quantity | Estimate | 95% interval |
|---|---|---|
| Grand-mean MRR | ||
| Grand-mean ECE | ||
| Grand-mean inj.-FN AUC-PR | ||
| Btwn.-teacher SD, MRR | ||
| Btwn.-teacher SD, ECE | ||
| Btwn.-teacher SD, AUC-PR |
| Judge | Model | Configuration |
|---|---|---|
| A | GPT-5.6 Sol ( gpt-5.6-sol ) | Medium reasoning, structured JSON, no tools |
| B | Claude Sonnet 5 ( claude-sonnet-5 ) | Adaptive thinking, structured JSON, no overrides |
| C | Gemini 2.5 Pro ( gemini-2.5-pro ) | Structured JSON, deterministic, no tools |
| Field | OpenAI | Anthropic | |
|---|---|---|---|
| Model | gpt-5.6-sol | claude-sonnet-5 | gemini-2.5-pro |
| API | /v1/responses | /v1/messages | generateContent |
| Max output | 256 | 512 | 512 |
| Decoding | effort med. | adaptive think | , top- |
| UTC date | 2026-08-12 | 2026-08-13 | 2026-08-14 |
| Audit items | 20,622 | 20,622 | 20,622 |
| Judge/rule | Coverage | Bal. acc. | Pos. prec. | Neg. prec. |
|---|---|---|---|---|
| GPT-5.6 Sol | ||||
| Claude Sonnet 5 | ||||
| Gemini 2.5 Pro | ||||
| Panel-MAJ | ||||
| Panel-HC |
| Judge/rule | Gold | T | F | U |
| GPT-5.6 Sol | Pos | 8,451 | 1,035 | 825 |
| Neg | 1,109 | 8,377 | 825 | |
| Claude Sonnet 5 | Pos | 8,625 | 1,067 | 619 |
| Neg | 969 | 8,723 | 619 | |
| Gemini 2.5 Pro | Pos | 8,140 | 1,140 | 1,031 |
| Neg | 1,227 | 8,053 | 1,031 |
| Judge/rule | Non-unc. | signed | 95% CI | raw |
|---|---|---|---|---|
| GPT-5.6 Sol | 18,972 | |||
| Claude Sonnet 5 | 19,384 | |||
| Gemini 2.5 Pro | 18,560 | |||
| Panel-HC signed | 13,776 |
| Dataset | Submitted | HC retained | HC pos. | Prevalence |
|---|---|---|---|---|
| FB15k-237 | 800 | 458 | 89 | |
| WN18RR | 800 | 421 | 46 | |
| CoDEx-M | 800 | 454 | 65 | |
| NELL-995 | 800 | 430 | 81 | |
| Hetionet | 800 | 453 | 73 | |
| Total | 4,000 | 2,216 | 354 |
| Stratum | Submitted | HC ret. | HC pos. | Cond. prev. |
|---|---|---|---|---|
| Type-compatible random | 1,000 | 575 | 30 | |
| BLADE-only top | 1,000 | 555 | 132 | |
| RotatE-only top | 1,000 | 530 | 83 | |
| Largest rank disagreement | 1,000 | 556 | 109 | |
| Total | 4,000 | 2,216 | 354 |
| Stratum | Prev. | RotatE ECE | BLADE ECE | BLADE AUC-PR | Full triage AUC-PR | |
|---|---|---|---|---|---|---|
| Type-compatible random | 575 | |||||
| BLADE-only top | 555 | |||||
| RotatE-only top | 530 | |||||
| Largest rank disagreement | 556 | |||||
| Pooled | 2,216 |
| Dataset | Prev. | RotatE ECE | BLADE ECE | BLADE AUC-PR | Full AUC-PR | |
|---|---|---|---|---|---|---|
| FB15k-237 | 458 | |||||
| WN18RR | 421 | |||||
| CoDEx-M | 454 | |||||
| NELL-995 | 430 | |||||
| Hetionet | 453 | |||||
| Pooled | 2,216 |
| Method | ECE | Brier | NLL | AUC-PR |
|---|---|---|---|---|
| RotatE + sel. post-hoc | ||||
| Five-model ensemble | ||||
| BLADE without teacher | ||||
| BLADE–RotatE post. mean |
| Triage signal | AUC-PR | |
|---|---|---|
| Posterior mean only | ||
| Teacher only | ||
| Mean + uncertainty | ||
| Mean + observation model | ||
| Full BLADE triage score |
| Label rule | Prevalence | BLADE ECE | Post. AUC-PR | Full-triage AUC-PR | |
|---|---|---|---|---|---|
| All-three Panel-HC | 2,216 | ||||
| GPT + Claude, no conflict | 2,520 | ||||
| GPT + Gemini, no conflict | 2,385 | ||||
| Claude + Gemini, no conflict | 2,456 | ||||
| Panel-MAJ expanded | 3,388 |
| Component | Added work |
|---|---|
| Verified CoDEx-M | 20,622 candidates per seed/method; no new annotation |
| KGE Calibrator | Two full-entity datasets; 20–40 CPU-hours incl. extraction |
| Difficulty prevalence | Evaluation-only if 50-negative anchor scores are retained; GPU-hours |
| Teacher uncertainty | Two extra teachers + ten extra KGC seed runs; 75–90 A100-hours |
| LLM audit + extension | 79,866 judge calls; 64M input and 8M output tokens |
KG Completion
Knowledge graph completion (KGC) predicts missing entities, relations, or facts from structured graphs and supporting evidence.
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