How Many and How Much? Contrastive Learning with Negative Samples for Knowledge Graph Embedding

Sooho Moon; Yunyong Ko

cs.LGOct 27, 2026

How Many and How Much? Contrastive Learning with Negative Samples for Knowledge Graph Embedding

Authors: Sooho Moon, Yunyong Ko

Organizations: Chung-Ang University Seoul, Korea

Abstract

Knowledge graph embedding (KGE), a fundamental technique for knowledge-centric Web and KG-augmented AI applications, is commonly trained through contrastive learning with negative samples to learn discriminative representations. Despite its empirical success, two crucial questions regarding negative samples remain underexplored: (Q1) how many negative samples should be used for each positive sample and (Q2) how much should each negative sample contribute to learning? To answer these questions, we propose RADAR, a novel contrastive learning framework for KGE models with two effective strategies, respectively: (1) Risk-aware negative budget allocation quantifies false-negative sampling risk by modeling an open-world KG as a stochastic partial observation of its closed-world counterpart and adaptively assigns a negative budget to each positive sample based on its risk; (2) Distribution-calibrated negative weighting assigns negative weights by calibrating the weighting strength for each positive based on two complementary characteristics of the negative-score distribution: dispersion and concentration. Extensive experiments on 3 real-world KGs with 4 KGE models reveal that RADAR achieves the best KGE performance on average across all model--KG combinations and reduces sampled false negatives by over 90% compared with conventional fixed-budget methods.

Figures & tables

Figure 1. Process of contrastive learning with negative samples for knowledge graph embedding.

Figure 2. Observations: (a) Varying numbers of false negatives across positive triples on FB15k237 ( Toutanova and Chen, 2015 ) , and (b) negative scores and their weights computed by Self-Adv ( Sun et al., 2019 ) for two positive triples (P1 and P2) with different score dispersion (

\sigma

) and concentration (shaded: top-10% negative scores).

Figure 3. Overview of RADAR . RADAR addresses (C1) “how many negatives to sample” through risk-aware negative budget allocation and (C2) “how much should each negative contribute” through distribution-calibrated negative weighting.

Figure 4. Relationship between dispersion (

\sigma_{\textbf{x}}

) and concentration (

C_{\textbf{x}}

) of negative-score distributions during training with Self-Adv on FB15k237. Each color represents the evolution of the negative-score distribution for the same positive.

Dataset	Method	RotatE		TransE		ComplEx		DistMult		A.R. $\downarrow$
Dataset	Method	MRR $\uparrow$	H@10 $\uparrow$	MRR $\uparrow$	H@10 $\uparrow$	MRR $\uparrow$	H@10 $\uparrow$	MRR $\uparrow$	H@10 $\uparrow$	A.R. $\downarrow$
FB15k237	KBGAN ∗ [NAACL’18]	-	-	29.4 $\pm\text{N/A}$	49.7 $\pm\text{N/A}$	28.2 $\pm\text{N/A}$	45.4 $\pm\text{N/A}$	26.7 $\pm\text{N/A}$	45.3 $\pm\text{N/A}$	-
	NSCaching ∗ [ICDE’19]	30.9 $\pm\text{N/A}$	48.6 $\pm\text{N/A}$	30.0 $\pm\text{N/A}$	47.4 $\pm\text{N/A}$	30.2 $\pm\text{N/A}$	48.1 $\pm\text{N/A}$	28.3 $\pm\text{N/A}$	45.6 $\pm\text{N/A}$	11.5
	DeMix-Adv ∗ [ISWC’23]	32.9 $\pm\text{N/A}$	51.8 $\pm\text{N/A}$	31.8 $\pm\text{N/A}$	51.0 $\pm\text{N/A}$	30.7 $\pm\text{N/A}$	47.9 $\pm\text{N/A}$	30.1 $\pm\text{N/A}$	47.0 $\pm\text{N/A}$	9.2
	M 2 ixKG ∗ [NN’24]	33.7 $\pm\text{N/A}$	53.2 $\pm\text{N/A}$	33.1 $\pm\text{N/A}$	52.9 $\pm\text{N/A}$	32.3 $\pm\text{N/A}$	51.6 $\pm\text{N/A}$	31.7 $\pm\text{N/A}$	50.3 $\pm\text{N/A}$	4.1
	IF-NS ∗ [KBS’25]	-	-	31.0 $\pm\text{N/A}$	48.9 $\pm\text{N/A}$	-	-	-	-	-

Table 1. KGE performance (MRR and H@10) comparison of RADAR with baselines. RADAR achieves the best average rank on all datasets.

*

indicates results reported in the original works. Bold and underline indicate the best and the second-best results, respectively. A.R. and OOM denote average rank and out of memory, respectively.

Panel of Figure 5 — Figure 5. The average number of false negatives sampled per positive during training ( $N_{max}=256$ ). RADAR consistently samples the fewest false negatives among all baselines.

Figure 6. KGE performance across relation cardinality categories for head and tail prediction. RADAR performs strongly on multi-valued relations.

Panel of Figure 7 — Figure 7. Performance–efficiency trade-off of RotatE and DistMult with each method on two KGs. RADAR achieves the highest performance in the shortest training time.

Method	TT $\downarrow$	Gain	MC $\downarrow$	Gain	MRR $\uparrow$
Uniform	1h 40m	0.0%	7.5GB	0.0%	29.5
Uniform SANS	1h 40m	0.0%	7.5GB	0.0%	29.8
Uniform RW-SANS	1h 40m	0.0%	7.5GB	0.0%	29.7
Self-Adv	1h 40m	0.0%	7.5GB	0.0%	33.6
Self-Adv SANS	1h 40m	0.0%	7.5GB	0.0%	33.6
Self-Adv RW-SANS	1h 40m	0.0%	7.5GB	0.0%	31.5

Table 2. Training time (TT) and GPU memory cost (MC) of RotatE with each method on FB15k237.

Dataset	Method	RotatE	TransE	ComplEx	DistMult
FB15k237	RADAR	35.1	34.7	35.7	35.4
	w/o RA	34.1 (-2.7%)	33.7 (-2.7%)	34.2 (-4.2%)	32.8 (-7.4%)
	w/o DW	33.1 (-5.5%)	32.5 (-6.2%)	31.7 (-11.1%)	31.0 (-12.4%)
WN18RR	RADAR	49.0	25.9	49.4	46.0
	w/o RA	47.8 (-2.5%)	23.8 (-8.4%)	47.7 (-3.6%)	44.5 (-3.1%)
	w/o DW	47.8 (-2.5%)	23.7 (-8.4%)	47.4 (-4.2%)	44.2 (-4.1%)

Table 3. Ablation study of RADAR . Ablating either of our strategies consistently degrades KGE performance.

Figure 8. Relative MRR gains over the corresponding counterparts, Self-Adv and Uniform. R, T, C, and D denote RotatE, TransE, ComplEx, and DistMult, respectively.

Panel of Figure 9 — Figure 9. Hyperparameter sensitivity analysis of RADAR .

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

	$\|\mathcal{E}\|$	$\|\mathcal{R}\|$	$\|\mathcal{T}\|$
FB15k237	14,541	237	272,115
WN18RR	40,943	11	86,835
YAGO3-10	123,182	37	1,079,040

Appendix

Table 4. Statistics of three KGs used in our experiments.

Panel of Figure 10 — Figure 10. Sensitivity of KGE performance to the two adjustment parameters, $\tau$ and $\omega$ , on WN18RR.

Dataset	Statistic	1-to-1	1-to-N	N-to-1	N-to-N
FB15k237	# Relations	17	26	86	108
	# Train triples	4,278 (1.6%)	12,536 (4.6%)	50,635 (18.6%)	204,666 (75.2%)
	# Test triples	192 (0.9%)	1,293 (6.3%)	4,508 (22.0%)	14,473 (70.7%)
WN18RR	# Relations	2	4	3	2
	# Train triples	1,218 (1.4%)	13,770 (15.9%)	40,833 (47.0%)	31,014 (35.7%)
	# Test triples	42 (1.3%)	475 (15.2%)	1,487 (47.4%)	1,130 (36.1%)

Appendix

Table 5. Statistics of relation cardinality.

Panel of Figure 11 — Figure 11. Negative sampling methods evaluated on different relation categories.

Panel of Figure 12 — Figure 12. Performance–efficiency trade-off of RADAR and baselines across all KGE models and datasets.

KG Embedding

Knowledge graph embedding (KGE) represents entities and relations as vectors or structured geometric objects for prediction and reasoning.

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FlowNeg: GFlowNet-Guided Diverse Hard Negative Sampling for Knowledge Graph Embedding

Ibne Farabi Shihab, Naoshin Anzum Hridi, Joyanta Jyoti Mondal

Department of Computer Science, Iowa State University, USA · Department of Computer Science and Engineering, BRAC University, Bangladesh · Department of Computer and Information Sciences, University of Delaware, USA

KG Embedding Hard Negative Mining KG Completion Generative Flow Networks

Open paper AskPDF arXiv

Negative sampling determines whether a knowledge graph embedding (KGE) model learns from informative counterexamples or wastes updates on implausible corruptions. Uniform negatives are diverse but easy, whereas hard-negative miners concentrate on few entities and collide more with held-out positives. We introduce FlowNeg, a context-conditioned hierarchical generative flow network that amortizes reward-proportional sampling without normalizing a composite reward over the entity set: given a positive triple and corruption side, it selects a type, then an entity. Its terminal reward combines bounded model-based hardness with a training-only structural score for held-out-positive collision, over a relation-specific type-compatible support. We derive the reward, specialize standard trajectory balance, and bound multiplicatively how residual imbalance perturbs terminal and mode probability. Across a descriptive five-seed grid of five architectures and five benchmarks, FlowNeg has higher mean MRR than EMU and than IF-NS in 24 of 25 cells (

+0.0172

and

+0.0160

on average). A separate 15-seed FB15k-237/RotatE control fixing negative count, diagnostic budget, and compute gives FlowNeg

0.359\pm0.001

MRR against

0.346\pm0.002

for EMU, with near-uniform fixed-partition diversity, high gradient informativeness, and low collision. The evidence supports mode-covering negative generation without treating structural similarity as an open-world truth oracle.

Abstract

KG Embedding

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