MEIM: Multi-partition Embedding Interaction iMproved beyond block term tensor format

This is a pure Python code implementing the MEIM knowledge graph embedding method in the paper MEIM: Multi-partition Embedding Interaction Beyond Block Term Format for Efficient and Expressive Link Prediction (IJCAI 2022). MEIM introduces two new aspects, namely independent core tensor for ensemble boosting effect and soft orthogonality for max-rank relational mapping, in addition to multi-partition embedding (MEI, ECAI 2020). The code is optimized for high performance in PyTorch, demonstrates several important KGE techniques and some recent state-of-the-art models including W2V, DistMult, CP, SimplE, ComplEx, RotatE, Quaternion, MEI, and MEIM.

Knowledge graph embedding methods (KGE) aim to learn low-dimensional vector representations of entities and relations in knowledge graphs. The models take input in the format of triples (h, t, r) denoting head entity, tail entity, and relation, respectively, and output their embedding vectors as well as solving the link prediction task. For more information, please see our paper.

Figure 1: Architecture of MEIM with independent core tensors and max-rank mapping matrices in three different views: Tucker format, parameterized bilinear format, and neural network format.

Installation

• Clone the repository to your local machine: git clone https://github.com/tranhungnghiep/MEIM-KGE/
• Go to the repository directory: cd MEIM-KGE/
• Install required packages, you may install in a separate environment: pip install -r requirements.txt

How to run

Go to the source directory (cd src/) and run the following commands.

To reproduce MEIM:

On WN18RR, MEIM 3x100:

python main.py --seed 7 --config_id "rep" --gpu 0 --model MEIM --in_path ../datasets/wn18rr/ --out_path ../result/ --K 3 --Ce 100 --Cr 100 --core_tensor nonshared --reuse_array torch1pin --sampling kvsall --loss_mode softmax-cross-entropy --batch_size 1024 --max_epoch 1000 --opt_method adam --amsgrad 0 --lr 3e-3 --lr_scheduler exp --lr_decay 0.99775 --lambda_ent 0.0 --lambda_rel 0.0 --lambda_params 0.0 --label_smooth 0.0 --constraint "" --to_constrain "" --mapping_constraint orthogonal --lambda_ortho 1e-1 --lambda_rowrelnorm 5e-5 --droprate_w 0.0 --droprate_r 0.0 --droprate_mr 0.0 --droprate_h 0.71 --droprate_mrh 0.67 --droprate_t 0.0 --norm bn --n_w 0 --n_r 0 --n_mr 0 --n_h 1 --n_mrh 1 --n_t 0 --n_sepK 1

On FB15K-237, MEIM 3x100:

python main.py --seed 7 --config_id "rep" --gpu 0 --model MEIM --in_path ../datasets/fb15k-237/ --out_path ../result/ --K 3 --Ce 100 --Cr 100 --core_tensor nonshared --reuse_array torch1pin --sampling 1vsall --loss_mode softmax-cross-entropy --batch_size 1024 --max_epoch 1000 --opt_method adam --amsgrad 1 --lr 3e-3 --lr_scheduler exp --lr_decay 0.99775 --lambda_ent 0.0 --lambda_rel 0.0 --lambda_params 0.0 --label_smooth 0.0 --constraint "" --to_constrain "" --mapping_constraint "" --lambda_ortho 0.0 --lambda_rowrelnorm 0.0 --droprate_w 0.0 --droprate_r 0.0 --droprate_mr 0.0 --droprate_h 0.66 --droprate_mrh 0.67 --droprate_t 0.0 --norm bn --n_w 0 --n_r 0 --n_mr 0 --n_h 1 --n_mrh 1 --n_t 0 --n_sepK 0

On YAGO3-10, MEIM 5x100:

python main.py --seed 7 --config_id "rep" --gpu 0 --model MEIM --in_path ../datasets/YAGO3-10/ --out_path ../result/ --K 5 --Ce 100 --Cr 100 --core_tensor nonshared --reuse_array torch1gpu --sampling 1vsall --loss_mode softmax-cross-entropy --batch_size 1024 --max_epoch 1000 --opt_method adam --amsgrad 1 --lr 3e-3 --lr_scheduler exp --lr_decay 0.995 --lambda_ent 0.0 --lambda_rel 0.0 --lambda_params 0.0 --label_smooth 0.0 --constraint "" --to_constrain "" --mapping_constraint orthogonal --lambda_ortho 1e-3 --lambda_rowrelnorm 0.0 --droprate_w 0.0 --droprate_r 0.0 --droprate_mr 0.0 --droprate_h 0.1 --droprate_mrh 0.15 --droprate_t 0.0 --norm bn --n_w 0 --n_r 0 --n_mr 0 --n_h 1 --n_mrh 1 --n_t 0 --n_sepK 0

To reproduce MEI with comparable sizes:

On WN18RR, MEI 3x115:

python main.py --seed 7 --config_id "rep" --gpu 0 --model MEI --in_path ../datasets/wn18rr/ --out_path ../result/ --check_period 5 --K 3 --Ce 115 --Cr 115 --core_tensor shared --reuse_array torch1pin --sampling kvsall --loss_mode softmax-cross-entropy --batch_size 1024 --max_epoch 1000 --opt_method adam --amsgrad 0 --lr 3e-3 --lr_scheduler exp --lr_decay 0.99775 --lambda_ent 0.0 --lambda_rel 0.0 --lambda_params 0.0 --label_smooth 0.0 --constraint "" --to_constrain "" --mapping_constraint "" --lambda_ortho 0 --lambda_rowrelnorm 0 --droprate_w 0.0 --droprate_r 0.0 --droprate_mr 0.0 --droprate_h 0.71 --droprate_mrh 0.67 --droprate_t 0.0 --norm bn --n_w 0 --n_r 0 --n_mr 0 --n_h 1 --n_mrh 1 --n_t 0 --n_sepK 1

On FB15K-237, MEI 3x124:

python main.py --seed 7 --config_id "rep" --gpu 0 --model MEI --in_path ../datasets/fb15k-237/ --out_path ../result/ --K 3 --Ce 124 --Cr 124 --core_tensor shared --reuse_array torch1pin --sampling 1vsall --loss_mode softmax-cross-entropy --batch_size 1024 --max_epoch 1000 --opt_method adam --amsgrad 1 --lr 3e-3 --lr_scheduler exp --lr_decay 0.99775 --lambda_ent 0.0 --lambda_rel 0.0 --lambda_params 0.0 --label_smooth 0.0 --constraint "" --to_constrain "" --mapping_constraint "" --lambda_ortho 0.0 --lambda_rowrelnorm 0.0 --droprate_w 0.0 --droprate_r 0.0 --droprate_mr 0.0 --droprate_h 0.66 --droprate_mrh 0.67 --droprate_t 0.0 --norm bn --n_w 0 --n_r 0 --n_mr 0 --n_h 1 --n_mrh 1 --n_t 0 --n_sepK 0

On YAGO3-10, MEI 5x106:

python main.py --seed 7 --config_id "rep" --gpu 0 --model MEI --in_path ../datasets/YAGO3-10/ --out_path ../result/ --K 5 --Ce 106 --Cr 106 --core_tensor shared --reuse_array torch1gpu --sampling 1vsall --loss_mode softmax-cross-entropy --batch_size 1024 --max_epoch 1000 --opt_method adam --amsgrad 1 --lr 3e-3 --lr_scheduler exp --lr_decay 0.995 --lambda_ent 0.0 --lambda_rel 0.0 --lambda_params 0.0 --label_smooth 0.0 --constraint "" --to_constrain "" --mapping_constraint "" --lambda_ortho 0.0 --lambda_rowrelnorm 0.0 --droprate_w 0.0 --droprate_r 0.0 --droprate_mr 0.0 --droprate_h 0.1 --droprate_mrh 0.15 --droprate_t 0.0 --norm bn --n_w 0 --n_r 0 --n_mr 0 --n_h 1 --n_mrh 1 --n_t 0 --n_sepK 0

Results

The above hyperparameters were tuned for MRR on the validation sets, higher MRR is better.

MEIM outperforms MEI, achieves new state-of-the-art results using quite small number of parameters.

WN18RR	MR	MRR	H@1	H@3	H@10
MEI 3x115, valid set	3114.822	0.481	0.447	0.493	0.544
MEIM 3x100, valid set	2117.390	0.499	0.460	0.513	0.574
MEI 3x115, test set	3267.743	0.481	0.444	0.496	0.551
MEIM 3x100, test set	2434.371	0.499	0.458	0.518	0.577

FB15K-237	MR	MRR	H@1	H@3	H@10
MEI 3x124, valid set	137.179	0.371	0.278	0.406	0.556
MEIM 3x100, valid set	131.311	0.375	0.282	0.410	0.562
MEI 3x124, test set	144.932	0.365	0.271	0.402	0.552
MEIM 3x100, test set	137.431	0.369	0.274	0.406	0.557

YAGO3-10	MR	MRR	H@1	H@3	H@10
MEI 5x106, valid set	854.727	0.581	0.511	0.621	0.709
MEIM 5x100, valid set	747.502	0.585	0.515	0.628	0.710
MEI 5x106, test set	755.723	0.578	0.505	0.622	0.709
MEIM 5x100, test set	747.490	0.585	0.514	0.625	0.716

How to cite

If you found this code or our work useful, please cite us.

• Hung Nghiep Tran and Atsuhiro Takasu. MEIM: Multi-partition Embedding Interaction Beyond Block Term Format for Efficient and Expressive Link Prediction. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), 2022.

  @inproceedings{tran_meimmultipartitionembedding_2022,
    title = {{MEIM}: {Multi}-partition {Embedding} {Interaction} {Beyond} {Block} {Term} {Format} for {Efficient} and {Expressive} {Link} {Prediction}},
    booktitle = {Proceedings of the {Thirty}-{First} {International} {Joint} {Conference} on {Artificial} {Intelligence}},
    author = {Tran, Hung Nghiep and Takasu, Atsuhiro},
    year = {2022},
    pages = {2262--2269},
    url = {https://arxiv.org/abs/2209.15597},
  }
  

• Hung Nghiep Tran and Atsuhiro Takasu. Multi-Partition Embedding Interaction with Block Term Format for Knowledge Graph Completion. In Proceedings of the European Conference on Artificial Intelligence (ECAI), 2020.

  @inproceedings{tran_multipartitionembeddinginteraction_2020,
    title = {Multi-{Partition} {Embedding} {Interaction} with {Block} {Term} {Format} for {Knowledge} {Graph} {Completion}},
    booktitle = {Proceedings of the {European} {Conference} on {Artificial} {Intelligence}},
    author = {Tran, Hung Nghiep and Takasu, Atsuhiro},
    year = {2020},
    pages = {833--840},
    url = {https://arxiv.org/abs/2006.16365},
  }
  

See also

• MEI-KGE, Multi-partition Embedding Interaction model: https://github.com/tranhungnghiep/MEI-KGE
• AnalyzeKGE, preliminary experiments and analysis: https://github.com/tranhungnghiep/AnalyzeKGE
• KG20C, a scholarly knowledge graph benchmark dataset: https://github.com/tranhungnghiep/KG20C