$\mathrm{Compl\epsilon x}$, $5^{\bigstar}\mathrm{\epsilon}$

This is the code for implementation of "(Feng et al. 2022) Sharing Parameter by Conjugation for Knowledge Graph Embeddings in Complex Space"

Our methods

Complex number employed in current Knowledge Graph Embedding (KGE) models enforces multiplicative constraint on representations; our method further adds conjugate constraintwithin the parameters. Note that we don't reduce the dimensions of the parameters, instead, we share the dimensions.

We economize 50% of the memory in relation embedding by sharing half of the parameters in the conjugate form. Our approach is at least comparable in accuracy to the baselines. In addition, our method reduces calculation in the regularization process, e.g., for the $5^{\bigstar}\mathrm{\epsilon}$ model, 31% of training time is saved on average for five benchmark datasets.

Methods

• Constrain the relations with:

• conjugate
• negative_conjugate
• vertical_conjugate
• horizontal_conjugate

Baseline models

• $\mathrm{ComplEx}$
• $5^{\bigstar}\mathrm{E}$

Datasets

• UMLS
• FB15K-237
• WN18RR
• YAGO3-10
• FB15K
• WN18

Implementation of the project

Prepare virtual environment

Setup virtual environment, and install required basic packages:

python -m venv .venv_kbc
source .venv_kbc/bin/activate
pip install -r requirements.txt

Install the kbc package into this environment. Please note that, you have to run this command to setup modified kbc package every time the model is modified:

python setup.py install

Prepare datasets

Download datasets:

cd kbc/scripts
chmod +x download_data.sh
./download_data.sh

Once the datasets are downloaded, add them to the package data folder by running the command below. This will create the required files to compute the filtered metrics:

python kbc/process_datasets.py

Running the code

python kbc/learn.py --dataset WN18RR --model FiveStarE_conjugate --regularizer N3 --optimizer Adagrad --max_epochs 100 --valid 50 --rank 500 --batch_size 100 --reg 1e-1 --init 1e-3 --learning_rate 1e-1 &> output/now.out &

Hyperparameters

Best hyperparameter settings for $5^{\bigstar}\mathrm{E}$

dataset	model	regularizer	optimizer	max_epochs	valid	rank	batch_size	reg	init	learning_rate
FB237	FiveStarE	N3	Adagrad	200	3	500	2000	1.E-01	1.E-03	1.E-02
WN18RR	FiveStarE	N3	Adagrad	600	3	500	1000	5.E-01	1.E-03	1.E-01
YAGO3-10	FiveStarE	N3	Adagrad	65	3	500	500	2.5E-03	1.E-03	1.E-01
FB15K	FiveStarE	N3	Adagrad	25	1	500	1000	1.0E-03	1.E-03	5.E-02
WN	FiveStarE	N3	Adagrad	400	3	500	500	5.E-02	1.E-03	1.E-01

Best hyperparameter settings for $5^{\bigstar}\mathrm{\epsilon}$

dataset	model	regularizer	optimizer	max_epochs	valid	rank	batch_size	reg	init	learning_rate
FB237	FiveStarE_conjugate	N3	Adagrad	640	3	500	1000	1.E-01	1.E-03	1.E-02
WN18RR	FiveStarE_conjugate	N3	Adagrad	300	3	500	1000	5.E-01	1.E-03	1.E-01
YAGO3-10	FiveStarE_conjugate	N3	Adagrad	60	3	500	1000	5.E-03	1.E-03	1.E-01
FB15K	FiveStarE_conjugate	N3	Adagrad	20	1	500	1000	2.5E-03	1.E-03	1.E-01
WN	FiveStarE_conjugate	N3	Adagrad	550	3	500	500	1.E-01	1.E-03	5.E-02

License

kbc is CC-BY-NC licensed, as found in the LICENSE file