GyroSPD

Code for the paper "Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices" accepted at NeurIPS 2021.

Requirements

• Python == 3.7
• Pytorch == 1.5.1: conda install pytorch==1.5.1 torchvision==0.6.1 [cpuonly | cudatoolkit=10.2] -c pytorch.
• Geoopt == 0.3.1: install from repository is advised
• tensorboardx
• tqdm

Running experiments

0. Init repo

sh init.sh

It will uncompress the Knowledge graphs and create the necessary folders. Datasets are taken from https://github.com/villmow/datasets_knowledge_embedding

1. Preprocess Dataset

python preprocess.py

This will preprocess all folders inside the data folder. It looks for "train", "valid", "test" files in tsv format with triples of "head relation tail"

2. Run Experiments

python -m torch.distributed.launch --nproc_per_node=N_CPUS --master_port=2055 train.py \\
            --n_procs=N_CPUS \\
            --data=PREP \\
            --run_id=RUN_ID \\
            --results_file=out/results.csv \\
            --model=MODEL \\
            --metric=riem \\
            --dims=10 \\
            --learning_rate=1e-4 \\
            --val_every=25 \\
            --patience=50 \\
            --batch_size=2048 \\
            --epochs=1000 \\
            --train_bias

Experiments can be run distributed over multiple CPUs/GPUs with N_CPUS. PREP must be the name of the folder inside data. Results will be reported in results_file with run_id as the name. For model and metric see Models and Metrics

Models and Metrics

The parameter --model can be set with:

• tgspd: Applies a scaling on the head embedding
• tgrotspd: Applies a rotation on the head embedding
• tgrefspd: Applies a reflection on the head embedding
• tgattnspd: Combines rotation and reflection with an attention mechanism

The parameter --metric can be set with:

• riem: Riemannian metric
• fone: Finsler One
• finf: Finsler Infinity

TODO

• Migrate to latest pytorch
• Remove geoopt dependency / Migrate to latest geoopt

Citation

The source code and data in this repository aims at facilitating the study of graph embeddings in the space of symmetric positive definite matrices. If you use the code/data, please cite it as follows:

@misc{lopez2021gyrospd,
      title={Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices}, 
      author={Federico L{\'o}pez and Beatrice Pozzetti and Steve Trettel and Michael Strube and Anna Wienhard},
      year={2021},
      eprint={2110.13475},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}