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Hyperbolic Embeddings

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Hyperbolic embedding implementations of Representation Tradeoffs for Hyperbolic Embeddings + product embedding implementations of Learning Mixed-Curvature Representations in Product Spaces

Hyperbolic embedding of binary tree


We use Docker to set up the environment for our code. See Docker/ for installation and launch instructions.

In this README, all instructions are assumed to be run inside the Docker container. All paths are relative to the /hyperbolics directory, and all commands are expected to be run from this directory.


The following programs and scripts expect the input graphs to exist in the /data/edges folder, e.g. /data/edges/phylo_tree.edges. All graphs that we report results on have been prepared and saved here.

Combinatorial construction

julia combinatorial/comb.jl --help
to see options. Example usage (for better results on this dataset, raise the precision):
julia combinatorial/comb.jl -d data/edges/phylo_tree.edges -m phylo_tree.r10.emb -e 1.0 -p 64 -r 10 -a -s

Pytorch optimizer

python pytorch/ learn --help
to see options. Optimizer requires torch >=0.4.1. Example usage:
python pytorch/ learn data/edges/phylo_tree.edges --batch-size 64 --dim 10 -l 5.0 --epochs 100 --checkpoint-freq 10 --subsample 16

Products of hyperbolic spaces with Euclidean and spherical spaces are also supported. E.g. adding flags

-euc 1 -edim 20 -sph 2 -sdim 10
embeds into a product of Euclidean space of dimension 20 with two copies of spherical space of dimension 10.

Experiment scripts

  • scripts/
    runs a full set of experiments for a list of datasets. Example usage (note: the default run settings take a long time to finish):
    python scripts/ phylo -d phylo_tree --epochs 20

    Currently, it executes the following experiments:

    1. The combinatorial construction with fixed precision in varying dimensions
    2. The combinatorial construction in dimension 2 (Sarkar's algorithm), with very high precision
    3. Pytorch optimizer in varying dimensions, random initialization
    4. Pytorch optimizer in varying dimensions, using the embedding produced by the combinatorial construction as initialization
  • The combinatorial constructor

    has an option for reporting the MAP and distortion statistics. However, this can be slow on larger datasets such as wordnet
    • scripts/
      provides an alternate method for computing stats that can leverage multiprocessing Example usage:
      python scripts/ phylo_tree -e 1.0 -r 2 -p 1024 -q 4
      to run on 4 cores

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