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Lorentz Embeddings

A pytorch implementation of Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry.

We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is substantially more efficient than in the Poincaré-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincaré embeddings, especially in low dimensions. Lastly, we apply our model to discover hierarchies in two real-world datasets: we show that an embedding in hyperbolic space can reveal important aspects of a company’s organizational structure as well as reveal historical relationships between language families.

An example of a binary tree being embedded in the Lorentz space and then visualized using Poincaré space. Binary Tree Embedding


Binary tree embedding and visualization.

# See this for more options
python --help

python bin_mat  # run binary tree

# plot the checkpoint's embeddings for all saved checkpoints
# in poincare space
python bin_mat -plot -ckpt ckpt  # plot only embeddings
python bin_mat -plot -ckpt ckpt -plot_graph  # plot graph also
python bin_mat -plot -ckpt ckpt -plot_graph  -overwrite_plots # overwrite plots
python bin_mat -plot -ckpt ckpt -plot_graph  -plot_size 10 # make a large plot

To embed an arbitrary graph

  1. Add a numpy matrix in the file with a unique name (my_graph for example). This represents a directed adjacency matrix
  2. Now you can simply call python my_graph to embed your graph.
  3. You can use tensorboard to watch the progress with tensorboard --logdir runs.
  4. You can plot the embeddings using python my_graph -plot -ckpt ckpt

For anything else python --help