HyperLib: Deep learning in the Hyperbolic space

Background

This library implements common Neural Network components in the hyperbolic space (using the Poincare model). The implementation of this library uses Tensorflow as a backend and can easily be used with Keras and is meant to help Data Scientists, Machine Learning Engineers, Researchers and others to implement hyperbolic neural networks.

You can also use this library for uses other than neural networks by using the mathematical functions available in the Poincare class. In the future we may implement components that can be used in models other than neural networks. You can learn more about Hyperbolic networks here, and in the references¹²³⁴.

Install

The recommended way to install is with pip

pip install hyperlib

To build from source, you need to compile the pybind11 extensions.
For example to build on linux:

conda -n hyperlib python=3.8 gxx_linux-64 pybind11
python setup.py install

Hyperlib works with python>=3.8 and tensorflow>=2.0.

Example Usage

Creating a hyperbolic neural network using Keras:

importtensorflowastffromtensorflowimportkerasfromhyperlib.nn.layers.lin_hypimportLinearHyperbolicfromhyperlib.nn.optimizers.rsgdimportRSGDfromhyperlib.manifold.poincareimportPoincare# Create layershyperbolic_layer_1=LinearHyperbolic(32, Poincare(), 1)
hyperbolic_layer_2=LinearHyperbolic(32, Poincare(), 1)
output_layer=LinearHyperbolic(10, Poincare(), 1)
# Create optimizeroptimizer=RSGD(learning_rate=0.1)
# Create model architecturemodel=tf.keras.models.Sequential([
hyperbolic_layer_1,
hyperbolic_layer_2,
output_layer
])
# Compile the model with the Riemannian optimizer model.compile(
optimizer=optimizer,
loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
metrics=[tf.keras.metrics.SparseCategoricalAccuracy()],
)

Using math functions on the Poincare ball:

importtensorflowastffromhyperlib.manifold.poincareimportPoincarep=Poincare()
# Create two matricesa=tf.constant([[5.0,9.4,3.0],[2.0,5.2,8.9],[4.0,7.2,8.9]])
b=tf.constant([[4.8,1.0,2.3]])
# Matrix multiplication on the Poincare ballcurvature=1p.mobius_matvec(a, b, curvature)

Embeddings

A big advantage of hyperbolic space is its ability to represent hierarchical data. There are several techniques for embedding data in hyperbolic space; the most common is gradient methods ⁵.

If your data has a natural metric you can also use TreeRep⁶. Input a symmetric distance matrix, or a compressed distance matrix

importnumpyasnpfromhyperlib.embedding.treerepimporttreerepfromhyperlib.embedding.sarkarimportsarkar_embedding# Example: immunological distances between 8 mammals by Sarichcompressed_metric=np.array([ 32., 48., 51., 50., 48., 98., 148., 26., 34., 29., 33., 84., 136., 42., 44., 44., 92., 152., 44., 38., 86., 142.,
42., 89., 142., 90., 142., 148.
])
# outputs a weighted networkx Graphtree=treerep(compressed_metric, return_networkx=True)
# embed the tree in 2D hyperbolic spaceroot=0embedding=sarkar_embedding(tree, root, tau=0.5)

Please see the examples directory for complete examples.

References

Footnotes

1. Chami, I., Ying, R., Ré, C. and Leskovec, J. Hyperbolic Graph Convolutional Neural Networks. NIPS 2019.↩

2. Nickel, M. and Kiela, D. Poincaré embeddings for learning hierarchical representations. NIPS 2017.↩

3. Khrulkov, Mirvakhabova, Ustinova, Oseledets, Lempitsky. Hyperbolic Image Embeddings.↩

4. Wei Peng, Varanka, Mostafa, Shi, Zhao. Hyperbolic Deep Neural Networks: A Survey.↩

5. De Sa et. al. Representation Tradeoffs for Hyperbolic Embeddings↩

6. Rishi Sonthalia and Anna Gilbert. Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embedding↩