Keras Graph Convolutions

A set of layers for graph convolutions in tensorflow keras that use ragged tensors.

Table of Contents

• General
• Installation
• Implementation details
• Literature
• Datasets
• Examples
• Tests

General

The package in kgcnn contains several layer classes to build up graph convolution models. Some models are given as an example. A documentation is generated in docs. This repo is still under construction. Any comments, suggestions or help are very welcome!

Installation

Clone repository https://github.com/aimat-lab/gcnn_keras and install with editable mode:

pip install -e ./gcnn_keras

or latest

pip install kgcnn

Implementation details

Representation

The most frequent usage for graph convolutions is either node or graph classifaction. As for their size, either a single large graph, e.g. citation network or small (batched) graphs like molecules have to be considered. Graphs can be represented by a connection index list plus feature information. Typical quantities in tensor format to describe a graph are listed below.

• n: Nodelist of shape ([batch],N,F) where N is the number of nodes and F is the node feature dimension.
• e: Edgelist of shape ([batch],M,Fe) where M is the number of edges and Fe is the edge feature dimension.
• m: Connectionlist of shape ([batch],M,2) where M is the number of edges. The indices denote a connection of incoming i and outgoing j node as (i,j).
• u: Graph state information of shape ([batch],F) where F denotes the feature dimension.

A major issue for graphs is their flexible size and shape, when using mini-batches. Here, for a graph implementation in the spirit of keras, the batch dimension should be kept also in between layes. This is realized by using ragged tensors. A complete set of layers that work solemnly with ragged tensors is given in ragged.

Many graph implementations use also a disjoint representation and sparse or padded tensors.

Input

In order to input batched tensors of variable length with keras, either zero-padding plus masking or ragged and sparse tensors can be used. Morover for more flexibility, a dataloader from tf.keras.utils.Sequence is often used to input disjoint graph representations. Tools for converting numpy or scipy arrays are found in utils.

Here, for ragged tensors, the nodelist of shape (batch,None,F) and edgelist of shape (batch,None,Fe) have one ragged dimension (None,). The graph structure is represented by an indexlist of shape (batch,None,2) with index of incoming i and outgoing j node as (i,j). The first index of incoming node i is usually expected to be sorted for faster pooling opertions, but can also be unsorted (see layer arguments). Furthermore the graph is directed, so an additional edge with (j,i) is required for undirected graphs. A ragged constant can be directly obtained from a list of numpy arrays: tf.ragged.constant(indices,ragged_rank=1,inner_shape=(2,)) which yields shape (batch,None,2).

Model

Models can be set up in a functional. Example message passing from fundamental operations:

import tensorflow as tf
import tensorflow.keras as ks
from kgcnn.layers.ragged.gather import GatherNodes
from kgcnn.layers.ragged.conv import DenseRagged  # Will most likely be supported by keras.Dense in the future
from kgcnn.layers.ragged.pooling import PoolingEdgesPerNode

feature_dim = 10
n = ks.layers.Input(shape=(None,feature_dim),name='node_input',dtype ="float32",ragged=True)
ei = ks.layers.Input(shape=(None,2),name='edge_index_input',dtype ="int64",ragged=True)

n_in_out = GatherNodes()([n,ei])
node_messages = DenseRagged(feature_dim)(n_in_out)
node_updates = PoolingEdgesPerNode()([n,node_messages,ei])
n_node_updates = ks.layers.Concatenate(axis=-1)([n,node_updates])
n_embedd = DenseRagged(feature_dim)(n_node_updates)

message_passing = ks.models.Model(inputs=[n,ei], outputs=n_embedd)

Literature

A version of the following models are implemented in literature:

• GCN: Semi-Supervised Classification with Graph Convolutional Networks by Kipf et al. (2016)
• INorp: Interaction Networks for Learning about Objects,Relations and Physics by Battaglia et al. (2016)
• Megnet: Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals by Chen et al. (2019)
• NMPN: Neural Message Passing for Quantum Chemistry by Gilmer et al. (2017)
• Schnet: SchNet – A deep learning architecture for molecules and materials by Schütt et al. (2017)
• Unet: Graph U-Nets by H. Gao and S. Ji (2019)

Datasets

In data there are simple data handling tools that are used for examples.

Examples

A set of example traing can be found in example