Building a Graph Convolutional Network

Author: Yulun Yao, Chien-Yu Lin

This article is an introductory tutorial to build a Graph Convolutional Network (GCN) with Relay.

In this tutorial, we will run our GCN on Cora dataset to demonstrate.

Cora dataset is a common benchmark for Graph Neural Networks (GNN) and frameworks that support GNN training and inference.

We directly load the dataset from DGL library to do the apples to apples comparison against DGL.

Please refer to DGL doc for DGL installation at https://docs.dgl.ai/install/index.html

and refer to PyTorch guide for PyTorch installation at https://pytorch.org/get-started/locally/

Define GCN in DGL with PyTorch backend

DGL example: https://github.com/dmlc/dgl/tree/master/examples/pytorch/gcn This part reuses the code from the above example

import torch
import torch.nn as nn
import torch.nn.functional as F
import dgl
from dgl.nn.pytorch import GraphConv

class GCN(nn.Module):
    def __init__(self,
                 g,
                 n_infeat,
                 n_hidden,
                 n_classes,
                 n_layers,
                 activation):
        super(GCN, self).__init__()
        self.g = g
        self.layers = nn.ModuleList()
        self.layers.append(GraphConv(n_infeat, n_hidden, activation=activation))
        for i in range(n_layers - 1):
            self.layers.append(GraphConv(n_hidden, n_hidden, activation=activation))
        self.layers.append(GraphConv(n_hidden, n_classes))

    def forward(self, features):
        h = features
        for i, layer in enumerate(self.layers):
            # handle api changes for differnt DGL version
            if dgl.__version__ > '0.3':
                h = layer(self.g, h)
            else:
                h = layer(h, self.g)
        return h

Define the functions to load dataset and evaluate accuracy

You may substitute this part with your own dataset, here we load data from DGL

from dgl.data import load_data
from collections import namedtuple

def load_dataset(dataset="cora"):
    args = namedtuple("args", ["dataset"])
    data = load_data(args(dataset))

    # Remove self-loops to avoid duplicate passing of a node's feature to itself
    g = data.graph
    g.remove_edges_from(g.selfloop_edges())
    g.add_edges_from(zip(g.nodes, g.nodes))

    return g, data


def evaluate(data, logits):
    test_mask = data.test_mask # the test set which isn't included in the training phase

    pred = logits.argmax(axis=1)
    acc = ((pred == data.labels) * test_mask).sum() / test_mask.sum()

    return acc

Load the data and set up model parameters

"""
Parameters
----------
dataset: str
    Name of dataset. You can choose from ['cora', 'citeseer', 'pubmed'].

num_layer: int
    number of hidden layers

num_hidden: int
    number of the hidden units in the hidden layer

infeat_dim: int
    dimension of the input features

num_classes: int
    dimension of model output (Number of classes)
"""
dataset = "cora"

g, data = load_dataset(dataset)

num_layers = 1
num_hidden = 16
infeat_dim = data.features.shape[1]
num_classes = data.num_labels

Set up the DGL-PyTorch model and get the golden results

The weights are trained with https://github.com/dmlc/dgl/blob/master/examples/pytorch/gcn/train.py

from tvm.contrib.download import download_testdata
from dgl import DGLGraph

features = torch.FloatTensor(data.features)
dgl_g = DGLGraph(g)

torch_model = GCN(dgl_g,
                  infeat_dim,
                  num_hidden,
                  num_classes,
                  num_layers,
                  F.relu)

# Download the pretrained weights
model_url = "https://homes.cs.washington.edu/~cyulin/media/gnn_model/gcn_%s.torch"%(dataset)
model_path = download_testdata(model_url, "gcn_%s.pickle"%(dataset), module='gcn_model')

# Load the weights into the model
torch_model.load_state_dict(torch.load(model_path))

Out:

File /workspace/.tvm_test_data/gcn_model/gcn_cora.pickle exists, skip.

Run the DGL model and test for accuracy

torch_model.eval()
with torch.no_grad():
    logits_torch = torch_model(features)
print("Print the first five outputs from DGL-PyTorch execution\n", logits_torch[:5])

acc = evaluate(data, logits_torch.numpy())
print("Test accuracy of DGL results: {:.2%}".format(acc))

Out:

/usr/local/lib/python3.6/dist-packages/dgl/base.py:18: UserWarning: Initializer is not set. Use zero initializer instead. To suppress this warning, use `set_initializer` to explicitly specify which initializer to use.
  warnings.warn(msg)
Print the first five outputs from DGL-PyTorch execution
 tensor([[-2.1450, -1.3411,  3.6003,  0.1190, -0.9690, -1.4138, -1.0221],
        [ 0.6063, -1.1822, -0.3693, -0.9476,  0.5819,  1.2295,  0.2738],
        [-1.0876,  0.0565, -0.2626, -0.9312,  2.7453, -0.0950, -0.6077],
        [-1.4724,  0.0105, -0.1038, -0.2135,  2.2795, -0.5208, -0.5848],
        [-1.6528, -1.2279,  0.0541,  3.6322, -1.6748, -1.6925,  0.1763]])
Test accuracy of DGL results: 81.40%

Define Graph Convolution Layer in Relay

To run GCN on TVM, we first need to implement Graph Convolution Layer.

You may refer to https://github.com/dmlc/dgl/blob/master/python/dgl/nn/mxnet/conv.py for a GraphConv Layer implemented in DGL with MXNet Backend

The layer is defined with below operations, note that we apply two transposes to keep adjacency matrix on right hand side of sparse_dense operator, this method is temporary and will be updated in next few weeks when we have sparse matrix transpose and support for left sparse operator.

\[\mbox{GraphConv}(A, H, W) = A * H * W = ((H * W)^t * A^t)^t = ((W^t * H^t) * A^t)^t\]
from tvm import relay
from tvm.contrib import graph_runtime
import tvm

def GraphConv(layer_name,
              input_dim,
              output_dim,
              adj,
              input,
              norm=None,
              bias=True,
              activation=None):
    """
    Parameters
    ----------
    layer_name: str
    Name of layer

    input_dim: int
    Input dimension per node feature

    output_dim: int,
    Output dimension per node feature

    adj: namedtuple,
    Graph representation (Adjacency Matrix) in Sparse Format (`data`, `indices`, `indptr`),
    where `data` has shape [num_nonzeros], indices` has shape [num_nonzeros], `indptr` has shape [num_nodes + 1]

    input: relay.Expr,
    Input feature to current layer with shape [num_nodes, input_dim]

    norm: relay.Expr,
    Norm passed to this layer to normalize features before and after Convolution.

    bias: bool
    Set bias to True to add bias when doing GCN layer

    activation: <function relay.op.nn>,
    Activation function applies to the output. e.g. relay.nn.{relu, sigmoid, log_softmax, softmax, leaky_relu}

    Returns
    ----------
    output: tvm.relay.Expr
    The Output Tensor for this layer [num_nodes, output_dim]
    """
    if norm is not None:
        input = relay.multiply(input, norm)

    weight = relay.var(layer_name + ".weight", shape=(input_dim, output_dim))
    weight_t = relay.transpose(weight)
    dense = relay.nn.dense(weight_t, input)
    output = relay.nn.sparse_dense(dense, adj)
    output_t = relay.transpose(output)
    if norm is not None:
        output_t = relay.multiply(output_t, norm)
    if bias is True:
        _bias = relay.var(layer_name + ".bias", shape=(output_dim, 1))
        output_t = relay.nn.bias_add(output_t, _bias, axis=-1)
    if activation is not None:
        output_t = activation(output_t)
    return output_t

Prepare the parameters needed in the GraphConv layers

import numpy as np
import networkx as nx

def prepare_params(g, data):
    params = {}
    params['infeats'] = data.features.astype('float32') # Only support float32 as feature for now

    # Generate adjacency matrix
    adjacency = nx.to_scipy_sparse_matrix(g)
    params['g_data'] = adjacency.data.astype('float32')
    params['indices'] = adjacency.indices.astype('int32')
    params['indptr'] = adjacency.indptr.astype('int32')

    # Normalization w.r.t. node degrees
    degs = [g.in_degree[i] for i in range(g.number_of_nodes())]
    params['norm'] = np.power(degs, -0.5).astype('float32')
    params['norm'] = params['norm'].reshape((params['norm'].shape[0], 1))

    return params

params = prepare_params(g, data)

# Check shape of features and the validity of adjacency matrix
assert len(params['infeats'].shape) == 2
assert params['g_data'] is not None and params['indices'] is not None and params['indptr'] is not None
assert params['infeats'].shape[0] == params['indptr'].shape[0] - 1

Put layers together

# Define input features, norms, adjacency matrix in Relay
infeats = relay.var("infeats", shape=data.features.shape)
norm = relay.Constant(tvm.nd.array(params['norm']))
g_data = relay.Constant(tvm.nd.array(params['g_data']))
indices = relay.Constant(tvm.nd.array(params['indices']))
indptr = relay.Constant(tvm.nd.array(params['indptr']))

Adjacency = namedtuple('Adjacency', ['data', 'indices', 'indptr'])
adj = Adjacency(g_data, indices, indptr)

# Construct the 2-layer GCN
layers = []
layers.append(GraphConv(
    layer_name="layers.0",
    input_dim=infeat_dim,
    output_dim=num_hidden,
    adj=adj,
    input=infeats,
    norm=norm,
    activation=relay.nn.relu
))
layers.append(GraphConv(
    layer_name="layers.1",
    input_dim=num_hidden,
    output_dim=num_classes,
    adj=adj,
    input=layers[-1],
    norm=norm,
    activation=None
))

# Analyze free variables and generate Relay function
output = layers[-1]
func = relay.Function(relay.analysis.free_vars(output), output)

Compile and run with TVM

Export the weigths from PyTorch model to Python Dict

model_params = {}
for param_tensor in torch_model.state_dict():
    model_params[param_tensor] = torch_model.state_dict()[param_tensor].numpy()

for i in range(num_layers+1):
    params["layers.%d.weight"%(i)] = model_params["layers.%d.weight"%(i)]
    params["layers.%d.bias"%(i)] = model_params["layers.%d.bias"%(i)]

# Set the TVM build target
target = 'llvm' # Currently only support `llvm` as target

# Build with Relay
with relay.build_config(opt_level=0): # Currently only support opt_level=0
    graph, lib, params = relay.build(func, target, params=params)

# Generate graph runtime
ctx = tvm.context(target, 0)
m = graph_runtime.create(graph, lib, ctx)
m.set_input(**params)

Run the TVM model, test for accuracy and verify with DGL

m.run()
logits_tvm = m.get_output(0).asnumpy()
print("Print the first five outputs from TVM execution\n", logits_tvm[:5])

labels = data.labels
test_mask = data.test_mask

acc = evaluate(data, logits_tvm)
print("Test accuracy of TVM results: {:.2%}".format(acc))

# Verify the results with the DGL model
tvm.testing.assert_allclose(logits_torch, logits_tvm, atol=1e-3)

Out:

Print the first five outputs from TVM execution
 [[-2.1450336  -1.341066    3.600258    0.11899108 -0.96899545 -1.4137654
  -1.0221214 ]
 [ 0.60626334 -1.182223   -0.36925027 -0.94760215  0.581874    1.2294779
   0.27382204]
 [-1.0875838   0.05650991 -0.2626103  -0.93124706  2.7452836  -0.09504303
  -0.6076888 ]
 [-1.4723883   0.01050094 -0.10382691 -0.21350211  2.27953    -0.52083516
  -0.5848303 ]
 [-1.6527934  -1.2278551   0.05413637  3.6321862  -1.6748215  -1.6924572
   0.176308  ]]
Test accuracy of TVM results: 81.40%

Total running time of the script: ( 0 minutes 7.415 seconds)

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