Hands-on 06: Graph data and GNNs: Tagging Higgs boson jets

This week, we will look at graph neural networks using the PyTorch Geometric library: https://pytorch-geometric.readthedocs.io/. See [] for more details.

import torch
import torch_geometric

device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
from tqdm.notebook import tqdm
import numpy as np

local = False

import yaml

with open("definitions.yml") as file:
    # The FullLoader parameter handles the conversion from YAML
    # scalar values to Python the dictionary format
    definitions = yaml.load(file, Loader=yaml.FullLoader)

features = definitions["features"]
spectators = definitions["spectators"]
labels = definitions["labels"]

nfeatures = definitions["nfeatures"]
nspectators = definitions["nspectators"]
nlabels = definitions["nlabels"]
ntracks = definitions["ntracks"]

Graph datasets

Here we have to define the graph dataset. We do this in a separate class following this example: https://pytorch-geometric.readthedocs.io/en/latest/notes/create_dataset.html#creating-larger-datasets

Formally, a graph is represented by a triplet \(\mathcal G = (\mathbf{u}, V, E)\), consisting of a graph-level, or global, feature vector \(\mathbf{u}\), a set of \(N^v\) nodes \(V\), and a set of \(N^e\) edges \(E\). The nodes are given by \(V = \{\mathbf{v}_i\}_{i=1:N^v}\), where \(\mathbf{v}_i\) represents the \(i\)th node’s attributes. The edges connect pairs of nodes and are given by \(E = \{\left(\mathbf{e}_k, r_k, s_k\right)\}_{k=1:N^e}\), where \(\mathbf{e}_k\) represents the \(k\)th edge’s attributes, and \(r_k\) and \(s_k\) are the indices of the “receiver” and “sender” nodes, respectively, connected by the \(k\)th edge (from the sender node to the receiver node). The receiver and sender index vectors are an alternative way of encoding the directed adjacency matrix.

from GraphDataset import GraphDataset

if local:
    file_names = ["/teams/DSC180A_FA20_A00/b06particlephysics/train/ntuple_merged_10.root"]
    file_names_test = ["/teams/DSC180A_FA20_A00/b06particlephysics/test/ntuple_merged_0.root"]
else:
    file_names = [
        "root://eospublic.cern.ch//eos/opendata/cms/datascience/HiggsToBBNtupleProducerTool/HiggsToBBNTuple_HiggsToBB_QCD_RunII_13TeV_MC/train/ntuple_merged_10.root"
    ]
    file_names_test = [
        "root://eospublic.cern.ch//eos/opendata/cms/datascience/HiggsToBBNtupleProducerTool/HiggsToBBNTuple_HiggsToBB_QCD_RunII_13TeV_MC/test/ntuple_merged_0.root"
    ]

graph_dataset = GraphDataset(
    "gdata_train", features, labels, spectators, n_events=1000, n_events_merge=1, file_names=file_names
)

test_dataset = GraphDataset(
    "gdata_test", features, labels, spectators, n_events=2000, n_events_merge=1, file_names=file_names_test
)

Processing...

/home/runner/work/phys139_239/phys139_239/notebooks/GraphDataset.py:120: UserWarning: Creating a tensor from a list of numpy.ndarrays is extremely slow. Please consider converting the list to a single numpy.ndarray with numpy.array() before converting to a tensor. (Triggered internally at /opt/conda/conda-bld/pytorch_1678402323377/work/torch/csrc/utils/tensor_new.cpp:245.)
  x = torch.tensor([feature_array[feat][i].to_numpy() for feat in self.features], dtype=torch.float).T

Done!
Processing...

Done!

Graph neural network

Here, we recapitulate the “graph network” (GN) formalism [], which generalizes various GNNs and other similar methods. GNs are graph-to-graph mappings, whose output graphs have the same node and edge structure as the input. Formally, a GN block contains three “update” functions, \(\phi\), and three “aggregation” functions, \(\rho\). The stages of processing in a single GN block are:

\( \begin{align} \mathbf{e}'_k &= \phi^e\left(\mathbf{e}_k, \mathbf{v}_{r_k}, \mathbf{v}_{s_k}, \mathbf{u} \right) & \mathbf{\bar{e}}'_i &= \rho^{e \rightarrow v}\left(E'_i\right) & \text{(Edge block),}\\ \mathbf{v}'_i &= \phi^v\left(\mathbf{\bar{e}}'_i, \mathbf{v}_i, \mathbf{u}\right) & \mathbf{\bar{e}}' &= \rho^{e \rightarrow u}\left(E'\right) & \text{(Node block),}\\ \mathbf{u}' &= \phi^u\left(\mathbf{\bar{e}}', \mathbf{\bar{v}}', \mathbf{u}\right) & \mathbf{\bar{v}}' &= \rho^{v \rightarrow u}\left(V'\right) &\text{(Global block).} \label{eq:gn-functions} \end{align} \)

where \(E'_i = \left\{\left(\mathbf{e}'_k, r_k, s_k \right)\right\}_{r_k=i,\; k=1:N^e}\) contains the updated edge features for edges whose receiver node is the \(i\)th node, \(E' = \bigcup_i E_i' = \left\{\left(\mathbf{e}'_k, r_k, s_k \right)\right\}_{k=1:N^e}\) is the set of updated edges, and \(V'=\left\{\mathbf{v}'_i\right\}_{i=1:N^v}\) is the set of updated nodes.

We will define an interaction network model similar to Ref. [1], but just modeling the particle-particle interactions. It will take as input all of the tracks (with 48 features) without truncating or zero-padding. Another modification is the use of batch normalization [] layers to improve the stability of the training.

import torch.nn as nn
import torch.nn.functional as F
import torch_geometric.transforms as T
from torch_geometric.nn import EdgeConv, global_mean_pool
from torch.nn import Sequential as Seq, Linear as Lin, ReLU, BatchNorm1d
from torch_scatter import scatter_mean
from torch_geometric.nn import MetaLayer

inputs = 48
hidden = 128
outputs = 2


class EdgeBlock(torch.nn.Module):
    def __init__(self):
        super(EdgeBlock, self).__init__()
        self.edge_mlp = Seq(Lin(inputs * 2, hidden), BatchNorm1d(hidden), ReLU(), Lin(hidden, hidden))

    def forward(self, src, dest, edge_attr, u, batch):
        out = torch.cat([src, dest], 1)
        return self.edge_mlp(out)


class NodeBlock(torch.nn.Module):
    def __init__(self):
        super(NodeBlock, self).__init__()
        self.node_mlp_1 = Seq(Lin(inputs + hidden, hidden), BatchNorm1d(hidden), ReLU(), Lin(hidden, hidden))
        self.node_mlp_2 = Seq(Lin(inputs + hidden, hidden), BatchNorm1d(hidden), ReLU(), Lin(hidden, hidden))

    def forward(self, x, edge_index, edge_attr, u, batch):
        row, col = edge_index
        out = torch.cat([x[row], edge_attr], dim=1)
        out = self.node_mlp_1(out)
        out = scatter_mean(out, col, dim=0, dim_size=x.size(0))
        out = torch.cat([x, out], dim=1)
        return self.node_mlp_2(out)


class GlobalBlock(torch.nn.Module):
    def __init__(self):
        super(GlobalBlock, self).__init__()
        self.global_mlp = Seq(Lin(hidden, hidden), BatchNorm1d(hidden), ReLU(), Lin(hidden, outputs))

    def forward(self, x, edge_index, edge_attr, u, batch):
        out = scatter_mean(x, batch, dim=0)
        return self.global_mlp(out)


class InteractionNetwork(torch.nn.Module):
    def __init__(self):
        super(InteractionNetwork, self).__init__()
        self.interactionnetwork = MetaLayer(EdgeBlock(), NodeBlock(), GlobalBlock())
        self.bn = BatchNorm1d(inputs)

    def forward(self, x, edge_index, batch):

        x = self.bn(x)
        x, edge_attr, u = self.interactionnetwork(x, edge_index, None, None, batch)
        return u


model = InteractionNetwork().to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Cell In[4], line 6
      4 from torch_geometric.nn import EdgeConv, global_mean_pool
      5 from torch.nn import Sequential as Seq, Linear as Lin, ReLU, BatchNorm1d
----> 6 from torch_scatter import scatter_mean
      7 from torch_geometric.nn import MetaLayer
      9 inputs = 48

ModuleNotFoundError: No module named 'torch_scatter'

Define training loop

@torch.no_grad()
def test(model, loader, total, batch_size, leave=False):
    model.eval()

    xentropy = nn.CrossEntropyLoss(reduction="mean")

    sum_loss = 0.0
    t = tqdm(enumerate(loader), total=total / batch_size, leave=leave)
    for i, data in t:
        data = data.to(device)
        y = torch.argmax(data.y, dim=1)
        batch_output = model(data.x, data.edge_index, data.batch)
        batch_loss_item = xentropy(batch_output, y).item()
        sum_loss += batch_loss_item
        t.set_description("loss = %.5f" % (batch_loss_item))
        t.refresh()  # to show immediately the update

    return sum_loss / (i + 1)


def train(model, optimizer, loader, total, batch_size, leave=False):
    model.train()

    xentropy = nn.CrossEntropyLoss(reduction="mean")

    sum_loss = 0.0
    t = tqdm(enumerate(loader), total=total / batch_size, leave=leave)
    for i, data in t:
        data = data.to(device)
        y = torch.argmax(data.y, dim=1)
        optimizer.zero_grad()
        batch_output = model(data.x, data.edge_index, data.batch)
        batch_loss = xentropy(batch_output, y)
        batch_loss.backward()
        batch_loss_item = batch_loss.item()
        t.set_description("loss = %.5f" % batch_loss_item)
        t.refresh()  # to show immediately the update
        sum_loss += batch_loss_item
        optimizer.step()

    return sum_loss / (i + 1)

Define training, validation, testing data generators

from torch_geometric.data import Data, DataListLoader, Batch
from torch.utils.data import random_split


def collate(items):
    l = sum(items, [])
    return Batch.from_data_list(l)


torch.manual_seed(0)
valid_frac = 0.20
full_length = len(graph_dataset)
valid_num = int(valid_frac * full_length)
batch_size = 32

train_dataset, valid_dataset = random_split(graph_dataset, [full_length - valid_num, valid_num])

train_loader = DataListLoader(train_dataset, batch_size=batch_size, pin_memory=True, shuffle=True)
train_loader.collate_fn = collate
valid_loader = DataListLoader(valid_dataset, batch_size=batch_size, pin_memory=True, shuffle=False)
valid_loader.collate_fn = collate
test_loader = DataListLoader(test_dataset, batch_size=batch_size, pin_memory=True, shuffle=False)
test_loader.collate_fn = collate


train_samples = len(train_dataset)
valid_samples = len(valid_dataset)
test_samples = len(test_dataset)
print(full_length)
print(train_samples)
print(valid_samples)
print(test_samples)

Train

import os.path as osp

n_epochs = 10
stale_epochs = 0
best_valid_loss = 99999
patience = 5
t = tqdm(range(0, n_epochs))

for epoch in t:
    loss = train(model, optimizer, train_loader, train_samples, batch_size, leave=bool(epoch == n_epochs - 1))
    valid_loss = test(model, valid_loader, valid_samples, batch_size, leave=bool(epoch == n_epochs - 1))
    print("Epoch: {:02d}, Training Loss:   {:.4f}".format(epoch, loss))
    print("           Validation Loss: {:.4f}".format(valid_loss))

    if valid_loss < best_valid_loss:
        best_valid_loss = valid_loss
        modpath = osp.join("interactionnetwork_best.pth")
        print("New best model saved to:", modpath)
        torch.save(model.state_dict(), modpath)
        stale_epochs = 0
    else:
        print("Stale epoch")
        stale_epochs += 1
    if stale_epochs >= patience:
        print("Early stopping after %i stale epochs" % patience)
        break

Evaluate on testing data

model.eval()
t = tqdm(enumerate(test_loader), total=test_samples / batch_size)
y_test = []
y_predict = []
for i, data in t:
    data = data.to(device)
    batch_output = model(data.x, data.edge_index, data.batch)
    y_predict.append(batch_output.detach().cpu().numpy())
    y_test.append(data.y.cpu().numpy())
y_test = np.concatenate(y_test)
y_predict = np.concatenate(y_predict)

from sklearn.metrics import roc_curve, auc
import matplotlib.pyplot as plt
import mplhep as hep

plt.style.use(hep.style.ROOT)
# create ROC curves
fpr_gnn, tpr_gnn, threshold_gnn = roc_curve(y_test[:, 1], y_predict[:, 1])

# plot ROC curves
plt.figure()
plt.plot(tpr_gnn, fpr_gnn, lw=2.5, label="GNN, AUC = {:.1f}%".format(auc(fpr_gnn, tpr_gnn) * 100))
plt.xlabel(r"True positive rate")
plt.ylabel(r"False positive rate")
plt.semilogy()
plt.ylim(0.001, 1)
plt.xlim(0, 1)
plt.grid(True)
plt.legend(loc="upper left")
plt.show()