Training: Quantum case

In this tutorial we will train a lambeq model to solve the relative pronoun classification task presented in [Lea2021]. The goal is to predict whether a noun phrase contains a subject-based or an object-based relative clause. The entries of this dataset are extracted from the RelPron dataset [Rea2016].

We will use an IQPAnsatz to convert string diagrams into quantum circuits. The pipeline uses tket as a backend.

If you have already gone through the classical training tutorial, you will see that there are only minor differences for the quantum case.

Download code

Preparation

We start with importing NumPy and specifying some training hyperparameters.

import os
import warnings

warnings.filterwarnings('ignore')
os.environ['TOKENIZERS_PARALLELISM'] = 'true'

Note

We disable warnings to filter out issues with the tqdm package used in jupyter notebooks. Furthermore, we have to specify whether we want to use parallel computation for the tokenizer used by the BobcatParser. None of the above impairs the performance of the code.

import numpy as np

BATCH_SIZE = 30
EPOCHS = 1000
SEED = 2

Input data

Let’s read the data and print some example sentences.

def read_data(filename):
    labels, sentences = [], []
    with open(filename) as f:
        for line in f:
            t = int(line[0])
            labels.append([t, 1-t])
            sentences.append(line[1:].strip())
    return labels, sentences


train_labels, train_data = read_data('../examples/datasets/rp_train_data.txt')
val_labels, val_data = read_data('../examples/datasets/rp_test_data.txt')

train_data[:5]

['organization that church establish .',
 'organization that team join .',
 'organization that company sell .',
 'organization that soldier serve .',
 'organization that sailor join .']

Targets are represented as 2-dimensional arrays:

train_labels[:5]

[[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]

Creating and parameterising diagrams

The first step is to convert sentences into string diagrams.

Note

We know that the specific dataset only consists of noun phrases, hence, we reduce potential parsing errors by restricting the parser to only return parse trees with the root categories N (noun) and NP (noun phrase).

from lambeq import BobcatParser

parser = BobcatParser(root_cats=('NP', 'N'), verbose='text')

raw_train_diagrams = parser.sentences2diagrams(train_data, suppress_exceptions=True)
raw_val_diagrams = parser.sentences2diagrams(val_data, suppress_exceptions=True)

Tagging sentences.
Parsing tagged sentences.
Turning parse trees to diagrams.
Tagging sentences.
Parsing tagged sentences.
Turning parse trees to diagrams.

Filter and simplify diagrams

We simplify the diagrams by calling normal_form() and filter out any diagrams that could not be parsed.

train_diagrams = [
    diagram.normal_form()
    for diagram in raw_train_diagrams if diagram is not None
]
val_diagrams = [
    diagram.normal_form()
    for diagram in raw_val_diagrams if diagram is not None
]

train_labels = [
    label for (diagram, label)
    in zip(raw_train_diagrams, train_labels)
    if diagram is not None]
val_labels = [
    label for (diagram, label)
    in zip(raw_val_diagrams, val_labels)
    if diagram is not None
]

Let’s see the form of the diagram for a relative clause on the subject of a sentence:

train_diagrams[0].draw(figsize=(9, 5), fontsize=12)

In object-based relative clauses the noun that follows the relative pronoun is the object of the sentence:

train_diagrams[-1].draw(figsize=(9, 5), fontsize=12)

Create circuits

In order to run the experiments on a quantum computer, we need to apply to string diagrams a quantum ansatz. For this experiment, we will use an IQPAnsatz, where noun wires (n) are represented by a one-qubit system, and sentence wires (s) are discarded (since we deal with noun phrases).

from lambeq import AtomicType, IQPAnsatz, remove_cups

ansatz = IQPAnsatz({AtomicType.NOUN: 1, AtomicType.SENTENCE: 0},
                   n_layers=1, n_single_qubit_params=3)

train_circuits = [ansatz(remove_cups(diagram)) for diagram in train_diagrams]
val_circuits =  [ansatz(remove_cups(diagram))  for diagram in val_diagrams]

train_circuits[0].draw(figsize=(9, 10))

Note that we remove the cups before parameterising the diagrams. By doing so, we reduce the number of :term:`post-selections <post-selection>, which makes the model computationally more efficient. The effect of cups removal on a string diagram is demonstrated below:

from discopy.drawing import equation

original_diagram = train_diagrams[0]
removed_cups_diagram = remove_cups(original_diagram)

equation(original_diagram, removed_cups_diagram, symbol='-->', figsize=(9, 6), asymmetry=0.3, fontsize=12)

Training

Instantiate the model

We will use a TketModel, which we initialise by passing all diagrams to the class method TketModel.from_diagrams(). The TketModel needs a backend configuration dictionary passed as a keyword argument to the initialisation method. This dictionary must contain entries for backend, compilation and shots. The backend is provided by pytket-extensions. In this example, we use Qiskit‘s AerBackend with 8192 shots.

from pytket.extensions.qiskit import AerBackend
from lambeq import TketModel

all_circuits = train_circuits + val_circuits

backend = AerBackend()
backend_config = {
    'backend': backend,
    'compilation': backend.default_compilation_pass(2),
    'shots': 8192
}

model = TketModel.from_diagrams(all_circuits, backend_config=backend_config)

Note

The model can also be instantiated by calling TketModel.from_checkpoint(), in case a pre-trained checkpoint is available.

Define loss and evaluation metric

We use standard binary cross-entropy as the loss. Optionally, we can provide a dictionary of callable evaluation metrics with the signature metric(y_hat, y).

loss = lambda y_hat, y: -np.sum(y * np.log(y_hat)) / len(y)  # binary cross-entropy loss

acc = lambda y_hat, y: np.sum(np.round(y_hat) == y) / len(y) / 2  # half due to double-counting
eval_metrics = {"acc": acc}

Initialise trainer

In lambeq, quantum pipelines are based on the QuantumTrainer class. Furthermore, we will use the standard lambeq SPSA optimizer, implemented in the SPSAOptimizer class. This needs three hyperameters:

• a: The initial learning rate (decays over time),

• c: The initial parameter shift scaling factor (decays over time),

• A: A stability constant, best choice is approx. 0.01 * number of training steps.

from lambeq import QuantumTrainer, SPSAOptimizer

trainer = QuantumTrainer(
    model,
    loss_function=loss,
    epochs=EPOCHS,
    optimizer=SPSAOptimizer,
    optim_hyperparams={'a': 0.05, 'c': 0.06, 'A':0.01*EPOCHS},
    evaluate_functions=eval_metrics,
    evaluate_on_train=True,
    verbose = 'text',
    seed=0
)

Create datasets

To facilitate data shuffling and batching, lambeq provides a native Dataset class. Shuffling is enabled by default, and if not specified, the batch size is set to the length of the dataset.

from lambeq import Dataset

train_dataset = Dataset(
            train_circuits,
            train_labels,
            batch_size=BATCH_SIZE)

val_dataset = Dataset(val_circuits, val_labels, shuffle=False)

Train

We can now pass the datasets to the fit() method of the trainer to start the training.

trainer.fit(train_dataset, val_dataset, evaluation_step=1, logging_step=100)

Epoch 1:     train/loss: 1.4088   valid/loss: 0.7565   train/acc: 0.6029   valid/acc: 0.7419
Epoch 100:   train/loss: 0.1892   valid/loss: 1.6061   train/acc: 0.9412   valid/acc: 0.6774
Epoch 200:   train/loss: 0.1210   valid/loss: 1.1567   train/acc: 0.9706   valid/acc: 0.7742
Epoch 300:   train/loss: 0.1091   valid/loss: 1.0711   train/acc: 1.0000   valid/acc: 0.7581
Epoch 400:   train/loss: 0.0938   valid/loss: 0.6084   train/acc: 1.0000   valid/acc: 0.7742
Epoch 500:   train/loss: 0.0830   valid/loss: 1.0892   train/acc: 0.9853   valid/acc: 0.7581
Epoch 600:   train/loss: 0.0793   valid/loss: 1.5707   train/acc: 0.9853   valid/acc: 0.7742
Epoch 700:   train/loss: 0.0719   valid/loss: 1.0649   train/acc: 0.9853   valid/acc: 0.8065
Epoch 800:   train/loss: 0.0752   valid/loss: 0.5992   train/acc: 0.9853   valid/acc: 0.7742
Epoch 900:   train/loss: 0.0612   valid/loss: 0.6363   train/acc: 0.9853   valid/acc: 0.7742
Epoch 1000:  train/loss: 0.0649   valid/loss: 0.9800   train/acc: 1.0000   valid/acc: 0.8065

Training completed!

Results

Finally, we visualise the results and evaluate the model on the test data.

import matplotlib.pyplot as plt

fig, ((ax_tl, ax_tr), (ax_bl, ax_br)) = plt.subplots(2, 2, sharex=True, sharey='row', figsize=(10, 6))
ax_tl.set_title('Training set')
ax_tr.set_title('Development set')
ax_bl.set_xlabel('Iterations')
ax_br.set_xlabel('Iterations')
ax_bl.set_ylabel('Accuracy')
ax_tl.set_ylabel('Loss')

colours = iter(plt.rcParams['axes.prop_cycle'].by_key()['color'])
ax_tl.plot(trainer.train_epoch_costs[::10], color=next(colours))
ax_bl.plot(trainer.train_results['acc'][::10], color=next(colours))
ax_tr.plot(trainer.val_costs[::10], color=next(colours))
ax_br.plot(trainer.val_results['acc'][::10], color=next(colours))

# print test accuracy
test_acc = acc(model(val_circuits), val_labels)
print('Validation accuracy:', test_acc.item())

Validation accuracy: 0.7419354838709677

See also:

• Training: Classical case

• Training: Hybrid case

• Advanced: Manual training