EffectiveDimension

class EffectiveDimension(qnn, weight_samples=1, input_samples=1)

Bases: object

This class computes the global effective dimension for a Qiskit NeuralNetwork following the definition used in [1].

References [1]: Abbas et al., The power of quantum neural networks. The power of QNNs.

Parameters:

• qnn (NeuralNetwork) – A Qiskit NeuralNetwork, with a specific dimension (num_weights) that will determine the shape of the Fisher Information Matrix (num_input_samples * num_weight_samples, num_weights, num_weights) used to compute the global effective dimension for a set of input_samples, of shape (num_input_samples, qnn_input_size), and weight_samples, of shape (num_weight_samples, num_weights).

• weight_samples (ndarray | int) – An array of neural network parameters (weights), of shape (num_weight_samples, num_weights), or an int to indicate the number of parameter sets to sample randomly from a uniform distribution. By default, weight_samples = 1.

• input_samples (ndarray | int) – An array of samples to the neural network, of shape (num_input_samples, qnn_input_size), or an int to indicate the number of input sets to sample randomly from a normal distribution. By default, input_samples = 1.

Attributes

input_samples

Returns network input samples.

weight_samples

Returns network weight samples.

Methods

get_effective_dimension(dataset_size)

This method computes the effective dimension for a dataset of size dataset_size. If an array is passed, then effective dimension computed for each value in the array.

Parameters:

dataset_size (List[int] | ndarray | int) – array of data sizes or a single integer value.

Returns:

array of effective dimensions for each dataset size in num_data.

Return type:

effective_dim

get_fisher_information(gradients, model_outputs)

This method computes the average Jacobian for every set of gradients and model output as shown in Abbas et al.

Parameters:

• gradients (ndarray) – A numpy array, result of the neural network’s backward pass, of shape (num_input_samples * num_weight_samples, output_size, num_weights).

• model_outputs (ndarray) – A numpy array, result of the neural networks’ forward pass, of shape (num_input_samples * num_weight_samples, output_size).

Returns:

A numpy array of shape

(num_input_samples * num_weight_samples, num_weights, num_weights) with the average Jacobian for every set of gradients and model output given.

Return type:

fisher

get_normalized_fisher(normalized_fisher)

This method computes the normalized Fisher Information Matrix and extracts its trace.

Parameters:

normalized_fisher (ndarray) – The Fisher Information Matrix to be normalized.

Returns:

The normalized Fisher Information Matrix, a numpy array of size

(num_input_samples, num_weights, num_weights).

fisher_trace: The trace of the Fisher Information Matrix

(before normalizing).

Return type:

normalized_fisher

run_monte_carlo()

This method computes the model’s Monte Carlo sampling for a set of input samples and weight samples.

Returns:

QNN gradient vector, result of backward passes, of shape

(num_input_samples * num_weight_samples, output_size, num_weights).

outputs: QNN output vector, result of forward passes, of shape

(num_input_samples * num_weight_samples, output_size).

Return type:

grads