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sf.apps.train.KL

class KL(data, vgbs)[source]

Bases: object

Kullback-Liebler divergence cost function.

In a standard unsupervised learning scenario, data are assumed to be sampled from an unknown distribution and a common goal is to learn that distribution. Training of a model distribution can be performed by minimizing the Kullback-Leibler (KL) divergence, which up to additive constants can be written as:

\[KL = -\frac{1}{T}\sum_S \log[P(S)],\]

where \(S\) is an element of the data, \(P(S)\) is the probability of observing that element when sampling from the GBS distribution, and \(T\) is the total number of elements in the data. For the GBS distribution in the WAW parametrization, the gradient of the KL divergence can be written as

\[\partial_\theta KL(\theta) = - \sum_{k=1}^m\frac{1}{w_k}(\langle n_k\rangle_{\text{data}}- \langle n_k\rangle_{\text{GBS}})\partial_\theta w_k,\]

where \(\langle n_k\rangle\) denotes the average photon numbers in mode k. This class provides methods to compute gradients and evaluate the cost function.

Example usage

>>> embedding = train.embed.Exp(4)
>>> A = np.ones((4, 4))
>>> vgbs = train.VGBS(A, 3, embedding, threshold=True)
>>> params = np.array([0.05, 0.1, 0.02, 0.01])
>>> data = np.zeros((4, 4))
>>> kl = cost.KL(data, vgbs)
>>> kl.evaluate(params)
-0.2866830267216749
>>> kl.grad(params)
array([-0.52812574, -0.5201932 , -0.53282312, -0.53437824])
Parameters

  • data (array) – Array of samples representing the training data

  • vgbs (train.VGBS) – Variational GBS class

evaluate(params)

Computes the value of the Kullback-Liebler divergence cost function.

grad(params)

Calculates the gradient of the Kullback-Liebler cost function with respect to the trainable parameters
evaluate(params)[source]

Computes the value of the Kullback-Liebler divergence cost function.

Example usage

>>> kl.evaluate(params)
-0.2866830267216749
Parameters

params (array) – the trainable parameters \(\theta\)

Returns

the value of the cost function

Return type

float

grad(params)[source]

Calculates the gradient of the Kullback-Liebler cost function with respect to the trainable parameters

Example usage

>>> kl.grad(params)
array([-0.52812574, -0.5201932 , -0.53282312, -0.53437824])
Parameters

params (array[float]) – the trainable parameters \(\theta\)

Returns

the gradient of the KL cost function with respect to \(\theta\)

Return type

array

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