theanets.regularizers.GaussianNoise

class theanets.regularizers.GaussianNoise(pattern='*:out', weight=0.0, rng=13)

Add isotropic Gaussian noise to one or more graph outputs.

Parameters:

rng : Theano random number generator, optional

A Theano random number generator to use for creating noise and dropout values. If not provided, a new generator will be produced for this layer.

Notes

This regularizer implements the modify_graph() method to “inject” noise into the loss function of a network. Suppose we were optimizing a linear regression model with one hidden layer under a mean squared error. The loss for an input/output pair \((x, y)\) would be:

\[\mathcal{L} = \| V(Wx + b) + c - y \|_2^2\]

where \(W (V)\) and \(b (c)\) are the weights and bias parameters of the first (and second) layers in the model.

If we regularized this model with Gaussian noise, the loss for this pair would be:

\[\mathcal{L} = \| V(W(x+\epsilon) + b) + c - y \|_2^2\]

where \(\epsilon \sim \mathcal{N}(0, \sigma^2)\) is isotropic random noise with standard deviation \(\sigma\).

This regularizer encourages the model to develop parameter settings that are robust to noisy inputs. There are some parallels to the Contractive regularizer, in that both models are thought to develop internal representations that are orthogonal to the manifold of the input data, so that noisy inputs are “pushed back” onto the manifold by the network.

References

[Vin10]

P. Vincent, H. Larochelle, Y. Bengio, & P.-A. Manzagol. (ICML 2008). “Extracting and composing robust features with denoising autoencoders.” http://oucsace.cs.ohiou.edu/~razvan/courses/dl6900/papers/vincent08.pdf

Examples

This regularizer can be specified at training or test time by providing the noise or input_noise or hidden_noise keyword arguments:

>>> net = theanets.Regression(...)

To apply this regularizer at training time to network inputs:

>>> net.train(..., input_noise=0.1)

And to apply the regularizer to hidden states of the network:

>>> net.train(..., hidden_noise=0.1)

To target specific network outputs, a pattern can be given manually:

>>> net.train(..., noise={'hid[23]:out': 0.1, 'in:out': 0.01})

To use this regularizer when running the model forward to generate a prediction:

>>> net.predict(..., input_noise=0.1)

The value associated with the input_noise or hidden_noise keyword arguments should be a scalar giving the standard deviation of the noise to apply. The value of the noise keyword argument should be a dictionary, whose keys provide glob-style output name patterns, and the corresponding values are the noise level.

__init__(pattern='*:out', weight=0.0, rng=13)

x.__init__(…) initializes x; see help(type(x)) for signature

Methods

__init__([pattern, weight, rng])	x.__init__(…) initializes x; see help(type(x)) for signature
log()	Log some diagnostic info about this regularizer.
loss(layers, outputs)	Compute a scalar term to add to the loss function for a model.
modify_graph(outputs)	Modify the outputs of a particular layer in the computation graph.

log()

Log some diagnostic info about this regularizer.

modify_graph(outputs)

Modify the outputs of a particular layer in the computation graph.

Parameters:

outputs : dict of Theano expressions

A map from string output names to the corresponding Theano expression. This dictionary contains the fully-scoped name of all outputs from a single layer in the computation graph.

This map is mutable, so any changes that the regularizer makes will be retained when the caller regains control.

Notes

This method is applied during graph-construction time to change the behavior of one or more layer outputs. For example, the BernoulliDropout class replaces matching outputs with an expression containing “masked” outputs, where some elements are randomly set to zero each time the expression is evaluated.

Any regularizer that needs to modify the structure of the computation graph should implement this method.