class neupy.algorithms.HessianDiagonal[source]

Hissian diagonal is a Hessian algorithm approximation which require only computation of hessian matrix diagonal elements and makes it invertion much easier and faster.

min_eigval : float

Set up minimum eigenvalue for Hessian diagonale matrix. After a few iteration elements will be extremly small and matrix inverse produce huge number in hessian diagonal elements. This parameter control diagonal elements size. Defaults to 1e-2.

connection : list, tuple or LayerConnection instance

Network’s architecture. There are a few ways to define it.

  • List of layers. For instance, [Input(2), Tanh(4), Relu(1)].
  • Construct layer connections. For instance, Input(2) > Tanh(4) > Relu(1).
  • Tuple of integers. Each integer defines Sigmoid layer and it’s input size. For instance, value (2, 4, 1) means that network has 3 layers with 2 input units, 4 hidden units and 1 output unit.
error : str or function

Error/loss function. Defaults to mse.

  • mae - Mean Absolute Error.
  • mse - Mean Squared Error.
  • rmse - Root Mean Squared Error.
  • msle - Mean Squared Logarithmic Error.
  • rmsle - Root Mean Squared Logarithmic Error.
  • categorical_crossentropy - Categorical cross entropy.
  • binary_crossentropy - Binary cross entropy.
  • binary_hinge - Binary hinge entropy.
  • categorical_hinge - Categorical hinge entropy.
  • Custom function which accepts two mandatory arguments. The first one is expected value and the second one is predicted value. Example:
def custom_func(expected, predicted):
    return expected - predicted
step : float

Learning rate, defaults to 0.1.

show_epoch : int or str

This property controls how often the network will display information about training. There are two main syntaxes for this property.

  • You can define it as a positive integer number. It defines how offen would you like to see summary output in terminal. For instance, number 100 mean that network shows summary at 100th, 200th, 300th … epochs.
  • String defines number of times you want to see output in terminal. For instance, value '2 times' mean that the network will show output twice with approximately equal period of epochs and one additional output would be after the finall epoch.

Defaults to 1.

shuffle_data : bool

If it’s True class shuffles all your training data before training your network, defaults to True.

epoch_end_signal : function

Calls this function when train epoch finishes.

train_end_signal : function

Calls this function when train process finishes.

verbose : bool

Property controls verbose output interminal. True enables informative output in the terminal and False - disable it. Defaults to False.

addons : list or None

The list of addon algortihms. None by default. If this option is not empty it will generate new class which will inherit all from this list. Support two types of addon algorithms: weight update and step update.

See also

BaseGradientDescent algorithm.
Newton’s method.


  • Method requires all training data during propagation, which means it’s not allowed to use mini-batches.


>>> import numpy as np
>>> from neupy import algorithms
>>> x_train = np.array([[1, 2], [3, 4]])
>>> y_train = np.array([[1], [0]])
>>> hdnet = algorithms.HessianDiagonal((2, 3, 1))
>>> hdnet.train(x_train, y_train)

Diabets dataset example

>>> import numpy as np
>>> from sklearn.model_selection import train_test_split
>>> from sklearn import datasets, preprocessing
>>> from neupy import algorithms, layers, environment
>>> from neupy.estimators import rmsle
>>> environment.reproducible()
>>> dataset = datasets.load_diabetes()
>>> data, target =,
>>> input_scaler = preprocessing.StandardScaler()
>>> target_scaler = preprocessing.StandardScaler()
>>> x_train, x_test, y_train, y_test = train_test_split(
...     input_scaler.fit_transform(data),
...     target_scaler.fit_transform(target),
...     test_size=0.2
... )
>>> nw = algorithms.HessianDiagonal(
...     connection=[
...         layers.Input(10),
...         layers.Sigmoid(20),
...         layers.Sigmoid(1),
...     ],
...     step=1.5,
...     shuffle_data=False,
...     verbose=False,
...     min_eigval=1e-10
... )
>>> nw.train(x_train, y_train, epochs=10)
>>> y_predict = nw.predict(x_test)
>>> error = rmsle(target_scaler.inverse_transform(y_test),
...               target_scaler.inverse_transform(y_predict).round())
>>> error
errors : ErrorHistoryList

Contains list of training errors. This object has the same properties as list and in addition there are three additional useful methods: last, previous and normalized.

train_errors : ErrorHistoryList

Alias to the errors attribute.

validation_errors : ErrorHistoryList

The same as errors attribute, but it contains only validation errors.

last_epoch : int

Value equals to the last trained epoch. After initialization it is equal to 0.


predict(input_data) Predicts output for the specified input.
train(input_train, target_train, input_test=None, target_test=None, epochs=100, epsilon=None) Train network. You can control network’s training procedure with epochs and epsilon parameters. The input_test and target_test should be presented both in case of you need to validate network’s training after each iteration.
fit(*args, **kwargs) Alias to the train method.

Initialize updates that would be applied after each training epoch.

min_eigval = None[source]
options = {'addons': Option(class_name='BaseGradientDescent', value=Property(name="addons")), 'epoch_end_signal': Option(class_name='BaseNetwork', value=Property(name="epoch_end_signal")), 'error': Option(class_name='ConstructibleNetwork', value=FunctionWithOptionsProperty(name="error")), 'min_eigval': Option(class_name='HessianDiagonal', value=ProperFractionProperty(name="min_eigval")), 'show_epoch': Option(class_name='BaseNetwork', value=ShowEpochProperty(name="show_epoch")), 'shuffle_data': Option(class_name='BaseNetwork', value=Property(name="shuffle_data")), 'step': Option(class_name='BaseNetwork', value=NumberProperty(name="step")), 'train_end_signal': Option(class_name='BaseNetwork', value=Property(name="train_end_signal")), 'verbose': Option(class_name='Verbose', value=VerboseProperty(name="verbose"))}[source]