class neupy.algorithms.Hessian[source]

Hessian gradient decent optimization, also known as Newton’s method. This algorithm uses second-order derivative (hessian matrix) in order to choose correct step during the training iteration. Because of this, method doesn’t have step parameter.

penalty_const : float

Inverse hessian could be singular matrix. For this reason algorithm include penalty that add to hessian matrix identity multiplied by defined constant. Defaults to 1.

network : 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)].
  • Constructed layers. For instance, Input(2) >> Tanh(4) >> Relu(1).
loss : 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
regularizer : function or None

Network’s regularizer.

show_epoch : int

This property controls how often the network will display information about training. It has to be defined as positive integer. For instance, number 100 mean that network shows summary at 1st, 100th, 200th, 300th … and last epochs.

Defaults to 1.

shuffle_data : bool

If it’s True than training data will be shuffled before the training. Defaults to True.

signals : dict, list or function

Function that will be triggered after certain events during the training.

verbose : bool

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

See also

Hessian diagonal approximation.


  • Method requires all training data during propagation, which means it cannot be trained with mini-batches.
  • This method calculates full hessian matrix which means it will compute matrix with NxN parameters, where N = number of parameters in the network.


>>> import numpy as np
>>> from neupy import algorithms
>>> from neupy.layers import *
>>> x_train = np.array([[1, 2], [3, 4]])
>>> y_train = np.array([[1], [0]])
>>> network = Input(2) >> Sigmoid(3) >> Sigmoid(1)
>>> optimizer = algorithms.Hessian(network)
>>> optimizer.train(x_train, y_train)
errors : list

Information about errors. It has two main attributes, namely train and valid. These attributes provide access to the training and validation errors respectively.

last_epoch : int

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

n_updates_made : int

Number of training updates applied to the network.


predict(X) Predicts output for the specified input.
train(X_train, y_train, X_test=None, y_test=None, epochs=100) Train network. You can control network’s training procedure with epochs parameter. The X_test and y_test should be presented both in case network’s validation required after each training epoch.
fit(*args, **kwargs) Alias to the train method.
options = {'loss': Option(class_name='BaseOptimizer', value=FunctionWithOptionsProperty(name="loss")), 'penalty_const': Option(class_name='Hessian', value=BoundedProperty(name="penalty_const")), 'regularizer': Option(class_name='BaseOptimizer', value=Property(name="regularizer")), 'show_epoch': Option(class_name='BaseNetwork', value=IntProperty(name="show_epoch")), 'shuffle_data': Option(class_name='BaseNetwork', value=Property(name="shuffle_data")), 'signals': Option(class_name='BaseNetwork', value=Property(name="signals")), 'target': Option(class_name='BaseOptimizer', value=Property(name="target")), 'verbose': Option(class_name='Verbose', value=VerboseProperty(name="verbose"))}[source]
penalty_const = None[source]
step = None[source]