plot_taylor_and_activation_potentials {nn2poly}

Plots activation potentials and Taylor expansion.

Description

Function that allows to take a NN and the data input values and plot the distribution of data activation potentials (sum of input values * weights) at all neurons together at each layer with the Taylor expansion used in the activation functions. If any layer is 'linear' (usually will be the output), then that layer will not be an approximation as Taylor expansion is not needed.

Usage

plot_taylor_and_activation_potentials(
  object,
  data,
  max_order,
  taylor_orders = 8,
  constraints,
  taylor_interval = 1.5,
  ...
)

Arguments

object

An object for which the computation of the NN2Poly algorithm is desired. Currently supports models from the following deep learning frameworks:

• tensorflow/keras models built as a sequential model.

• torch/luz models built as a sequential model.

It also supports a named list as input which allows to introduce by hand a model from any other source. This list should be of length L (number of hidden layers + 1) containing the weights matrix for each layer. Each element of the list should be named as the activation function used at each layer. Currently supported activation functions are "tanh", "softplus", "sigmoid" and "linear".

At any layer l, the expected shape of such matrices is of the form (h_{(l-1)} + 1)*(h_l), that is, the number of rows is the number of neurons in the previous layer plus the bias vector, and the number of columns is the number of neurons in the current layer L. Therefore, each column corresponds to the weight vector affecting each neuron in that layer. The bias vector should be in the first row.

data

Matrix or data frame containing the predictor variables (X) to be used as input to compute their activation potentials. The response variable column should not be included.

max_order

integer that determines the maximum order that will be forced in the final polynomial, discarding terms of higher order that would naturally arise when considering all Taylor expansions allowed by taylor_orders.

taylor_orders

integer or vector of length L that sets the degree at which Taylor expansion is truncated at each layer. If a single value is used, that value is set for each non linear layer and 1 for linear at each layer activation function. Default set to 8.

constraints

Boolean parameter determining if the NN is constrained (TRUE) or not (FALSE). This only modifies the plots title to show "constrained" or "unconstrained" respectively.

taylor_interval

optional parameter determining the interval in which the Taylor expansion is represented. Default is 1.5.

...

Additional parameters.

Value

A list of plots.