rational.mxnet

class rational.mxnet.Rational(approx_func='leaky_relu', degrees=(5, 4), cuda=False, version='A', trainable=True, name=None, **kwargs)[source]

Rational Activation Function, inheriting from mxnet.gluon.HybridBlock.

Parameters

  • approx_func (str) –

    The name of the approximated function for initialisation.

    The different functions are available in rational.rationals_config.json.

    Default: leaky_relu

  • degrees (tuple of int) –

    The degrees of the numerator (P) and denominator (Q).

    Default (5, 4)

  • cuda (bool) –

    whether to execute on cuda device.

    NOTE: THIS PARAMETER IS CURRENTLY NOT CONSIDERED.

    CUDA GPUS ARE USED WHEN IT IS POSSIBLE

  • version (str) –

    Version of Rational to use. Rational(x) = P(x)/Q(x), where P(x) = (a_0 + a_1 * x + a_2 * x^2 + … + a_n * x^n) and

    A: Q(x) = (1 + |b_0 * x| + | b_1 * x^2| + … + | b_m * x^{m+1}|)

    B: Q(x) = (1 + |b_0 * x + b_1 * x^2 + … + b_m * x^{m + 1}|)

    C: Q(x) = (0.1 + |b_0 + b_1 * x + b_2 * x^2 + … + b_m * x^m|)

    D: like B with noised coefficients b_i

    Default A

  • trainable (bool) –

    Whether the weights are trainable, i.e, if they are updated during backward pass.

    Default True

Returns

Rational hybrid block

Return type

HybridBlock

best_fit(functions_list, x=None, show=False)

Compute the distance between the rational and the functions in functions_list, and return the one with the minimal the distance.

Parameters

  • functions_list (list of callable) – The function you want to fit to rational.

  • x (array) –

    The range on which the curves of the functions are fitted together.

    Default None

  • show (bool) –

    If True, plots the final fitted function and rational (using matplotlib).

    Default False

Returns

((a, b, c, d), dist) with:

a, b, c, d: the parameters to adjust the function (vertical and horizontal scales and bias)

dist: The final distance between the rational function and the fitted one

Return type

tuple

capture(name='snapshot_0', x=None, fitted_function=True, other_func=None, returns=False)

Captures a snapshot of the rational functions and related in the snapshot_list variable (or returns it if returns=True).

Parameters

  • name (str) –

    Name of the snapshot.

    Default "snapshot_0"

  • x (range) –

    The range to print the function on.

    Default None

  • fitted_function (bool) –

    If True, displays the best fitted function if searched. Otherwise, returns it.

    Default True

  • other_funcs (callable) – another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value.

  • returns (bool) –

    If True, returns the snapshot. Otherwise, saves it in self.snapshot_list

    Default False

classmethod capture_all(name='snapshot_0', x=None, fitted_function=True, other_func=None, returns=False)

Captures a snapshot of every instanciated rational functions and related in the snapshot_list variable (or returns a list of them if returns=True).

Parameters

  • name (str) –

    Name of the snapshot.

    Default "snapshot_0"

  • x (range) –

    The range to print the function on.

    Default None

  • fitted_function (bool) –

    If True, displays the best fitted function if searched. Otherwise, returns it.

    Default True

  • other_funcs (callable) – another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value.

  • returns (bool) –

    If True, returns the snapshot. Otherwise, saves it in self.snapshot_list

    Default False

export_evolution_graph(path='rational_evolution.gif', animated=True, other_func=None)

Creates and saves an animated graph of the function evolution based on the successive snapshots saved in snapshot_list.

Parameters

  • path (str) –

    Complete path with name of the figure.

    Default "rational_evolution.gif"

  • animated (bool) –

    Complete path with name of the figure.

    Default True

  • other_func (callable) –

    another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value.

    Default None

classmethod export_evolution_graphs(path='rationals_evolution.gif', together=True, layout='auto', animated=True, other_func=None)

Creates and saves an animated graph of the function evolution based on the successive snapshots saved in snapshot_list for each instanciated rational function.

Parameters

  • path (str) –

    Complete path with name of the figure.

    Default "rationals_evolution.gif"

  • together (bool) –

    If True, the graphs of every functions are stored in different files.

    Default True

  • layout (tuple or 'auto') –

    Grid layout of the figure. If “auto”, one is generated. (see layout).

    Default "auto"

  • animated (bool) –

    If True, creates an animated gif, else, different files are created.

    Default True

  • other_func (callable) –

    another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value.

    Default None

export_graph(path='rational_function.svg', snap_number=- 1, other_func=None)

Saves one graph of the function based on the last snapshot (by default, and if available).

Parameters

  • path (str) –

    Complete path with name of the figure.

    Default "rational_functions.svg"

  • together (bool) –

    If True, the graphs of every functions are stored in different files.

    Default True

  • layout (tuple or 'auto') – Grid layout of the figure. If “auto”, one is generated. (see layout). Default auto

  • snap_number (int) –

    The snap to take in snapshot_list for each function.

    Default -1 (last)

  • other_func (callable) – another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value. Default None

classmethod export_graphs(path='rational_functions.svg', together=True, layout='auto', snap_number=- 1, other_func=None)

Saves one or more graph(s) of the function based on the last snapshot (by default, and if available) for each instanciated rational function.

Parameters

  • path (str) –

    Complete path with name of the figure.

    Default "rational_functions.svg"

  • together (bool) –

    If True, the graphs of every functions are stored in different files.

    Default True

  • layout (tuple or 'auto') – Grid layout of the figure. If “auto”, one is generated. (see layout). Default "auto"

  • snap_number (int) –

    The snap to take in snapshot_list for each function.

    Default -1 (last)

  • other_func (callable) – another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value. Default None

fit(function, x=None, show=False)

Compute the parameters a, b, c, and d to have the neurally equivalent function of the provided one as close as possible to this rational function.

Parameters

  • function (callable) – The function you want to fit to rational.

  • x (array) –

    The range on which the curves of the functions are fitted together.

    Default None

  • show (bool) –

    If True, plots the final fitted function and rational (using matplotlib).

    Default False

Returns

((a, b, c, d), dist) with:

a, b, c, d: the parameters to adjust the function (vertical and horizontal scales and bias)

dist: The final distance between the rational function and the fitted one

Return type

tuple

hybrid_forward(F, x, numerator, denominator)[source]

Overrides to construct symbolic graph for this Block.

Parameters

  • x (Symbol or NDArray) – The first input tensor.

  • *args (list of Symbol or list of NDArray) – Additional input tensors.

numpy()[source]

Returns a numpy version of this activation function.

show(x=None, fitted_function=True, other_func=None, display=True, tolerance=0.001, title=None, axis=None)

Shows a graph of the function (or returns it if returns=True).

Parameters

  • x (range) –

    The range to print the function on.

    Default None

  • fitted_function (bool) –

    If True, displays the best fitted function if searched. Otherwise, returns it.

    Default True

  • other_funcs (callable) – another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value.

  • display (bool) –

    If True, displays the plot. Otherwise, returns the figure.

    Default False

  • tolerance (float) –

    If the input histogram is used, it will be pruned.

    Every bin containg less than tolerance of the total input is pruned out. (Reduces noise). Default 0.001

  • title (str) – If not None, a title for the figure Default None

  • axis (matplotlib.pyplot.axis) – axis to be plotted on. If None, creates one automatically. Default None

classmethod show_all(x=None, fitted_function=True, other_func=None, display=True, tolerance=0.001, title=None, axes=None, layout='auto')

Shows a graph of the all instanciated rational functions (or returns it if returns=True).

Parameters

  • x (range) –

    The range to print the function on.

    Default None

  • fitted_function (bool) –

    If True, displays the best fitted function if searched. Otherwise, returns it.

    Default True

  • other_funcs (callable) – another function to be plotted or a list of other callable functions or a dictionary with the function name as key and the callable as value.

  • display (bool) –

    If True, displays the plot. Otherwise, returns the figure.

    Default False

  • tolerance (float) –

    If the input histogram is used, it will be pruned.

    Every bin containg less than tolerance of the total input is pruned out. (Reduces noise). Default 0.001

  • title (str) – If not None, a title for the figure Default None

  • axes (matplotlib.pyplot.axis) –

    On ax or a list of axes to be plotted on.

    If None, creates them automatically (see layout).

    Default None

  • layout (tuple or 'auto') –

    Grid layout of the figure. If “auto”, one is generated.

    Default "auto"