mlpractical/mlp/layers.py

# -*- coding: utf-8 -*-
"""Layer definitions.

This module defines classes which encapsulate a single layer.

These layers map input activations to output activation with the `fprop`
method and map gradients with repsect to outputs to gradients with respect to
their inputs with the `bprop` method.

Some layers will have learnable parameters and so will additionally define
methods for getting and setting parameter and calculating gradients with
respect to the layer parameters.
"""

import numpy as np
import mlp.initialisers as init


class Layer(object):
    """Abstract class defining the interface for a layer."""

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        raise NotImplementedError()

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        raise NotImplementedError()


class LayerWithParameters(Layer):
    """Abstract class defining the interface for a layer with parameters."""

    def grads_wrt_params(self, inputs, grads_wrt_outputs):
        """Calculates gradients with respect to layer parameters.

        Args:
            inputs: Array of inputs to layer of shape (batch_size, input_dim).
            grads_wrt_to_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            List of arrays of gradients with respect to the layer parameters
            with parameter gradients appearing in same order in tuple as
            returned from `get_params` method.
        """
        raise NotImplementedError()

    def params_penalty(self):
        """Returns the parameter dependent penalty term for this layer.

        If no parameter-dependent penalty terms are set this returns zero.
        """
        raise NotImplementedError()

    @property
    def params(self):
        """Returns a list of parameters of layer.

        Returns:
            List of current parameter values. This list should be in the
            corresponding order to the `values` argument to `set_params`.
        """
        raise NotImplementedError()

    @params.setter
    def params(self, values):
        """Sets layer parameters from a list of values.

        Args:
            values: List of values to set parameters to. This list should be
                in the corresponding order to what is returned by `get_params`.
        """
        raise NotImplementedError()


class AffineLayer(LayerWithParameters):
    """Layer implementing an affine tranformation of its inputs.

    This layer is parameterised by a weight matrix and bias vector.
    """

    def __init__(self, input_dim, output_dim,
                 weights_initialiser=init.UniformInit(-0.1, 0.1),
                 biases_initialiser=init.ConstantInit(0.),
                 weights_penalty=None, biases_penalty=None):
        """Initialises a parameterised affine layer.

        Args:
            input_dim (int): Dimension of inputs to the layer.
            output_dim (int): Dimension of the layer outputs.
            weights_initialiser: Initialiser for the weight parameters.
            biases_initialiser: Initialiser for the bias parameters.
            weights_penalty: Weights-dependent penalty term (regulariser) or
                None if no regularisation is to be applied to the weights.
            biases_penalty: Biases-dependent penalty term (regulariser) or
                None if no regularisation is to be applied to the biases.
        """
        self.input_dim = input_dim
        self.output_dim = output_dim
        self.weights = weights_initialiser((self.output_dim, self.input_dim))
        self.biases = biases_initialiser(self.output_dim)
        self.weights_penalty = weights_penalty
        self.biases_penalty = biases_penalty

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        For inputs `x`, outputs `y`, weights `W` and biases `b` the layer
        corresponds to `y = W.dot(x) + b`.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        return self.weights.dot(inputs.T).T + self.biases

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        return grads_wrt_outputs.dot(self.weights)

    def grads_wrt_params(self, inputs, grads_wrt_outputs):
        """Calculates gradients with respect to layer parameters.

        Args:
            inputs: array of inputs to layer of shape (batch_size, input_dim)
            grads_wrt_to_outputs: array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim)

        Returns:
            list of arrays of gradients with respect to the layer parameters
            `[grads_wrt_weights, grads_wrt_biases]`.
        """

        grads_wrt_weights = np.dot(grads_wrt_outputs.T, inputs)
        grads_wrt_biases = np.sum(grads_wrt_outputs, axis=0)

        if self.weights_penalty is not None:
            grads_wrt_weights += self.weights_penalty.grad(self.weights)

        if self.biases_penalty is not None:
            grads_wrt_biases += self.biases_penalty.grad(self.biases)

        return [grads_wrt_weights, grads_wrt_biases]

    def params_penalty(self):
        """Returns the parameter dependent penalty term for this layer.

        If no parameter-dependent penalty terms are set this returns zero.
        """
        params_penalty = 0
        if self.weights_penalty is not None:
            params_penalty += self.weights_penalty(self.weights)
        if self.biases_penalty is not None:
            params_penalty += self.biases_penalty(self.biases)
        return params_penalty

    @property
    def params(self):
        """A list of layer parameter values: `[weights, biases]`."""
        return [self.weights, self.biases]

    @params.setter
    def params(self, values):
        self.weights = values[0]
        self.biases = values[1]

    def __repr__(self):
        return 'AffineLayer(input_dim={0}, output_dim={1})'.format(
            self.input_dim, self.output_dim)


class SigmoidLayer(Layer):
    """Layer implementing an element-wise logistic sigmoid transformation."""

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        For inputs `x` and outputs `y` this corresponds to
        `y = 1 / (1 + exp(-x))`.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        return 1. / (1. + np.exp(-inputs))

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        return grads_wrt_outputs * outputs * (1. - outputs)

    def __repr__(self):
        return 'SigmoidLayer'


class ReluLayer(Layer):
    """Layer implementing an element-wise rectified linear transformation."""

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        For inputs `x` and outputs `y` this corresponds to `y = max(0, x)`.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        return np.maximum(inputs, 0.)

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        return (outputs > 0) * grads_wrt_outputs

    def __repr__(self):
        return 'ReluLayer'


class TanhLayer(Layer):
    """Layer implementing an element-wise hyperbolic tangent transformation."""

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        For inputs `x` and outputs `y` this corresponds to `y = tanh(x)`.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        return np.tanh(inputs)

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        return (1. - outputs**2) * grads_wrt_outputs

    def __repr__(self):
        return 'TanhLayer'


class SoftmaxLayer(Layer):
    """Layer implementing a softmax transformation."""

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        For inputs `x` and outputs `y` this corresponds to

            `y = exp(x) / sum(exp(x))`.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        # subtract max inside exponential to improve numerical stability -
        # when we divide through by sum this term cancels
        exp_inputs = np.exp(inputs - inputs.max(-1)[:, None])
        return exp_inputs / exp_inputs.sum(-1)[:, None]

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        return (outputs * (grads_wrt_outputs -
                           (grads_wrt_outputs * outputs).sum(-1)[:, None]))

    def __repr__(self):
        return 'SoftmaxLayer'


class RadialBasisFunctionLayer(Layer):
    """Layer implementing projection to a grid of radial basis functions."""

    def __init__(self, grid_dim, intervals=[[0., 1.]]):
        """Creates a radial basis function layer object.

        Args:
            grid_dim: Integer specifying how many basis function to use in
                grid across input space per dimension (so total number of
                basis functions will be grid_dim**input_dim)
            intervals: List of intervals (two element lists or tuples)
                specifying extents of axis-aligned region in input-space to
                tile basis functions in grid across. For example for a 2D input
                space spanning [0, 1] x [0, 1] use intervals=[[0, 1], [0, 1]].
        """
        num_basis = grid_dim**len(intervals)
        self.centres = np.array(np.meshgrid(*[
            np.linspace(low, high, grid_dim) for (low, high) in intervals])
        ).reshape((len(intervals), -1))
        self.scales = np.array([
            [(high - low) * 1. / grid_dim] for (low, high) in intervals])

    def fprop(self, inputs):
        """Forward propagates activations through the layer transformation.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).

        Returns:
            outputs: Array of layer outputs of shape (batch_size, output_dim).
        """
        return np.exp(-(inputs[..., None] - self.centres[None, ...])**2 /
                      self.scales**2).reshape((inputs.shape[0], -1))

    def bprop(self, inputs, outputs, grads_wrt_outputs):
        """Back propagates gradients through a layer.

        Given gradients with respect to the outputs of the layer calculates the
        gradients with respect to the layer inputs.

        Args:
            inputs: Array of layer inputs of shape (batch_size, input_dim).
            outputs: Array of layer outputs calculated in forward pass of
                shape (batch_size, output_dim).
            grads_wrt_outputs: Array of gradients with respect to the layer
                outputs of shape (batch_size, output_dim).

        Returns:
            Array of gradients with respect to the layer inputs of shape
            (batch_size, input_dim).
        """
        num_basis = self.centres.shape[1]
        return -2 * (
            ((inputs[..., None] - self.centres[None, ...]) / self.scales**2) *
            grads_wrt_outputs.reshape((inputs.shape[0], -1, num_basis))
        ).sum(-1)

    def __repr__(self):
        return 'RadialBasisFunctionLayer(grid_dim={0})'.format(self.grid_dim)