EVOLUTION-MANAGER

Edit File: kernelized.py

# Copyright 2019 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== # pylint: disable=g-classes-have-attributes """Keras layers that implement explicit (approximate) kernel feature maps.""" from __future__ import absolute_import from __future__ import division from __future__ import print_function import numpy as np import six from tensorflow.python.framework import dtypes from tensorflow.python.framework import ops from tensorflow.python.framework import tensor_shape from tensorflow.python.keras import initializers from tensorflow.python.keras.engine import base_layer from tensorflow.python.keras.engine import input_spec from tensorflow.python.ops import gen_math_ops from tensorflow.python.ops import init_ops from tensorflow.python.ops import nn from tensorflow.python.util.tf_export import keras_export _SUPPORTED_RBF_KERNEL_TYPES = ['gaussian', 'laplacian'] @keras_export('keras.layers.experimental.RandomFourierFeatures') class RandomFourierFeatures(base_layer.Layer): r"""Layer that projects its inputs into a random feature space. This layer implements a mapping from input space to a space with `output_dim` dimensions, which approximates shift-invariant kernels. A kernel function `K(x, y)` is shift-invariant if `K(x, y) == k(x - y)` for some function `k`. Many popular Radial Basis Functions (RBF), including Gaussian and Laplacian kernels, are shift-invariant. The implementation of this layer is based on the following paper: ["Random Features for Large-Scale Kernel Machines"]( https://people.eecs.berkeley.edu/~brecht/papers/07.rah.rec.nips.pdf) by Ali Rahimi and Ben Recht. The distribution from which the parameters of the random features map (layer) are sampled determines which shift-invariant kernel the layer approximates (see paper for more details). You can use the distribution of your choice. The layer supports out-of-the-box approximation sof the following two RBF kernels: - Gaussian: `K(x, y) == exp(- square(x - y) / (2 * square(scale)))` - Laplacian: `K(x, y) = exp(-abs(x - y) / scale))` **Note:** Unlike what is described in the paper and unlike what is used in the Scikit-Learn implementation, the output of this layer does not apply the `sqrt(2 / D)` normalization factor. **Usage:** Typically, this layer is used to "kernelize" linear models by applying a non-linear transformation (this layer) to the input features and then training a linear model on top of the transformed features. Depending on the loss function of the linear model, the composition of this layer and the linear model results to models that are equivalent (up to approximation) to kernel SVMs (for hinge loss), kernel logistic regression (for logistic loss), kernel linear regression (for squared loss), etc. Examples: A kernel multinomial logistic regression model with Gaussian kernel for MNIST: ```python model = keras.Sequential([ keras.Input(shape=(784,)), RandomFourierFeatures( output_dim=4096, scale=10., kernel_initializer='gaussian'), layers.Dense(units=10, activation='softmax'), ]) model.compile( optimizer='adam', loss='categorical_crossentropy', metrics=['categorical_accuracy'] ) ``` A quasi-SVM classifier for MNIST: ```python model = keras.Sequential([ keras.Input(shape=(784,)), RandomFourierFeatures( output_dim=4096, scale=10., kernel_initializer='gaussian'), layers.Dense(units=10), ]) model.compile( optimizer='adam', loss='hinge', metrics=['categorical_accuracy'] ) ``` To use another kernel, just replace the layer creation line with: ```python random_features_layer = RandomFourierFeatures( output_dim=500, kernel_initializer=<my_initializer>, scale=..., ...) ``` Arguments: output_dim: Positive integer, the dimension of the layer's output, i.e., the number of random features used to approximate the kernel. kernel_initializer: Determines the distribution of the parameters of the random features map (and therefore the kernel approximated by the layer). It can be either a string identifier or a Keras `Initializer` instance. Currently only 'gaussian' and 'laplacian' are supported string identifiers (case insensitive). Note that the kernel matrix is not trainable. scale: For Gaussian and Laplacian kernels, this corresponds to a scaling factor of the corresponding kernel approximated by the layer (see concrete definitions above). When provided, it should be a positive float. If None, a default value is used: if the kernel initializer is set to "gaussian", `scale` defaults to `sqrt(input_dim / 2)`, otherwise, it defaults to 1.0. Both the approximation error of the kernel and the classification quality are sensitive to this parameter. If `trainable` is set to `True`, this parameter is learned end-to-end during training and the provided value serves as the initial value. **Note:** When features from this layer are fed to a linear model, by making `scale` trainable, the resulting optimization problem is no longer convex (even if the loss function used by the linear model is convex). trainable: Whether the scaling parameter of the layer should be trainable. Defaults to `False`. name: String, name to use for this layer. """ def __init__(self, output_dim, kernel_initializer='gaussian', scale=None, trainable=False, name=None, **kwargs): if output_dim <= 0: raise ValueError( '`output_dim` should be a positive integer. Given: {}.'.format( output_dim)) if isinstance(kernel_initializer, six.string_types): if kernel_initializer.lower() not in _SUPPORTED_RBF_KERNEL_TYPES: raise ValueError( 'Unsupported kernel type: \'{}\'. Supported kernel types: {}.' .format(kernel_initializer, _SUPPORTED_RBF_KERNEL_TYPES)) if scale is not None and scale <= 0.0: raise ValueError('When provided, `scale` should be a positive float. ' 'Given: {}.'.format(scale)) super(RandomFourierFeatures, self).__init__( trainable=trainable, name=name, **kwargs) self.output_dim = output_dim self.kernel_initializer = kernel_initializer self.scale = scale def build(self, input_shape): input_shape = tensor_shape.TensorShape(input_shape) # TODO(sibyl-vie3Poto): Allow higher dimension inputs. Currently the input is expected # to have shape [batch_size, dimension]. if input_shape.rank != 2: raise ValueError( 'The rank of the input tensor should be 2. Got {} instead.'.format( input_shape.ndims)) if input_shape.dims[1].value is None: raise ValueError( 'The last dimension of the inputs to `RandomFourierFeatures` ' 'should be defined. Found `None`.') self.input_spec = input_spec.InputSpec( ndim=2, axes={1: input_shape.dims[1].value}) input_dim = input_shape.dims[1].value kernel_initializer = _get_random_features_initializer( self.kernel_initializer, shape=(input_dim, self.output_dim)) self.unscaled_kernel = self.add_weight( name='unscaled_kernel', shape=(input_dim, self.output_dim), dtype=dtypes.float32, initializer=kernel_initializer, trainable=False) self.bias = self.add_weight( name='bias', shape=(self.output_dim,), dtype=dtypes.float32, initializer=init_ops.random_uniform_initializer( minval=0.0, maxval=2 * np.pi, dtype=dtypes.float32), trainable=False) if self.scale is None: self.scale = _get_default_scale(self.kernel_initializer, input_dim) self.kernel_scale = self.add_weight( name='kernel_scale', shape=(1,), dtype=dtypes.float32, initializer=init_ops.constant_initializer(self.scale), trainable=True, constraint='NonNeg') super(RandomFourierFeatures, self).build(input_shape) def call(self, inputs): inputs = ops.convert_to_tensor_v2_with_dispatch(inputs, dtype=self.dtype) inputs = gen_math_ops.cast(inputs, dtypes.float32) kernel = (1.0 / self.kernel_scale) * self.unscaled_kernel outputs = gen_math_ops.mat_mul(inputs, kernel) outputs = nn.bias_add(outputs, self.bias) return gen_math_ops.cos(outputs) def compute_output_shape(self, input_shape): input_shape = tensor_shape.TensorShape(input_shape) input_shape = input_shape.with_rank(2) if input_shape.dims[-1].value is None: raise ValueError( 'The innermost dimension of input shape must be defined. Given: %s' % input_shape) return input_shape[:-1].concatenate(self.output_dim) def get_config(self): kernel_initializer = self.kernel_initializer if not isinstance(kernel_initializer, six.string_types): kernel_initializer = initializers.serialize(kernel_initializer) config = { 'output_dim': self.output_dim, 'kernel_initializer': kernel_initializer, 'scale': self.scale, } base_config = super(RandomFourierFeatures, self).get_config() return dict(list(base_config.items()) + list(config.items())) def _get_random_features_initializer(initializer, shape): """Returns Initializer object for random features.""" def _get_cauchy_samples(loc, scale, shape): probs = np.random.uniform(low=0., high=1., size=shape) return loc + scale * np.tan(np.pi * (probs - 0.5)) random_features_initializer = initializer if isinstance(initializer, six.string_types): if initializer.lower() == 'gaussian': random_features_initializer = init_ops.random_normal_initializer( stddev=1.0) elif initializer.lower() == 'laplacian': random_features_initializer = init_ops.constant_initializer( _get_cauchy_samples(loc=0.0, scale=1.0, shape=shape)) else: raise ValueError( 'Unsupported kernel type: \'{}\'. Supported kernel types: {}.'.format( random_features_initializer, _SUPPORTED_RBF_KERNEL_TYPES)) return random_features_initializer def _get_default_scale(initializer, input_dim): if (isinstance(initializer, six.string_types) and initializer.lower() == 'gaussian'): return np.sqrt(input_dim / 2.0) return 1.0