Creating depthwise separable convolutions in Keras

Creating depthwise separable convolutions in Keras

In a recent blog post, we took a look at separable convolutions. When you separate your convolutional kernels in a depthwise way, you can substantially reduce the required amount of resources for your machine learning project.

The best thing: presumably, this is all without losing the predictive power of the traditional convolutional neural network.

In this blog, we’ll adapt a neural network that we trained earlier to illustrate the following:

How to create a depthwise separable convolutional neural network in Keras.

We’ll first briefly review traditional convolutions, depthwise separable convolutions and how they improve the training process of your neural network. We then move towards adapting a ConvNet that we created earlier, for performing classifications with the MNIST dataset. The best thing: we can even compare the two in terms of performance and time required for completing the training.

Note that the code for this blog post is also available on GitHub.

A brief review: what is a depthwise separable convolutional layer?

Suppose that you’re working with some traditional convolutional kernels, like the ones in this image:

If your 15×15 pixels image is RGB, and by consequence has 3 channels, you’ll need (15-3+1) x (15-3+1) x 3 x 3 x 3 x N = 4563N multiplications to complete the full interpretation of one image. If you’re working with ten kernels, so N = 10, you’ll need over 45000 multiplications. Today, 20 to 50 kernels are not uncommon, datasets often span thousands of images and neural networks often compose multiple convolutional layers in their architecture.

That’s many resources you’ll need, possibly draining you from funds that might have been spent better.

Enter depthwise separable convolutional layers:

With those, you essentially split your N traditional kernels into depthwise convolutions and pointwise convolutions. In the first subprocess, you convolve with M filters on a layer basis, adding the kernels ‘pointwise’ in the second subprocess.

While achieving the same result, you’ll need only 9633 convolutions as we’ve seen in our other blog post.

Depthwise separable convolutional layers may therefore greatly optimize your learning process without giving in on accuracy, since essentially the same operation is performed.

We’ll test this premise today, in this blog. We’ll adapt a traditional CNN classifier created in a previous blog to use SeparableConv2D instead of the traditional Conv2D. What’s more, we’ll cover each of the configuration settings in detail, to augment the Keras docs for SeparableConv2D.

Training with SeparableConv2D instead of Conv2D using the same model architecture and the same dataset allows us to compare the two in terms of performance and training time without much interference from architecture-specific factors or configuration-specific factors. This ensures that the comparison is as fair as possible.

Allright, let’s go!

Adapting our traditional MNIST CNN

Next, we’ll adapt the traditional CNN we created for classifying instances of the MNIST dataset. As we recall, the MNIST dataset stands for Modified National Institute of Standards and Technology and contains thousands of 28 x 28 pixel images of the digits 0-9. We first present the Keras code for the traditional CNN. Then, we introduce the SeparableConv2D layer and explain its configuration options. Finally, before we move on to the training and comparison stages, we show you how to adapt a normal CNN to use depthwise separable convolutions.

The traditional CNN

This was the traditional CNN that we used in the other blog

import keras
from keras.datasets import mnist
from keras.models import Sequential
from keras.layers import Dense, Dropout, Flatten
from keras.layers import Conv2D, MaxPooling2D
from keras import backend as K

# Model configuration
img_width, img_height = 28, 28
batch_size = 250
no_epochs = 25
no_classes = 10
validation_split = 0.2
verbosity = 1

# Load MNIST dataset
(input_train, target_train), (input_test, target_test) = mnist.load_data()

# Reshape data based on channels first / channels last strategy.
# This is dependent on whether you use TF, Theano or CNTK as backend.
# Source: https://github.com/keras-team/keras/blob/master/examples/mnist_cnn.py
if K.image_data_format() == 'channels_first':
    input_train = input_train.reshape(input_train.shape[0], 1, img_width, img_height)
    input_test = input_test.reshape(input_test.shape[0], 1, img_width, img_height)
    input_shape = (1, img_width, img_height)
else:
    input_train = input_train.reshape(input_train.shape[0], img_width, img_height, 1)
    input_test = input_test.reshape(input_test.shape[0], img_width, img_height, 1)
    input_shape = (img_width, img_height, 1)

# Parse numbers as floats
input_train = input_train.astype('float32')
input_test = input_test.astype('float32')

# Convert them into black or white: [0, 1].
input_train = input_train / 255
input_test = input_test / 255

# Convert target vectors to categorical targets
target_train = keras.utils.to_categorical(target_train, no_classes)
target_test = keras.utils.to_categorical(target_test, no_classes)

# Create the model
model = Sequential()
model.add(Conv2D(32, kernel_size=(3, 3), activation='relu', input_shape=input_shape))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))
model.add(Conv2D(64, kernel_size=(3, 3), activation='relu'))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))
model.add(Flatten())
model.add(Dense(256, activation='relu'))
model.add(Dense(no_classes, activation='softmax'))

# Compile the model
model.compile(loss=keras.losses.categorical_crossentropy,
              optimizer=keras.optimizers.Adam(),
              metrics=['accuracy'])

# Fit data to model
model.fit(input_train, target_train,
          batch_size=batch_size,
          epochs=no_epochs,
          verbose=verbosity,
          validation_split=validation_split)

# Generate generalization metrics
score = model.evaluate(input_test, target_test, verbose=0)
print(f'Test loss: {score[0]} / Test accuracy: {score[1]}')

Briefly reviewing the code, this is what happens:

  • Firstly, all the dependencies are imported into your Python script: Keras itself, the MNIST dataset (which is embedded in Keras), the Sequential API, and the layers that we’ll need.
  • Secondly, we specify the configuration of our model. Mainly, we cover hyperparameters and the shape of our data (by specifying image size).
  • Thirdly, the MNIST dataset is loaded.
  • Fourthly, we decide (thanks to this default model) whether your framework utilizes a channels first or channels last approach. Since Keras can run on top of either TensorFlow, Theano and CNTK, this is necessary in order to guarantee that it always runs.
  • Fifthly, we parse numbers as floats (this benefits training on GPUs), convert the images into grayscale (to make them color-agnostic, which benefits classification of new instances) and convert target vectors (which are scalars) into categorical data (vectors deciding for each possible target, in this case scalars 0-9, whether it belongs to that category yes/no). More about to_categorical here.
  • Sixthly, we do one of the most important things: we specify the model architecture. Our model makes use of the Sequential API provided by Keras and stacks all layers on top of each other, in line with this API. We employ Conv2D twice, followed by Max Pooling and Dropout, before we flatten the abstract feature map and classify the data by means of densely-connected layers.
  • Seventhly, we configure the model and fit the data. We specify hyperparameters such as the loss function (categorical crossentropy), the optimizer, additional metrics, batch size, number of epochs and validation split.
  • Eightly, and finally, we add model evaluation. Since during training validation loss is computed, we can fairly accurately assess the predictive power of our model. However, it can overfit, which means that it no longer works as well with data that the model has never seen before. By means of the testing set, we can test our model. In the other blog, test accuracy was as high as training (validation) accuracy. Test loss was even lower (which is better). That’s great.

SeparableConv2D in Keras

Now that we understand what happens in the model code, we can introduce the SeparableConv2D convolutional layer in Keras, which implements depthwise separable convolution for two-dimensional data (such as images).

The layer is very similar to the traditional Conv2D layer. It can be added to your Keras model easily and, as we saw above, it performs mostly the same trick. However, it comes with some separation-specific configuration options that must be set before training is commenced. The Keras website defines the SeparableConv2D layer as follows:

keras.layers.SeparableConv2D(filters, kernel_size, strides=(1, 1), padding='valid', data_format=None, dilation_rate=(1, 1), depth_multiplier=1, activation=None, use_bias=True, depthwise_initializer='glorot_uniform', pointwise_initializer='glorot_uniform', bias_initializer='zeros', depthwise_regularizer=None, pointwise_regularizer=None, bias_regularizer=None, activity_regularizer=None, depthwise_constraint=None, pointwise_constraint=None, bias_constraint=None)

Where all the configuration options mean the following:

  • Filters: the number of output filters (or traditional ‘kernels’ length in the situation above);
  • Kernel size: either an integer (if the spatial dimensions are the same) or a tuple of integers (if they are not). Hence, both 3 and (3, 3) represent a 3x3xN kernel.
  • Stride: how fast the kernel will convolve over your input image. If 1, it will move pixel by pixel, whereas with larger values, it will skip certain convolutions in order to be faster.
  • Padding: use no padding (valid; might even drop rows if the kernel size and stride don’t match up) or padding equally distributed left, right, up and down (same) in order to fully cover the input images.
  • Data format: whether your image input is channels_first or channels_last. By default, this is defined as channels_last.
  • Dilation rate: as a simple example, a convolution over a grayscale image is usually a mxn block of which the convolving pixels are grouped tightly together; really as a mxn block. When you specify dilations of > 1, what you will see is that the distance between the convolving pixels increases and that the convolution is dilated, as if you’re no longer looking directly to the image but continuously from the edge. Dilation has empirically shown to improve model training in some cases, so it may be worth playing with this parameter.
  • Depth multiplier: how many depthwise convolutions must be performed over the channels of the input image. Traditionally, this is 1, as we’ve seen in the drawing above. However, you might wish to manually set this to a larger value. Note that you must accomodate for the required resources, though.
  • Activation function: well, this one speaks for itself – which activation function you’ll use to (very likely) add nonlinearity to your deep learning model.
  • Whether bias must be used: bias might help you steer your result a bit into the right direction if you cannot find a proper decision boundary with gradient-optimized weights only. By default, bias is used.
  • Depthwise, pointwise and bias initializers: which weight initialization strategy is used for the neuron’s vectors representing the depthwise and pointwise convolutions and the accompanying bias vectors. By default, this is zeros for bias (which is fine) and Glorot uniform or Xavier for the depthwise and pointwise convolutions. Watch out in that case when you use ReLU for activating your network, especially when you train with much data.
  • Depthwise, pointwise and bias regularizers: which regularization techniques are applied to the depthwise and pointwise convolutions and the accompanying bias, to keep the training process balanced.
  • Activity regularizer: which regularization technique is applied to the output of the layer, i.e. what flows out of the activation function. This is different than the other regularizers, which are applied within the layer.
  • Depthwise, pointwise and bias constraints: constraints applied to the depthwise and pointwise convolution and the layer bias vector.

Adapting the CNN to use depthwise separable convolutions

Now that we understand how to create a depthwise separable convolutional layer in Keras and how to configure it, we’ll move on to adapting the CNN from above to use depthwise separable convolutions.

And that’s really simple – we’ll just adapt the Conv2D layers to use SeparableConv2D and add the extra configuration that we need.

Eventually, we then end up with this:

import keras
from keras.datasets import mnist
from keras.models import Sequential
from keras.layers import Dense, Dropout, Flatten
from keras.layers import SeparableConv2D, MaxPooling2D
from keras import backend as K

# Model configuration
img_width, img_height = 28, 28
batch_size = 250
no_epochs = 25
no_classes = 10
validation_split = 0.2
verbosity = 1

# Load MNIST dataset
(input_train, target_train), (input_test, target_test) = mnist.load_data()

# Reshape data based on channels first / channels last strategy.
# This is dependent on whether you use TF, Theano or CNTK as backend.
# Source: https://github.com/keras-team/keras/blob/master/examples/mnist_cnn.py
if K.image_data_format() == 'channels_first':
    input_train = input_train.reshape(input_train.shape[0], 1, img_width, img_height)
    input_test = input_test.reshape(input_test.shape[0], 1, img_width, img_height)
    input_shape = (1, img_width, img_height)
else:
    input_train = input_train.reshape(input_train.shape[0], img_width, img_height, 1)
    input_test = input_test.reshape(input_test.shape[0], img_width, img_height, 1)
    input_shape = (img_width, img_height, 1)

# Parse numbers as floats
input_train = input_train.astype('float32')
input_test = input_test.astype('float32')

# Convert them into black or white: [0, 1].
input_train = input_train / 255
input_test = input_test / 255

# Convert target vectors to categorical targets
target_train = keras.utils.to_categorical(target_train, no_classes)
target_test = keras.utils.to_categorical(target_test, no_classes)

# Create the model
model = Sequential()
model.add(SeparableConv2D(32, kernel_size=(3, 3), activation='relu', input_shape=input_shape))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))
model.add(SeparableConv2D(64, kernel_size=(3, 3), activation='relu'))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))
model.add(Flatten())
model.add(Dense(256, activation='relu'))
model.add(Dense(no_classes, activation='softmax'))

# Compile the model
model.compile(loss=keras.losses.categorical_crossentropy,
              optimizer=keras.optimizers.Adam(),
              metrics=['accuracy'])

# Fit data to model
model.fit(input_train, target_train,
          batch_size=batch_size,
          epochs=no_epochs,
          verbose=verbosity,
          validation_split=validation_split)

# Generate generalization metrics
score = model.evaluate(input_test, target_test, verbose=0)
print(f'Test loss: {score[0]} / Test accuracy: {score[1]}')

A small note on Conv1D and Conv3D

Although this blog post shows you how to create a depthwise separable convolutional neural network based on a Conv2D layer, it’s of course also possible to use separable convolutions in 1D: Conv1D can be replaced with SeparableConv1D. So far, there is no such thing as a SeparableConv3D available in Keras.

Training the neural network

Let’s go & train our model to see how it performs!

Software dependencies you’ll need to install first

I quote my usual advice about software dependencies from another blog –


We always start with listing certain dependencies that you’ll need to install before you can run the model on your machine. Those are for today:

A version of Python that can run Keras and one of the backends (TensorFlow, Theano or CNTK);
One of these backends;
Keras itself.
If you wish to generate plots, it’s also wise to install Numpy (if it’s not a peer dependency of the previous ones) and Matplotlib.

Preferably, you’ll install these in an Anaconda environment. Read here how to do that.

Running your model

Create a file that is called e.g. model_depthwise_separable.py and store it somewhere (possibly besides the regular CNN you created before). Subsequently open up a terminal and cd to the particular folder. Issue the command python model_depthwise_separable.py to start training. Note that if you’re using Anaconda that you must activate your Keras environment first, with conda activate <environment_name>, in my case e.g. conda activate tensorflow_gpu.

Traditional vs Depthwise separable CNN: performance comparison

This is the output of training the depthwise separable CNN:

Epoch 1/25
48000/48000 [==============================] - 9s 198us/step - loss: 0.5469 - acc: 0.8535 - val_loss: 0.1651 - val_acc: 0.9510
Epoch 2/25
48000/48000 [==============================] - 4s 84us/step - loss: 0.1720 - acc: 0.9459 - val_loss: 0.1176 - val_acc: 0.9648
Epoch 3/25
48000/48000 [==============================] - 4s 85us/step - loss: 0.1310 - acc: 0.9597 - val_loss: 0.0889 - val_acc: 0.9734
Epoch 4/25
48000/48000 [==============================] - 4s 85us/step - loss: 0.1072 - acc: 0.9658 - val_loss: 0.0853 - val_acc: 0.9740
Epoch 5/25
48000/48000 [==============================] - 4s 86us/step - loss: 0.0939 - acc: 0.9710 - val_loss: 0.0721 - val_acc: 0.9781
Epoch 6/25
48000/48000 [==============================] - 4s 87us/step - loss: 0.0811 - acc: 0.9747 - val_loss: 0.0626 - val_acc: 0.9815
Epoch 7/25
48000/48000 [==============================] - 4s 87us/step - loss: 0.0734 - acc: 0.9773 - val_loss: 0.0588 - val_acc: 0.9821
Epoch 8/25
48000/48000 [==============================] - 4s 86us/step - loss: 0.0695 - acc: 0.9783 - val_loss: 0.0530 - val_acc: 0.9843
Epoch 9/25
48000/48000 [==============================] - 4s 88us/step - loss: 0.0616 - acc: 0.9797 - val_loss: 0.0512 - val_acc: 0.9853
Epoch 10/25
48000/48000 [==============================] - 4s 89us/step - loss: 0.0557 - acc: 0.9827 - val_loss: 0.0520 - val_acc: 0.9838
Epoch 11/25
48000/48000 [==============================] - 4s 89us/step - loss: 0.0525 - acc: 0.9825 - val_loss: 0.0485 - val_acc: 0.9857
Epoch 12/25
48000/48000 [==============================] - 4s 92us/step - loss: 0.0477 - acc: 0.9845 - val_loss: 0.0491 - val_acc: 0.9844
Epoch 13/25
48000/48000 [==============================] - 4s 93us/step - loss: 0.0445 - acc: 0.9849 - val_loss: 0.0484 - val_acc: 0.9852
Epoch 14/25
48000/48000 [==============================] - 4s 91us/step - loss: 0.0404 - acc: 0.9863 - val_loss: 0.0456 - val_acc: 0.9868
Epoch 15/25
48000/48000 [==============================] - 4s 90us/step - loss: 0.0385 - acc: 0.9869 - val_loss: 0.0449 - val_acc: 0.9859
Epoch 16/25
48000/48000 [==============================] - 4s 91us/step - loss: 0.0349 - acc: 0.9887 - val_loss: 0.0467 - val_acc: 0.9857
Epoch 17/25
48000/48000 [==============================] - 4s 94us/step - loss: 0.0337 - acc: 0.9886 - val_loss: 0.0430 - val_acc: 0.9871
Epoch 18/25
48000/48000 [==============================] - 5s 95us/step - loss: 0.0298 - acc: 0.9902 - val_loss: 0.0406 - val_acc: 0.9881
Epoch 19/25
48000/48000 [==============================] - 5s 94us/step - loss: 0.0300 - acc: 0.9900 - val_loss: 0.0434 - val_acc: 0.9872
Epoch 20/25
48000/48000 [==============================] - 5s 95us/step - loss: 0.0269 - acc: 0.9906 - val_loss: 0.0410 - val_acc: 0.9884
Epoch 21/25
48000/48000 [==============================] - 5s 96us/step - loss: 0.0269 - acc: 0.9912 - val_loss: 0.0407 - val_acc: 0.9883
Epoch 22/25
48000/48000 [==============================] - 5s 96us/step - loss: 0.0255 - acc: 0.9914 - val_loss: 0.0420 - val_acc: 0.9874
Epoch 23/25
48000/48000 [==============================] - 5s 104us/step - loss: 0.0230 - acc: 0.9928 - val_loss: 0.0443 - val_acc: 0.9869
Epoch 24/25
48000/48000 [==============================] - 5s 99us/step - loss: 0.0209 - acc: 0.9926 - val_loss: 0.0418 - val_acc: 0.9890
Epoch 25/25
48000/48000 [==============================] - 5s 95us/step - loss: 0.0211 - acc: 0.9931 - val_loss: 0.0419 - val_acc: 0.9881
Test loss: 0.03642239146179636 / Test accuracy: 0.9886

Accuracy performance

Those are the last five epochs from the traditional CNN together with its test evaluation performance:

Epoch 20/25
48000/48000 [==============================] - 4s 84us/step - loss: 0.0094 - acc: 0.9968 - val_loss: 0.0281 - val_acc: 0.9924
Epoch 21/25
48000/48000 [==============================] - 4s 85us/step - loss: 0.0098 - acc: 0.9966 - val_loss: 0.0306 - val_acc: 0.9923
Epoch 22/25
48000/48000 [==============================] - 4s 84us/step - loss: 0.0094 - acc: 0.9967 - val_loss: 0.0320 - val_acc: 0.9921
Epoch 23/25
48000/48000 [==============================] - 4s 85us/step - loss: 0.0068 - acc: 0.9979 - val_loss: 0.0347 - val_acc: 0.9917
Epoch 24/25
48000/48000 [==============================] - 5s 100us/step - loss: 0.0074 - acc: 0.9974 - val_loss: 0.0347 - val_acc: 0.9916
Epoch 25/25
48000/48000 [==============================] - 4s 85us/step - loss: 0.0072 - acc: 0.9975 - val_loss: 0.0319 - val_acc: 0.9925

Test loss: 0.02579820747410522 / Test accuracy: 0.9926

The depthwise separable convolution seems to perform slightly worse on both validation accuracy (~0.04 in the last five epochs vs ~0.03 in the last five traditional epochs) and test loss (~0.026 against ~0.036). This may be caused by the initialization of your weights (which, by setting your starting point uniquely, may impact how the model performs even towards the end).

I therefore ran the model multiple times. This was the output of the 25th epoch and the evaluation step for five re-runs:

Epoch 25/25
48000/48000 [==============================] - 5s 97us/step - loss: 0.0218 - acc: 0.9927 - val_loss: 0.0445 - val_acc: 0.9873
Test loss: 0.03588760701002175 / Test accuracy: 0.9883

Epoch 25/25
48000/48000 [==============================] - 5s 99us/step - loss: 0.0230 - acc: 0.9918 - val_loss: 0.0392 - val_acc: 0.9893
Test loss: 0.03982483066770946 / Test accuracy: 0.9886

Epoch 25/25
48000/48000 [==============================] - 6s 128us/step - loss: 0.0189 - acc: 0.9934 - val_loss: 0.0396 - val_acc: 0.9883
Test loss: 0.03224361159349937 / Test accuracy: 0.9895

Epoch 25/25
48000/48000 [==============================] - 5s 107us/step - loss: 0.0281 - acc: 0.9903 - val_loss: 0.0432 - val_acc: 0.9874
Test loss: 0.04041151546177571 / Test accuracy: 0.9869

Epoch 25/25
48000/48000 [==============================] - 5s 98us/step - loss: 0.0308 - acc: 0.9893 - val_loss: 0.0461 - val_acc: 0.9875
Test loss: 0.04591406463075546 / Test accuracy: 0.9852

On average, test loss is 0.038852 and validation loss is similar. This is still worse than the traditional Conv2D layer. Oops. You might wish to experiment with Conv2D and SeparableConv2D first before you choose to do large-scale training.

Why this is the case might be explained through the number of trainable parameters. Since fewer multiplications are necessary, fewer parameters are to be trained. This might result in the model becoming unable to capture the underlying patterns in the data set.

In our model, neither adding a layer or removing one helps improve validation and test loss. You might thus really wish to test between Conv2D and SeparableConv2D first.

Time performance: it’s slower than Conv2D (with TensorFlow)

What’s more interesting is that despite the many fewer multiplications the depthwise separable convolutional layer trains slower than the traditional Conv2D layer. Although theoretically impossible, it’s a practical reality, possibly removing all the benefits from the spectrum (especially with large datasets, small training time deterioration per epoch turns into large deviations with many epochs). However, this seems to be some issue with TensorFlow:

Also experiencing that SeparableConv2d is slower than Conv2d in Keras. The number of input_channels does not seem to matter, I tested 32-2048 and in all cases the Conv2d is faster. Interestingly, in the SeparableConv2d-model the number parameters is lower as well as the FLOPS. Still this does not seem to have the wanted affect on the inference.

Source: gitman88 (2019), https://github.com/tensorflow/tensorflow/issues/12132#issuecomment-471880273

I’m really curious whether you also experience this issue when you run the depthwise separable ConvNet with Theano or CTNK. It might be the case that you don’t and that the depthwise convolutional layer is faster. If you have those installed, I would be really happy to hear your findings in the comments section below 👇 I can then edit my post 😊

Summary

In this blog, we’ve seen how a (2D) depthwise separable convolutional layer can be implemented by Keras by means of the SeparableConv2D layer. For this to work well, we briefly recapped depthwise separable convolutions and their split into depthwise and pointwise convolutions. We also explained the Keras configuration for the SeparableConv2D layer and showed how to implement one by adapting a previous CNN based classifier we created before – see e.g. GitHub for the code.

The fact that they were very similar in terms of data and configuration allowed us to compare the results. The performance of the depthwise separable convolution seems to be a bit lower than the traditional layer, perhaps due to underfitting given the fewer multiplications and, hence, fewer amount of trainable parameters. Similarly, its time performance was lower, presumably due to an issue with TensorFlow that performs the numerical operations. Therefore: choose wisely and test first!

I hope you’ve learnt something today – at least, I thought it was interesting to find deviating performance that directly opposes the theoretical benefits of the depthwise separable layer. Let’s hope the issue with TensorFlow is repaired relatively soon. Until then, happy engineering! 😎

References

Keras. (n.d.). Convolutional Layers. Retrieved from https://keras.io/layers/convolutional/

Keras. (n.d.). Constraints. Retrieved from https://keras.io/constraints/

Keras-team/keras. (n.d.). Trains a simple convnet on the MNIST dataset. Retrieved from https://github.com/keras-team/keras/blob/master/examples/mnist_cnn.py

Gitman88. (2019). slim.separable_conv2d is too slow · Issue #12132 · tensorflow/tensorflow. Retrieved from https://github.com/tensorflow/tensorflow/issues/12132#issuecomment-471880273

Alexvicegrab. (n.d.). SeparableConv3D · Issue #5639 · keras-team/keras. Retrieved from https://github.com/keras-team/keras/issues/5639

Ceballos, F. (2019, September 8). Installing a Python Based Machine Learning Environment in Windows 10. Retrieved from https://towardsdatascience.com/installing-keras-tensorflow-using-anaconda-for-machine-learning-44ab28ff39cb

MachineCurve. (2019, September 23). Understanding separable convolutions. Retrieved from https://machinecurve.com/index.php/2019/09/23/understanding-separable-convolutions/

MachineCurve. (2019, May 30). Convolutional Neural Networks and their components for computer vision. Retrieved from https://machinecurve.com/index.php/2018/12/07/convolutional-neural-networks-and-their-components-for-computer-vision/

MachineCurve. (2019, September 24). How to create a CNN classifier with Keras? Retrieved from https://machinecurve.com/index.php/2019/09/17/how-to-create-a-cnn-classifier-with-keras/

MachineCurve. (2019, July 27). How to create a basic MLP classifier with the Keras Sequential API – Small detour: categorical cross entropy. Retrieved from https://machinecurve.com/index.php/2019/07/27/how-to-create-a-basic-mlp-classifier-with-the-keras-sequential-api/#small-detour-categorical-cross-entropy

MachineCurve. (2019, September 4). ReLU, Sigmoid and Tanh: today’s most used activation functions. Retrieved from https://machinecurve.com/index.php/2019/09/04/relu-sigmoid-and-tanh-todays-most-used-activation-functions/

MachineCurve. (2019, August 22). What is weight initialization? Retrieved from https://machinecurve.com/index.php/2019/08/22/what-is-weight-initialization/

MachineCurve. (2019, September 18). He/Xavier initialization & activation functions: choose wisely. Retrieved from https://machinecurve.com/index.php/2019/09/16/he-xavier-initialization-activation-functions-choose-wisely/

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