In this notebook we will play with Feed-Forward FC-NN (Fully Connected Neural Network) for a classification task: Image Classification on MNIST Dataset
RECALL
In the FC-NN, the output of each layer is computed using the activations from the previous one, as follows:
$$h_{i} = \sigma(W_i h_{i-1} + b_i)$$where ${h}_i$ is the activation vector from the $i$-th layer (or the input data for $i=0$), ${W}_i$ and ${b}_i$ are the weight matrix and the bias vector for the $i$-th layer, respectively.
To regularize the model, we will also insert a Dropout layer between consecutive hidden layers.
Dropout works by “dropping out” some unit activations in a given layer, that is setting them to zero with a given probability.
Our loss function will be the categorical crossentropy.
Keras supports two different kind of models: the Sequential model and the Graph model. The former is used to build linear stacks of layer (so each layer has one input and one output), and the latter supports any kind of connection graph.
In our case we build a Sequential model with three Dense (aka fully connected) layers, with some Dropout. Notice that the output layer has the softmax activation function.
The resulting model is actually a function of its own inputs implemented using the Keras backend.
We apply the binary crossentropy loss and choose SGD as the optimizer.
Please remind that Keras supports a variety of different optimizers and loss functions, which you may want to check out.
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from keras.models import Sequential
from keras.layers.core import Dense, Dropout
from keras.optimizers import SGD
nb_classes = 10
# FC@512+relu -> DropOut(0.2) -> FC@512+relu -> DropOut(0.2) -> FC@nb_classes+softmax
# ... your Code Here
In [1]:
# Decomment and Execute this cell to get the solution
# %load solutions/sol_221_1.py
keras.dataset)We will train our model on the MNIST dataset, which consists of 60,000 28x28 grayscale images of the 10 digits, along with a test set of 10,000 images.
Since this dataset is provided with Keras, we just ask the keras.dataset model for training and test data.
We will:
The binary_crossentropy loss expects a one-hot-vector as input, therefore we apply the to_categorical function from keras.utilis to convert integer labels to one-hot-vectors.
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from keras.datasets import mnist
from keras.utils import np_utils
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train.reshape(60000, 784)
X_test = X_test.reshape(10000, 784)
X_train = X_train.astype("float32")
X_test = X_test.astype("float32")
X_train /= 255
X_test /= 255
# convert class vectors to binary class matrices
Y_train = np_utils.to_categorical(y_train, 10)
Y_test = np_utils.to_categorical(y_test, 10)
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network_history = model.fit(X_train, Y_train, batch_size=128,
epochs=100, verbose=1, validation_data=(X_test, Y_test))
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import matplotlib.pyplot as plt
%matplotlib inline
plt.figure()
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.plot(network_history.history['loss'])
plt.plot(network_history.history['val_loss'])
plt.legend(['Training', 'Validation'])
plt.figure()
plt.xlabel('Epochs')
plt.ylabel('Accuracy')
plt.plot(network_history.history['acc'])
plt.plot(network_history.history['val_acc'])
plt.legend(['Training', 'Validation'], loc='lower right')
After 100 epochs, we get a 98.8% validation accuracy.
If you continue training, at some point the validation loss will start to increase: that is when the model starts to overfit.
It is always necessary to monitor training and validation loss during the training of any kind of Neural Network, either to detect overfitting or to evaluate the behaviour of the model (any clue on how to do it??)
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# %load solutions/sol_221_2.py