Let's implement the handwritten digits classification with Keras, again using dense FC layers only. This time we shall use one more hidden layer, along with a dropout layer. The next code block shows how to implement the classifier with a few lines of code using the keras.models Sequential() function. We can simply add the layers sequentially to the model. There are a couple of hidden layers introduced, with each of them having 200 nodes along with a dropout in between, with 15% dropout rate. This time, let's use the Adam optimizer (which uses momentum to accelerate SGD). Let's fit the model on the training dataset with 10 epochs (one pass over the entire input dataset). As can be seen, with this simple change in the architecture, an accuracy of 98.04% is obtained on the test images of MNIST:

import keras
from keras.models import Sequential
from keras.layers import Dense, Flatten, Dropout
from keras.layers.convolutional import Conv2D, MaxPooling2D
from keras.utils import to_categorical

# import data
from keras.datasets import mnist
# load data
(X_train, y_train), (X_test, y_test) = mnist.load_data()
print(X_train.shape, X_test.shape)
# (60000, 28, 28) (10000, 28, 28)
# reshape to be [samples][pixels][width][height]
X_train = X_train.reshape(X_train.shape[0], 28, 28, 1).astype('float32')
X_test = X_test.reshape(X_test.shape[0], 28, 28, 1).astype('float32')
X_train = X_train / 255 # normalize training data
X_test = X_test / 255 # normalize test data
y_train = to_categorical(y_train) # to one-hot-encoding of the labels
y_test = to_categorical(y_test)
num_classes = y_test.shape[1] # number of categories

def FC_model(): 
    # create model
    model = Sequential()
    model.add(Flatten(input_shape=(28, 28, 1)))
    model.add(Dense(200, activation='relu'))
    model.add(Dropout(0.15))
    model.add(Dense(200, activation='relu'))
    model.add(Dense(num_classes, activation='softmax')) 
    # compile model

    model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])
    return model

# build the model
model = FC_model()
model.summary()
# fit the model
model.fit(X_train, y_train, validation_data=(X_test, y_test), epochs=10, batch_size=200, verbose=2)
# evaluate the model
scores = model.evaluate(X_test, y_test, verbose=0)
print("Accuracy: {} 
 Error: {}".format(scores[1], 100-scores[1]*100))

# _________________________________________________________________
# Layer (type)                 Output Shape              Param #   
# =================================================================
# flatten_1 (Flatten)         (None, 784)               0         
# _________________________________________________________________
# dense_1 (Dense)             (None, 200)               157000    
# ________________________________________________________________
# dropout_1 (Dropout)         (None, 200)               0         
# ________________________________________________________________
# dense_2 (Dense)             (None, 200)               40200     
# ________________________________________________________________
# dense_3 (Dense)             (None, 10)                2010      
# =================================================================
# Total params: 199,210
# Trainable params: 199,210
# Non-trainable params: 0
# _________________________________________________________________
# Train on 60000 samples, validate on 10000 samples
# Epoch 1/10
#  - 3s - loss: 0.3487 - acc: 0.9010 - val_loss: 0.1474 - val_acc: 0.9562
# Epoch 2/10
#  - 2s - loss: 0.1426 - acc: 0.9580 - val_loss: 0.0986 - val_acc: 0.9700
# Epoch 3/10
#  - 2s - loss: 0.0976 - acc: 0.9697 - val_loss: 0.0892 - val_acc: 0.9721
# Epoch 4/10
#  - 2s - loss: 0.0768 - acc: 0.9762 - val_loss: 0.0829 - val_acc: 0.9744
# Epoch 5/10
#  - 2s - loss: 0.0624 - acc: 0.9806 - val_loss: 0.0706 - val_acc: 0.9774
# Epoch 6/10
#  - 2s - loss: 0.0516 - acc: 0.9838 - val_loss: 0.0655 - val_acc: 0.9806
# Epoch 7/10
#  - 2s - loss: 0.0438 - acc: 0.9861 - val_loss: 0.0692 - val_acc: 0.9788
# Epoch 8/10
#  - 2s - loss: 0.0387 - acc: 0.9874 - val_loss: 0.0623 - val_acc: 0.9823
# Epoch 9/10
#  - 2s - loss: 0.0341 - acc: 0.9888 - val_loss: 0.0695 - val_acc: 0.9781
# Epoch 10/10
#  - 2s - loss: 0.0299 - acc: 0.9899 - val_loss: 0.0638 - val_acc: 0.9804
# Accuracy: 0.9804 
# Error: 1.9599999999999937