notebook.community



In [1]:

    
%matplotlib inline
import keras

from keras.layers         import Dense
from keras.models         import Model
from keras.models         import Sequential
from keras.utils.np_utils import to_categorical

from collections import Counter

import numpy             as np
import matplotlib.pyplot as plt









    



Using TensorFlow backend.



In [2]:

    
max_iter = 50
seq_fn   = lambda z, c: z ** 2 + c



In [3]:

    
def iterate_sequence(seq_fn, max_iter, c):
    return 1 if c.real > 0 else 0



In [4]:

    
def iterate_sequence(seq_fn, max_iter, c):
    z = c
    for i in range(max_iter):
        z = seq_fn(z, c)
        if (z.real * z.real + z.imag * z.imag) > 4:
            return 1
    return 0

Model results visualization



In [5]:

    
def generate_X(unit):
    c_list = []
    width  = 3 * unit
    height = 2 * unit
    
    for x in range(height):
        im = x * 2. / height - 1 
        for y in range(width):
            re = y * 3. / width - 2
            c_list.append(np.array([re, im]))
    
    return np.stack(c_list)



In [6]:

    
def generate_visualization(model, unit):
    width  = 3 * unit
    height = 2 * unit
    X      = generate_X(unit)
    y      = model.predict_classes(X, batch_size = 64)
    
    return y.reshape((2 * unit, 3 * unit))



In [7]:

    
class FakeModel():
    def predict_classes(self, X, **kwargs):
        return np.array([iterate_sequence(seq_fn, max_iter, complex(*sample)) for sample in X])



In [8]:

    
fake_model = FakeModel()
res        = generate_visualization(fake_model, 48)
plt.imshow(res)









    Out[8]:





<matplotlib.image.AxesImage at 0x7fb702effba8>

Training samples generation



In [9]:

    
nb_samples = 100000



In [10]:

    
samples       = np.random.rand(nb_samples, 2)
samples[:, 0] = samples[:, 0] * 3 - 2
samples[:, 1] = samples[:, 1] * 2 - 1



In [11]:

    
sample_img = np.array([iterate_sequence(seq_fn, max_iter, complex(*sample)) for sample in samples])



In [12]:

    
outside = samples[sample_img == 1]
inside  = samples[sample_img == 0][np.random.choice(samples.shape[0] - outside.shape[0], outside.shape[0])] 
X       = np.concatenate([inside, outside])
y       = np.concatenate([np.zeros(inside.shape[0]), np.zeros(outside.shape[0]) + 1]).astype(np.int32)
y       = to_categorical(y)

Model definition



In [13]:

    
model = Sequential([
    Dense(512, input_dim = 2, activation = 'relu'),
    Dense(512, activation = 'relu'),
    Dense(512, activation = 'relu'),
    Dense(512, activation = 'relu'),
    Dense(512, activation = 'relu'),
    Dense(512, activation = 'relu'),
    Dense(512, activation = 'relu'),
    Dense(2, activation = 'softmax')
])



In [14]:

    
model.compile('adam', 'binary_crossentropy')



In [17]:

    
model.fit(X, y, nb_epoch = 3, batch_size = 256, shuffle = True)









    



Epoch 1/3
147044/147044 [==============================] - 4s - loss: 0.0641     
Epoch 2/3
147044/147044 [==============================] - 4s - loss: 0.0632     
Epoch 3/3
147044/147044 [==============================] - 4s - loss: 0.0603     






    Out[17]:





<keras.callbacks.History at 0x7fb6e46c5710>



In [18]:

    
res = generate_visualization(model, 32)
plt.imshow(res)









    



5504/6144 [=========================>....] - ETA: 0s





    Out[18]:





<matplotlib.image.AxesImage at 0x7fb6e464b7f0>



In [19]:

    
model.optimizer.lr = 0.0001



In [20]:

    
model.fit(X, y, nb_epoch = 3, batch_size = 256, shuffle = True)









    



Epoch 1/3
147044/147044 [==============================] - 4s - loss: 0.0590     
Epoch 2/3
147044/147044 [==============================] - 4s - loss: 0.0588     
Epoch 3/3
147044/147044 [==============================] - 4s - loss: 0.0569     






    Out[20]:





<keras.callbacks.History at 0x7fb752afcd68>



In [21]:

    
model.fit(X, y, nb_epoch = 3, batch_size = 256, shuffle = True)









    



Epoch 1/3
147044/147044 [==============================] - 4s - loss: 0.0547     
Epoch 2/3
147044/147044 [==============================] - 4s - loss: 0.0553     
Epoch 3/3
147044/147044 [==============================] - 4s - loss: 0.0529     






    Out[21]:





<keras.callbacks.History at 0x7fb7031920b8>



In [22]:

    
plt.imshow(generate_visualization(model, 32))









    



5568/6144 [==========================>...] - ETA: 0s





    Out[22]:





<matplotlib.image.AxesImage at 0x7fb6cd685fd0>



In [23]:

    
model.optimizer.lr = 1e-5



In [24]:

    
model.fit(X, y, nb_epoch = 3, batch_size = 256, shuffle = True)









    



Epoch 1/3
147044/147044 [==============================] - 4s - loss: 0.0532     
Epoch 2/3
147044/147044 [==============================] - 4s - loss: 0.0525     
Epoch 3/3
147044/147044 [==============================] - 4s - loss: 0.0518     






    Out[24]:





<keras.callbacks.History at 0x7fb6e4711198>



In [25]:

    
model.fit(X, y, nb_epoch = 3, batch_size = 256, shuffle = True)









    



Epoch 1/3
147044/147044 [==============================] - 4s - loss: 0.0512     
Epoch 2/3
147044/147044 [==============================] - 4s - loss: 0.0501     
Epoch 3/3
147044/147044 [==============================] - 4s - loss: 0.0492     






    Out[25]:





<keras.callbacks.History at 0x7fb6e46c5588>



In [26]:

    
model.fit(X, y, nb_epoch = 3, batch_size = 256, shuffle = True)









    



Epoch 1/3
147044/147044 [==============================] - 4s - loss: 0.0495     
Epoch 2/3
147044/147044 [==============================] - 4s - loss: 0.0483     
Epoch 3/3
147044/147044 [==============================] - 4s - loss: 0.0466     






    Out[26]:





<keras.callbacks.History at 0x7fb6cd69c710>



In [27]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0472     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0471     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0464     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0467     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0458     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0464     






    Out[27]:





<keras.callbacks.History at 0x7fb6cd69cc18>



In [28]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0453     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0447     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0442     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0442     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0442     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0423     






    Out[28]:





<keras.callbacks.History at 0x7fb6cd69c748>



In [31]:

    
plt.imshow(generate_visualization(model, 128))









    



96832/98304 [============================>.] - ETA: 0s





    Out[31]:





<matplotlib.image.AxesImage at 0x7fb6cc0376a0>



In [32]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0436     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0433     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0431     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0434     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0426     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0421     






    Out[32]:





<keras.callbacks.History at 0x7fb6e4711748>



In [33]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0419     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0413     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0407     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0408     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0404     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0411     






    Out[33]:





<keras.callbacks.History at 0x7fb6cc0502e8>



In [34]:

    
model.optimizer.lr = 1e-6



In [35]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0403     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0406     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0405     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0403     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0458     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0405     






    Out[35]:





<keras.callbacks.History at 0x7fb6cc050128>



In [36]:

    
plt.imshow(generate_visualization(model, 256))









    



392576/393216 [============================>.] - ETA: 0s 





    Out[36]:





<matplotlib.image.AxesImage at 0x7fb6ad0f02e8>



In [37]:

    
model.optimizer.lr = 1e-7



In [38]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0397     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0397     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0395     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0393     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0395     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0383     






    Out[38]:





<keras.callbacks.History at 0x7fb6cd6c7710>



In [39]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0384     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0389     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0382     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0384     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0379     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0372     






    Out[39]:





<keras.callbacks.History at 0x7fb6c61d0198>



In [40]:

    
model.fit(X, y, nb_epoch = 6, batch_size = 256, shuffle = True)









    



Epoch 1/6
147044/147044 [==============================] - 4s - loss: 0.0383     
Epoch 2/6
147044/147044 [==============================] - 4s - loss: 0.0385     
Epoch 3/6
147044/147044 [==============================] - 4s - loss: 0.0376     
Epoch 4/6
147044/147044 [==============================] - 4s - loss: 0.0380     
Epoch 5/6
147044/147044 [==============================] - 4s - loss: 0.0376     
Epoch 6/6
147044/147044 [==============================] - 4s - loss: 0.0367     






    Out[40]:





<keras.callbacks.History at 0x7fb6c61f4828>



In [41]:

    
plt.imshow(generate_visualization(model, 256))









    



392768/393216 [============================>.] - ETA: 0s 





    Out[41]:





<matplotlib.image.AxesImage at 0x7fb6c6b4cef0>



In [ ]: