Are these models equivalent?

Question

Main question: I define the same model in two different ways. Why do I get different results? They seem to be the same model.

Secondary question (answered below) If I run the code again, I get different results again. I have set the seed at the beginning to fix the randomness. Why is that happening?

import numpy as np
np.random.seed(1)
from keras.models import Model, Sequential
from keras.layers import Input, Dense

model1= Sequential([
     Dense(20, activation='sigmoid',kernel_initializer='glorot_normal', 
               input_shape=(2,)),
     Dense(2,  activation='linear', kernel_initializer='glorot_normal'),
])

model1.compile(optimizer='adam', loss='mean_squared_error')

ipt    = Input(shape=(2,))
x      = Dense(20, activation='sigmoid', kernel_initializer='glorot_normal')(ipt)
out    = Dense(2,  activation='linear',  kernel_initializer='glorot_normal')(x)
model2 = Model(ipt, out)

model2.compile(optimizer='adam', loss='mean_squared_error')

x_train=np.array([[1,2],[3,4],[3,4]])

model1.fit(x_train, x_train,epochs=2, validation_split=0.1, shuffle=False)
model2.fit(x_train, x_train,epochs=2, validation_split=0.1, shuffle=False)

The first time, the output is:

2/2 [==============================] - 0s 68ms/step - loss: 14.4394 - val_loss: 21.5747
Epoch 2/2

2/2 [==============================] - 0s 502us/step - loss: 14.3199 - val_loss: 21.4163
Train on 2 samples, validate on 1 samples
Epoch 1/2

2/2 [==============================] - 0s 72ms/step - loss: 11.0523 - val_loss: 17.7059
Epoch 2/2

2/2 [==============================] - 0s 491us/step - loss: 10.9833 - val_loss: 17.5785

The second time, the output is:

2/2 [==============================] - 0s 80ms/step - loss: 14.4394 - val_loss: 21.5747
Epoch 2/2

2/2 [==============================] - 0s 501us/step - loss: 14.3199 - val_loss: 21.4163
Train on 2 samples, validate on 1 samples
Epoch 1/2

2/2 [==============================] - 0s 72ms/step - loss: 11.0523 - val_loss: 17.6733
Epoch 2/2

2/2 [==============================] - 0s 485us/step - loss: 10.9597 - val_loss: 17.5459

---

Update after reading the answer: By the answer below, one of my questions has been answered. I changed the beginning of my code to:

import numpy as np
np.random.seed(1)
import random
random.seed(2)
import tensorflow as tf
tf.set_random_seed(3)

And, now I am getting the same numbers as before. So, it is stable. But, my main question has remained unanswered. Why at each time, the two equivalent models give different results?

Here is the result I get every time:

results 1:

Epoch 1/2

2/2 [==============================] - 0s 66ms/sample - loss: 11.9794 - val_loss: 18.9925
Epoch 2/2

2/2 [==============================] - 0s 268us/sample - loss: 11.8813 - val_loss: 18.8572

results 2:

Epoch 1/2

2/2 [==============================] - 0s 67ms/sample - loss: 5.4743 - val_loss: 9.3471
Epoch 2/2

2/2 [==============================] - 0s 3ms/sample - loss: 5.4108 - val_loss: 9.2497

Answer 1

The problem's rooted in the expected vs. actual behavior of model definition and randomness. To see what's going on, we must understand how "RNG" works:

• A "random number generator" (RNG) is actually a function that produces numbers such that they map onto a probability distribution 'in the long run'
• When the RNG function, e.g. RNG() is called, it returns a "random" value and increments its internal counter by 1. Call this counter n - then: random_value = RNG(n)
• When you set a SEED, you set n according to the value of that seed (but not to that seed); we can represent this difference via + c in the counter
• c will be a constant produced by a non-linear, but deterministic, function of the seed: f(seed)

import numpy as np

np.random.seed(4)         # internal counter = 0 + c
print(np.random.random()) # internal counter = 1 + c
print(np.random.random()) # internal counter = 2 + c
print(np.random.random()) # internal counter = 3 + c

np.random.seed(4)         # internal counter = 0 + c
print(np.random.random()) # internal counter = 1 + c
print(np.random.random()) # internal counter = 2 + c
print(np.random.random()) # internal counter = 3 + c

0.9670298390136767
0.5472322491757223
0.9726843599648843

0.9670298390136767
0.5472322491757223
0.9726843599648843

Suppose model1 has 100 weights, and you set a seed (n = 0 + c). After model1 is built, your counter is at 100 + c. If you don't reset the seed, even if you build model2 with the exact same code, the models will differ - as model2's weights are initialized per n from 100 + c to 200 + c.

---

Additional info:

There are three seeds to ensure better randomness:

import numpy as np
np.random.seed(1)         # for Numpy ops
import random 
random.seed(2)            # for Python ops
import tensorflow as tf
tf.set_random_seed(3)     # for tensorfow ops - e.g. Dropout masks

This'll give pretty good reproducibility, but not perfect if you're using a GPU - due to parallelism of operations; this video explains it well. For even better reproducibility, set your PYHTONHASHSEED - that and other info in the official Keras FAQ.

"Perfect" reproducibility is rather redundant, as your results should agree within .1% majority of the time - but if you really need it, likely the only way currently is to switch to CPU and stop using CUDA - but that'll slow down training tremendously (by x10+).

---

Sources of randomness:

• Weight initializations (every default Keras initializer uses randomness)
• Noise layers (Dropout, GaussianNoise, etc)
• Hashing for hash-based operations, e.g. item order in a set or dict
• GPU parallelism (see linked video)

---

Model randomness demo:

import numpy as np
np.random.seed(4)

model1_init_weights = [np.random.random(), np.random.random(), np.random.random()]
model2_init_weights = [np.random.random(), np.random.random(), np.random.random()]
print("model1_init_weights:", model1_init_weights)
print("model2_init_weights:", model2_init_weights)

model1_init_weights: [0.9670298390136767, 0.5472322491757223, 0.9726843599648843]
model2_init_weights: [0.7148159936743647, 0.6977288245972708, 0.21608949558037638]

Restart kernel. Now run this:

import numpy as np
np.random.seed(4)

model2_init_weights = [np.random.random(), np.random.random(), np.random.random()]
model1_init_weights = [np.random.random(), np.random.random(), np.random.random()]
print("model1_init_weights:", model1_init_weights)
print("model2_init_weights:", model2_init_weights)

model1_init_weights: [0.7148159936743647, 0.6977288245972708, 0.21608949558037638]
model2_init_weights: [0.9670298390136767, 0.5472322491757223, 0.9726843599648843]

Thus, flipping the order of model1 and model2 in your code also flips the losses. This is because the seed does not reset itself between the two models' definitions, so your weight initializations are totally different.

If you wish them to be the same, reset the seed before defining EACH MODEL, and before FITTING each model - and use a handy function like below. But your best bet is to restart the kernel and work in separate .py files.

def reset_seeds():
    np.random.seed(1)
    random.seed(2)
    tf.set_random_seed(3)
    print("RANDOM SEEDS RESET")