keras 网络不训练

Question

First time I try to make the simplest net. I train it for XOR. It does not work absolutely. Tryed everithing: different activation functions, number of layers, neurons, epoches, batches, optimisers... Everytime result is 1,1,1,1 (accuracy=0.5). Please, help! What I do wrong?

from keras.models import Sequential
from keras.layers import Dense
from tensorflow import keras
import numpy as np

X = np.array([  [0,0],
                [0,1],
                [1,0],
                [1,1] ])
Y = np.array([[1,0,0,1]]).T

model = Sequential()
model.add(Dense(10, input_dim=2, activation='relu'))
model.add(Dense(10, activation='relu'))  
model.add(Dense(1, activation='softmax')) 

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

#Traiting a model
model.fit(X, Y, epochs=100, batch_size=len(X))

# Prediction
predictions = model.predict(X)
print(predictions)

I noticed, that there are always 1/1 at the left side of the output. But, I guess, there must be something like 4/4. May be this is the reason? But I can't understand how to fix it...

Tail of output:

...
...
Epoch 97/100
1/1 [==============================] - 0s 1ms/step - loss: 0.0000e+00 - accuracy: 0.5000
Epoch 98/100
1/1 [==============================] - 0s 1ms/step - loss: 0.0000e+00 - accuracy: 0.5000
Epoch 99/100
1/1 [==============================] - 0s 1ms/step - loss: 0.0000e+00 - accuracy: 0.5000
Epoch 100/100
1/1 [==============================] - 0s 1ms/step - loss: 0.0000e+00 - accuracy: 0.5000
1/1 [==============================] - 0s 165ms/step - loss: 0.0000e+00 - accuracy: 0.5000
[0.0, 0.5]
[[1.]
[1.]
[1.]
[1.]]

Answer 1

Thank you very much to all!

Here the working net below. Strange, that it takes too long time for training! I remember, I did the same task but without Keras several years ago. Training was almost instantly (of course without any GPU). But here "Adam optimisation" (with "fast relu" I managed to do only 4 layers net). Seems that that functions has the opposit effect for such simple tasks.

from keras.models import Sequential
from keras import initializers
 
from keras.layers import Dense
from tensorflow import keras
import numpy as np
 
X = np.array([0,0,
              0,1,
              1,0,
              1,1] )
 
X = X.reshape(4,2).astype("float32")
 
Y = np.array([1,
              0,
              0,
              1] )
Y = Y.reshape(4,1).astype("float32")
 
init_2 = initializers.TruncatedNormal(mean=0.0, stddev=0.05, seed=12345)
 
model = Sequential()
model.add(Dense(4, input_dim=2, activation='sigmoid', kernel_initializer=init_2, bias_initializer=init_2))
model.add(Dense(1, activation='sigmoid', kernel_initializer=init_2, bias_initializer=init_2)) 
 
model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])
 
 
#Traiting a model
model.fit(X, Y, epochs=7000, batch_size=4, verbose=0)
 
scores = model.evaluate(X, Y)
print(scores)
 
# Prediction
predictions = model.predict(X)
print(predictions)