Trying to get simple Keras neural net example to work

Question

I've been fooling-around trying to get simple examples that I create working, because I find the examples given with large complicated datasets to be hard to grasp intuitively. The program below takes a list of weights [x_0 x_1 ... x_n] and uses them to create a random scattering of points on a plane with some random noise added in. I then train the simple neural nets on this data and check the results.

When I do this with the Graph models everything works perfectly, the loss score goes down to zero predictably as the model converges on the weights given. However, when I try to use a sequential model, nothing happens. Code below

If you want I can post my other script that uses the Graph instead of sequential and show that it finds the input weights perfectly.

#!/usr/bin/env python
from keras.models import Sequential, Graph
from keras.layers.core import Dense, Dropout, Activation
from keras.optimizers import SGD
import numpy as np
import theano, sys

NUM_TRAIN = 100000
NUM_TEST = 10000
INDIM = 3

mn = 1

def myrand(a, b) :
    return (b)*(np.random.random_sample()-0.5)+a

def get_data(count, ws, xno, bounds=100, rweight=0.0) :
    xt = np.random.rand(count, len(ws))
    xt = np.multiply(bounds, xt)
    yt = np.random.rand(count, 1)
    ws = np.array(ws, dtype=np.float)
    xno = np.array([float(xno) + rweight*myrand(-mn, mn) for x in xt], dtype=np.float)
    yt = np.dot(xt, ws)
    yt = np.add(yt, xno)

    return (xt, yt)


if __name__ == '__main__' :
    if len(sys.argv) > 1 :
       EPOCHS = int(sys.argv[1])
       XNO = float(sys.argv[2])
       WS = [float(x) for x in sys.argv[3:]]
       mx = max([abs(x) for x in (WS+[XNO])])
       mn = min([abs(x) for x in (WS+[XNO])])
       mn = min(1, mn)
       WS = [float(x)/mx for x in WS]
       XNO = float(XNO)/mx
       INDIM = len(WS)
    else :
        INDIM = 3
        WS = [2.0, 1.0, 0.5]
        XNO = 2.2

    X_test, y_test = get_data(10000, WS, XNO, 10000, rweight=0.4)
    X_train, y_train = get_data(100000, WS, XNO, 10000)

    model = Sequential()
    model.add(Dense(INDIM, input_dim=INDIM, init='uniform', activation='tanh'))
    model.add(Dropout(0.5))
    model.add(Dense(2, init='uniform', activation='tanh'))
    model.add(Dropout(0.5))
    model.add(Dense(1, init='uniform', activation='softmax'))

    sgd = SGD(lr=0.1, decay=1e-6, momentum=0.9, nesterov=True)
    model.compile(loss='mean_squared_error', optimizer=sgd)

    model.fit(X_train, y_train, shuffle="batch", show_accuracy=True, nb_epoch=EPOCHS)
    score, acc = model.evaluate(X_test, y_test, batch_size=16, show_accuracy=True)
    print score
    print acc

    predict_data = np.random.rand(100*100, INDIM)
    predictions = model.predict(predict_data)

    for x in range(len(predict_data)) :
        print "%s --> %s" % (str(predict_data[x]), str(predictions[x]))

The output is as follows

$ ./keras_hello.py 20 10 5 4 3 2 1
Using gpu device 0: GeForce GTX 970 (CNMeM is disabled)
Epoch 1/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 2/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 3/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 4/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 5/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 6/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 7/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 8/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 9/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 10/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 11/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 12/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 13/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 14/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 15/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 16/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 17/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 18/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 19/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
Epoch 20/20
100000/100000 [==============================] - 0s - loss: 60726734.3061 - acc: 1.0000     
10000/10000 [==============================] - 0s     
60247198.6661
1.0
[ 0.06698217  0.70033048  0.4317502   0.78504855  0.26173543] --> [ 1.]
[ 0.28940025  0.21746189  0.93097653  0.94885535  0.56790348] --> [ 1.]
[ 0.69430499  0.1622601   0.22802859  0.75709315  0.88948355] --> [ 1.]
[ 0.90714721  0.99918648  0.31404901  0.83920051  0.84081288] --> [ 1.]
[ 0.02214092  0.03132355  0.14417082  0.33901317  0.91491426] --> [ 1.]
[ 0.31426055  0.80830795  0.46686523  0.58353359  0.50000842] --> [ 1.]
[ 0.27649579  0.77914451  0.33572287  0.08703303  0.50865592] --> [ 1.]
[ 0.99280349  0.24028343  0.05556034  0.31411902  0.41912574] --> [ 1.]
[ 0.91897031  0.96840695  0.23561379  0.16005505  0.06567748] --> [ 1.]
[ 0.27392867  0.44021533  0.44129147  0.40658522  0.47582736] --> [ 1.]
[ 0.82063221  0.95182938  0.64210378  0.69578691  0.2946907 ] --> [ 1.]
[ 0.12672415  0.35700418  0.89303047  0.80726545  0.79870725] --> [ 1.]
[ 0.6662085   0.41358115  0.76637022  0.82093095  0.76973305] --> [ 1.]
[ 0.96201937  0.29706843  0.22856618  0.59924945  0.05653825] --> [ 1.]
[ 0.34120276  0.71866377  0.18758929  0.52424856  0.64061623] --> [ 1.]
[ 0.25471237  0.35001821  0.63248632  0.45442404  0.96967989] --> [ 1.]
[ 0.79390087  0.00100834  0.49645204  0.55574269  0.33487764] --> [ 1.]
[ 0.41330261  0.38061826  0.33766183  0.23133121  0.80999653] --> [ 1.]
[ 0.49603561  0.33414841  0.10180184  0.9227252   0.35073833] --> [ 1.]
[ 0.17960345  0.05259438  0.565135    0.40465603  0.91518233] --> [ 1.]
[ 0.36129943  0.903603    0.63047644  0.96553285  0.94006713] --> [ 1.]
[ 0.7150973   0.93945141  0.31802763  0.15849441  0.92902078] --> [ 1.]
[ 0.23730571  0.65360248  0.68776259  0.79697206  0.86814652] --> [ 1.]
[ 0.47414382  0.75421265  0.32531333  0.43218305  0.4680773 ] --> [ 1.]
[ 0.4887811   0.66130135  0.79913557  0.68948405  0.48376372] --> [ 1.]
....

Answer 1

The reason for the huge error is that your labels are not binary and very large, but the output of softmax is binary. For instance, if the label is 10000 but you can only predict something between 0 and 1, there will be huge error regardless of what you predict. Did you mean activation='linear' in the last layer, to do a regression? Or did you want to put your labels through a softmax at the end of get_data()?