神经网络损失不准确

Question

I trained a model for neural network to find the roots of the quadratic equation (discriminant >= 0) But when I checked the same on my example, even the loss is small it is showing a far from exact answer.

Loss graph:

My example:

 a = 1 b = -2 c = -24 model.predict(np.array([[a/max,b/max,c/max]])) * max Out[421]: array([[-15.218947 , -1.3733944]], dtype=float32) #but should be 6 and -4 

Look here please:

import numpy as np

from keras.models import Sequential
from keras.layers.core import Dense, Activation
from keras.utils import np_utils
from keras.layers import Dropout

x_in = np.array([]).reshape(0,3)
x_answer = np.array([]).reshape(0,2)

for i in range(300):
    a = np.random.randint(-1000,1000)
    b = np.random.randint(-1000,1000)
    c = np.random.randint(-1000,1000)
    D = np.power(b,2)-4*a*c
    if(a != 0):
        if(D >= 0):
            x1 = (-b+np.sqrt(D))/(2*a)
            x2 = (-b-np.sqrt(D))/(2*a)
            x_in = np.concatenate((x_in,[[a,b,c]]))
            x_answer = np.concatenate((x_answer,[[x1,x2]]))

np.random.seed()

NB_EPOCH = 300
VERBOSE = 1

x_in = np.asarray(x_in, dtype=np.float32)
x_answer = np.asarray(x_answer, dtype=np.float32)

min_in = np.nanmin(x_in)
min_answ = np.nanmin(x_answer)
min = -1000 #np.min(np.array([min_in,min_answ]))

max_in = np.nanmax(x_in)
max_answ = np.nanmax(x_answer)
max = 1000 #np.max(np.array([max_in,max_answ]))

x_in /= max
x_answer /= max

model = Sequential()
model.add(Dense(30, input_dim = 3, activation='relu'))
#model.add(Dropout(0.2))
model.add(Dense(40, activation='softmax'))
#model.add(Dropout(0.2))

model.add(Dense(50, activation='linear'))
model.add(Dense(2))

model.compile(loss='mse', optimizer='adam')

history = model.fit(x_in, x_answer, epochs=NB_EPOCH, verbose=VERBOSE)

UPDATE:

what to do?

Answer 1

I think that 300 training points is too few for a parameter space of (2000)**3 possible parameter values of a, b and c. You could try to give it more training data.