3
$\begingroup$

Just for practice, i've tried to create a super-basic neural network script (one neuron for each layer, didn't want to deal with matrices for the sake of simplicity, not that I don't know how to). I've implemented a squared error loss function, sigmoid activation and the derivatives. Of course i created a feedforward function, and a backprop function to calculate the deltas.

import random
import math

LEARNING_RATE = 0.1
TRAINING_EPOCHS = 10_000  #just a reason to make it incompatible with python2

def sigmoid(x):
    return 1/(1 + math.exp(-x))   #activation

def der_sigmoid(x):
    return x * (1 - x)          #derivative for already applied activation

def cost(x):
    return x * x          #squared error

def der_cost(x):
    return 2 * x          #derivative of squared error


w1 = 2 * random.random() - 1
w2 = 2 * random.random() - 1      #initializing weights

b1 = 0       #biases
b2 = 0

def feedforward(x, w1, w2, b1, b2):
    h = sigmoid((x * w1) + b1) 
    y = sigmoid((h * w2) + b2)        #feedforward

    return h, y

def backprop(q_set, a_set, w1, w2, b1, b2):
    rand_choice = random.randint(0, len(q_set) - 1)

    curr_q = q_set[rand_choice]            #choosing random pair from dataset
    curr_a = a_set[rand_choice]

    h, yHat = feedforward(curr_q, w1, w2, b1, b2)       #calculating guess

    E = yHat - curr_a     #Error

    loss = cost(E)     #Calculating cost, just because
    #print(loss)

    gradient_y = der_cost(E)      #calculating the derivative of the cost for the output layer

    gradient_h = gradient_y * w2   #backpropagating the derivative

    delta_w2 = gradient_y * der_sigmoid(yHat) * w2 * LEARNING_RATE
    delta_w1 = gradient_h * der_sigmoid(h) * w1 * LEARNING_RATE       #calculating weight deltas

    delta_b2 = gradient_y * der_sigmoid(yHat) * LEARNING_RATE         #bias deltas
    delta_b1 = gradient_h * der_sigmoid(h) * LEARNING_RATE

    return delta_b1, delta_b2, delta_w1, delta_w2

set_q = [1,2,3,4,5,6,7,8,9]   
set_a = [0,1,0,1,0,1,0,1,0]     #1 for even, 0 for odd

for i in range(len(set_q)):
    set_q[i] /= max(set_q)     #normalizing the qset between 0 and 1

print(feedforward(5, w1, w2, b1, b2))
print(feedforward(16, w1, w2, b1, b2))        #testing initial predictions

for i in range(TRAINING_EPOCHS):
    delta_b1, delta_b2, delta_w1, delta_w2 = backprop(set_q, set_a, w1, w2, b1, b2)

    w1 -= delta_w1
    w2 -= delta_w2       #applying deltas

    b1 -= delta_b1
    b2 -= delta_b2

print(feedforward(5, w1, w2, b1, b2))       #testing
print(feedforward(16, w1, w2, b1, b2))      #why is this output almost the same?

and, as you already guessed, my problem is that even after training, this pseudo-network doesn't converge, instead it keeps giving the same result (or almost) for any input. What's my mistake? (of course I already tried with various parameters and datasets, but still nothing) Thank you in advance

$\endgroup$

1 Answer 1

2
$\begingroup$

Your gradient calculations are probably wrong. Let the forward pass be: $$\begin{align}h&=\sigma(wx_1+b_1)\\y&=\sigma(hw_2+b_2)\\L&=(y-a)^2=E^2\end{align}$$ Then, the derivatives wrt $w_i$ is going to be: $$\begin{align}\frac{dL}{dw_1}&=\frac{\partial L}{\partial y}\frac{\partial y}{\partial w_2}=\underbrace{2Ey(1-y)}_{\delta_2}h\\\frac{d L}{d w_2}&=\frac{\partial L}{\partial y}\frac{\partial y}{\partial h}\frac{\partial h}{\partial w_1}=2Ey(1-y)w_2h(1-h)x=\delta_2w_2h(1-h)x\end{align}$$

I couldn't see this calculation in your code.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.