The Forward-Forward Algorithm: Some Preliminary Investigations [pdf]
Can someone work with this?<p>#using the Forward-Forward algorithm to train a neural network to classify positive and negative data
#the positive data is real data and the negative data is generated by the network itself
#the network is trained to have high goodness for positive data and low goodness for negative data
#the goodness is measured by the sum of the squared activities in a layer
#the network is trained to correctly classify input vectors as positive data or negative data
#the probability that an input vector is positive is given by applying the logistic function, σ to the goodness, minus some threshold, θ
#the negative data may be predicted by the neural net using top-down connections, or it may be supplied externally<p>import numpy as np<p># Define the activation function and its derivative
def activation(x):
    return np.maximum(0, x)<p>def activation_derivative(x):
    return 1. * (x &gt; 0)<p># Define the goodness function (the sum of the squared activities in a layer)
def goodness(x):
    return np.sum(x*2)<p># Define the forward pass for the positive data
def forward_pass_positive(X, W1, W2):
    # Forward pass
    a1 = activation(np.dot(X, W1))
    a2 = activation(np.dot(a1, W2))
    return a1, a2<p># Define the forward pass for the negative data
def forward_pass_negative(X, W1, W2):
    # Forward pass
    a1 = activation(np.dot(X, W1))
    a2 = activation(np.dot(a1, W2))
    return a1, a2<p># Define the learning rate
learning_rate = 0.01<p># Define the threshold for the goodness
theta = 0.1<p># Define the number of epochs
epochs = 100<p># Generate the positive data
X = np.array([[0, 0, 1],
                [0, 1, 1],
                [1, 0, 1],
                [1, 1, 1]])<p># Generate the negative data
Xn = np.array([[0, 0, 0],
                [0, 1, 0],
                [1, 0, 0],
                [1, 1, 0]])<p># Initialize the weights
W1 = 2<i>np.random.random((3, 4)) - 1
W2 = 2</i>np.random.random((4, 1)) - 1<p># Perform the positive and negative passes for each epoch
for j in range(epochs):<p><pre><code>    # Forward pass for the positive data
    a1, a2 = forward_pass_positive(X, W1, W2)

    # Forward pass for the negative data
    a1n, a2n = forward_pass_negative(Xn, W1, W2)

    # Calculate the goodness for the positive data
    g1 = goodness(a1)
    g2 = goodness(a2)

    # Calculate the goodness for the negative data
    g1n = goodness(a1n)
    g2n = goodness(a2n)

    # Calculate the probability that the input vector is positive data
    p1 = 1&#x2F;(1 + np.exp(-(g1 - theta)))
    p2 = 1&#x2F;(1 + np.exp(-(g2 - theta)))

    # Calculate the probability that the input vector is negative data
    p1n = 1&#x2F;(1 + np.exp(-(g1n - theta)))
    p2n = 1&#x2F;(1 + np.exp(-(g2n - theta)))

    # Calculate the error for the positive data
    error2 = p2 - 1
    error1 = p1 - 1

    # Calculate the error for the negative data
    error2n = p2n - 0
    error1n = p1n - 0

    # Calculate the delta for the positive data
    delta2 = error2 * activation_derivative(a2)
    delta1 = error1 * activation_derivative(a1)

    # Calculate the delta for the negative data
    delta2n = error2n * activation_derivative(a2n)
    delta1n = error1n * activation_derivative(a1n)

    # Calculate the change in the weights for the positive data
    dW2 = learning_rate * a1.T.dot(delta2)
    dW1 = learning_rate * X.T.dot(delta1)

    # Calculate the change in the weights for the negative data
    dW2n = learning_rate * a1n.T.dot(delta2n)
    dW1n = learning_rate * Xn.T.dot(delta1n)

    # Update the weights for the positive data
    W2 += dW2
    W1 += dW1

    # Update the weights for the negative data
    W2 += dW2n
    W1 += dW1n
</code></pre>
# Print the weights
print(&quot;W1 = &quot;, W1)
print(&quot;W2 = &quot;, W2)<p># Print the goodness for the positive data
print(&quot;g1 = &quot;, g1)
print(&quot;g2 = &quot;, g2)<p># Print the goodness for the negative data
print(&quot;g1n = &quot;, g1n)
print(&quot;g2n = &quot;, g2n)<p># Print the probability that the input vector is positive data
print(&quot;p1 = &quot;, p1)
print(&quot;p2 = &quot;, p2)<p># Print the probability that the input vector is negative data
print(&quot;p1n = &quot;, p1n)
print(&quot;p2n = &quot;, p2n)