by jordn on 12/1/22, 9:36 PM with 10 comments
by CGamesPlay on 12/2/22, 11:33 AM
by candiodari on 12/2/22, 2:17 PM
This is the main source of performance bottlenecks and also an obvious difference between natural and artificial neural networks. The brain does not even seem to have error signals, and we also can't seem to find any signal going in the opposite direction of propagation. It requires that you have an error signal ... and that means it requires knowing the right answer to the problem the algorithm is trying to solve. Also quite important to some companies: sending data in 2 directions through the network places serious limitations on parallelization of neural network training. It is one of the big causes that Google/Facebook/MS(OpenAI)/... only seem to have a 1y or less headstart over the rest of the industry, despite billions of investment.
Forward - forward tries to do online learning by training the network to differentiate between real and fake-but-really-realistic signals with data going in the same direction every time.
by arc-in-space on 12/2/22, 9:12 AM
by gauddasa on 12/2/22, 2:24 PM
by joko42 on 12/2/22, 11:58 AM
by KunzEgg on 12/7/22, 2:26 AM
#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
import numpy as np
# Define the activation function and its derivative def activation(x): return np.maximum(0, x)
def activation_derivative(x): return 1. * (x > 0)
# Define the goodness function (the sum of the squared activities in a layer) def goodness(x): return np.sum(x*2)
# 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
# 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
# Define the learning rate learning_rate = 0.01
# Define the threshold for the goodness theta = 0.1
# Define the number of epochs epochs = 100
# Generate the positive data X = np.array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
# Generate the negative data Xn = np.array([[0, 0, 0], [0, 1, 0], [1, 0, 0], [1, 1, 0]])
# Initialize the weights W1 = 2np.random.random((3, 4)) - 1 W2 = 2np.random.random((4, 1)) - 1
# Perform the positive and negative passes for each epoch for j in range(epochs):
# 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/(1 + np.exp(-(g1 - theta)))
p2 = 1/(1 + np.exp(-(g2 - theta)))
# Calculate the probability that the input vector is negative data
p1n = 1/(1 + np.exp(-(g1n - theta)))
p2n = 1/(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
# Print the goodness for the positive data print("g1 = ", g1) print("g2 = ", g2)
# Print the goodness for the negative data print("g1n = ", g1n) print("g2n = ", g2n)
# Print the probability that the input vector is positive data print("p1 = ", p1) print("p2 = ", p2)
# Print the probability that the input vector is negative data print("p1n = ", p1n) print("p2n = ", p2n)
by KunzEgg on 12/7/22, 2:26 AM
import numpy as np
# Define the activation function and its derivative def activation(x): return np.maximum(0, x)
def activation_derivative(x): return 1. * (x > 0)
# Define the goodness function (the sum of the squared activities in a layer) def goodness(x): return np.sum(x*2)
# 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
# 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
# Define the learning rate learning_rate = 0.01
# Define the threshold for the goodness theta = 0.1
# Define the number of epochs epochs = 100
# Generate the positive data X = np.array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
# Generate the negative data Xn = np.array([[0, 0, 0], [0, 1, 0], [1, 0, 0], [1, 1, 0]])
# Initialize the weights W1 = 2np.random.random((3, 4)) - 1 W2 = 2np.random.random((4, 1)) - 1
# Perform the positive and negative passes for each epoch for j in range(epochs):
# 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/(1 + np.exp(-(g1 - theta)))
p2 = 1/(1 + np.exp(-(g2 - theta)))
# Calculate the probability that the input vector is negative data
p1n = 1/(1 + np.exp(-(g1n - theta)))
p2n = 1/(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
# Print the goodness for the positive data print("g1 = ", g1) print("g2 = ", g2)
# Print the goodness for the negative data print("g1n = ", g1n) print("g2n = ", g2n)
# Print the probability that the input vector is positive data print("p1 = ", p1) print("p2 = ", p2)
# Print the probability that the input vector is negative data print("p1n = ", p1n) print("p2n = ", p2n)