def solve_xor_complex(learning_pulses, epochs, output_to_csv=False):
hrs_set_voltage = -4
spike = 1
false_negative = 1
false_positive = -1
training_voltage = 1
input_spikes_1 = [0, 0, 1, 1]
input_spikes_2 = [0, 1, 0, 1]
targets = [0, 1, 1, 0]
# Create a network with 2 input neurons, 3 hidden layer neurons
# and 1 output neuron. The input neurons are simulated by their spikes.
hidden_neuron_1 = neuron.Neuron()
hidden_neuron_2 = neuron.Neuron()
hidden_neuron_3 = neuron.Neuron()
output_neuron = neuron.Neuron()
# Create 7 synapses with pos_input_synapse_ij representing the excitatory
# connection between the input neuron i and the hidden neuron j, and
# pos_hidden_synapse_k representing the excitatory connection between
# the hidden neuron k and the output neuron.
pos_input_synapse_11 = memristor.Memristor()
pos_input_synapse_13 = memristor.Memristor()
pos_input_synapse_22 = memristor.Memristor()
pos_input_synapse_23 = memristor.Memristor()
pos_hidden_synapse_1 = memristor.Memristor()
pos_hidden_synapse_2 = memristor.Memristor()
pos_hidden_synapse_3 = memristor.Memristor()
# Create 7 synapses with neg_input_synapse_ij representing the inhibitory
# connection between the input neuron i and the hidden neuron j, and
# neg_hidden_synapse_k representing the inhibitory connection between
# the hidden neuron k and the output neuron.
neg_input_synapse_11 = memristor.Memristor()
neg_input_synapse_13 = memristor.Memristor()
neg_input_synapse_22 = memristor.Memristor()
neg_input_synapse_23 = memristor.Memristor()
neg_hidden_synapse_1 = memristor.Memristor()
neg_hidden_synapse_2 = memristor.Memristor()
neg_hidden_synapse_3 = memristor.Memristor()
# Set all the synapses to a high resistance state.
pos_input_synapse_11.set_resistance(hrs_set_voltage)
pos_input_synapse_13.set_resistance(hrs_set_voltage)
pos_input_synapse_22.set_resistance(hrs_set_voltage)
pos_input_synapse_23.set_resistance(hrs_set_voltage)
pos_hidden_synapse_1.set_resistance(hrs_set_voltage)
pos_hidden_synapse_2.set_resistance(hrs_set_voltage)
pos_hidden_synapse_3.set_resistance(hrs_set_voltage)
neg_input_synapse_11.set_resistance(hrs_set_voltage)
neg_input_synapse_13.set_resistance(hrs_set_voltage)
neg_input_synapse_22.set_resistance(hrs_set_voltage)
neg_input_synapse_23.set_resistance(hrs_set_voltage)
neg_hidden_synapse_1.set_resistance(hrs_set_voltage)
neg_hidden_synapse_2.set_resistance(hrs_set_voltage)
neg_hidden_synapse_3.set_resistance(hrs_set_voltage)
c_11 = []
c_13 = []
c_22 = []
c_23 = []
hidden_spikes_1 = []
hidden_spikes_2 = []
hidden_spikes_3 = []
z_1 = []
z_2 = []
z_3 = []
output_spikes = []
errors = []
squared_errors = []
epoch_numbers = []
for epoch_number in range(1, epochs + 1):
for spike_1, spike_2, target in zip(input_spikes_1, input_spikes_2,
targets):
epoch_numbers.append(epoch_number)
# The current pos_c_ij passes through the pos_input_synapse_ij.
# The input voltage is 1 V if the input neuron fired, else it is 0 V.
pos_c_11 = spike_1 / pos_input_synapse_11.read_resistance()
pos_c_13 = spike_1 / pos_input_synapse_13.read_resistance()
pos_c_22 = spike_2 / pos_input_synapse_22.read_resistance()
pos_c_23 = spike_2 / pos_input_synapse_23.read_resistance()
# The current neg_c_ij passes through the neg_input_synapse_ij.
# The current is inverted to represent the inhibitory connection.
# The input voltage is 1 V if the input neuron fired, else it is 0 V.
neg_c_11 = utility.invert(spike_1 /
neg_input_synapse_11.read_resistance())
neg_c_13 = utility.invert(spike_1 /
neg_input_synapse_13.read_resistance())
neg_c_22 = utility.invert(spike_2 /
neg_input_synapse_22.read_resistance())
neg_c_23 = utility.invert(spike_2 /
neg_input_synapse_23.read_resistance())
c_11.append(pos_c_11 + neg_c_11)
c_13.append(pos_c_13 + neg_c_13)
c_22.append(pos_c_22 + neg_c_22)
c_23.append(pos_c_23 + neg_c_23)
hidden_spikes_1.append(hidden_neuron_1.apply_current(c_11[-1]))
hidden_spikes_2.append(hidden_neuron_2.apply_current(c_22[-1]))
hidden_spikes_3.append(
hidden_neuron_3.apply_current(c_13[-1] + c_23[-1]))
# The curent pos_z_i passes through the pos_hidden_synapse_i.
# The input voltage is 1 V if the hidden neuron fired, else it is 0 V.
pos_z_1 = hidden_spikes_1[
-1] / pos_hidden_synapse_1.read_resistance()
pos_z_2 = hidden_spikes_2[
-1] / pos_hidden_synapse_2.read_resistance()
pos_z_3 = hidden_spikes_3[
-1] / pos_hidden_synapse_3.read_resistance()
# The curent neg_z_i passes through the neg_hidden_synapse_i.
# The current is inverted to represent the inhibitory connection.
# The input voltage is 1 V if the hidden neuron fired, else it is 0 V.
neg_z_1 = utility.invert(hidden_spikes_1[-1] /
neg_hidden_synapse_1.read_resistance())
neg_z_2 = utility.invert(hidden_spikes_2[-1] /
neg_hidden_synapse_2.read_resistance())
neg_z_3 = utility.invert(hidden_spikes_3[-1] /
neg_hidden_synapse_3.read_resistance())
z_1.append(pos_z_1 + neg_z_1)
z_2.append(pos_z_2 + neg_z_2)
z_3.append(pos_z_3 + neg_z_3)
output_spikes.append(
output_neuron.apply_current(z_1[-1] + z_2[-1] + z_3[-1]))
errors.append(target - output_spikes[-1])
squared_errors.append(errors[-1]**2)
# Update the synapses based on the error.
# If the output neuron should have fired and it did not,
# then strengthen the excitatory hidden synapses of the
# hidden neurons that fired. Otherwise, do the equivalent
# update for the input synapses of the input neurons that fired.
if errors[-1] == false_negative:
if hidden_spikes_1[-1] == spike or hidden_spikes_2[
-1] == spike or hidden_spikes_3[-1] == spike:
if hidden_spikes_1[-1] == spike:
for _ in range(learning_pulses):
pos_hidden_synapse_1.apply_voltage(
training_voltage)
if hidden_spikes_2[-1] == spike:
for _ in range(learning_pulses):
pos_hidden_synapse_2.apply_voltage(
training_voltage)
if hidden_spikes_3[-1] == spike:
for _ in range(learning_pulses):
pos_hidden_synapse_3.apply_voltage(
training_voltage)
else:
if spike_1 == spike:
for _ in range(learning_pulses):
pos_input_synapse_11.apply_voltage(
training_voltage)
pos_input_synapse_13.apply_voltage(
training_voltage)
if spike_2 == spike:
for _ in range(learning_pulses):
pos_input_synapse_22.apply_voltage(
training_voltage)
pos_input_synapse_23.apply_voltage(
training_voltage)
# If the output neuron should not have fired and it did, then
# strengthen the inhibitory hidden synapses of the hidden neurons
# that fired.
elif errors[-1] == false_positive:
if hidden_spikes_1[-1] == spike:
for _ in range(learning_pulses):
neg_hidden_synapse_1.apply_voltage(training_voltage)
if hidden_spikes_2[-1] == spike:
for _ in range(learning_pulses):
neg_hidden_synapse_2.apply_voltage(training_voltage)
if hidden_spikes_3[-1] == spike:
for _ in range(learning_pulses):
neg_hidden_synapse_3.apply_voltage(training_voltage)
# Store the data into a data frame.
data = pd.DataFrame()
data["input_spike_1"] = input_spikes_1 * epochs
data["input_spike_2"] = input_spikes_2 * epochs
data["c_11"] = c_11
data["c_13"] = c_13
data["c_22"] = c_22
data["c_23"] = c_23
data["hidden_spike_1"] = hidden_spikes_1
data["hidden_spike_2"] = hidden_spikes_2
data["hidden_spike_3"] = hidden_spikes_3
data["z_1"] = z_1
data["z_2"] = z_2
data["z_3"] = z_3
data["output_spike"] = output_spikes
data["target"] = targets * epochs
data["error"] = errors
data["squared_error"] = squared_errors
data["epoch"] = epoch_numbers
data["learning_pulses"] = [learning_pulses] * epochs * 4
data["training_voltage"] = [training_voltage] * epochs * 4
if output_to_csv:
utility.save_data(data, "./output", "solve-xor-complex")
# Plot the MSE as a function of epoch.
utility.plot_mse(data)
def model_xor():
lrs_set_voltage = 1
input_spikes_1 = [0, 0, 1, 1]
input_spikes_2 = [0, 1, 0, 1]
targets = [0, 1, 1, 0]
# Create a network with 2 input neurons, 2 hidden layer neurons
# and 1 output neuron. The input neurons are simulated by their spikes.
hidden_neuron_1 = neuron.Neuron()
hidden_neuron_2 = neuron.Neuron()
output_neuron = neuron.Neuron()
# Create 6 synapses with input_synapse_ij representing the connection
# between the input neuron i and the hidden neuron j, and hidden_synapse_k
# representing the connection between the hidden neuron k and the output neuron.
# The inhibitory synapses are input_synapse_12 and input_synapse_21.
input_synapse_11 = memristor.Memristor()
input_synapse_12 = memristor.Memristor()
input_synapse_21 = memristor.Memristor()
input_synapse_22 = memristor.Memristor()
hidden_synapse_1 = memristor.Memristor()
hidden_synapse_2 = memristor.Memristor()
# Set all the synapses to a low resistance state.
input_synapse_11.set_resistance(lrs_set_voltage)
input_synapse_12.set_resistance(lrs_set_voltage)
input_synapse_21.set_resistance(lrs_set_voltage)
input_synapse_22.set_resistance(lrs_set_voltage)
hidden_synapse_1.set_resistance(lrs_set_voltage)
hidden_synapse_2.set_resistance(lrs_set_voltage)
c_11 = []
c_12 = []
c_21 = []
c_22 = []
hidden_spikes_1 = []
hidden_spikes_2 = []
z_1 = []
z_2 = []
output_spikes = []
for spike_1, spike_2 in zip(input_spikes_1, input_spikes_2):
# The current c_ij passes through the input_synapse_ij.
# The current in the inhibitory synapses is inverted.
# The input voltage is 1 V if the input neuron
# fired, else it is 0 V.
c_11.append(spike_1 / input_synapse_11.read_resistance())
c_12.append(
utility.invert(spike_1 / input_synapse_12.read_resistance()))
c_21.append(
utility.invert(spike_2 / input_synapse_21.read_resistance()))
c_22.append(spike_2 / input_synapse_22.read_resistance())
hidden_spikes_1.append(
hidden_neuron_1.apply_current(c_11[-1] + c_21[-1]))
hidden_spikes_2.append(
hidden_neuron_2.apply_current(c_12[-1] + c_22[-1]))
# The current z_i passes through the hidden_synapse_i.
# The input voltage is 1 V if the hidden neuron fired, else it is 0 V.
z_1.append(hidden_spikes_1[-1] / hidden_synapse_1.read_resistance())
z_2.append(hidden_spikes_2[-1] / hidden_synapse_2.read_resistance())
output_spikes.append(output_neuron.apply_current(z_1[-1] + z_2[-1]))
# Store the data into a data frame.
data = pd.DataFrame()
data["input_spike_1"] = input_spikes_1
data["input_spike_2"] = input_spikes_2
data["c_11"] = c_11
data["c_12"] = c_12
data["c_21"] = c_21
data["c_22"] = c_22
data["hidden_spike_1"] = hidden_spikes_1
data["hidden_spike_2"] = hidden_spikes_2
data["z_1"] = z_1
data["z_2"] = z_2
data["output_spike"] = output_spikes
data["target"] = targets
print(data)
def solve_xor(learning_pulses,
epochs,
learn_hidden_synapses=False,
output_to_csv=False):
lrs_set_voltage = 1
hrs_set_voltage = -4
spike = 1
false_negative = 1
false_positive = -1
training_voltage = 1
input_spikes_1 = [0, 0, 1, 1]
input_spikes_2 = [0, 1, 0, 1]
targets = [0, 1, 1, 0]
# Create a network with 2 input neurons, 2 hidden layer neurons
# and 1 output neuron. The input neurons are simulated by their spikes.
hidden_neuron_1 = neuron.Neuron()
hidden_neuron_2 = neuron.Neuron()
output_neuron = neuron.Neuron()
# Create 6 synapses with input_synapse_ij representing the connection
# between the input neuron i and the hidden neuron j, and hidden_synapse_k
# representing the connection between the hidden neuron k and the output neuron.
# The inhibitory synapse is hidden_synapse_2.
input_synapse_11 = memristor.Memristor()
input_synapse_12 = memristor.Memristor()
input_synapse_21 = memristor.Memristor()
input_synapse_22 = memristor.Memristor()
hidden_synapse_1 = memristor.Memristor()
hidden_synapse_2 = memristor.Memristor()
# Set all the input synapses to a high resistance state.
input_synapse_11.set_resistance(hrs_set_voltage)
input_synapse_12.set_resistance(hrs_set_voltage)
input_synapse_21.set_resistance(hrs_set_voltage)
input_synapse_22.set_resistance(hrs_set_voltage)
# If the resistance values at the hidden synapses are going to be learned,
# then set all the hidden synapses to a high resistance state. Otherwise set
# all the hidden synapses to a low resistance state.
if learn_hidden_synapses:
hidden_synapse_1.set_resistance(hrs_set_voltage)
hidden_synapse_2.set_resistance(hrs_set_voltage)
else:
hidden_synapse_1.set_resistance(lrs_set_voltage)
hidden_synapse_2.set_resistance(lrs_set_voltage)
c_11 = []
c_12 = []
c_21 = []
c_22 = []
hidden_spikes_1 = []
hidden_spikes_2 = []
z_1 = []
z_2 = []
output_spikes = []
errors = []
squared_errors = []
epoch_numbers = []
for epoch_number in range(1, epochs + 1):
for spike_1, spike_2, target in zip(input_spikes_1, input_spikes_2,
targets):
epoch_numbers.append(epoch_number)
# The current c_ij passes through the input_synapse_ij.
# The input voltage is 1 V if the input neuron fired, else it is 0 V.
c_11.append(spike_1 / input_synapse_11.read_resistance())
c_12.append(spike_1 / input_synapse_12.read_resistance())
c_21.append(spike_2 / input_synapse_21.read_resistance())
c_22.append(spike_2 / input_synapse_22.read_resistance())
hidden_spikes_1.append(
hidden_neuron_1.apply_current(c_11[-1] + c_21[-1]))
hidden_spikes_2.append(
hidden_neuron_2.apply_current(c_12[-1] + c_22[-1]))
# The curent z_i passes through the hidden_synapse_i.
# The current in the inhibitory synapse is inverted.
# The input voltage is 1 V if the hidden neuron
# fired, else it is 0 V.
z_1.append(hidden_spikes_1[-1] /
hidden_synapse_1.read_resistance())
z_2.append(
utility.invert(hidden_spikes_2[-1] /
hidden_synapse_2.read_resistance()))
output_spikes.append(output_neuron.apply_current(z_1[-1] +
z_2[-1]))
errors.append(target - output_spikes[-1])
squared_errors.append(errors[-1]**2)
# Update the synapses based on the error.
# If the output neuron should have fired and it did not,
# then strengthen hidden synapse 1 if hidden neuron 1 fired
# and if the resistance values at the hidden synapses are to be learned.
# Otherwise strengthen the input synapses of the input neurons that fired
# and that are connected to hidden neuron 1.
if errors[-1] == false_negative:
if hidden_spikes_1[-1] == spike and learn_hidden_synapses:
for _ in range(learning_pulses):
hidden_synapse_1.apply_voltage(training_voltage)
else:
if spike_1 == spike:
for _ in range(learning_pulses):
input_synapse_11.apply_voltage(training_voltage)
if spike_2 == spike:
for _ in range(learning_pulses):
input_synapse_21.apply_voltage(training_voltage)
# If the output neuron should not have fired and it did,
# then do the equivalent update for hidden synapse 2 or
# for the input synapses that are connected to hidden neuron 2.
elif errors[-1] == false_positive:
if hidden_spikes_2[-1] == spike and learn_hidden_synapses:
for _ in range(learning_pulses):
hidden_synapse_2.apply_voltage(training_voltage)
else:
if spike_1 == spike:
for _ in range(learning_pulses):
input_synapse_12.apply_voltage(training_voltage)
if spike_2 == spike:
for _ in range(learning_pulses):
input_synapse_22.apply_voltage(training_voltage)
# Store the data into a data frame.
data = pd.DataFrame()
data["input_spike_1"] = input_spikes_1 * epochs
data["input_spike_2"] = input_spikes_2 * epochs
data["c_11"] = c_11
data["c_12"] = c_12
data["c_21"] = c_21
data["c_22"] = c_22
data["hidden_spike_1"] = hidden_spikes_1
data["hidden_spike_2"] = hidden_spikes_2
data["z_1"] = z_1
data["z_2"] = z_2
data["output_spike"] = output_spikes
data["target"] = targets * epochs
data["error"] = errors
data["squared_error"] = squared_errors
data["epoch"] = epoch_numbers
data["learning_pulses"] = [learning_pulses] * epochs * 4
data["training_voltage"] = [training_voltage] * epochs * 4
data["learn_hidden_synapses"] = [learn_hidden_synapses] * epochs * 4
if output_to_csv:
utility.save_data(data, "./output", "solve-xor")
# Plot the MSE as a function of epoch.
utility.plot_mse(data)
'[losses] mean': loss_mean.item(),
'[losses] var': loss_var.item(),
}
return info
# return loss_mean + loss_var
# ======= Optimize =======
lr = 0.1
steps = 100
optimizer = torch.optim.Adam([A, b], lr=lr)
utility.invert(
[X_B],
loss_fn,
optimizer,
steps=steps,
plot=True,
track_grad_norm=True,
)
# ======= Result =======
X_B_proc = reconstruct(X_B).detach()
print("After Reconstruction:")
print("Cross Entropy of B:", gmm.cross_entropy(X_B_proc).item())
print("Cross Entropy of undistorted B:", gmm.cross_entropy(X_B_orig).item())
plt.scatter(X_A[:, 0], X_A[:, 1], c=cmaps[0], label="target data A")
plt.scatter(X_B_proc[:, 0],
X_B_proc[:, 1],
c=cmaps[1],
label="reconstructed data B")
plt.scatter(X_B_orig[:, 0],
def solve_xor_complex_noisy_snn(learning_pulses, epochs, output_to_csv=False):
hrs_set_voltage = -4
current_application_time = 500
spike = 1
training_voltage = 1
true = 20
false = 0
input_spikes_1 = [false, false, true, true]
input_spikes_2 = [false, true, false, true]
targets = [false, true, true, false]
# Create a network with 2 input neurons, 2 hidden layer neurons
# and 1 output neuron. The input neurons are simulated by their spikes.
hidden_neuron_1 = spiking_neuron.SpikingNeuron()
hidden_neuron_2 = spiking_neuron.SpikingNeuron()
output_neuron = spiking_neuron.SpikingNeuron()
# Create 6 synapses with pos_input_synapse_ij representing the excitatory
# connection between the input neuron i and the hidden neuron j, and
# pos_hidden_synapse_k representing the excitatory connection between
# the hidden neuron k and the output neuron.
pos_input_synapse_11 = memristor.Memristor()
pos_input_synapse_12 = memristor.Memristor()
pos_input_synapse_21 = memristor.Memristor()
pos_input_synapse_22 = memristor.Memristor()
pos_hidden_synapse_1 = memristor.Memristor()
pos_hidden_synapse_2 = memristor.Memristor()
# Create 6 synapses with neg_input_synapse_ij representing the inhibitory
# connection between the input neuron i and the hidden neuron j, and
# neg_hidden_synapse_k representing the inhibitory connection between
# the hidden neuron k and the output neuron.
neg_input_synapse_11 = memristor.Memristor()
neg_input_synapse_12 = memristor.Memristor()
neg_input_synapse_21 = memristor.Memristor()
neg_input_synapse_22 = memristor.Memristor()
neg_hidden_synapse_1 = memristor.Memristor()
neg_hidden_synapse_2 = memristor.Memristor()
# Set all the synapses to a high resistance state.
pos_input_synapse_11.set_resistance(hrs_set_voltage)
pos_input_synapse_12.set_resistance(hrs_set_voltage)
pos_input_synapse_21.set_resistance(hrs_set_voltage)
pos_input_synapse_22.set_resistance(hrs_set_voltage)
pos_hidden_synapse_1.set_resistance(hrs_set_voltage)
pos_hidden_synapse_2.set_resistance(hrs_set_voltage)
neg_input_synapse_11.set_resistance(hrs_set_voltage)
neg_input_synapse_12.set_resistance(hrs_set_voltage)
neg_input_synapse_21.set_resistance(hrs_set_voltage)
neg_input_synapse_22.set_resistance(hrs_set_voltage)
neg_hidden_synapse_1.set_resistance(hrs_set_voltage)
neg_hidden_synapse_2.set_resistance(hrs_set_voltage)
c_11 = []
c_12 = []
c_21 = []
c_22 = []
hidden_spikes_1 = []
hidden_spikes_2 = []
z_1 = []
z_2 = []
output_spikes = []
errors = []
squared_errors = []
epoch_numbers = []
for epoch_number in range(1, epochs + 1):
for spikes_1, spikes_2, target in zip(input_spikes_1, input_spikes_2, targets):
epoch_numbers.append(epoch_number)
# The normalized noisy current c_ij passes through the input_synapse_ij. The input
# voltage is 1 V if the input neuron fired as many pulses as the encoding of
# TRUE or more, else it is 0 V.
pos_c_11 = utility.add_noise(utility.normalize(utility.burst(spikes_1, true)
/ pos_input_synapse_11.read_resistance()))
pos_c_12 = utility.add_noise(utility.normalize(utility.burst(spikes_1, true)
/ pos_input_synapse_12.read_resistance()))
pos_c_21 = utility.add_noise(utility.normalize(utility.burst(spikes_2, true)
/ pos_input_synapse_21.read_resistance()))
pos_c_22 = utility.add_noise(utility.normalize(utility.burst(spikes_2, true)
/ pos_input_synapse_22.read_resistance()))
# The normalized noisy current neg_c_ij passes through the neg_input_synapse_ij.
# The current is inverted to represent the inhibitory connection. The input
# voltage is 1 V if the input neuron fired as many pulses as the encoding
# of TRUE or more, else it is 0 V.
neg_c_11 = utility.invert(utility.add_noise(utility.normalize(utility.burst(spikes_1, true)
/ neg_input_synapse_11.read_resistance())))
neg_c_12 = utility.invert(utility.add_noise(utility.normalize(utility.burst(spikes_1, true)
/ neg_input_synapse_12.read_resistance())))
neg_c_21 = utility.invert(utility.add_noise(utility.normalize(utility.burst(spikes_2, true)
/ neg_input_synapse_21.read_resistance())))
neg_c_22 = utility.invert(utility.add_noise(utility.normalize(utility.burst(spikes_2, true)
/ neg_input_synapse_22.read_resistance())))
c_11.append(pos_c_11 + neg_c_11)
c_12.append(pos_c_12 + neg_c_12)
c_21.append(pos_c_21 + neg_c_21)
c_22.append(pos_c_22 + neg_c_22)
hidden_spikes_1.append(hidden_neuron_1.apply_current(c_11[-1] + c_21[-1],
current_application_time)[0].count(spike))
hidden_spikes_2.append(hidden_neuron_2.apply_current(c_12[-1] + c_22[-1],
current_application_time)[0].count(spike))
# The normalized noisy curent pos_z_i passes through the pos_hidden_synapse_i.
# The input voltage is 1 V if the hidden neuron fired as many pulses as
# the encoding of TRUE or more, else it is 0 V.
pos_z_1 = utility.add_noise(utility.normalize(utility.burst(hidden_spikes_1[-1], true)
/ pos_hidden_synapse_1.read_resistance()))
pos_z_2 = utility.add_noise(utility.normalize(utility.burst(hidden_spikes_2[-1], true)
/ pos_hidden_synapse_2.read_resistance()))
# The normalized noisy curent neg_z_i passes through the neg_hidden_synapse_i.
# The current is inverted to represent the inhibitory connection. The
# input voltage is 1 V if the hidden neuron fired as many pulses as the
# encoding of TRUE or more, else it is 0 V.
neg_z_1 = utility.invert(utility.add_noise(utility.normalize(utility.burst(hidden_spikes_1[-1], true)
/ neg_hidden_synapse_1.read_resistance())))
neg_z_2 = utility.invert(utility.add_noise(utility.normalize(utility.burst(hidden_spikes_2[-1], true)
/ neg_hidden_synapse_2.read_resistance())))
z_1.append(pos_z_1 + neg_z_1)
z_2.append(pos_z_2 + neg_z_2)
output_spikes.append(output_neuron.apply_current(z_1[-1] + z_2[-1],
current_application_time)[0].count(spike))
errors.append(target - output_spikes[-1])
squared_errors.append(errors[-1] ** 2)
# Update the synapses based on the error.
# If the output neuron should have fired more times and it did not,
# then strengthen the excitatory hidden synapses of the hidden neurons
# that fired as many pulses as the encoding of TRUE or more. Otherwise,
# do the equivalent update for the input synapses of the input neurons
# that fired as many pulses as the encoding of TRUE or more.
if utility.is_false_negative(errors[-1]):
if utility.burst(hidden_spikes_1[-1], true) or utility.burst(hidden_spikes_2[-1], true):
if utility.burst(hidden_spikes_1[-1], true):
for _ in range(learning_pulses):
pos_hidden_synapse_1.apply_voltage(training_voltage)
if utility.burst(hidden_spikes_2[-1], true):
for _ in range(learning_pulses):
pos_hidden_synapse_2.apply_voltage(training_voltage)
else:
if utility.burst(spikes_1, true):
for _ in range(learning_pulses):
pos_input_synapse_11.apply_voltage(training_voltage)
pos_input_synapse_12.apply_voltage(training_voltage)
if utility.burst(spikes_2, true):
for _ in range(learning_pulses):
pos_input_synapse_21.apply_voltage(training_voltage)
pos_input_synapse_22.apply_voltage(training_voltage)
# If the output neuron should not have fired and it did, then strengthen
# the inhibitory hidden synapses of the hidden neurons that fired as many
# pulses as the encoding of TRUE or more.
elif utility.is_false_positive(errors[-1]):
if utility.burst(hidden_spikes_1[-1], true):
for _ in range(learning_pulses):
neg_hidden_synapse_1.apply_voltage(training_voltage)
if utility.burst(hidden_spikes_2[-1], true):
for _ in range(learning_pulses):
neg_hidden_synapse_2.apply_voltage(training_voltage)
# The neurons are resting until the next input.
hidden_neuron_1.rest()
hidden_neuron_2.rest()
output_neuron.rest()
# Store the data into a data frame.
data = pd.DataFrame()
data["input_spikes_1"] = input_spikes_1 * epochs
data["input_spikes_2"] = input_spikes_2 * epochs
data["c_11"] = c_11
data["c_12"] = c_12
data["c_21"] = c_21
data["c_22"] = c_22
data["hidden_spikes_1"] = hidden_spikes_1
data["hidden_spikes_2"] = hidden_spikes_2
data["z_1"] = z_1
data["z_2"] = z_2
data["output_spikes"] = output_spikes
data["target"] = targets * epochs
data["error"] = errors
data["squared_error"] = squared_errors
data["epoch"] = epoch_numbers
data["learning_pulses"] = [learning_pulses] * epochs * 4
data["training_voltage"] = [training_voltage] * epochs * 4
data["current_application_time"] = [current_application_time] * epochs * 4
if output_to_csv:
utility.save_data(data, "./output", "solve-xor-complex-noisy-snn")
# Plot the MSE as a function of epoch.
utility.plot_mse(data)
def model_xor_snn():
hrs_set_voltage = -4
positive_bias = 1
fixing_pulses = 37 * 10 ** 4
current_application_time = 500
spike = 1
true = 20
false = 0
input_spikes_1 = [false, false, true, true]
input_spikes_2 = [false, true, false, true]
targets = [false, true, true, false]
# Create a network with 2 input neurons, 2 hidden layer neurons
# and 1 output neuron. The input neurons are simulated by their spikes.
hidden_neuron_1 = spiking_neuron.SpikingNeuron()
hidden_neuron_2 = spiking_neuron.SpikingNeuron()
output_neuron = spiking_neuron.SpikingNeuron()
# Create 6 synapses with input_synapse_ij representing the connection
# between the input neuron i and the hidden neuron j, and hidden_synapse_k
# representing the connection between the hidden neuron k and the output neuron.
# The inhibitory synapses are input_synapse_12 and input_synapse_21.
input_synapse_11 = memristor.Memristor()
input_synapse_12 = memristor.Memristor()
input_synapse_21 = memristor.Memristor()
input_synapse_22 = memristor.Memristor()
hidden_synapse_1 = memristor.Memristor()
hidden_synapse_2 = memristor.Memristor()
# Set all the synapses to a high resistance state.
input_synapse_11.set_resistance(hrs_set_voltage)
input_synapse_12.set_resistance(hrs_set_voltage)
input_synapse_21.set_resistance(hrs_set_voltage)
input_synapse_22.set_resistance(hrs_set_voltage)
hidden_synapse_1.set_resistance(hrs_set_voltage)
hidden_synapse_2.set_resistance(hrs_set_voltage)
# Fix the resistance values in the synapses by applying consecutive
# positive bias voltage pulses.
for _ in range(fixing_pulses):
input_synapse_11.apply_voltage(positive_bias)
input_synapse_12.apply_voltage(positive_bias)
input_synapse_21.apply_voltage(positive_bias)
input_synapse_22.apply_voltage(positive_bias)
hidden_synapse_1.apply_voltage(positive_bias)
hidden_synapse_2.apply_voltage(positive_bias)
c_11 = []
c_12 = []
c_21 = []
c_22 = []
hidden_spikes_1 = []
hidden_spikes_2 = []
z_1 = []
z_2 = []
output_spikes = []
for spikes_1, spikes_2 in zip(input_spikes_1, input_spikes_2):
# The normalized current c_ij passes through the input_synapse_ij.
# The current in the inhibitory synapses is inverted. The input voltage
# is 1 V if the input neuron fired as many pulses as the encoding of TRUE
# or more, else it is 0 V.
c_11.append(utility.normalize(utility.burst(spikes_1, true) / input_synapse_11.read_resistance()))
c_12.append(utility.invert(utility.normalize(utility.burst(spikes_1, true) / input_synapse_12.read_resistance())))
c_21.append(utility.invert(utility.normalize(utility.burst(spikes_2, true) / input_synapse_21.read_resistance())))
c_22.append(utility.normalize(utility.burst(spikes_2, true) / input_synapse_22.read_resistance()))
hidden_spikes_1.append(hidden_neuron_1.apply_current(c_11[-1] + c_21[-1],
current_application_time)[0].count(spike))
hidden_spikes_2.append(hidden_neuron_2.apply_current(c_12[-1] + c_22[-1],
current_application_time)[0].count(spike))
# The normalized curent z_i passes through the hidden_synapse_i. The
# input voltage is 1 V if the hidden neuron fired as many pulses as
# the encoding of TRUE or more, else it is 0 V.
z_1.append(utility.normalize(utility.burst(hidden_spikes_1[-1], true) / hidden_synapse_1.read_resistance()))
z_2.append(utility.normalize(utility.burst(hidden_spikes_2[-1], true) / hidden_synapse_2.read_resistance()))
output_spikes.append(output_neuron.apply_current(z_1[-1] + z_2[-1],
current_application_time)[0].count(spike))
# The neurons are resting until the next input.
hidden_neuron_1.rest()
hidden_neuron_2.rest()
output_neuron.rest()
# Store the data into a data frame.
data = pd.DataFrame()
data["input_spikes_1"] = input_spikes_1
data["input_spikes_2"] = input_spikes_2
data["c_11"] = c_11
data["c_12"] = c_12
data["c_21"] = c_21
data["c_22"] = c_22
data["hidden_spikes_1"] = hidden_spikes_1
data["hidden_spikes_2"] = hidden_spikes_2
data["z_1"] = z_1
data["z_2"] = z_2
data["output_spikes"] = output_spikes
data["target"] = targets
data["current_application_time"] = [current_application_time] * 4
print(data)
def solve_xor_snn(learning_pulses, epochs, learn_hidden_synapses=False, output_to_csv=False):
hrs_set_voltage = -4
positive_bias = 1
fixing_pulses = 37 * 10 ** 4
current_application_time = 500
spike = 1
true = 20
false = 0
training_voltage = 1
input_spikes_1 = [false, false, true, true]
input_spikes_2 = [false, true, false, true]
targets = [false, true, true, false]
# Create a network with 2 input neurons, 2 hidden layer neurons
# and 1 output neuron. The input neurons are simulated by their spikes.
hidden_neuron_1 = spiking_neuron.SpikingNeuron()
hidden_neuron_2 = spiking_neuron.SpikingNeuron()
output_neuron = spiking_neuron.SpikingNeuron()
# Create 6 synapses with input_synapse_ij representing the connection
# between the input neuron i and the hidden neuron j, and hidden_synapse_k
# representing the connection between the hidden neuron k and the output neuron.
# The inhibitory synapse is hidden_synapse_2.
input_synapse_11 = memristor.Memristor()
input_synapse_12 = memristor.Memristor()
input_synapse_21 = memristor.Memristor()
input_synapse_22 = memristor.Memristor()
hidden_synapse_1 = memristor.Memristor()
hidden_synapse_2 = memristor.Memristor()
# Set all the synapses to a high resistance state.
input_synapse_11.set_resistance(hrs_set_voltage)
input_synapse_12.set_resistance(hrs_set_voltage)
input_synapse_21.set_resistance(hrs_set_voltage)
input_synapse_22.set_resistance(hrs_set_voltage)
hidden_synapse_1.set_resistance(hrs_set_voltage)
hidden_synapse_2.set_resistance(hrs_set_voltage)
# If the resistance values at the hidden synapses are not going
# to be learned, then fix them by applying consecutive positive
# bias voltage pulses.
if not learn_hidden_synapses:
for _ in range(fixing_pulses):
hidden_synapse_1.apply_voltage(positive_bias)
hidden_synapse_2.apply_voltage(positive_bias)
c_11 = []
c_12 = []
c_21 = []
c_22 = []
hidden_spikes_1 = []
hidden_spikes_2 = []
z_1 = []
z_2 = []
output_spikes = []
errors = []
squared_errors = []
epoch_numbers = []
for epoch_number in range(1, epochs + 1):
for spikes_1, spikes_2, target in zip(input_spikes_1, input_spikes_2, targets):
epoch_numbers.append(epoch_number)
# The normalized current c_ij passes through the input_synapse_ij.
# The input voltage is 1 V if the input neuron fired as many pulses
# as the encoding of TRUE or more, else it is 0 V.
c_11.append(utility.normalize(utility.burst(spikes_1, true) / input_synapse_11.read_resistance()))
c_12.append(utility.normalize(utility.burst(spikes_1, true) / input_synapse_12.read_resistance()))
c_21.append(utility.normalize(utility.burst(spikes_2, true) / input_synapse_21.read_resistance()))
c_22.append(utility.normalize(utility.burst(spikes_2, true) / input_synapse_22.read_resistance()))
hidden_spikes_1.append(hidden_neuron_1.apply_current(c_11[-1] + c_21[-1],
current_application_time)[0].count(spike))
hidden_spikes_2.append(hidden_neuron_2.apply_current(c_12[-1] + c_22[-1],
current_application_time)[0].count(spike))
# The normalized current z_i passes through the hidden_synapse_i.
# The current in the inhibitory synapse is inverted. The input
# voltage is 1 V if the hidden neuron fired as many pulses as
# the encoding of TRUE or more, else it is 0 V.
z_1.append(utility.normalize(utility.burst(hidden_spikes_1[-1], true) / hidden_synapse_1.read_resistance()))
z_2.append(utility.invert(utility.normalize(utility.burst(hidden_spikes_2[-1], true)
/ hidden_synapse_2.read_resistance())))
output_spikes.append(output_neuron.apply_current(z_1[-1] + z_2[-1],
current_application_time)[0].count(spike))
errors.append(target - output_spikes[-1])
squared_errors.append(errors[-1] ** 2)
# Update the synapses based on the error.
# If the output neuron should have fired more times and it did not,
# then strengthen hidden synapse 1 if hidden neuron 1 fired as many
# pulses as the encoding of TRUE or more and if the resistance values
# at the hidden synapses are to be learned. Otherwise strengthen the
# input synapses of the input neurons that fired as many pulses as the
# encoding of TRUE or more and that are connected to hidden neuron 1.
if utility.is_false_negative(errors[-1]):
if utility.burst(hidden_spikes_1[-1], true) and learn_hidden_synapses:
for _ in range(learning_pulses):
hidden_synapse_1.apply_voltage(training_voltage)
else:
if utility.burst(spikes_1, true):
for _ in range(learning_pulses):
input_synapse_11.apply_voltage(training_voltage)
if utility.burst(spikes_2, true):
for _ in range(learning_pulses):
input_synapse_21.apply_voltage(training_voltage)
# If the output neuron should not have fired and it did, then do the
# equivalent update for hidden synapse 2 or for the input synapses that
# are connected to hidden neuron 2.
elif utility.is_false_positive(errors[-1]):
if utility.burst(hidden_spikes_2[-1], true) and learn_hidden_synapses:
for _ in range(learning_pulses):
hidden_synapse_2.apply_voltage(training_voltage)
else:
if utility.burst(spikes_1, true):
for _ in range(learning_pulses):
input_synapse_12.apply_voltage(training_voltage)
if utility.burst(spikes_2, true):
for _ in range(learning_pulses):
input_synapse_22.apply_voltage(training_voltage)
# The neurons are resting until the next input.
hidden_neuron_1.rest()
hidden_neuron_2.rest()
output_neuron.rest()
# Store the data into a data frame.
data = pd.DataFrame()
data["input_spikes_1"] = input_spikes_1 * epochs
data["input_spikes_2"] = input_spikes_2 * epochs
data["c_11"] = c_11
data["c_12"] = c_12
data["c_21"] = c_21
data["c_22"] = c_22
data["hidden_spikes_1"] = hidden_spikes_1
data["hidden_spikes_2"] = hidden_spikes_2
data["z_1"] = z_1
data["z_2"] = z_2
data["output_spikes"] = output_spikes
data["target"] = targets * epochs
data["error"] = errors
data["squared_error"] = squared_errors
data["epoch"] = epoch_numbers
data["learning_pulses"] = [learning_pulses] * epochs * 4
data["training_voltage"] = [training_voltage] * epochs * 4
data["learn_hidden_synapses"] = [learn_hidden_synapses] * epochs * 4
data["current_application_time"] = [current_application_time] * epochs * 4
if output_to_csv:
utility.save_data(data, "./output", "solve-xor-snn")
# Plot the MSE as a function of epoch.
utility.plot_mse(data)