Nengo PES learning

nengo_gui

my model schematic

code

import nengo
import numpy as np


# 1 neuorn

X_small = 0.2*np.random.rand(401)
Y_small = 3*X_small + 0.02*np.random.randn(len(X_small))

# plt.scatter(X_small[:160],Y_small[:160])
# plt.title("train data")
# plt.show()

# plt.scatter(X_small[160:],Y_small[160:])
# plt.title("test data")
# plt.show()


# many neuron
def inhibit(t):
    return 1.0 if t > 32 else 0.0

model = nengo.Network()
with model:
    process_x = nengo.processes.PresentInput(X_small, presentation_time=0.1)
    process_y = nengo.processes.PresentInput(Y_small, presentation_time=0.1)
    x_train = nengo.Node(process_x)
    y_train = nengo.Node(process_y)

    pre = nengo.Ensemble(1000, dimensions=1)

    nengo.Connection(x_train, pre)

    post = nengo.Ensemble(1000, dimensions=1)
    
    conn = nengo.Connection(pre, post)

    input_data = nengo.Probe(x_train)
    label_data = nengo.Probe(y_train)

    pre_p = nengo.Probe(pre, synapse=0.005)
    post_p = nengo.Probe(post, synapse=0.005)
    # pre_p = nengo.Probe(pre)
    # post_p = nengo.Probe(post)

    error = nengo.Ensemble(1000, dimensions=1)

    nengo.Connection(post, error)
    nengo.Connection(y_train, error, transform=-1)

    conn.learning_rule_type = nengo.PES()

    nengo.Connection(error, conn.learning_rule)

    inhib = nengo.Node(inhibit)
    nengo.Connection(inhib, error.neurons, transform=[[-1]] * error.n_neurons)

#dt = 0.001 (default)
# with nengo.Simulator(model) as sim:
#     sim.run(20.0)

regression 결과물

실패
- single neuron || data_input(duration = 0.001)
  i) 첫시도 neuron ensemble 에서 single neuron (n=1) || data input 그대로 적용 (duration = 0.001)
  ii) 두번째 시도 neuron ensemble(n=1000) || data input 그대로 적용 (duration = 0.001)

y = 3x

결과물

neuron ensemble (n=1000), data input duration= 0.2

input data

train and test result1

train and test result2

code

#data
X_small = 0.2*np.random.rand(201)
Y_small = 3*X_small + 0.02*np.random.randn(len(X_small))

########## model ##########

# test시 learning inhibition
def inhibit(t):
    return 1.0 if t > 32 else 0.0

model = nengo.Network()
with model:
    process_x = nengo.processes.PresentInput(X_small, presentation_time=0.2)
    process_y = nengo.processes.PresentInput(Y_small, presentation_time=0.2)
    x_train = nengo.Node(process_x)
    y_train = nengo.Node(process_y)

    pre = nengo.Ensemble(1000, dimensions=1)

    nengo.Connection(x_train, pre)

    post = nengo.Ensemble(1000, dimensions=1)
    
    conn = nengo.Connection(pre, post)

    input_data = nengo.Probe(x_train)
    label_data = nengo.Probe(y_train)

    pre_p = nengo.Probe(pre, synapse=0.01)
    post_p = nengo.Probe(post, synapse=0.01)
    # pre_p = nengo.Probe(pre)
    # post_p = nengo.Probe(post)

    error = nengo.Ensemble(1000, dimensions=1)

    nengo.Connection(post, error)
    nengo.Connection(y_train, error, transform=-1)

    conn.learning_rule_type = nengo.PES()

    nengo.Connection(error, conn.learning_rule)

    inhib = nengo.Node(inhibit)
    nengo.Connection(inhib, error.neurons, transform=[[-1]] * error.n_neurons)

#dt = 0.001 (default)
with nengo.Simulator(model) as sim:
    sim.run(40.0)

########## result ##########

plt.figure(figsize=(12, 6))

end_t = sim.trange().shape[0]
train_index = range(200,int(end_t*0.75),200)
test_index = range(int(end_t*0.75)+200,end_t,200)

plt.subplot(1, 2, 1)
plt.scatter(sim.data[input_data].T[0][train_index],sim.data[label_data].T[0][train_index], c='k', label='train_data')
plt.plot([0,0.2],[0,0.6], c='r',linestyle='dashed',linewidth=2,label='ground truth')
plt.scatter(sim.data[pre_p].T[0][train_index],sim.data[post_p].T[0][train_index], c='b', label='model_train')
plt.ylabel("training process")
plt.legend(loc='best')


plt.subplot(1,2,2)
plt.scatter(sim.data[input_data].T[0][test_index],sim.data[label_data].T[0][test_index], c='k', label='test_data')
plt.plot([0,0.2],[0,0.6], c='r',linestyle='dashed',linewidth=2,label='ground truth')
plt.scatter(sim.data[pre_p].T[0][test_index],sim.data[post_p].T[0][test_index], c='b', label='model_test')
plt.ylabel("test process")
plt.legend(loc='best')

Dependency of the number of neurons
- neuron 1개
- neuron 10개
- neuron 100개

y = x^2

결과물

neuron ensemble (n=1000), data input duration= 0.2

input data

train and test result

code

#data
X_small = np.random.rand(401)-0.5
Y_small = X_small**2 + 0.01*np.random.randn(len(X_small))


########## model ##########

# test시 learning inhibition
def inhibit(t):
    return 1.0 if t > 64 else 0.0

model = nengo.Network()
with model:
    process_x = nengo.processes.PresentInput(X_small, presentation_time=0.2)
    process_y = nengo.processes.PresentInput(Y_small, presentation_time=0.2)
    x_train = nengo.Node(process_x)
    y_train = nengo.Node(process_y)

    pre = nengo.Ensemble(1000, dimensions=1)

    nengo.Connection(x_train, pre)

    post = nengo.Ensemble(1000, dimensions=1)
    
    conn = nengo.Connection(pre, post)

    input_data = nengo.Probe(x_train)
    label_data = nengo.Probe(y_train)

    pre_p = nengo.Probe(pre, synapse=0.01)
    post_p = nengo.Probe(post, synapse=0.01)
    # pre_p = nengo.Probe(pre)
    # post_p = nengo.Probe(post)

    error = nengo.Ensemble(1000, dimensions=1)

    nengo.Connection(post, error)
    nengo.Connection(y_train, error, transform=-1)

    conn.learning_rule_type = nengo.PES()

    nengo.Connection(error, conn.learning_rule)

    inhib = nengo.Node(inhibit)
    nengo.Connection(inhib, error.neurons, transform=[[-1]] * error.n_neurons)

#dt = 0.001 (default)
with nengo.Simulator(model) as sim:
    sim.run(80.0)


########## result ##########

plt.figure(figsize=(12, 6))

end_t = sim.trange().shape[0]
train_index = range(200,int(end_t*0.75),200)
test_index = range(int(end_t*0.75)+200,end_t,200)

gt_x = np.arange(-0.5,0.5,0.01)
gt_y = gt_x**2

plt.subplot(1, 2, 1)
plt.scatter(sim.data[input_data].T[0][train_index],sim.data[label_data].T[0][train_index], c='k', label='train_data')
plt.plot(gt_x,gt_y, c='r',linestyle='dashed',linewidth=3,label='ground truth')
plt.scatter(sim.data[pre_p].T[0][train_index],sim.data[post_p].T[0][train_index], c='b', label='model_train')
plt.ylabel("training process")
plt.legend(loc='best')
plt.ylim([-0.2,0.5])


plt.subplot(1,2,2)
plt.scatter(sim.data[input_data].T[0][test_index],sim.data[label_data].T[0][test_index], c='k', label='test_data')
plt.plot(gt_x,gt_y, c='r',linestyle='dashed',linewidth=3,label='ground truth')
plt.scatter(sim.data[pre_p].T[0][test_index],sim.data[post_p].T[0][test_index], c='b', label='model_test')
plt.ylabel("test process")
plt.legend(loc='best')
plt.ylim([-0.2,0.5])

기타 느낀점

간단한 regression도 구현하기 위해 많은 뉴런이 필요함... → 효율이...?!

$y=x^2$ 구현하기 위해서 layer 쌓아야 할줄 알았는데 안그래도됌. → 생각해보니 많은 뉴런 + LIF rate coding 이어서 가능했던거 같음. 다른 복잡한 함수면 layer 쌓아햐 할꺼 같음

post_probe 가 0~1 보는데, 작은 값일때 더 잘 하는 느낌.

input data 가 어느정도 duration이 필요한데 어느정도가 좋을지는..

조절할만한 parameter가 data_duration, neuron_number, learning_rate

이제 할일

bekolay master thesis chapter 3,4 읽기

PES learning layer 쌓기

MNIST classification

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nengo-6주차

Nengo PES learning

nengo_gui

regression 결과물

기타 느낀점

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