Using the trained weights in an ensemble of neurons

On the function points branch of nengo
On the vision branch of nengo_extras



In [2]:

    
import nengo
import numpy as np
import cPickle
from nengo_extras.data import load_mnist
from nengo_extras.vision import Gabor, Mask
from matplotlib import pylab
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import scipy.ndimage
from scipy.ndimage.interpolation import rotate

Load the MNIST database



In [3]:

    
# --- load the data
img_rows, img_cols = 28, 28

(X_train, y_train), (X_test, y_test) = load_mnist()

X_train = 2 * X_train - 1  # normalize to -1 to 1
X_test = 2 * X_test - 1  # normalize to -1 to 1

Each digit is represented by a one hot vector where the index of the 1 represents the number



In [4]:

    
temp = np.diag([1]*10)

ZERO = temp[0]
ONE =  temp[1]
TWO =  temp[2]
THREE= temp[3]
FOUR = temp[4]
FIVE = temp[5]
SIX =  temp[6]
SEVEN =temp[7]
EIGHT= temp[8]
NINE = temp[9]

labels =[ZERO,ONE,TWO,THREE,FOUR,FIVE,SIX,SEVEN,EIGHT,NINE]

dim =28

Load the saved weight matrices that were created by training the model



In [6]:

    
label_weights = cPickle.load(open("label_weights_choose_enc1000.p", "rb"))
activity_to_img_weights = cPickle.load(open("activity_to_img_weights_choose_enc1000.p", "rb"))
#rotated_clockwise_after_encoder_weights =  cPickle.load(open("rotated_clockwise_after_encoder_weights_rot_enc1000.p", "r"))
rotated_counter_after_encoder_weights =  cPickle.load(open("rotated_counter_after_encoder_weights_choose_enc1000.p", "r"))

#identity_after_encoder_weights = cPickle.load(open("identity_after_encoder_weights1000.p","r"))


#rotation_clockwise_weights = cPickle.load(open("rotation_clockwise_weights1000.p","rb"))
#rotation_counter_weights = cPickle.load(open("rotation_weights1000.p","rb"))



In [5]:

    
#Training with filters used on train images
#low_pass_weights = cPickle.load(open("low_pass_weights1000.p", "rb"))
#rotated_counter_after_encoder_weights_noise = cPickle.load(open("rotated_after_encoder_weights_counter_filter_noise5000.p", "r"))
#rotated_counter_after_encoder_weights_filter = cPickle.load(open("rotated_after_encoder_weights_counter_filter5000.p", "r"))

Functions to perform the inhibition of each ensemble



In [6]:

    
#A value of zero gives no inhibition

def inhibit_rotate_clockwise(t):
    if t < 0.5:
        return dim**2
    else:
        return 0
    
def inhibit_rotate_counter(t):
    if t < 0.5:
        return 0
    else:
        return dim**2
    
def inhibit_identity(t):
    if t < 0.3:
        return dim**2
    else:
        return dim**2



In [13]:

    
def intense(img):
    newImg = img.copy()
    newImg[newImg < 0] = -1
    newImg[newImg > 0] = 1
    return newImg

def node_func(t,x):
    #clean = scipy.ndimage.gaussian_filter(x, sigma=1)
    #clean = scipy.ndimage.median_filter(x, 3)
    clean = intense(x)
    return clean



In [14]:

    
#Create stimulus at horizontal
weight = np.dot(label_weights,activity_to_img_weights)

img = np.dot(THREE,weight)

img = scipy.ndimage.rotate(img.reshape(28,28),90).ravel()

pylab.imshow(img.reshape(28,28),cmap="gray")
plt.show()

The network where the mental imagery and rotation occurs

The state, seed and ensemble parameters (including encoders) must all be the same for the saved weight matrices to work
The number of neurons (n_hid) must be the same as was used for training
The input must be shown for a short period of time to be able to view the rotation
The recurrent connection must be from the neurons because the weight matices were trained on the neuron activities



In [7]:

    
rng = np.random.RandomState(9)
n_hid = 1000
model = nengo.Network(seed=3)
with model:
    #Stimulus only shows for brief period of time
    stim = nengo.Node(lambda t: THREE if t < 0.1 else 0) #nengo.processes.PresentInput(labels,1))# For cycling through input
    
    #Starting the image at horizontal
    #stim = nengo.Node(lambda t:img if t< 0.1 else 0)
    
    ens_params = dict(
        eval_points=X_train,
        neuron_type=nengo.LIF(), #Why not use LIF?
        intercepts=nengo.dists.Choice([-0.5]),
        max_rates=nengo.dists.Choice([100]),
        )
        
    
    # linear filter used for edge detection as encoders, more plausible for human visual system
    #encoders = Gabor().generate(n_hid, (11, 11), rng=rng)
    #encoders = Mask((28, 28)).populate(encoders, rng=rng, flatten=True)

    '''
    degrees = 6
    #must have same number of excoders as neurons (Want each random encoder to have same encoder at every angle)
    encoders = Gabor().generate(n_hid/(360/degrees), (11, 11), rng=rng)
    encoders = Mask((28, 28)).populate(encoders, rng=rng, flatten=True)

    rotated_encoders = encoders.copy()


    #For each randomly generated encoder, create the same encoder at every angle (increments chosen by degree)
    for encoder in encoders:
        rotated_encoders = np.append(rotated_encoders, [encoder],axis =0)
        for i in range(1,59):
            #new_gabor = rotate(encoder.reshape(28,28),degrees*i,reshape = False).ravel()
            rotated_encoders = np.append(rotated_encoders, [rotate(encoder.reshape(28,28),degrees*i,reshape = False).ravel()],axis =0)
            #rotated_encoders = np.append(rotated_encoders, [encoder],axis =0)
'''
    rotated_encoders = cPickle.load(open("encoders.p", "r"))
    
    #Num of neurons does not divide evenly with 6 degree increments, so add random encoders
    extra_encoders = Gabor().generate(n_hid - len(rotated_encoders), (11, 11), rng=rng)
    extra_encoders = Mask((28, 28)).populate(extra_encoders, rng=rng, flatten=True)
    all_encoders = np.append(rotated_encoders, extra_encoders, axis =0)

    encoders = all_encoders
    

    #Ensemble that represents the image with different transformations applied to it
    ens = nengo.Ensemble(n_hid, dim**2, seed=3, encoders=encoders, **ens_params)
    

    #Connect stimulus to ensemble, transform using learned weight matrices
    nengo.Connection(stim, ens, transform = np.dot(label_weights,activity_to_img_weights).T)
    #nengo.Connection(stim, ens) #for rotated stim
    
    
    #Recurrent connection on the neurons of the ensemble to perform the rotation
    nengo.Connection(ens.neurons, ens.neurons, transform = rotated_counter_after_encoder_weights.T, synapse=0.1)      
    #nengo.Connection(ens.neurons, ens.neurons, transform = low_pass_weights.T, synapse=0.1)      

    #Identity ensemble
    #ens_iden = nengo.Ensemble(n_hid,dim**2, seed=3, encoders=encoders, **ens_params)
    #Rotation ensembles
    #ens_clock_rot = nengo.Ensemble(n_hid,dim**2,seed=3,encoders=encoders, **ens_params)
    ens_counter_rot = nengo.Ensemble(n_hid,dim**2,seed=3,encoders=encoders, **ens_params)
    
    
    #Inhibition nodes
    #inhib_iden = nengo.Node(inhibit_identity)
    #inhib_clock_rot = nengo.Node(inhibit_rotate_clockwise)
    #inhib_counter_rot = nengo.Node(inhibit_rotate_counter)

    #Connect the main ensemble to each manipulation ensemble and back with appropriate transformation
    #Identity
    #nengo.Connection(ens.neurons, ens_iden.neurons,transform=identity_after_encoder_weights.T,synapse=0.1)
    #nengo.Connection(ens_iden.neurons, ens.neurons,transform=identity_after_encoder_weights.T,synapse=0.1)
    #Clockwise
    #nengo.Connection(ens.neurons, ens_clock_rot.neurons, transform = rotated_clockwise_after_encoder_weights.T,synapse=0.1)
    #nengo.Connection(ens_clock_rot.neurons, ens.neurons, transform = rotated_clockwise_after_encoder_weights.T,synapse = 0.1)
    #Counter-clockwise
    #nengo.Connection(ens.neurons, ens_counter_rot.neurons, transform = rotated_counter_after_encoder_weights.T, synapse=0.1)
    #nengo.Connection(ens_counter_rot.neurons, ens.neurons, transform = rotated_counter_after_encoder_weights.T, synapse=0.1)
    #nengo.Connection(ens_counter_rot.neurons, ens.neurons, transform = rotated_counter_after_encoder_weights_filter.T, synapse=0.1)
    
    #nengo.Connection(ens.neurons, ens_counter_rot.neurons, transform = low_pass_weights.T, synapse=0.1)
    #nengo.Connection(ens_counter_rot.neurons, ens.neurons, transform = low_pass_weights.T, synapse=0.1)

    #Clean up by a node
    #n = nengo.Node(node_func, size_in=dim**2)
    #nengo.Connection(ens.neurons,n,transform=activity_to_img_weights.T, synapse=0.1)
    #nengo.Connection(n,ens_counter_rot,synapse=0.1)

    #Connect the inhibition nodes to each manipulation ensemble
    #nengo.Connection(inhib_iden, ens_iden.neurons, transform=[[-1]] * n_hid)
    #nengo.Connection(inhib_clock_rot, ens_clock_rot.neurons, transform=[[-1]] * n_hid)
    #nengo.Connection(inhib_counter_rot, ens_counter_rot.neurons, transform=[[-1]] * n_hid)

    
    #Collect output, use synapse for smoothing
    probe = nengo.Probe(ens.neurons,synapse=0.1)



In [8]:

    
sim = nengo.Simulator(model)



In [9]:

    
sim.run(5)









    



Simulation finished in 0:00:12.

The following is not part of the brain model, it is used to view the output for the ensemble

Since it's probing the neurons themselves, the output must be transformed from neuron activity to visual image



In [10]:

    
'''Animation for Probe output'''
fig = plt.figure()

output_acts = []
for act in sim.data[probe]:
    output_acts.append(np.dot(act,activity_to_img_weights))

def updatefig(i):
    im = pylab.imshow(np.reshape(output_acts[i],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'),animated=True)
    
    return im,

ani = animation.FuncAnimation(fig, updatefig, interval=0.1, blit=True)
plt.show()









    



---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-10-d4eda138fd3f> in <module>()
     12 
     13 ani = animation.FuncAnimation(fig, updatefig, interval=0.1, blit=True)
---> 14 plt.show()

C:\Python27\lib\site-packages\matplotlib\pyplot.pyc in show(*args, **kw)
    242     """
    243     global _show
--> 244     return _show(*args, **kw)
    245 
    246 

C:\Python27\lib\site-packages\matplotlib\backend_bases.pyc in __call__(self, block)
    190 
    191         if not is_interactive() or get_backend() == 'WebAgg':
--> 192             self.mainloop()
    193 
    194     def mainloop(self):

C:\Python27\lib\site-packages\matplotlib\backends\backend_tkagg.pyc in mainloop(self)
     72 class Show(ShowBase):
     73     def mainloop(self):
---> 74         Tk.mainloop()
     75 
     76 show = Show()

C:\Python27\lib\lib-tk\Tkinter.pyc in mainloop(n)
    412 def mainloop(n=0):
    413     """Run the main loop of Tcl."""
--> 414     _default_root.tk.mainloop(n)
    415 
    416 getint = int

AttributeError: 'NoneType' object has no attribute 'tk'



In [11]:

    
#ouput_acts = sim.data[probe]

plt.subplot(261)
plt.title("100")
pylab.imshow(np.reshape(output_acts[100],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(262)
plt.title("500")
pylab.imshow(np.reshape(output_acts[500],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(263)
plt.title("1000")
pylab.imshow(np.reshape(output_acts[1000],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(264)
plt.title("1500")
pylab.imshow(np.reshape(output_acts[1500],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(265)
plt.title("2000")
pylab.imshow(np.reshape(output_acts[2000],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(266)
plt.title("2500")
pylab.imshow(np.reshape(output_acts[2500],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(267)
plt.title("3000")
pylab.imshow(np.reshape(output_acts[3000],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(268)
plt.title("3500")
pylab.imshow(np.reshape(output_acts[3500],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(269)
plt.title("4000")
pylab.imshow(np.reshape(output_acts[4000],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(2,6,10)
plt.title("4500")
pylab.imshow(np.reshape(output_acts[4500],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(2,6,11)
plt.title("5000")
pylab.imshow(np.reshape(output_acts[4999],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))


plt.show()

Pickle the probe's output if it takes a long time to run



In [ ]:

    
#The filename includes the number of neurons and which digit is being rotated
filename = "mental_rotation_output_ONE_"  + str(n_hid) + ".p"
cPickle.dump(sim.data[probe], open( filename , "wb" ) )

Testing



In [171]:

    
testing = np.dot(ONE,np.dot(label_weights,activity_to_img_weights))
testing = output_acts[300]
plt.subplot(131)
pylab.imshow(np.reshape(testing,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

#Get image
#testing = np.dot(ONE,np.dot(label_weights,activity_to_img_weights))
#noise = np.random.random([28,28]).ravel()
testing = node_func(0,testing)

plt.subplot(132)
pylab.imshow(np.reshape(testing,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))


#Get activity of image
_, testing_act = nengo.utils.ensemble.tuning_curves(ens, sim, inputs=testing)

#Get encoder outputs
testing_filter = np.dot(testing_act,rotated_counter_after_encoder_weights_filter)

#Get activities
testing_filter = ens.neuron_type.rates(testing_filter, sim.data[ens].gain, sim.data[ens].bias)

for i in range(5):
    testing_filter = np.dot(testing_filter,rotated_counter_after_encoder_weights_filter)
    testing_filter = ens.neuron_type.rates(testing_filter, sim.data[ens].gain, sim.data[ens].bias)
    testing_filter = np.dot(testing_filter,activity_to_img_weights)
    testing_filter = node_func(0,testing_filter)
    _, testing_filter = nengo.utils.ensemble.tuning_curves(ens, sim, inputs=testing_filter)


#testing_rotate = np.dot(testing_rotate,rotation_weights)

testing_filter = np.dot(testing_filter,activity_to_img_weights)

plt.subplot(133)
pylab.imshow(np.reshape(testing_filter,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

plt.show()



In [ ]:

    
plt.subplot(121)
pylab.imshow(np.reshape(X_train[0],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

#Get activity of image
_, testing_act = nengo.utils.ensemble.tuning_curves(ens, sim, inputs=X_train[0])

testing_rotate = np.dot(testing_act,activity_to_img_weights)

plt.subplot(122)
pylab.imshow(np.reshape(testing_rotate,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

plt.show()

Just for fun



In [ ]:

    
letterO = np.dot(ZERO,np.dot(label_weights,activity_to_img_weights))
plt.subplot(161)
pylab.imshow(np.reshape(letterO,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

letterL = np.dot(SEVEN,label_weights)
for _ in range(30):
    letterL = np.dot(letterL,rotation_weights)
letterL = np.dot(letterL,activity_to_img_weights)
plt.subplot(162)
pylab.imshow(np.reshape(letterL,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

letterI = np.dot(ONE,np.dot(label_weights,activity_to_img_weights))
plt.subplot(163)
pylab.imshow(np.reshape(letterI,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.subplot(165)
pylab.imshow(np.reshape(letterI,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

letterV = np.dot(SEVEN,label_weights)
for _ in range(40):
    letterV = np.dot(letterV,rotation_weights)
letterV = np.dot(letterV,activity_to_img_weights)
plt.subplot(164)
pylab.imshow(np.reshape(letterV,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

letterA = np.dot(SEVEN,label_weights)
for _ in range(10):
    letterA = np.dot(letterA,rotation_weights)
letterA = np.dot(letterA,activity_to_img_weights)
plt.subplot(166)
pylab.imshow(np.reshape(letterA,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))

plt.show()