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main_1d_20190924.py
518 lines (422 loc) · 17.9 KB
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main_1d_20190924.py
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#author: Zhiqin Xu 许志钦
#email: xuzhiqin@sjtu.edu.cn
#2019-09-24
# coding: utf-8
'''
Reference:
1 Training behavior of deep neural network in frequency domain: https://arxiv.org/abs/1807.01251
2 Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks: https://arxiv.org/abs/1901.06523
3 Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks: https://arxiv.org/abs/1905.10264
4 Theory of the Frequency Principle for General Deep Neural Networks: https://arxiv.org/abs/1906.09235
'''
#author: Zhiqin Xu 许志钦
#email: xuzhiqin@sjtu.edu
#2019-09-24
# coding: utf-8
#import sys
import matplotlib
matplotlib.use('Agg')
# In[2]:
import pickle
import time, os
import shutil
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
from BasicFunc import mySaveFig, univAprox
from BasicFunc import my_fft, SelectPeakIndex
# In[3]:
isShowPic=0
Leftp=0.18
Bottomp=0.18
Widthp=0.88-Leftp
Heightp=0.9-Bottomp
pos=[Leftp,Bottomp,Widthp,Heightp]
ComputeStepFFT=20
LowFreqDrawAdd=1e-5 # for plot. plot y+this number, in case of 0 in log-log
SD=0.0 ### noise standard deviation in sample data, used in the fitting function
# y_name='|x|'
#y_name='sigmoid'
y_name='sinx'
# y_name='inv x'
def sigmoid(xx):
return (1 / (1 + np.exp(-xx)))
def func0(xx,SD):
y_sin=np.sin(xx)+np.sin(4*xx)#+np.sin(5*xx)
return y_sin
### discretized the func0 by sin_div
def func_to_approx(xx,sin_div,SD):
y_sin=func0(xx,SD)
if sin_div==0:
return y_sin
out_y = np.round(y_sin/sin_div)
out_y2 = out_y * sin_div
return out_y2
R_variable={} ### used for saved all parameters and data
### mkdir a folder to save all output
R_variable['iscontinue']=0
if R_variable['iscontinue']:
FolderName='Errordata/%s/'%('50129')
else:
BaseDir = 'Errordata/'
subFolderName = '%s'%(int(np.absolute(np.random.normal([1])*100000))//int(1))
FolderName = '%s%s/'%(BaseDir,subFolderName)
if not os.path.isdir(BaseDir):
os.mkdir(BaseDir)
os.mkdir(FolderName)
os.mkdir('%smodel/'%(FolderName))
R_variable['FolderName']=FolderName
### initialization standard deviation
R_variable['astddev']=0.05 # for weight
R_variable['bstddev']=0.05 # for bias terms2
### the length to discretized the continuous function
R_variable['sin_div']=0
### noise standard deviation in sample data, used in the fitting function
R_variable['SD']=SD
### hidden layer structure
# R_variable['hidden_units']=[20,10]
# R_variable['hidden_units']=[40,20]
R_variable['hidden_units']=[200,200,200,100]
#R_variable['hidden_units']=[1500,1500,500,500]
#R_variable['hidden_units']=[1]
# R_variable['hidden_units']=[800,800,400,400]
R_variable['learning_rate']=2e-5
R_variable['learning_rateDecay']=0
R_variable['rateDecayStep']=2000
### setup for activation function
R_variable['seed']=0
R_variable['ActFuc']=1 ### 0: ReLU; 1: Tanh; 3:sin;4: x**5,, 5: sigmoid 6 sigmoid derivate
R_variable['train_size']=61; ### training size
R_variable['batch_size']=int(np.floor(R_variable['train_size'])) ### batch size
R_variable['test_size']=int(201) ### test size
R_variable['x_start']=-10 #math.pi*3 ### start point of input
R_variable['x_end']=10 #math.pi*3 ### end point of input
R_variable['isRec_y_test']=0
R_variable['isFFT']=1 #compute FFT or not
R_variable['ismovie']=0 # make a training movie
R_variable['tol']=3e-3
R_variable['Total_Step']=600000 ### the training step. Set a big number, if it converges, can manually stop training
R_variable['Record_Step']=1 ### every R_step compute Entropy or other values
R_variable['id']=0 ### index for how many step recorded
R_variable['y_name']=y_name ### the target fitting function
R_variable['FolderName']=FolderName ### folder for save images
# initialization for variables
x_end=R_variable['x_end']
R_variable['test_inputs'] =np.reshape(np.linspace(R_variable['x_start'], R_variable['x_end'], num=R_variable['test_size'],
endpoint=True),[R_variable['test_size'],1])
R_variable['train_inputs']=np.reshape(np.linspace(R_variable['x_start'], R_variable['x_end'], num=R_variable['train_size'],
endpoint=True),[R_variable['train_size'],1])
# ###randomly select training set from test set
# indperm = np.random.permutation(test_size)
# ind = indperm[0:Size_in]
# R_variable['train_inputs']=R_variable['test_inputs'][ind]
# ###randomly select training set from test set
R_variable['loss_test']=[]
R_variable['loss_train']=[]
R_variable['fft_fit_test']=[]
R_variable['fft_true_test']=[]
R_variable['fft_0_train']=[]
R_variable['fft_fit_train']=[]
R_variable['fft_true_train']=[]
R_variable['fft_0_test']=[]
R_variable['y_test_all']=[]
R_variable['y_train_all']=[]
R_variable['y_test']=[]
R_variable['y_true_test']=[]
sin_div=R_variable['sin_div']
test_inputs=R_variable['test_inputs']
train_inputs=R_variable['train_inputs']
t0=time.time()
# In[16]:
y_0_test = func0(test_inputs,0)
y_0_train = func0(train_inputs,0)
y_true_test = func_to_approx(test_inputs,R_variable['sin_div'],R_variable['SD'])
y_true_train = func_to_approx(train_inputs,R_variable['sin_div'],R_variable['SD'])
R_variable['y_0_train']=y_0_train
R_variable['y_0_test']=y_0_test
R_variable['y_true_test']= y_true_test
R_variable['y_true_train']=y_true_train
if R_variable['isFFT']:
fft_0_test=my_fft(y_0_test,ComputeStepFFT)
R_variable['fft_0_test']=fft_0_test
fft_0_train=my_fft(y_0_train,ComputeStepFFT)
R_variable['fft_0_train']=fft_0_train
fft_true_test=my_fft(y_true_test,ComputeStepFFT)
R_variable['fft_true_test']=fft_true_test
fft_true_train=my_fft(y_true_train,ComputeStepFFT)
R_variable['fft_true_train']=fft_true_train
### compute a FFT for FFT Training.
fft_y_true_train=np.fft.fft(np.squeeze(y_true_train))
if R_variable['isFFT']:
Sel_fre_true=np.array(R_variable['fft_true_train'][0:ComputeStepFFT])
Peak_ind1=SelectPeakIndex(Sel_fre_true, endpoint=False)
Peak_ind=Peak_ind1
Hand_Add_peak=[1] # sometimes, first few points are also very important. such as x^2
Hand_Add_peak=[]
Peak_ind=np.concatenate([Peak_ind,Hand_Add_peak],axis=0)
Peak_ind=np.sort(Peak_ind)
Peak_len=len(Peak_ind)
Peak_ind=np.int32(Peak_ind)
Peak_id=0 # count peak for peak training
#tf.reset_default_graph()
with tf.variable_scope('Graph',reuse=tf.AUTO_REUSE) as scope:
# Our inputs will be a batch of values taken by our functions
x = tf.placeholder(tf.float32, shape=[None, 1], name="x")
y_true = tf.placeholder_with_default(input=[[0.0]], shape=[None, 1], name="y")
y,w_Sess,b_Sess,L2w_all_out = univAprox(x, R_variable['hidden_units'],
astddev=R_variable['astddev'],bstddev=R_variable['bstddev'],
ActFuc=R_variable['ActFuc'],seed=R_variable['seed'])
with tf.variable_scope('Loss',reuse=tf.AUTO_REUSE):
loss=tf.reduce_mean(tf.square(y - y_true))
# We define our train operation using the Adam optimizer
learning_rate=R_variable['learning_rate']
adam = tf.train.AdamOptimizer(learning_rate=learning_rate)
train_op = adam.minimize(loss)
# train_op = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
saver = tf.train.Saver()
config = tf.ConfigProto()
config.gpu_options.allow_growth=True
sess = tf.Session(config=config)
if R_variable['iscontinue']:
saver.restore(sess, "%smodel/model.ckpt"%(FolderName))
else:
sess.run(tf.global_variables_initializer())
for i in range(R_variable['Total_Step']):
if (i) % R_variable['Record_Step'] == 0:
y_test, loss_test_tmp,w_tmp,b_tmp= sess.run([y,loss,w_Sess,b_Sess],
feed_dict={x: test_inputs, y_true: y_true_test})
y_train,loss_train_tmp = sess.run([y,loss],feed_dict={x: train_inputs, y_true: y_true_train})
if i==0:
y_test_ini=y_test
R_variable['y_test_ini']=y_test_ini
R_variable['loss_test'].append(loss_test_tmp)
R_variable['loss_train'].append(loss_train_tmp)
if R_variable['isRec_y_test']:
R_variable['y_test_all'].append(np.squeeze(y_test))
if R_variable['isFFT']:
R_variable['fft_fit_test'].append(my_fft(y_test,ComputeStepFFT))
R_variable['fft_fit_train'].append(my_fft(y_train,ComputeStepFFT))
if loss_train_tmp<R_variable['tol']:
print('total step:%s; total error:%s'%(i,loss_train_tmp))
break
indperm = np.random.permutation(R_variable['train_size'])
ind = indperm[0:R_variable['batch_size']]
_ = sess.run(train_op, feed_dict={x: train_inputs[ind], y_true: y_true_train[ind]})
if (i%250==0 and i<2000000):
print('batch: %d, test loss: %f' % (i + 1, R_variable['loss_test'][-1]))
print('batch: %d, train loss: %f' % (i + 1, R_variable['loss_train'][-1]))
R_variable['y_test']=y_test
R_variable['y_train']=y_train
t1=time.time()
print('time cost:%s'%(t1-t0))
shutil.rmtree('%smodel/'%(FolderName))
os.mkdir('%smodel/'%(FolderName))
save_path = saver.save(sess, "%smodel/model.ckpt"%(FolderName))
with open('%s/objs.pkl'%(FolderName), 'wb') as f: # Python 3: open(..., 'wb')
pickle.dump(R_variable, f, protocol=4)
text_file = open("%s/Output.txt"%(FolderName), "w")
for para in R_variable:
if np.size(R_variable[para])>20:
continue
text_file.write('%s: %s\n'%(para,R_variable[para]))
text_file.close()
plt.figure()
ax=plt.gca()
plt.plot(train_inputs, y_train,'m.', label='Train_fit')
plt.plot(train_inputs, R_variable['y_true_train'],'b-', label='Train_true')
plt.legend(fontsize=16)
plt.xlabel('x',fontsize=18)
plt.ylabel('y',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.title('epoch: %s'%(i),fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%sytrain%s'%(R_variable['FolderName'],i)
mySaveFig(plt,fntmp,ax=ax,iseps=0)
plt.figure()
ax=plt.gca()
plt.plot(test_inputs, y_test,'r.', label='Test_fit')
plt.plot(test_inputs, R_variable['y_true_test'],'g-', label='Test_true')
plt.legend(fontsize=16)
plt.xlabel('x',fontsize=18)
plt.ylabel('y',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.title('epoch: %s'%(i),fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%sytest%s'%(R_variable['FolderName'],i)
mySaveFig(plt,fntmp,ax=ax,iseps=0)
plt.figure()
ax = plt.gca()
y1 = R_variable['loss_test']
y2 = R_variable['loss_train']
plt.plot(y1,'ro',label='Test')
plt.plot(y2,'g*',label='Train')
#ax.set_xscale('log')
ax.set_yscale('log')
plt.xlabel('epoch',fontsize=18)
plt.ylabel('loss',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.legend(fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%sloss'%(FolderName)
mySaveFig(plt,fntmp,ax=ax,isax=1,iseps=0)
if R_variable['isFFT']:
plt.figure()
ax=plt.gca()
y1 = R_variable['fft_true_train'] / R_variable['train_size']
y2 = R_variable['fft_fit_train'][-1] / R_variable['train_size']
plt.semilogy(y1+LowFreqDrawAdd,'ro-',label='Trn_true')
plt.semilogy(y2+LowFreqDrawAdd,'g*-',label='Trn_fit')
plt.xlabel('freq index',fontsize=18)
plt.ylabel('|FFT|',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.legend(fontsize=18)
plt.title('Train, epoch: %s'%(i),fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%strainfft%s'%(FolderName,i)
mySaveFig(plt, fntmp,ax=ax,iseps=0)
plt.figure()
ax=plt.gca()
y1 = R_variable['fft_true_test'] / R_variable['test_size']
y2 = R_variable['fft_fit_test'][-1] / R_variable['test_size']
plt.semilogy(y1+LowFreqDrawAdd,'ro-',label='Trn_true')
plt.semilogy(y2+LowFreqDrawAdd,'g*-',label='Trn_fit')
plt.xlabel('freq index',fontsize=18)
plt.ylabel('|FFT|',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.legend(fontsize=18)
plt.title('Test, epoch: %s'%(i),fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%stestfft%s'%(FolderName,i)
mySaveFig(plt, fntmp,ax=ax,iseps=0)
print("for over")
R_variable['traintime']=time.time()-t0
print(R_variable['traintime'])
#save data
with open('%s/objs.pkl'%(FolderName), 'wb') as f: # Python 3: open(..., 'wb')
pickle.dump(R_variable, f, protocol=4)
text_file = open("%s/Output.txt"%(FolderName), "w")
for para in R_variable:
if np.size(R_variable[para])>20:
# print(para)
continue
text_file.write('%s: %s\n'%(para,R_variable[para]))
text_file.close()
#with open('objs.pkl', 'rb') as f: # Python 3: open(..., 'rb')
# R_variable = pickle.load(f)
#FolderName=''
test_inputs=R_variable['test_inputs']
plt.figure()
ax=plt.gca()
plt.plot(test_inputs, R_variable['y_test_ini'],'g-', label='initial')
plt.legend(fontsize=18)
ax.set_xlabel('x',fontsize=18)
ax.set_ylabel('y',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
ax.set_position(pos, which='both')
fntmp = '%sy_ini'%(FolderName)
mySaveFig(plt, fntmp,ax=ax)
plt.figure()
ax=plt.gca()
plt.plot(train_inputs, y_train,'m.', label='Train_fit')
plt.plot(train_inputs, R_variable['y_true_train'],'b-', label='Train_true')
plt.legend(fontsize=16)
plt.xlabel('x',fontsize=18)
plt.ylabel('y',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.title('epoch: %s'%(i),fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%sytrain'%(R_variable['FolderName'])
mySaveFig(plt,fntmp,ax=ax,iseps=0)
plt.figure()
ax=plt.gca()
plt.plot(test_inputs, y_test,'r.', label='Test_fit')
plt.plot(test_inputs, R_variable['y_true_test'],'g-', label='Test_true')
plt.legend(fontsize=16)
plt.xlabel('x',fontsize=18)
plt.ylabel('y',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.title('epoch: %s'%(i),fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%sytest'%(R_variable['FolderName'])
mySaveFig(plt,fntmp,ax=ax,iseps=0)
plt.figure()
ax = plt.gca()
y1 = R_variable['loss_test']
y2 = R_variable['loss_train']
plt.plot(y1,'ro',label='Test')
plt.plot(y2,'g*',label='Train')
#ax.set_xscale('log')
ax.set_yscale('log')
plt.xlabel('epoch',fontsize=18)
plt.ylabel('loss',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
plt.legend(fontsize=18)
ax.set_position(pos, which='both')
fntmp = '%sloss'%(FolderName)
mySaveFig(plt,fntmp,ax=ax,isax=1,iseps=0)
plt.figure()
ax=plt.gca()
plt.plot(test_inputs, R_variable['y_true_test'],'b-', label='true')
plt.legend(fontsize=16)
ax.set_xlabel('x',fontsize=18)
ax.set_ylabel('y',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
ax.set_position(pos, which='both')
fntmp = '%sy_true'%(FolderName)
mySaveFig(plt, fntmp,ax=ax,iseps=0)
if R_variable['isFFT']:
UsedPeak=np.arange(len(Peak_ind))
# plot fft with important peak
plt.figure()
ax=plt.gca()
ind = np.arange(ComputeStepFFT)
y1 = R_variable['fft_true_train']/R_variable['train_size']
plt.semilogy( y1[0:ComputeStepFFT],'r-',label='Trn_true')
UsedPeaktmp=np.arange(len(Peak_ind))
plt.semilogy(Peak_ind[UsedPeak],y1[Peak_ind[UsedPeak]]+1e-6,'ks')
plt.ylim([1e-5,10])
ax.set_xlabel('freq index',fontsize=18)
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
ax.set_position(pos, which='both')
fntmp = '%sfftPeak'%(FolderName)
mySaveFig(plt, fntmp,ax=ax,iseps=0)
d_step_fft_true_train_all=np.zeros([ComputeStepFFT,len(R_variable['fft_fit_train'])])
abs_err_all=np.zeros([ComputeStepFFT,len(R_variable['fft_fit_train'])])
fft_train_fitAll=np.asarray(np.abs(R_variable['fft_fit_train']))
for itfes in range(ComputeStepFFT):
tmp1=fft_train_fitAll[:,itfes]
tmp2=R_variable['fft_true_train'][itfes]
d_step_fft_true_train_all[itfes,:] = (np.absolute(tmp1-tmp2))/(1e-5+tmp2)
abs_err_all[itfes,:] = np.absolute(tmp1-tmp2)
DrawDis=1
DrawLastStep=len(R_variable['fft_fit_train'])
z_min=0.1
z_max=1
plt.figure()
ax=plt.gca()
im=plt.pcolor(d_step_fft_true_train_all[Peak_ind[UsedPeak],:DrawLastStep:DrawDis], cmap='RdBu', vmin=z_min, vmax=z_max)
ax.set_xlabel('epoch',fontsize=18)
ax.set_ylabel('freq peak index',fontsize=18)
#ax.set_xscale('log')
#ax.set_xlim([1,10])
plt.rc('xtick',labelsize=18)
plt.rc('ytick',labelsize=18)
ax.set_yticks([0,1,2])
ax.set_position(pos, which='both')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(im, cax=cax,ticks=[0,0.2,0.4,0.6,0.8,1])
fntmp = '%speakerror'%(FolderName)
mySaveFig(plt, fntmp,ax=ax,iseps=0)