Deep Calibration: learning local stochastic volatility from price data¶
Instead of learning maps from parameters to prices as we have seen in a first approach, or learning directly the solution of the inverse problem, see Andres Hernandez's work Model calibration with neural networks, or work of Cuchiero et al., we can in case of local stochastic volatility models choose a third approach (this is joint work with Christa Cuchiero and Wahid Khosrawi-Sardroudi):
Consider the model $$ dS_t = \alpha_t \sigma(t,S_t) dW_t $$ with initial value $ S_0 $. We can set up the problem to infer the local volatility function $ \sigma $ from derivatives's prices in the following machine learning fashion: try to find a function $ \sigma $, given as neural network, and hedges $ H^{(K,T)} $ such that $$ \sum_{(K,T)} E\big[{((S_T-K)_+ - C_{\text{market}}(K,T) - (H^{(K,T)}\bullet S)_t)}^2\big] \rightarrow \text{min!} $$ Notice that the sum is running over a finite set of price data points. The problem can possibly solve the calibration problem but one has to learn the local volatility function and the hedges simultanously.
Let us see in the sequel if this can work out. We shall use notation which reminds the above formulation.
In [146]:
import numpy as np
import tensorflow as tf
from keras.models import Sequential
from keras.layers import Input, Dense, Conv2D, Concatenate, Dropout, Subtract, \
Flatten, MaxPooling2D, Multiply, Lambda, Add, Dot
from keras.backend import constant
from keras import optimizers
from keras.engine.topology import Layer
from keras.models import Model
from keras.layers import Input
from keras import initializers
from keras.constraints import max_norm
import keras.backend as K
First we create two identical models where either only hedges or local volatilities can be trained.
In [147]:
m = 10 # layer dimension
n = 2 # number of layers for local volatility
N = 20 # time discretization (should fit to maturities)
maturities = [1.] # list of maturities in years
T = 1.0
layers = []
layersatT = []
for j in range(len(maturities)):
for i in range(n):
if i < 1:
nodes = m
else:
nodes = 1
layer = Dense(nodes, activation='tanh', trainable=False,
kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',
bias_initializer='random_normal')
layersatT = layersatT + [layer]
layers = layers + [layersatT]
#P = {(1.0,1.0): 0.4, (1.1,1.0):0.2, (0.9,1.0):0.5,
# (1.0,0.5): 0.2, (1.1,0.5):0.1, (0.9,0.5):0.3}
P= {(0.9, 0.5): 0.20042534,
(0.9, 1.0): 0.23559685,
(1.0, 0.5): 0.16312157,
(1.0, 1.0): 0.20771958,
(1.1, 0.5): 0.13154241,
(1.1, 1.0): 0.18236567}
hedges = {}
hedgeskey =[]
for key in P.keys():
for j in range(N):
hedge = Dense(nodes, activation='tanh', trainable=True,
kernel_initializer=initializers.RandomNormal(0,0.1),#kernel_initializer='random_normal',
bias_initializer='random_normal')
hedgeskey = hedgeskey + [hedge]
hedges[key] = hedgeskey
start = 0
In [148]:
keylist = list(P.keys())
price = Input(shape=(1,))
hedgepf = [Input(shape=(1,)) for l in range(len(P.keys()))]
inputs = [price] + hedgepf
inputshelper = []
hedgeratio = {}
hedge = {}
pricekey = [0 for l in range(len(P.keys()))]
normal = tf.distributions.Normal(loc=0., scale=1.)
def BS(x):
price=x[0]
vola=x[1]
return normal.cdf((K.log(K.abs(price)/key[0])-0.5*(key[1]-j*T/N)*vola**2)/(0.0001+np.sqrt(key[1]-j*T/N)*vola))
# increases computational time
for i in range(len(maturities)):
for j in range(start,N):
if maturities[i] >= j*T/N:
helper0 = layers[i][0](price)
for k in range(1,2):
helper0 = layers[i][k](helper0) # local vol applied to price at time j*T/N
BMincr = Input(shape=(1,)) # BM increment
stochvol = Input(shape=(1,)) # stochvol value
helper1 = Multiply()([helper0,BMincr])
helper1 = Lambda(lambda x: x * np.sqrt(T/N))(helper1)
priceincr = Multiply()([helper1,stochvol]) # new price increment
for l in range(len(P.keys())):
key = keylist[l]
hedgeratio[key] = hedges[key][j](price)
BSstrategy = Lambda(BS)([price,helper0])
hedgeratio[key] = Add()([hedgeratio[key],BSstrategy])
hedge[key] = Multiply()([priceincr,hedgeratio[key]])
hedgepf[l] = Add()([hedgepf[l],hedge[key]])
if key[1]==((j+1)*T/N): # the option expires
helper2 = Lambda(lambda x : 0.5*(abs(x-key[0])+x-key[0]))(price)
helper2 = Subtract()([helper2,hedgepf[l]]) # payoff minus hedge
pricekey[l] = helper2
price = Add()([price,priceincr]) #new price after one time step
inputshelper = inputshelper + [stochvol]
inputs = inputs + [BMincr]
else:
start = j
break
inputs = inputs + inputshelper
pricekey = Concatenate()(pricekey)
localvol_trainhedge = Model(inputs=inputs, outputs=pricekey)
Pay attention here: don't jump back and forth when defining models since layer lists come with the same names, so the order of execution is important!
In [149]:
layers = []
layersatT = []
for j in range(len(maturities)):
for i in range(2):
if i < 1:
nodes = m
else:
nodes = 1
layer = Dense(nodes, activation='tanh', trainable=True,
kernel_initializer=initializers.RandomNormal(0,1),#kernel_initializer='random_normal',
bias_initializer='random_normal')
layersatT = layersatT + [layer1]
layers = layers + [layersatT]
hedges = {}
hedgeskey =[]
for key in P.keys():
for j in range(N):
hedge = Dense(nodes, activation='tanh', trainable=False,
kernel_initializer=initializers.RandomNormal(0,0.1),#kernel_initializer='random_normal',
bias_initializer='random_normal')
hedgeskey = hedgeskey + [hedge]
hedges[key] = hedgeskey
start = 0
In [150]:
keylist = list(P.keys())
price = Input(shape=(1,))
hedgepf = [Input(shape=(1,)) for l in range(len(P.keys()))]
inputs = [price] + hedgepf
inputshelper = []
hedgeratio = {}
hedge = {}
pricekey = [0 for l in range(len(P.keys()))]
for i in range(len(maturities)):
for j in range(start,N):
if maturities[i] >= j*T/N:
layers[i][0].trainable=True
helper0 = layers[i][0](price)
for k in range(1,2):
layers[i][k].trainable=True
helper0 = layers[i][k](helper0)
BMincr = Input(shape=(1,))
stochvol = Input(shape=(1,))
helper1 = Multiply()([helper0,BMincr])
helper1 = Lambda(lambda x: x * np.sqrt(T/N))(helper1)
priceincr = Multiply()([helper1,stochvol])
for l in range(len(P.keys())):
key = keylist[l]
hedges[key][j].trainable=False
hedgeratio[key] = hedges[key][j](price)
BSstrategy = Lambda(BS)([price,helper0])
hedgeratio[key] = Add()([hedgeratio[key],BSstrategy])
hedge[key] = Multiply()([priceincr,hedgeratio[key]])
hedgepf[l] = Add()([hedgepf[l],hedge[key]])
if key[1]==((j+1)*T/N):
helper2 = Lambda(lambda x : 0.5*(abs(x-key[0])+x-key[0]))(price)
helper2 = Subtract()([helper2,hedgepf[l]])
pricekey[l] = helper2
price = Add()([price,priceincr])
inputshelper = inputshelper + [stochvol]
inputs = inputs + [BMincr]
else:
start = j
break
inputs = inputs + inputshelper
pricekey = Concatenate()(pricekey)
localvol_trainlocvol = Model(inputs=inputs, outputs=pricekey)
In [151]:
localvol_trainlocvol.summary()
____________________________________________________________________________________________________
Layer (type) Output Shape Param # Connected to
====================================================================================================
input_1391 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
dense_3173 (Dense) (None, 10) 20 input_1391[0][0]
add_7088[0][0]
add_7101[0][0]
add_7114[0][0]
add_7127[0][0]
add_7140[0][0]
add_7153[0][0]
add_7166[0][0]
add_7179[0][0]
add_7192[0][0]
add_7205[0][0]
add_7218[0][0]
add_7231[0][0]
add_7244[0][0]
add_7257[0][0]
add_7270[0][0]
add_7283[0][0]
add_7296[0][0]
add_7309[0][0]
add_7322[0][0]
____________________________________________________________________________________________________
dense_3174 (Dense) (None, 1) 11 dense_3173[0][0]
dense_3173[1][0]
dense_3173[2][0]
dense_3173[3][0]
dense_3173[4][0]
dense_3173[5][0]
dense_3173[6][0]
dense_3173[7][0]
dense_3173[8][0]
dense_3173[9][0]
dense_3173[10][0]
dense_3173[11][0]
dense_3173[12][0]
dense_3173[13][0]
dense_3173[14][0]
dense_3173[15][0]
dense_3173[16][0]
dense_3173[17][0]
dense_3173[18][0]
dense_3173[19][0]
____________________________________________________________________________________________________
input_1398 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4654 (Multiply) (None, 1) 0 dense_3174[0][0]
input_1398[0][0]
____________________________________________________________________________________________________
lambda_3886 (Lambda) (None, 1) 0 multiply_4654[0][0]
____________________________________________________________________________________________________
input_1399 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4655 (Multiply) (None, 1) 0 lambda_3886[0][0]
input_1399[0][0]
____________________________________________________________________________________________________
add_7088 (Add) (None, 1) 0 input_1391[0][0]
multiply_4655[0][0]
____________________________________________________________________________________________________
input_1400 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4662 (Multiply) (None, 1) 0 dense_3174[1][0]
input_1400[0][0]
____________________________________________________________________________________________________
lambda_3893 (Lambda) (None, 1) 0 multiply_4662[0][0]
____________________________________________________________________________________________________
input_1401 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4663 (Multiply) (None, 1) 0 lambda_3893[0][0]
input_1401[0][0]
____________________________________________________________________________________________________
add_7101 (Add) (None, 1) 0 add_7088[0][0]
multiply_4663[0][0]
____________________________________________________________________________________________________
input_1402 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4670 (Multiply) (None, 1) 0 dense_3174[2][0]
input_1402[0][0]
____________________________________________________________________________________________________
lambda_3900 (Lambda) (None, 1) 0 multiply_4670[0][0]
____________________________________________________________________________________________________
input_1403 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4671 (Multiply) (None, 1) 0 lambda_3900[0][0]
input_1403[0][0]
____________________________________________________________________________________________________
add_7114 (Add) (None, 1) 0 add_7101[0][0]
multiply_4671[0][0]
____________________________________________________________________________________________________
input_1404 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4678 (Multiply) (None, 1) 0 dense_3174[3][0]
input_1404[0][0]
____________________________________________________________________________________________________
lambda_3907 (Lambda) (None, 1) 0 multiply_4678[0][0]
____________________________________________________________________________________________________
input_1405 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4679 (Multiply) (None, 1) 0 lambda_3907[0][0]
input_1405[0][0]
____________________________________________________________________________________________________
add_7127 (Add) (None, 1) 0 add_7114[0][0]
multiply_4679[0][0]
____________________________________________________________________________________________________
input_1406 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4686 (Multiply) (None, 1) 0 dense_3174[4][0]
input_1406[0][0]
____________________________________________________________________________________________________
lambda_3914 (Lambda) (None, 1) 0 multiply_4686[0][0]
____________________________________________________________________________________________________
input_1407 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4687 (Multiply) (None, 1) 0 lambda_3914[0][0]
input_1407[0][0]
____________________________________________________________________________________________________
add_7140 (Add) (None, 1) 0 add_7127[0][0]
multiply_4687[0][0]
____________________________________________________________________________________________________
input_1408 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4694 (Multiply) (None, 1) 0 dense_3174[5][0]
input_1408[0][0]
____________________________________________________________________________________________________
lambda_3921 (Lambda) (None, 1) 0 multiply_4694[0][0]
____________________________________________________________________________________________________
input_1409 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4695 (Multiply) (None, 1) 0 lambda_3921[0][0]
input_1409[0][0]
____________________________________________________________________________________________________
add_7153 (Add) (None, 1) 0 add_7140[0][0]
multiply_4695[0][0]
____________________________________________________________________________________________________
input_1410 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4702 (Multiply) (None, 1) 0 dense_3174[6][0]
input_1410[0][0]
____________________________________________________________________________________________________
lambda_3928 (Lambda) (None, 1) 0 multiply_4702[0][0]
____________________________________________________________________________________________________
input_1411 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4703 (Multiply) (None, 1) 0 lambda_3928[0][0]
input_1411[0][0]
____________________________________________________________________________________________________
add_7166 (Add) (None, 1) 0 add_7153[0][0]
multiply_4703[0][0]
____________________________________________________________________________________________________
input_1412 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4710 (Multiply) (None, 1) 0 dense_3174[7][0]
input_1412[0][0]
____________________________________________________________________________________________________
lambda_3935 (Lambda) (None, 1) 0 multiply_4710[0][0]
____________________________________________________________________________________________________
input_1413 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4711 (Multiply) (None, 1) 0 lambda_3935[0][0]
input_1413[0][0]
____________________________________________________________________________________________________
add_7179 (Add) (None, 1) 0 add_7166[0][0]
multiply_4711[0][0]
____________________________________________________________________________________________________
input_1414 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4718 (Multiply) (None, 1) 0 dense_3174[8][0]
input_1414[0][0]
____________________________________________________________________________________________________
lambda_3942 (Lambda) (None, 1) 0 multiply_4718[0][0]
____________________________________________________________________________________________________
input_1415 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4719 (Multiply) (None, 1) 0 lambda_3942[0][0]
input_1415[0][0]
____________________________________________________________________________________________________
add_7192 (Add) (None, 1) 0 add_7179[0][0]
multiply_4719[0][0]
____________________________________________________________________________________________________
input_1416 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4726 (Multiply) (None, 1) 0 dense_3174[9][0]
input_1416[0][0]
____________________________________________________________________________________________________
lambda_3949 (Lambda) (None, 1) 0 multiply_4726[0][0]
____________________________________________________________________________________________________
input_1417 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4727 (Multiply) (None, 1) 0 lambda_3949[0][0]
input_1417[0][0]
____________________________________________________________________________________________________
add_7205 (Add) (None, 1) 0 add_7192[0][0]
multiply_4727[0][0]
____________________________________________________________________________________________________
input_1418 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4734 (Multiply) (None, 1) 0 dense_3174[10][0]
input_1418[0][0]
____________________________________________________________________________________________________
lambda_3959 (Lambda) (None, 1) 0 multiply_4734[0][0]
____________________________________________________________________________________________________
input_1419 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4735 (Multiply) (None, 1) 0 lambda_3959[0][0]
input_1419[0][0]
____________________________________________________________________________________________________
add_7218 (Add) (None, 1) 0 add_7205[0][0]
multiply_4735[0][0]
____________________________________________________________________________________________________
input_1420 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4742 (Multiply) (None, 1) 0 dense_3174[11][0]
input_1420[0][0]
____________________________________________________________________________________________________
lambda_3966 (Lambda) (None, 1) 0 multiply_4742[0][0]
____________________________________________________________________________________________________
input_1421 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4743 (Multiply) (None, 1) 0 lambda_3966[0][0]
input_1421[0][0]
____________________________________________________________________________________________________
add_7231 (Add) (None, 1) 0 add_7218[0][0]
multiply_4743[0][0]
____________________________________________________________________________________________________
input_1422 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4750 (Multiply) (None, 1) 0 dense_3174[12][0]
input_1422[0][0]
____________________________________________________________________________________________________
lambda_3973 (Lambda) (None, 1) 0 multiply_4750[0][0]
____________________________________________________________________________________________________
input_1423 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4751 (Multiply) (None, 1) 0 lambda_3973[0][0]
input_1423[0][0]
____________________________________________________________________________________________________
add_7244 (Add) (None, 1) 0 add_7231[0][0]
multiply_4751[0][0]
____________________________________________________________________________________________________
input_1424 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4758 (Multiply) (None, 1) 0 dense_3174[13][0]
input_1424[0][0]
____________________________________________________________________________________________________
lambda_3980 (Lambda) (None, 1) 0 multiply_4758[0][0]
____________________________________________________________________________________________________
input_1425 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4759 (Multiply) (None, 1) 0 lambda_3980[0][0]
input_1425[0][0]
____________________________________________________________________________________________________
add_7257 (Add) (None, 1) 0 add_7244[0][0]
multiply_4759[0][0]
____________________________________________________________________________________________________
input_1426 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4766 (Multiply) (None, 1) 0 dense_3174[14][0]
input_1426[0][0]
____________________________________________________________________________________________________
lambda_3987 (Lambda) (None, 1) 0 multiply_4766[0][0]
____________________________________________________________________________________________________
input_1427 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4767 (Multiply) (None, 1) 0 lambda_3987[0][0]
input_1427[0][0]
____________________________________________________________________________________________________
add_7270 (Add) (None, 1) 0 add_7257[0][0]
multiply_4767[0][0]
____________________________________________________________________________________________________
input_1428 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4774 (Multiply) (None, 1) 0 dense_3174[15][0]
input_1428[0][0]
____________________________________________________________________________________________________
lambda_3994 (Lambda) (None, 1) 0 multiply_4774[0][0]
____________________________________________________________________________________________________
input_1429 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4775 (Multiply) (None, 1) 0 lambda_3994[0][0]
input_1429[0][0]
____________________________________________________________________________________________________
add_7283 (Add) (None, 1) 0 add_7270[0][0]
multiply_4775[0][0]
____________________________________________________________________________________________________
input_1430 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
dense_3175 (Dense) (None, 1) 2 input_1391[0][0]
input_1391[0][0]
input_1391[0][0]
input_1391[0][0]
input_1391[0][0]
input_1391[0][0]
____________________________________________________________________________________________________
multiply_4782 (Multiply) (None, 1) 0 dense_3174[16][0]
input_1430[0][0]
____________________________________________________________________________________________________
lambda_3888 (Lambda) (None, 1) 0 input_1391[0][0]
dense_3174[0][0]
____________________________________________________________________________________________________
lambda_3890 (Lambda) (None, 1) 0 input_1391[0][0]
dense_3174[0][0]
____________________________________________________________________________________________________
lambda_3892 (Lambda) (None, 1) 0 input_1391[0][0]
dense_3174[0][0]
____________________________________________________________________________________________________
dense_3176 (Dense) (None, 1) 2 add_7088[0][0]
add_7088[0][0]
add_7088[0][0]
add_7088[0][0]
add_7088[0][0]
add_7088[0][0]
____________________________________________________________________________________________________
lambda_4001 (Lambda) (None, 1) 0 multiply_4782[0][0]
____________________________________________________________________________________________________
input_1431 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
add_7078 (Add) (None, 1) 0 dense_3175[1][0]
lambda_3888[0][0]
____________________________________________________________________________________________________
lambda_3895 (Lambda) (None, 1) 0 add_7088[0][0]
dense_3174[1][0]
____________________________________________________________________________________________________
add_7082 (Add) (None, 1) 0 dense_3175[3][0]
lambda_3890[0][0]
____________________________________________________________________________________________________
lambda_3897 (Lambda) (None, 1) 0 add_7088[0][0]
dense_3174[1][0]
____________________________________________________________________________________________________
add_7086 (Add) (None, 1) 0 dense_3175[5][0]
lambda_3892[0][0]
____________________________________________________________________________________________________
lambda_3899 (Lambda) (None, 1) 0 add_7088[0][0]
dense_3174[1][0]
____________________________________________________________________________________________________
dense_3177 (Dense) (None, 1) 2 add_7101[0][0]
add_7101[0][0]
add_7101[0][0]
add_7101[0][0]
add_7101[0][0]
add_7101[0][0]
____________________________________________________________________________________________________
multiply_4783 (Multiply) (None, 1) 0 lambda_4001[0][0]
input_1431[0][0]
____________________________________________________________________________________________________
input_1393 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4657 (Multiply) (None, 1) 0 multiply_4655[0][0]
add_7078[0][0]
____________________________________________________________________________________________________
add_7091 (Add) (None, 1) 0 dense_3176[1][0]
lambda_3895[0][0]
____________________________________________________________________________________________________
lambda_3902 (Lambda) (None, 1) 0 add_7101[0][0]
dense_3174[2][0]
____________________________________________________________________________________________________
input_1395 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4659 (Multiply) (None, 1) 0 multiply_4655[0][0]
add_7082[0][0]
____________________________________________________________________________________________________
add_7095 (Add) (None, 1) 0 dense_3176[3][0]
lambda_3897[0][0]
____________________________________________________________________________________________________
lambda_3904 (Lambda) (None, 1) 0 add_7101[0][0]
dense_3174[2][0]
____________________________________________________________________________________________________
input_1397 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4661 (Multiply) (None, 1) 0 multiply_4655[0][0]
add_7086[0][0]
____________________________________________________________________________________________________
add_7099 (Add) (None, 1) 0 dense_3176[5][0]
lambda_3899[0][0]
____________________________________________________________________________________________________
lambda_3906 (Lambda) (None, 1) 0 add_7101[0][0]
dense_3174[2][0]
____________________________________________________________________________________________________
dense_3178 (Dense) (None, 1) 2 add_7114[0][0]
add_7114[0][0]
add_7114[0][0]
add_7114[0][0]
add_7114[0][0]
add_7114[0][0]
____________________________________________________________________________________________________
add_7296 (Add) (None, 1) 0 add_7283[0][0]
multiply_4783[0][0]
____________________________________________________________________________________________________
add_7079 (Add) (None, 1) 0 input_1393[0][0]
multiply_4657[0][0]
____________________________________________________________________________________________________
multiply_4665 (Multiply) (None, 1) 0 multiply_4663[0][0]
add_7091[0][0]
____________________________________________________________________________________________________
add_7104 (Add) (None, 1) 0 dense_3177[1][0]
lambda_3902[0][0]
____________________________________________________________________________________________________
lambda_3909 (Lambda) (None, 1) 0 add_7114[0][0]
dense_3174[3][0]
____________________________________________________________________________________________________
add_7083 (Add) (None, 1) 0 input_1395[0][0]
multiply_4659[0][0]
____________________________________________________________________________________________________
multiply_4667 (Multiply) (None, 1) 0 multiply_4663[0][0]
add_7095[0][0]
____________________________________________________________________________________________________
add_7108 (Add) (None, 1) 0 dense_3177[3][0]
lambda_3904[0][0]
____________________________________________________________________________________________________
lambda_3911 (Lambda) (None, 1) 0 add_7114[0][0]
dense_3174[3][0]
____________________________________________________________________________________________________
add_7087 (Add) (None, 1) 0 input_1397[0][0]
multiply_4661[0][0]
____________________________________________________________________________________________________
multiply_4669 (Multiply) (None, 1) 0 multiply_4663[0][0]
add_7099[0][0]
____________________________________________________________________________________________________
add_7112 (Add) (None, 1) 0 dense_3177[5][0]
lambda_3906[0][0]
____________________________________________________________________________________________________
lambda_3913 (Lambda) (None, 1) 0 add_7114[0][0]
dense_3174[3][0]
____________________________________________________________________________________________________
dense_3179 (Dense) (None, 1) 2 add_7127[0][0]
add_7127[0][0]
add_7127[0][0]
add_7127[0][0]
add_7127[0][0]
add_7127[0][0]
____________________________________________________________________________________________________
add_7092 (Add) (None, 1) 0 add_7079[0][0]
multiply_4665[0][0]
____________________________________________________________________________________________________
multiply_4673 (Multiply) (None, 1) 0 multiply_4671[0][0]
add_7104[0][0]
____________________________________________________________________________________________________
add_7117 (Add) (None, 1) 0 dense_3178[1][0]
lambda_3909[0][0]
____________________________________________________________________________________________________
lambda_3916 (Lambda) (None, 1) 0 add_7127[0][0]
dense_3174[4][0]
____________________________________________________________________________________________________
add_7096 (Add) (None, 1) 0 add_7083[0][0]
multiply_4667[0][0]
____________________________________________________________________________________________________
multiply_4675 (Multiply) (None, 1) 0 multiply_4671[0][0]
add_7108[0][0]
____________________________________________________________________________________________________
add_7121 (Add) (None, 1) 0 dense_3178[3][0]
lambda_3911[0][0]
____________________________________________________________________________________________________
lambda_3918 (Lambda) (None, 1) 0 add_7127[0][0]
dense_3174[4][0]
____________________________________________________________________________________________________
add_7100 (Add) (None, 1) 0 add_7087[0][0]
multiply_4669[0][0]
____________________________________________________________________________________________________
multiply_4677 (Multiply) (None, 1) 0 multiply_4671[0][0]
add_7112[0][0]
____________________________________________________________________________________________________
add_7125 (Add) (None, 1) 0 dense_3178[5][0]
lambda_3913[0][0]
____________________________________________________________________________________________________
lambda_3920 (Lambda) (None, 1) 0 add_7127[0][0]
dense_3174[4][0]
____________________________________________________________________________________________________
dense_3180 (Dense) (None, 1) 2 add_7140[0][0]
add_7140[0][0]
add_7140[0][0]
add_7140[0][0]
add_7140[0][0]
add_7140[0][0]
____________________________________________________________________________________________________
input_1432 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
add_7105 (Add) (None, 1) 0 add_7092[0][0]
multiply_4673[0][0]
____________________________________________________________________________________________________
multiply_4681 (Multiply) (None, 1) 0 multiply_4679[0][0]
add_7117[0][0]
____________________________________________________________________________________________________
add_7130 (Add) (None, 1) 0 dense_3179[1][0]
lambda_3916[0][0]
____________________________________________________________________________________________________
lambda_3923 (Lambda) (None, 1) 0 add_7140[0][0]
dense_3174[5][0]
____________________________________________________________________________________________________
add_7109 (Add) (None, 1) 0 add_7096[0][0]
multiply_4675[0][0]
____________________________________________________________________________________________________
multiply_4683 (Multiply) (None, 1) 0 multiply_4679[0][0]
add_7121[0][0]
____________________________________________________________________________________________________
add_7134 (Add) (None, 1) 0 dense_3179[3][0]
lambda_3918[0][0]
____________________________________________________________________________________________________
lambda_3925 (Lambda) (None, 1) 0 add_7140[0][0]
dense_3174[5][0]
____________________________________________________________________________________________________
add_7113 (Add) (None, 1) 0 add_7100[0][0]
multiply_4677[0][0]
____________________________________________________________________________________________________
multiply_4685 (Multiply) (None, 1) 0 multiply_4679[0][0]
add_7125[0][0]
____________________________________________________________________________________________________
add_7138 (Add) (None, 1) 0 dense_3179[5][0]
lambda_3920[0][0]
____________________________________________________________________________________________________
lambda_3927 (Lambda) (None, 1) 0 add_7140[0][0]
dense_3174[5][0]
____________________________________________________________________________________________________
dense_3181 (Dense) (None, 1) 2 add_7153[0][0]
add_7153[0][0]
add_7153[0][0]
add_7153[0][0]
add_7153[0][0]
add_7153[0][0]
____________________________________________________________________________________________________
multiply_4790 (Multiply) (None, 1) 0 dense_3174[17][0]
input_1432[0][0]
____________________________________________________________________________________________________
add_7118 (Add) (None, 1) 0 add_7105[0][0]
multiply_4681[0][0]
____________________________________________________________________________________________________
multiply_4689 (Multiply) (None, 1) 0 multiply_4687[0][0]
add_7130[0][0]
____________________________________________________________________________________________________
add_7143 (Add) (None, 1) 0 dense_3180[1][0]
lambda_3923[0][0]
____________________________________________________________________________________________________
lambda_3930 (Lambda) (None, 1) 0 add_7153[0][0]
dense_3174[6][0]
____________________________________________________________________________________________________
add_7122 (Add) (None, 1) 0 add_7109[0][0]
multiply_4683[0][0]
____________________________________________________________________________________________________
multiply_4691 (Multiply) (None, 1) 0 multiply_4687[0][0]
add_7134[0][0]
____________________________________________________________________________________________________
add_7147 (Add) (None, 1) 0 dense_3180[3][0]
lambda_3925[0][0]
____________________________________________________________________________________________________
lambda_3932 (Lambda) (None, 1) 0 add_7153[0][0]
dense_3174[6][0]
____________________________________________________________________________________________________
add_7126 (Add) (None, 1) 0 add_7113[0][0]
multiply_4685[0][0]
____________________________________________________________________________________________________
multiply_4693 (Multiply) (None, 1) 0 multiply_4687[0][0]
add_7138[0][0]
____________________________________________________________________________________________________
add_7151 (Add) (None, 1) 0 dense_3180[5][0]
lambda_3927[0][0]
____________________________________________________________________________________________________
lambda_3934 (Lambda) (None, 1) 0 add_7153[0][0]
dense_3174[6][0]
____________________________________________________________________________________________________
dense_3182 (Dense) (None, 1) 2 add_7166[0][0]
add_7166[0][0]
add_7166[0][0]
add_7166[0][0]
add_7166[0][0]
add_7166[0][0]
____________________________________________________________________________________________________
lambda_4008 (Lambda) (None, 1) 0 multiply_4790[0][0]
____________________________________________________________________________________________________
input_1433 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
add_7131 (Add) (None, 1) 0 add_7118[0][0]
multiply_4689[0][0]
____________________________________________________________________________________________________
multiply_4697 (Multiply) (None, 1) 0 multiply_4695[0][0]
add_7143[0][0]
____________________________________________________________________________________________________
add_7156 (Add) (None, 1) 0 dense_3181[1][0]
lambda_3930[0][0]
____________________________________________________________________________________________________
lambda_3937 (Lambda) (None, 1) 0 add_7166[0][0]
dense_3174[7][0]
____________________________________________________________________________________________________
add_7135 (Add) (None, 1) 0 add_7122[0][0]
multiply_4691[0][0]
____________________________________________________________________________________________________
multiply_4699 (Multiply) (None, 1) 0 multiply_4695[0][0]
add_7147[0][0]
____________________________________________________________________________________________________
add_7160 (Add) (None, 1) 0 dense_3181[3][0]
lambda_3932[0][0]
____________________________________________________________________________________________________
lambda_3939 (Lambda) (None, 1) 0 add_7166[0][0]
dense_3174[7][0]
____________________________________________________________________________________________________
add_7139 (Add) (None, 1) 0 add_7126[0][0]
multiply_4693[0][0]
____________________________________________________________________________________________________
multiply_4701 (Multiply) (None, 1) 0 multiply_4695[0][0]
add_7151[0][0]
____________________________________________________________________________________________________
add_7164 (Add) (None, 1) 0 dense_3181[5][0]
lambda_3934[0][0]
____________________________________________________________________________________________________
lambda_3941 (Lambda) (None, 1) 0 add_7166[0][0]
dense_3174[7][0]
____________________________________________________________________________________________________
dense_3183 (Dense) (None, 1) 2 add_7179[0][0]
add_7179[0][0]
add_7179[0][0]
add_7179[0][0]
add_7179[0][0]
add_7179[0][0]
____________________________________________________________________________________________________
multiply_4791 (Multiply) (None, 1) 0 lambda_4008[0][0]
input_1433[0][0]
____________________________________________________________________________________________________
add_7144 (Add) (None, 1) 0 add_7131[0][0]
multiply_4697[0][0]
____________________________________________________________________________________________________
multiply_4705 (Multiply) (None, 1) 0 multiply_4703[0][0]
add_7156[0][0]
____________________________________________________________________________________________________
add_7169 (Add) (None, 1) 0 dense_3182[1][0]
lambda_3937[0][0]
____________________________________________________________________________________________________
lambda_3944 (Lambda) (None, 1) 0 add_7179[0][0]
dense_3174[8][0]
____________________________________________________________________________________________________
add_7148 (Add) (None, 1) 0 add_7135[0][0]
multiply_4699[0][0]
____________________________________________________________________________________________________
multiply_4707 (Multiply) (None, 1) 0 multiply_4703[0][0]
add_7160[0][0]
____________________________________________________________________________________________________
add_7173 (Add) (None, 1) 0 dense_3182[3][0]
lambda_3939[0][0]
____________________________________________________________________________________________________
lambda_3946 (Lambda) (None, 1) 0 add_7179[0][0]
dense_3174[8][0]
____________________________________________________________________________________________________
add_7152 (Add) (None, 1) 0 add_7139[0][0]
multiply_4701[0][0]
____________________________________________________________________________________________________
multiply_4709 (Multiply) (None, 1) 0 multiply_4703[0][0]
add_7164[0][0]
____________________________________________________________________________________________________
add_7177 (Add) (None, 1) 0 dense_3182[5][0]
lambda_3941[0][0]
____________________________________________________________________________________________________
lambda_3948 (Lambda) (None, 1) 0 add_7179[0][0]
dense_3174[8][0]
____________________________________________________________________________________________________
dense_3184 (Dense) (None, 1) 2 add_7192[0][0]
add_7192[0][0]
add_7192[0][0]
add_7192[0][0]
add_7192[0][0]
add_7192[0][0]
____________________________________________________________________________________________________
add_7309 (Add) (None, 1) 0 add_7296[0][0]
multiply_4791[0][0]
____________________________________________________________________________________________________
add_7157 (Add) (None, 1) 0 add_7144[0][0]
multiply_4705[0][0]
____________________________________________________________________________________________________
multiply_4713 (Multiply) (None, 1) 0 multiply_4711[0][0]
add_7169[0][0]
____________________________________________________________________________________________________
add_7182 (Add) (None, 1) 0 dense_3183[1][0]
lambda_3944[0][0]
____________________________________________________________________________________________________
lambda_3952 (Lambda) (None, 1) 0 add_7192[0][0]
dense_3174[9][0]
____________________________________________________________________________________________________
add_7161 (Add) (None, 1) 0 add_7148[0][0]
multiply_4707[0][0]
____________________________________________________________________________________________________
multiply_4715 (Multiply) (None, 1) 0 multiply_4711[0][0]
add_7173[0][0]
____________________________________________________________________________________________________
add_7186 (Add) (None, 1) 0 dense_3183[3][0]
lambda_3946[0][0]
____________________________________________________________________________________________________
lambda_3955 (Lambda) (None, 1) 0 add_7192[0][0]
dense_3174[9][0]
____________________________________________________________________________________________________
add_7165 (Add) (None, 1) 0 add_7152[0][0]
multiply_4709[0][0]
____________________________________________________________________________________________________
multiply_4717 (Multiply) (None, 1) 0 multiply_4711[0][0]
add_7177[0][0]
____________________________________________________________________________________________________
add_7190 (Add) (None, 1) 0 dense_3183[5][0]
lambda_3948[0][0]
____________________________________________________________________________________________________
lambda_3958 (Lambda) (None, 1) 0 add_7192[0][0]
dense_3174[9][0]
____________________________________________________________________________________________________
lambda_3887 (Lambda) (None, 1) 0 input_1391[0][0]
dense_3174[0][0]
____________________________________________________________________________________________________
add_7170 (Add) (None, 1) 0 add_7157[0][0]
multiply_4713[0][0]
____________________________________________________________________________________________________
multiply_4721 (Multiply) (None, 1) 0 multiply_4719[0][0]
add_7182[0][0]
____________________________________________________________________________________________________
add_7195 (Add) (None, 1) 0 dense_3184[1][0]
lambda_3952[0][0]
____________________________________________________________________________________________________
dense_3185 (Dense) (None, 1) 2 add_7205[0][0]
add_7205[0][0]
add_7205[0][0]
____________________________________________________________________________________________________
lambda_3961 (Lambda) (None, 1) 0 add_7205[0][0]
dense_3174[10][0]
____________________________________________________________________________________________________
lambda_3889 (Lambda) (None, 1) 0 input_1391[0][0]
dense_3174[0][0]
____________________________________________________________________________________________________
add_7174 (Add) (None, 1) 0 add_7161[0][0]
multiply_4715[0][0]
____________________________________________________________________________________________________
multiply_4723 (Multiply) (None, 1) 0 multiply_4719[0][0]
add_7186[0][0]
____________________________________________________________________________________________________
add_7199 (Add) (None, 1) 0 dense_3184[3][0]
lambda_3955[0][0]
____________________________________________________________________________________________________
lambda_3963 (Lambda) (None, 1) 0 add_7205[0][0]
dense_3174[10][0]
____________________________________________________________________________________________________
lambda_3891 (Lambda) (None, 1) 0 input_1391[0][0]
dense_3174[0][0]
____________________________________________________________________________________________________
add_7178 (Add) (None, 1) 0 add_7165[0][0]
multiply_4717[0][0]
____________________________________________________________________________________________________
multiply_4725 (Multiply) (None, 1) 0 multiply_4719[0][0]
add_7190[0][0]
____________________________________________________________________________________________________
add_7203 (Add) (None, 1) 0 dense_3184[5][0]
lambda_3958[0][0]
____________________________________________________________________________________________________
lambda_3965 (Lambda) (None, 1) 0 add_7205[0][0]
dense_3174[10][0]
____________________________________________________________________________________________________
add_7076 (Add) (None, 1) 0 dense_3175[0][0]
lambda_3887[0][0]
____________________________________________________________________________________________________
lambda_3894 (Lambda) (None, 1) 0 add_7088[0][0]
dense_3174[1][0]
____________________________________________________________________________________________________
input_1434 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
add_7183 (Add) (None, 1) 0 add_7170[0][0]
multiply_4721[0][0]
____________________________________________________________________________________________________
multiply_4729 (Multiply) (None, 1) 0 multiply_4727[0][0]
add_7195[0][0]
____________________________________________________________________________________________________
add_7208 (Add) (None, 1) 0 dense_3185[1][0]
lambda_3961[0][0]
____________________________________________________________________________________________________
dense_3186 (Dense) (None, 1) 2 add_7218[0][0]
add_7218[0][0]
add_7218[0][0]
____________________________________________________________________________________________________
lambda_3968 (Lambda) (None, 1) 0 add_7218[0][0]
dense_3174[11][0]
____________________________________________________________________________________________________
add_7080 (Add) (None, 1) 0 dense_3175[2][0]
lambda_3889[0][0]
____________________________________________________________________________________________________
lambda_3896 (Lambda) (None, 1) 0 add_7088[0][0]
dense_3174[1][0]
____________________________________________________________________________________________________
add_7187 (Add) (None, 1) 0 add_7174[0][0]
multiply_4723[0][0]
____________________________________________________________________________________________________
multiply_4731 (Multiply) (None, 1) 0 multiply_4727[0][0]
add_7199[0][0]
____________________________________________________________________________________________________
add_7212 (Add) (None, 1) 0 dense_3185[3][0]
lambda_3963[0][0]
____________________________________________________________________________________________________
lambda_3970 (Lambda) (None, 1) 0 add_7218[0][0]
dense_3174[11][0]
____________________________________________________________________________________________________
add_7084 (Add) (None, 1) 0 dense_3175[4][0]
lambda_3891[0][0]
____________________________________________________________________________________________________
lambda_3898 (Lambda) (None, 1) 0 add_7088[0][0]
dense_3174[1][0]
____________________________________________________________________________________________________
add_7191 (Add) (None, 1) 0 add_7178[0][0]
multiply_4725[0][0]
____________________________________________________________________________________________________
multiply_4733 (Multiply) (None, 1) 0 multiply_4727[0][0]
add_7203[0][0]
____________________________________________________________________________________________________
add_7216 (Add) (None, 1) 0 dense_3185[5][0]
lambda_3965[0][0]
____________________________________________________________________________________________________
lambda_3972 (Lambda) (None, 1) 0 add_7218[0][0]
dense_3174[11][0]
____________________________________________________________________________________________________
input_1392 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4656 (Multiply) (None, 1) 0 multiply_4655[0][0]
add_7076[0][0]
____________________________________________________________________________________________________
add_7089 (Add) (None, 1) 0 dense_3176[0][0]
lambda_3894[0][0]
____________________________________________________________________________________________________
lambda_3901 (Lambda) (None, 1) 0 add_7101[0][0]
dense_3174[2][0]
____________________________________________________________________________________________________
multiply_4798 (Multiply) (None, 1) 0 dense_3174[18][0]
input_1434[0][0]
____________________________________________________________________________________________________
add_7196 (Add) (None, 1) 0 add_7183[0][0]
multiply_4729[0][0]
____________________________________________________________________________________________________
multiply_4737 (Multiply) (None, 1) 0 multiply_4735[0][0]
add_7208[0][0]
____________________________________________________________________________________________________
add_7221 (Add) (None, 1) 0 dense_3186[1][0]
lambda_3968[0][0]
____________________________________________________________________________________________________
dense_3187 (Dense) (None, 1) 2 add_7231[0][0]
add_7231[0][0]
add_7231[0][0]
____________________________________________________________________________________________________
lambda_3975 (Lambda) (None, 1) 0 add_7231[0][0]
dense_3174[12][0]
____________________________________________________________________________________________________
input_1394 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4658 (Multiply) (None, 1) 0 multiply_4655[0][0]
add_7080[0][0]
____________________________________________________________________________________________________
add_7093 (Add) (None, 1) 0 dense_3176[2][0]
lambda_3896[0][0]
____________________________________________________________________________________________________
lambda_3903 (Lambda) (None, 1) 0 add_7101[0][0]
dense_3174[2][0]
____________________________________________________________________________________________________
add_7200 (Add) (None, 1) 0 add_7187[0][0]
multiply_4731[0][0]
____________________________________________________________________________________________________
multiply_4739 (Multiply) (None, 1) 0 multiply_4735[0][0]
add_7212[0][0]
____________________________________________________________________________________________________
add_7225 (Add) (None, 1) 0 dense_3186[3][0]
lambda_3970[0][0]
____________________________________________________________________________________________________
lambda_3977 (Lambda) (None, 1) 0 add_7231[0][0]
dense_3174[12][0]
____________________________________________________________________________________________________
input_1396 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
multiply_4660 (Multiply) (None, 1) 0 multiply_4655[0][0]
add_7084[0][0]
____________________________________________________________________________________________________
add_7097 (Add) (None, 1) 0 dense_3176[4][0]
lambda_3898[0][0]
____________________________________________________________________________________________________
lambda_3905 (Lambda) (None, 1) 0 add_7101[0][0]
dense_3174[2][0]
____________________________________________________________________________________________________
add_7204 (Add) (None, 1) 0 add_7191[0][0]
multiply_4733[0][0]
____________________________________________________________________________________________________
multiply_4741 (Multiply) (None, 1) 0 multiply_4735[0][0]
add_7216[0][0]
____________________________________________________________________________________________________
add_7229 (Add) (None, 1) 0 dense_3186[5][0]
lambda_3972[0][0]
____________________________________________________________________________________________________
lambda_3979 (Lambda) (None, 1) 0 add_7231[0][0]
dense_3174[12][0]
____________________________________________________________________________________________________
add_7077 (Add) (None, 1) 0 input_1392[0][0]
multiply_4656[0][0]
____________________________________________________________________________________________________
multiply_4664 (Multiply) (None, 1) 0 multiply_4663[0][0]
add_7089[0][0]
____________________________________________________________________________________________________
add_7102 (Add) (None, 1) 0 dense_3177[0][0]
lambda_3901[0][0]
____________________________________________________________________________________________________
lambda_3908 (Lambda) (None, 1) 0 add_7114[0][0]
dense_3174[3][0]
____________________________________________________________________________________________________
lambda_4015 (Lambda) (None, 1) 0 multiply_4798[0][0]
____________________________________________________________________________________________________
input_1435 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
add_7209 (Add) (None, 1) 0 add_7196[0][0]
multiply_4737[0][0]
____________________________________________________________________________________________________
multiply_4745 (Multiply) (None, 1) 0 multiply_4743[0][0]
add_7221[0][0]
____________________________________________________________________________________________________
add_7234 (Add) (None, 1) 0 dense_3187[1][0]
lambda_3975[0][0]
____________________________________________________________________________________________________
dense_3188 (Dense) (None, 1) 2 add_7244[0][0]
add_7244[0][0]
add_7244[0][0]
____________________________________________________________________________________________________
lambda_3982 (Lambda) (None, 1) 0 add_7244[0][0]
dense_3174[13][0]
____________________________________________________________________________________________________
add_7081 (Add) (None, 1) 0 input_1394[0][0]
multiply_4658[0][0]
____________________________________________________________________________________________________
multiply_4666 (Multiply) (None, 1) 0 multiply_4663[0][0]
add_7093[0][0]
____________________________________________________________________________________________________
add_7106 (Add) (None, 1) 0 dense_3177[2][0]
lambda_3903[0][0]
____________________________________________________________________________________________________
lambda_3910 (Lambda) (None, 1) 0 add_7114[0][0]
dense_3174[3][0]
____________________________________________________________________________________________________
add_7213 (Add) (None, 1) 0 add_7200[0][0]
multiply_4739[0][0]
____________________________________________________________________________________________________
multiply_4747 (Multiply) (None, 1) 0 multiply_4743[0][0]
add_7225[0][0]
____________________________________________________________________________________________________
add_7238 (Add) (None, 1) 0 dense_3187[3][0]
lambda_3977[0][0]
____________________________________________________________________________________________________
lambda_3984 (Lambda) (None, 1) 0 add_7244[0][0]
dense_3174[13][0]
____________________________________________________________________________________________________
add_7085 (Add) (None, 1) 0 input_1396[0][0]
multiply_4660[0][0]
____________________________________________________________________________________________________
multiply_4668 (Multiply) (None, 1) 0 multiply_4663[0][0]
add_7097[0][0]
____________________________________________________________________________________________________
add_7110 (Add) (None, 1) 0 dense_3177[4][0]
lambda_3905[0][0]
____________________________________________________________________________________________________
lambda_3912 (Lambda) (None, 1) 0 add_7114[0][0]
dense_3174[3][0]
____________________________________________________________________________________________________
add_7217 (Add) (None, 1) 0 add_7204[0][0]
multiply_4741[0][0]
____________________________________________________________________________________________________
multiply_4749 (Multiply) (None, 1) 0 multiply_4743[0][0]
add_7229[0][0]
____________________________________________________________________________________________________
add_7242 (Add) (None, 1) 0 dense_3187[5][0]
lambda_3979[0][0]
____________________________________________________________________________________________________
lambda_3986 (Lambda) (None, 1) 0 add_7244[0][0]
dense_3174[13][0]
____________________________________________________________________________________________________
add_7090 (Add) (None, 1) 0 add_7077[0][0]
multiply_4664[0][0]
____________________________________________________________________________________________________
multiply_4672 (Multiply) (None, 1) 0 multiply_4671[0][0]
add_7102[0][0]
____________________________________________________________________________________________________
add_7115 (Add) (None, 1) 0 dense_3178[0][0]
lambda_3908[0][0]
____________________________________________________________________________________________________
lambda_3915 (Lambda) (None, 1) 0 add_7127[0][0]
dense_3174[4][0]
____________________________________________________________________________________________________
multiply_4799 (Multiply) (None, 1) 0 lambda_4015[0][0]
input_1435[0][0]
____________________________________________________________________________________________________
add_7222 (Add) (None, 1) 0 add_7209[0][0]
multiply_4745[0][0]
____________________________________________________________________________________________________
multiply_4753 (Multiply) (None, 1) 0 multiply_4751[0][0]
add_7234[0][0]
____________________________________________________________________________________________________
add_7247 (Add) (None, 1) 0 dense_3188[1][0]
lambda_3982[0][0]
____________________________________________________________________________________________________
dense_3189 (Dense) (None, 1) 2 add_7257[0][0]
add_7257[0][0]
add_7257[0][0]
____________________________________________________________________________________________________
lambda_3989 (Lambda) (None, 1) 0 add_7257[0][0]
dense_3174[14][0]
____________________________________________________________________________________________________
add_7094 (Add) (None, 1) 0 add_7081[0][0]
multiply_4666[0][0]
____________________________________________________________________________________________________
multiply_4674 (Multiply) (None, 1) 0 multiply_4671[0][0]
add_7106[0][0]
____________________________________________________________________________________________________
add_7119 (Add) (None, 1) 0 dense_3178[2][0]
lambda_3910[0][0]
____________________________________________________________________________________________________
lambda_3917 (Lambda) (None, 1) 0 add_7127[0][0]
dense_3174[4][0]
____________________________________________________________________________________________________
add_7226 (Add) (None, 1) 0 add_7213[0][0]
multiply_4747[0][0]
____________________________________________________________________________________________________
multiply_4755 (Multiply) (None, 1) 0 multiply_4751[0][0]
add_7238[0][0]
____________________________________________________________________________________________________
add_7251 (Add) (None, 1) 0 dense_3188[3][0]
lambda_3984[0][0]
____________________________________________________________________________________________________
lambda_3991 (Lambda) (None, 1) 0 add_7257[0][0]
dense_3174[14][0]
____________________________________________________________________________________________________
add_7098 (Add) (None, 1) 0 add_7085[0][0]
multiply_4668[0][0]
____________________________________________________________________________________________________
multiply_4676 (Multiply) (None, 1) 0 multiply_4671[0][0]
add_7110[0][0]
____________________________________________________________________________________________________
add_7123 (Add) (None, 1) 0 dense_3178[4][0]
lambda_3912[0][0]
____________________________________________________________________________________________________
lambda_3919 (Lambda) (None, 1) 0 add_7127[0][0]
dense_3174[4][0]
____________________________________________________________________________________________________
add_7230 (Add) (None, 1) 0 add_7217[0][0]
multiply_4749[0][0]
____________________________________________________________________________________________________
multiply_4757 (Multiply) (None, 1) 0 multiply_4751[0][0]
add_7242[0][0]
____________________________________________________________________________________________________
add_7255 (Add) (None, 1) 0 dense_3188[5][0]
lambda_3986[0][0]
____________________________________________________________________________________________________
lambda_3993 (Lambda) (None, 1) 0 add_7257[0][0]
dense_3174[14][0]
____________________________________________________________________________________________________
add_7103 (Add) (None, 1) 0 add_7090[0][0]
multiply_4672[0][0]
____________________________________________________________________________________________________
multiply_4680 (Multiply) (None, 1) 0 multiply_4679[0][0]
add_7115[0][0]
____________________________________________________________________________________________________
add_7128 (Add) (None, 1) 0 dense_3179[0][0]
lambda_3915[0][0]
____________________________________________________________________________________________________
lambda_3922 (Lambda) (None, 1) 0 add_7140[0][0]
dense_3174[5][0]
____________________________________________________________________________________________________
add_7322 (Add) (None, 1) 0 add_7309[0][0]
multiply_4799[0][0]
____________________________________________________________________________________________________
add_7235 (Add) (None, 1) 0 add_7222[0][0]
multiply_4753[0][0]
____________________________________________________________________________________________________
multiply_4761 (Multiply) (None, 1) 0 multiply_4759[0][0]
add_7247[0][0]
____________________________________________________________________________________________________
add_7260 (Add) (None, 1) 0 dense_3189[1][0]
lambda_3989[0][0]
____________________________________________________________________________________________________
dense_3190 (Dense) (None, 1) 2 add_7270[0][0]
add_7270[0][0]
add_7270[0][0]
____________________________________________________________________________________________________
lambda_3996 (Lambda) (None, 1) 0 add_7270[0][0]
dense_3174[15][0]
____________________________________________________________________________________________________
add_7107 (Add) (None, 1) 0 add_7094[0][0]
multiply_4674[0][0]
____________________________________________________________________________________________________
multiply_4682 (Multiply) (None, 1) 0 multiply_4679[0][0]
add_7119[0][0]
____________________________________________________________________________________________________
add_7132 (Add) (None, 1) 0 dense_3179[2][0]
lambda_3917[0][0]
____________________________________________________________________________________________________
lambda_3924 (Lambda) (None, 1) 0 add_7140[0][0]
dense_3174[5][0]
____________________________________________________________________________________________________
add_7239 (Add) (None, 1) 0 add_7226[0][0]
multiply_4755[0][0]
____________________________________________________________________________________________________
multiply_4763 (Multiply) (None, 1) 0 multiply_4759[0][0]
add_7251[0][0]
____________________________________________________________________________________________________
add_7264 (Add) (None, 1) 0 dense_3189[3][0]
lambda_3991[0][0]
____________________________________________________________________________________________________
lambda_3998 (Lambda) (None, 1) 0 add_7270[0][0]
dense_3174[15][0]
____________________________________________________________________________________________________
add_7111 (Add) (None, 1) 0 add_7098[0][0]
multiply_4676[0][0]
____________________________________________________________________________________________________
multiply_4684 (Multiply) (None, 1) 0 multiply_4679[0][0]
add_7123[0][0]
____________________________________________________________________________________________________
add_7136 (Add) (None, 1) 0 dense_3179[4][0]
lambda_3919[0][0]
____________________________________________________________________________________________________
lambda_3926 (Lambda) (None, 1) 0 add_7140[0][0]
dense_3174[5][0]
____________________________________________________________________________________________________
add_7243 (Add) (None, 1) 0 add_7230[0][0]
multiply_4757[0][0]
____________________________________________________________________________________________________
multiply_4765 (Multiply) (None, 1) 0 multiply_4759[0][0]
add_7255[0][0]
____________________________________________________________________________________________________
add_7268 (Add) (None, 1) 0 dense_3189[5][0]
lambda_3993[0][0]
____________________________________________________________________________________________________
lambda_4000 (Lambda) (None, 1) 0 add_7270[0][0]
dense_3174[15][0]
____________________________________________________________________________________________________
add_7116 (Add) (None, 1) 0 add_7103[0][0]
multiply_4680[0][0]
____________________________________________________________________________________________________
multiply_4688 (Multiply) (None, 1) 0 multiply_4687[0][0]
add_7128[0][0]
____________________________________________________________________________________________________
add_7141 (Add) (None, 1) 0 dense_3180[0][0]
lambda_3922[0][0]
____________________________________________________________________________________________________
lambda_3929 (Lambda) (None, 1) 0 add_7153[0][0]
dense_3174[6][0]
____________________________________________________________________________________________________
add_7248 (Add) (None, 1) 0 add_7235[0][0]
multiply_4761[0][0]
____________________________________________________________________________________________________
multiply_4769 (Multiply) (None, 1) 0 multiply_4767[0][0]
add_7260[0][0]
____________________________________________________________________________________________________
add_7273 (Add) (None, 1) 0 dense_3190[1][0]
lambda_3996[0][0]
____________________________________________________________________________________________________
dense_3191 (Dense) (None, 1) 2 add_7283[0][0]
add_7283[0][0]
add_7283[0][0]
____________________________________________________________________________________________________
lambda_4003 (Lambda) (None, 1) 0 add_7283[0][0]
dense_3174[16][0]
____________________________________________________________________________________________________
add_7120 (Add) (None, 1) 0 add_7107[0][0]
multiply_4682[0][0]
____________________________________________________________________________________________________
multiply_4690 (Multiply) (None, 1) 0 multiply_4687[0][0]
add_7132[0][0]
____________________________________________________________________________________________________
add_7145 (Add) (None, 1) 0 dense_3180[2][0]
lambda_3924[0][0]
____________________________________________________________________________________________________
lambda_3931 (Lambda) (None, 1) 0 add_7153[0][0]
dense_3174[6][0]
____________________________________________________________________________________________________
add_7252 (Add) (None, 1) 0 add_7239[0][0]
multiply_4763[0][0]
____________________________________________________________________________________________________
multiply_4771 (Multiply) (None, 1) 0 multiply_4767[0][0]
add_7264[0][0]
____________________________________________________________________________________________________
add_7277 (Add) (None, 1) 0 dense_3190[3][0]
lambda_3998[0][0]
____________________________________________________________________________________________________
lambda_4005 (Lambda) (None, 1) 0 add_7283[0][0]
dense_3174[16][0]
____________________________________________________________________________________________________
add_7124 (Add) (None, 1) 0 add_7111[0][0]
multiply_4684[0][0]
____________________________________________________________________________________________________
multiply_4692 (Multiply) (None, 1) 0 multiply_4687[0][0]
add_7136[0][0]
____________________________________________________________________________________________________
add_7149 (Add) (None, 1) 0 dense_3180[4][0]
lambda_3926[0][0]
____________________________________________________________________________________________________
lambda_3933 (Lambda) (None, 1) 0 add_7153[0][0]
dense_3174[6][0]
____________________________________________________________________________________________________
add_7256 (Add) (None, 1) 0 add_7243[0][0]
multiply_4765[0][0]
____________________________________________________________________________________________________
multiply_4773 (Multiply) (None, 1) 0 multiply_4767[0][0]
add_7268[0][0]
____________________________________________________________________________________________________
add_7281 (Add) (None, 1) 0 dense_3190[5][0]
lambda_4000[0][0]
____________________________________________________________________________________________________
lambda_4007 (Lambda) (None, 1) 0 add_7283[0][0]
dense_3174[16][0]
____________________________________________________________________________________________________
add_7129 (Add) (None, 1) 0 add_7116[0][0]
multiply_4688[0][0]
____________________________________________________________________________________________________
multiply_4696 (Multiply) (None, 1) 0 multiply_4695[0][0]
add_7141[0][0]
____________________________________________________________________________________________________
add_7154 (Add) (None, 1) 0 dense_3181[0][0]
lambda_3929[0][0]
____________________________________________________________________________________________________
lambda_3936 (Lambda) (None, 1) 0 add_7166[0][0]
dense_3174[7][0]
____________________________________________________________________________________________________
add_7261 (Add) (None, 1) 0 add_7248[0][0]
multiply_4769[0][0]
____________________________________________________________________________________________________
multiply_4777 (Multiply) (None, 1) 0 multiply_4775[0][0]
add_7273[0][0]
____________________________________________________________________________________________________
add_7286 (Add) (None, 1) 0 dense_3191[1][0]
lambda_4003[0][0]
____________________________________________________________________________________________________
dense_3192 (Dense) (None, 1) 2 add_7296[0][0]
add_7296[0][0]
add_7296[0][0]
____________________________________________________________________________________________________
lambda_4010 (Lambda) (None, 1) 0 add_7296[0][0]
dense_3174[17][0]
____________________________________________________________________________________________________
input_1436 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
add_7133 (Add) (None, 1) 0 add_7120[0][0]
multiply_4690[0][0]
____________________________________________________________________________________________________
multiply_4698 (Multiply) (None, 1) 0 multiply_4695[0][0]
add_7145[0][0]
____________________________________________________________________________________________________
add_7158 (Add) (None, 1) 0 dense_3181[2][0]
lambda_3931[0][0]
____________________________________________________________________________________________________
lambda_3938 (Lambda) (None, 1) 0 add_7166[0][0]
dense_3174[7][0]
____________________________________________________________________________________________________
add_7265 (Add) (None, 1) 0 add_7252[0][0]
multiply_4771[0][0]
____________________________________________________________________________________________________
multiply_4779 (Multiply) (None, 1) 0 multiply_4775[0][0]
add_7277[0][0]
____________________________________________________________________________________________________
add_7290 (Add) (None, 1) 0 dense_3191[3][0]
lambda_4005[0][0]
____________________________________________________________________________________________________
lambda_4012 (Lambda) (None, 1) 0 add_7296[0][0]
dense_3174[17][0]
____________________________________________________________________________________________________
add_7137 (Add) (None, 1) 0 add_7124[0][0]
multiply_4692[0][0]
____________________________________________________________________________________________________
multiply_4700 (Multiply) (None, 1) 0 multiply_4695[0][0]
add_7149[0][0]
____________________________________________________________________________________________________
add_7162 (Add) (None, 1) 0 dense_3181[4][0]
lambda_3933[0][0]
____________________________________________________________________________________________________
lambda_3940 (Lambda) (None, 1) 0 add_7166[0][0]
dense_3174[7][0]
____________________________________________________________________________________________________
add_7269 (Add) (None, 1) 0 add_7256[0][0]
multiply_4773[0][0]
____________________________________________________________________________________________________
multiply_4781 (Multiply) (None, 1) 0 multiply_4775[0][0]
add_7281[0][0]
____________________________________________________________________________________________________
add_7294 (Add) (None, 1) 0 dense_3191[5][0]
lambda_4007[0][0]
____________________________________________________________________________________________________
lambda_4014 (Lambda) (None, 1) 0 add_7296[0][0]
dense_3174[17][0]
____________________________________________________________________________________________________
add_7142 (Add) (None, 1) 0 add_7129[0][0]
multiply_4696[0][0]
____________________________________________________________________________________________________
multiply_4704 (Multiply) (None, 1) 0 multiply_4703[0][0]
add_7154[0][0]
____________________________________________________________________________________________________
add_7167 (Add) (None, 1) 0 dense_3182[0][0]
lambda_3936[0][0]
____________________________________________________________________________________________________
lambda_3943 (Lambda) (None, 1) 0 add_7179[0][0]
dense_3174[8][0]
____________________________________________________________________________________________________
add_7274 (Add) (None, 1) 0 add_7261[0][0]
multiply_4777[0][0]
____________________________________________________________________________________________________
multiply_4785 (Multiply) (None, 1) 0 multiply_4783[0][0]
add_7286[0][0]
____________________________________________________________________________________________________
add_7299 (Add) (None, 1) 0 dense_3192[1][0]
lambda_4010[0][0]
____________________________________________________________________________________________________
dense_3193 (Dense) (None, 1) 2 add_7309[0][0]
add_7309[0][0]
add_7309[0][0]
____________________________________________________________________________________________________
lambda_4017 (Lambda) (None, 1) 0 add_7309[0][0]
dense_3174[18][0]
____________________________________________________________________________________________________
multiply_4806 (Multiply) (None, 1) 0 dense_3174[19][0]
input_1436[0][0]
____________________________________________________________________________________________________
add_7146 (Add) (None, 1) 0 add_7133[0][0]
multiply_4698[0][0]
____________________________________________________________________________________________________
multiply_4706 (Multiply) (None, 1) 0 multiply_4703[0][0]
add_7158[0][0]
____________________________________________________________________________________________________
add_7171 (Add) (None, 1) 0 dense_3182[2][0]
lambda_3938[0][0]
____________________________________________________________________________________________________
lambda_3945 (Lambda) (None, 1) 0 add_7179[0][0]
dense_3174[8][0]
____________________________________________________________________________________________________
add_7278 (Add) (None, 1) 0 add_7265[0][0]
multiply_4779[0][0]
____________________________________________________________________________________________________
multiply_4787 (Multiply) (None, 1) 0 multiply_4783[0][0]
add_7290[0][0]
____________________________________________________________________________________________________
add_7303 (Add) (None, 1) 0 dense_3192[3][0]
lambda_4012[0][0]
____________________________________________________________________________________________________
lambda_4019 (Lambda) (None, 1) 0 add_7309[0][0]
dense_3174[18][0]
____________________________________________________________________________________________________
add_7150 (Add) (None, 1) 0 add_7137[0][0]
multiply_4700[0][0]
____________________________________________________________________________________________________
multiply_4708 (Multiply) (None, 1) 0 multiply_4703[0][0]
add_7162[0][0]
____________________________________________________________________________________________________
add_7175 (Add) (None, 1) 0 dense_3182[4][0]
lambda_3940[0][0]
____________________________________________________________________________________________________
lambda_3947 (Lambda) (None, 1) 0 add_7179[0][0]
dense_3174[8][0]
____________________________________________________________________________________________________
add_7282 (Add) (None, 1) 0 add_7269[0][0]
multiply_4781[0][0]
____________________________________________________________________________________________________
multiply_4789 (Multiply) (None, 1) 0 multiply_4783[0][0]
add_7294[0][0]
____________________________________________________________________________________________________
add_7307 (Add) (None, 1) 0 dense_3192[5][0]
lambda_4014[0][0]
____________________________________________________________________________________________________
lambda_4021 (Lambda) (None, 1) 0 add_7309[0][0]
dense_3174[18][0]
____________________________________________________________________________________________________
add_7155 (Add) (None, 1) 0 add_7142[0][0]
multiply_4704[0][0]
____________________________________________________________________________________________________
multiply_4712 (Multiply) (None, 1) 0 multiply_4711[0][0]
add_7167[0][0]
____________________________________________________________________________________________________
add_7180 (Add) (None, 1) 0 dense_3183[0][0]
lambda_3943[0][0]
____________________________________________________________________________________________________
lambda_3950 (Lambda) (None, 1) 0 add_7192[0][0]
dense_3174[9][0]
____________________________________________________________________________________________________
add_7287 (Add) (None, 1) 0 add_7274[0][0]
multiply_4785[0][0]
____________________________________________________________________________________________________
multiply_4793 (Multiply) (None, 1) 0 multiply_4791[0][0]
add_7299[0][0]
____________________________________________________________________________________________________
add_7312 (Add) (None, 1) 0 dense_3193[1][0]
lambda_4017[0][0]
____________________________________________________________________________________________________
lambda_4022 (Lambda) (None, 1) 0 multiply_4806[0][0]
____________________________________________________________________________________________________
input_1437 (InputLayer) (None, 1) 0
____________________________________________________________________________________________________
dense_3194 (Dense) (None, 1) 2 add_7322[0][0]
add_7322[0][0]
add_7322[0][0]
____________________________________________________________________________________________________
lambda_4024 (Lambda) (None, 1) 0 add_7322[0][0]
dense_3174[19][0]
____________________________________________________________________________________________________
add_7159 (Add) (None, 1) 0 add_7146[0][0]
multiply_4706[0][0]
____________________________________________________________________________________________________
multiply_4714 (Multiply) (None, 1) 0 multiply_4711[0][0]
add_7171[0][0]
____________________________________________________________________________________________________
add_7184 (Add) (None, 1) 0 dense_3183[2][0]
lambda_3945[0][0]
____________________________________________________________________________________________________
lambda_3953 (Lambda) (None, 1) 0 add_7192[0][0]
dense_3174[9][0]
____________________________________________________________________________________________________
add_7291 (Add) (None, 1) 0 add_7278[0][0]
multiply_4787[0][0]
____________________________________________________________________________________________________
multiply_4795 (Multiply) (None, 1) 0 multiply_4791[0][0]
add_7303[0][0]
____________________________________________________________________________________________________
add_7316 (Add) (None, 1) 0 dense_3193[3][0]
lambda_4019[0][0]
____________________________________________________________________________________________________
lambda_4027 (Lambda) (None, 1) 0 add_7322[0][0]
dense_3174[19][0]
____________________________________________________________________________________________________
add_7163 (Add) (None, 1) 0 add_7150[0][0]
multiply_4708[0][0]
____________________________________________________________________________________________________
multiply_4716 (Multiply) (None, 1) 0 multiply_4711[0][0]
add_7175[0][0]
____________________________________________________________________________________________________
add_7188 (Add) (None, 1) 0 dense_3183[4][0]
lambda_3947[0][0]
____________________________________________________________________________________________________
lambda_3956 (Lambda) (None, 1) 0 add_7192[0][0]
dense_3174[9][0]
____________________________________________________________________________________________________
add_7295 (Add) (None, 1) 0 add_7282[0][0]
multiply_4789[0][0]
____________________________________________________________________________________________________
multiply_4797 (Multiply) (None, 1) 0 multiply_4791[0][0]
add_7307[0][0]
____________________________________________________________________________________________________
add_7320 (Add) (None, 1) 0 dense_3193[5][0]
lambda_4021[0][0]
____________________________________________________________________________________________________
lambda_4030 (Lambda) (None, 1) 0 add_7322[0][0]
dense_3174[19][0]
____________________________________________________________________________________________________
add_7168 (Add) (None, 1) 0 add_7155[0][0]
multiply_4712[0][0]
____________________________________________________________________________________________________
multiply_4720 (Multiply) (None, 1) 0 multiply_4719[0][0]
add_7180[0][0]
____________________________________________________________________________________________________
add_7193 (Add) (None, 1) 0 dense_3184[0][0]
lambda_3950[0][0]
____________________________________________________________________________________________________
add_7300 (Add) (None, 1) 0 add_7287[0][0]
multiply_4793[0][0]
____________________________________________________________________________________________________
multiply_4801 (Multiply) (None, 1) 0 multiply_4799[0][0]
add_7312[0][0]
____________________________________________________________________________________________________
multiply_4807 (Multiply) (None, 1) 0 lambda_4022[0][0]
input_1437[0][0]
____________________________________________________________________________________________________
add_7325 (Add) (None, 1) 0 dense_3194[1][0]
lambda_4024[0][0]
____________________________________________________________________________________________________
add_7172 (Add) (None, 1) 0 add_7159[0][0]
multiply_4714[0][0]
____________________________________________________________________________________________________
multiply_4722 (Multiply) (None, 1) 0 multiply_4719[0][0]
add_7184[0][0]
____________________________________________________________________________________________________
add_7197 (Add) (None, 1) 0 dense_3184[2][0]
lambda_3953[0][0]
____________________________________________________________________________________________________
add_7304 (Add) (None, 1) 0 add_7291[0][0]
multiply_4795[0][0]
____________________________________________________________________________________________________
multiply_4803 (Multiply) (None, 1) 0 multiply_4799[0][0]
add_7316[0][0]
____________________________________________________________________________________________________
add_7329 (Add) (None, 1) 0 dense_3194[3][0]
lambda_4027[0][0]
____________________________________________________________________________________________________
add_7176 (Add) (None, 1) 0 add_7163[0][0]
multiply_4716[0][0]
____________________________________________________________________________________________________
multiply_4724 (Multiply) (None, 1) 0 multiply_4719[0][0]
add_7188[0][0]
____________________________________________________________________________________________________
add_7201 (Add) (None, 1) 0 dense_3184[4][0]
lambda_3956[0][0]
____________________________________________________________________________________________________
add_7308 (Add) (None, 1) 0 add_7295[0][0]
multiply_4797[0][0]
____________________________________________________________________________________________________
multiply_4805 (Multiply) (None, 1) 0 multiply_4799[0][0]
add_7320[0][0]
____________________________________________________________________________________________________
add_7333 (Add) (None, 1) 0 dense_3194[5][0]
lambda_4030[0][0]
____________________________________________________________________________________________________
add_7181 (Add) (None, 1) 0 add_7168[0][0]
multiply_4720[0][0]
____________________________________________________________________________________________________
multiply_4728 (Multiply) (None, 1) 0 multiply_4727[0][0]
add_7193[0][0]
____________________________________________________________________________________________________
add_7313 (Add) (None, 1) 0 add_7300[0][0]
multiply_4801[0][0]
____________________________________________________________________________________________________
multiply_4809 (Multiply) (None, 1) 0 multiply_4807[0][0]
add_7325[0][0]
____________________________________________________________________________________________________
add_7185 (Add) (None, 1) 0 add_7172[0][0]
multiply_4722[0][0]
____________________________________________________________________________________________________
multiply_4730 (Multiply) (None, 1) 0 multiply_4727[0][0]
add_7197[0][0]
____________________________________________________________________________________________________
add_7317 (Add) (None, 1) 0 add_7304[0][0]
multiply_4803[0][0]
____________________________________________________________________________________________________
multiply_4811 (Multiply) (None, 1) 0 multiply_4807[0][0]
add_7329[0][0]
____________________________________________________________________________________________________
add_7189 (Add) (None, 1) 0 add_7176[0][0]
multiply_4724[0][0]
____________________________________________________________________________________________________
multiply_4732 (Multiply) (None, 1) 0 multiply_4727[0][0]
add_7201[0][0]
____________________________________________________________________________________________________
add_7321 (Add) (None, 1) 0 add_7308[0][0]
multiply_4805[0][0]
____________________________________________________________________________________________________
multiply_4813 (Multiply) (None, 1) 0 multiply_4807[0][0]
add_7333[0][0]
____________________________________________________________________________________________________
lambda_3951 (Lambda) (None, 1) 0 add_7192[0][0]
____________________________________________________________________________________________________
add_7194 (Add) (None, 1) 0 add_7181[0][0]
multiply_4728[0][0]
____________________________________________________________________________________________________
lambda_4025 (Lambda) (None, 1) 0 add_7322[0][0]
____________________________________________________________________________________________________
add_7326 (Add) (None, 1) 0 add_7313[0][0]
multiply_4809[0][0]
____________________________________________________________________________________________________
lambda_3954 (Lambda) (None, 1) 0 add_7192[0][0]
____________________________________________________________________________________________________
add_7198 (Add) (None, 1) 0 add_7185[0][0]
multiply_4730[0][0]
____________________________________________________________________________________________________
lambda_4028 (Lambda) (None, 1) 0 add_7322[0][0]
____________________________________________________________________________________________________
add_7330 (Add) (None, 1) 0 add_7317[0][0]
multiply_4811[0][0]
____________________________________________________________________________________________________
lambda_3957 (Lambda) (None, 1) 0 add_7192[0][0]
____________________________________________________________________________________________________
add_7202 (Add) (None, 1) 0 add_7189[0][0]
multiply_4732[0][0]
____________________________________________________________________________________________________
lambda_4031 (Lambda) (None, 1) 0 add_7322[0][0]
____________________________________________________________________________________________________
add_7334 (Add) (None, 1) 0 add_7321[0][0]
multiply_4813[0][0]
____________________________________________________________________________________________________
subtract_175 (Subtract) (None, 1) 0 lambda_3951[0][0]
add_7194[0][0]
____________________________________________________________________________________________________
subtract_178 (Subtract) (None, 1) 0 lambda_4025[0][0]
add_7326[0][0]
____________________________________________________________________________________________________
subtract_176 (Subtract) (None, 1) 0 lambda_3954[0][0]
add_7198[0][0]
____________________________________________________________________________________________________
subtract_179 (Subtract) (None, 1) 0 lambda_4028[0][0]
add_7330[0][0]
____________________________________________________________________________________________________
subtract_177 (Subtract) (None, 1) 0 lambda_3957[0][0]
add_7202[0][0]
____________________________________________________________________________________________________
subtract_180 (Subtract) (None, 1) 0 lambda_4031[0][0]
add_7334[0][0]
____________________________________________________________________________________________________
concatenate_30 (Concatenate) (None, 6) 0 subtract_175[0][0]
subtract_178[0][0]
subtract_176[0][0]
subtract_179[0][0]
subtract_177[0][0]
subtract_180[0][0]
====================================================================================================
Total params: 71
Trainable params: 31
Non-trainable params: 40
____________________________________________________________________________________________________
Here we use a very small amount of training data just for purposes of illustration even though it works relatively well. Below we consecutively train hedges or local volatilities.
In [152]:
Ltrain = 10**4
xtrain =([np.ones(Ltrain)] + [np.zeros(Ltrain) for key in keylist]+
[np.random.normal(0,1,Ltrain) for i in range(N)]+
[np.ones(Ltrain) for i in range(N)])
ytrain=np.zeros((Ltrain,len(P.keys())))
for i in range(Ltrain):
for l in range(len(P.keys())):
key = keylist[l]
ytrain[i,l]= P[key]
In the sequel the actual training is performed:
In [153]:
import matplotlib.pyplot as plt
localvol_trainhedge.compile(optimizer='adam',
loss='mean_squared_error')
localvol_trainlocvol.compile(optimizer='adam',
loss='mean_squared_error')
for i in range(5):
localvol_trainhedge.fit(x=xtrain,y=ytrain, epochs=15,verbose=True)
x = localvol_trainhedge.get_weights()
localvol_trainlocvol.set_weights(x)
localvol_trainlocvol.fit(x=xtrain,y=ytrain, epochs=5,verbose=True)
plt.hist(localvol_trainhedge.predict(xtrain)[:,0])
plt.show()
print(np.mean(localvol_trainhedge.predict(xtrain)[:,0]))
y = localvol_trainlocvol.get_weights()
localvol_trainhedge.set_weights(y)
Epoch 1/15 10000/10000 [==============================] - 25s - loss: 0.1271 Epoch 2/15 10000/10000 [==============================] - 3s - loss: 0.1090 Epoch 3/15 10000/10000 [==============================] - 3s - loss: 0.0992 Epoch 4/15 10000/10000 [==============================] - 3s - loss: 0.0905 Epoch 5/15 10000/10000 [==============================] - 2s - loss: 0.0826 Epoch 6/15 10000/10000 [==============================] - 3s - loss: 0.0755 Epoch 7/15 10000/10000 [==============================] - 3s - loss: 0.0691 Epoch 8/15 10000/10000 [==============================] - 3s - loss: 0.0635 Epoch 9/15 10000/10000 [==============================] - 3s - loss: 0.0584 Epoch 10/15 10000/10000 [==============================] - 3s - loss: 0.0540 Epoch 11/15 10000/10000 [==============================] - 3s - loss: 0.0501 Epoch 12/15 10000/10000 [==============================] - 3s - loss: 0.0467 Epoch 13/15 10000/10000 [==============================] - 3s - loss: 0.0437 Epoch 14/15 10000/10000 [==============================] - 3s - loss: 0.0411 Epoch 15/15 10000/10000 [==============================] - 3s - loss: 0.0387 Epoch 1/5 10000/10000 [==============================] - 37s - loss: 0.0227 Epoch 2/5 10000/10000 [==============================] - 6s - loss: 0.0212 Epoch 3/5 10000/10000 [==============================] - 6s - loss: 0.0207 Epoch 4/5 10000/10000 [==============================] - 10s - loss: 0.0189 Epoch 5/5 10000/10000 [==============================] - 6s - loss: 0.0178
0.27073652 Epoch 1/15 10000/10000 [==============================] - 3s - loss: 0.0141 Epoch 2/15 10000/10000 [==============================] - 3s - loss: 0.0126 Epoch 3/15 10000/10000 [==============================] - 3s - loss: 0.0125 Epoch 4/15 10000/10000 [==============================] - 3s - loss: 0.0125 Epoch 5/15 10000/10000 [==============================] - 3s - loss: 0.0124 Epoch 6/15 10000/10000 [==============================] - 3s - loss: 0.0123 Epoch 7/15 10000/10000 [==============================] - 3s - loss: 0.0123 Epoch 8/15 10000/10000 [==============================] - 2s - loss: 0.0122 Epoch 9/15 10000/10000 [==============================] - 3s - loss: 0.0121 Epoch 10/15 10000/10000 [==============================] - 3s - loss: 0.0120 Epoch 11/15 10000/10000 [==============================] - 3s - loss: 0.0120 Epoch 12/15 10000/10000 [==============================] - 3s - loss: 0.0119 Epoch 13/15 10000/10000 [==============================] - 3s - loss: 0.0118 Epoch 14/15 10000/10000 [==============================] - 3s - loss: 0.0118 Epoch 15/15 10000/10000 [==============================] - 3s - loss: 0.0117 Epoch 1/5 10000/10000 [==============================] - 6s - loss: 0.0113 Epoch 2/5 10000/10000 [==============================] - 6s - loss: 0.0112 Epoch 3/5 10000/10000 [==============================] - 9s - loss: 0.0112 Epoch 4/5 10000/10000 [==============================] - 6s - loss: 0.0112 Epoch 5/5 10000/10000 [==============================] - 6s - loss: 0.0112
0.18796247 Epoch 1/15 10000/10000 [==============================] - 3s - loss: 0.0110 Epoch 2/15 10000/10000 [==============================] - 3s - loss: 0.0110 Epoch 3/15 10000/10000 [==============================] - 3s - loss: 0.0110 Epoch 4/15 10000/10000 [==============================] - 3s - loss: 0.0110 Epoch 5/15 10000/10000 [==============================] - 4s - loss: 0.0109 Epoch 6/15 10000/10000 [==============================] - 3s - loss: 0.0109 Epoch 7/15 10000/10000 [==============================] - 3s - loss: 0.0109 Epoch 8/15 10000/10000 [==============================] - 3s - loss: 0.0109 Epoch 9/15 10000/10000 [==============================] - 3s - loss: 0.0109 Epoch 10/15 10000/10000 [==============================] - 3s - loss: 0.0109 Epoch 11/15 10000/10000 [==============================] - 4s - loss: 0.0109 Epoch 12/15 10000/10000 [==============================] - 5s - loss: 0.0109 Epoch 13/15 10000/10000 [==============================] - 4s - loss: 0.0108 Epoch 14/15 10000/10000 [==============================] - 3s - loss: 0.0108 Epoch 15/15 10000/10000 [==============================] - 3s - loss: 0.0108 Epoch 1/5 10000/10000 [==============================] - 8s - loss: 0.0108 Epoch 2/5 10000/10000 [==============================] - 8s - loss: 0.0108 Epoch 3/5 10000/10000 [==============================] - 7s - loss: 0.0108 Epoch 4/5 10000/10000 [==============================] - 8s - loss: 0.0108 Epoch 5/5 10000/10000 [==============================] - 8s - loss: 0.0108
0.17364338 Epoch 1/15 10000/10000 [==============================] - 3s - loss: 0.0108 Epoch 2/15 10000/10000 [==============================] - 3s - loss: 0.0108 Epoch 3/15 10000/10000 [==============================] - 4s - loss: 0.0108 Epoch 4/15 10000/10000 [==============================] - 3s - loss: 0.0108 Epoch 5/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 6/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 7/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 8/15 10000/10000 [==============================] - 4s - loss: 0.0107 Epoch 9/15 10000/10000 [==============================] - 4s - loss: 0.0107 Epoch 10/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 11/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 12/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 13/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 14/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 15/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 1/5 10000/10000 [==============================] - 7s - loss: 0.0107 Epoch 2/5 10000/10000 [==============================] - 8s - loss: 0.0107 Epoch 3/5 10000/10000 [==============================] - 8s - loss: 0.0107 Epoch 4/5 10000/10000 [==============================] - 10s - loss: 0.0107 Epoch 5/5 10000/10000 [==============================] - 9s - loss: 0.0107
0.17294763 Epoch 1/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 2/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 3/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 4/15 10000/10000 [==============================] - 3s - loss: 0.0107 Epoch 5/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 6/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 7/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 8/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 9/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 10/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 11/15 10000/10000 [==============================] - 3s - loss: 0.0106 Epoch 12/15 10000/10000 [==============================] - 4s - loss: 0.0106 Epoch 13/15 10000/10000 [==============================] - 5s - loss: 0.0106 Epoch 14/15 10000/10000 [==============================] - 4s - loss: 0.0106 Epoch 15/15 10000/10000 [==============================] - 4s - loss: 0.0106 Epoch 1/5 10000/10000 [==============================] - 8s - loss: 0.0106 Epoch 2/5 10000/10000 [==============================] - 6s - loss: 0.0106 Epoch 3/5 10000/10000 [==============================] - 6s - loss: 0.0106 Epoch 4/5 10000/10000 [==============================] - 7s - loss: 0.0105 Epoch 5/5 10000/10000 [==============================] - 7s - loss: 0.0105
0.17700884
Hedging helps to reduce variance tremendously, whence we are able to go for a classical means square calibration approach, which is implemented below with a custom loss function.
In [154]:
def custom_loss(y_true,y_pred):
return K.mean((K.mean(y_pred,axis=0)-K.mean(y_true,axis=0))**2)
localvol_trainlocvol.compile(optimizer='adam',
loss=custom_loss)
In [158]:
for i in range(10):
localvol_trainlocvol.fit(x=xtrain,y=ytrain, epochs=5, verbose=True,batch_size=10**4)
plt.hist(localvol_trainlocvol.predict(xtrain)[:,:])
plt.show()
print(np.mean(localvol_trainlocvol.predict(xtrain)[:,:],axis=0))
Epoch 1/5 10000/10000 [==============================] - 0s - loss: 1.7071e-05 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 1.4733e-05 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 1.2625e-05 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 1.0753e-05 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 9.1196e-06
[0.19766045 0.2352989 0.15941346 0.2061147 0.12752648 0.17992648] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 7.7151e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 6.5300e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 5.5497e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 4.7529e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 4.1238e-06
[0.19882971 0.23690218 0.16048893 0.20758782 0.12848227 0.18125945] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 3.6407e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 3.2854e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 3.0373e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 2.8780e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 2.7919e-06
[0.1996602 0.23803909 0.16125116 0.20863296 0.12916146 0.18220441] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 2.7618e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 2.7738e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 2.8156e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 2.8773e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 2.9517e-06
[0.20015445 0.23871522 0.16170453 0.20925388 0.12956533 0.18276557] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 3.0291e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 3.1069e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 3.1767e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 3.2394e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 3.2908e-06
[0.20036927 0.2390097 0.16190232 0.20952344 0.12974094 0.18300998] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 3.3301e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 3.3584e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 3.3730e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 3.3763e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 3.3702e-06
[0.20038432 0.23903024 0.16191632 0.20954241 0.12975426 0.18302672] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 3.3543e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 3.3306e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 3.3006e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 3.2659e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 3.2274e-06
[0.2002782 0.23888339 0.16181938 0.20940886 0.1296677 0.1829058 ] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 3.1874e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 3.1449e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 3.1034e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 3.0620e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 3.0222e-06
[0.20011768 0.23866326 0.16167204 0.20920657 0.12953676 0.18272291] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 2.9854e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 2.9507e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 2.9188e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 2.8895e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 2.8636e-06
[0.19995114 0.23843387 0.16151938 0.20899665 0.12940088 0.18253349] Epoch 1/5 10000/10000 [==============================] - 0s - loss: 2.8419e-06 Epoch 2/5 10000/10000 [==============================] - 0s - loss: 2.8221e-06 Epoch 3/5 10000/10000 [==============================] - 0s - loss: 2.8059e-06 Epoch 4/5 10000/10000 [==============================] - 0s - loss: 2.7922e-06 Epoch 5/5 10000/10000 [==============================] - 0s - loss: 2.7806e-06
[0.19980825 0.23823719 0.16138901 0.20881638 0.12928516 0.18237126]
In [161]:
Ltest = 10**6
xtest =([np.ones(Ltest)] + [np.zeros(Ltest) for key in keylist]+
[np.random.normal(0,1,Ltest) for i in range(N)]+
[np.ones(Ltest) for i in range(N)])
ytest=np.zeros((Ltest,len(P.keys())))
for i in range(Ltest):
for l in range(len(P.keys())):
key = keylist[l]
ytest[i,l]= P[key]
In [162]:
plt.hist(localvol_trainlocvol.predict(xtest)[:,:])
plt.show()
print(np.mean(localvol_trainlocvol.predict(xtest)[:,:],axis=0))
[0.20017254 0.23855153 0.16223146 0.20956783 0.13054265 0.18354742]
In [81]:
P
Out[81]:
{(0.9, 0.5): 0.20042534,
(0.9, 1.0): 0.23559685,
(1.0, 0.5): 0.16312157,
(1.0, 1.0): 0.20771958,
(1.1, 0.5): 0.13154241,
(1.1, 1.0): 0.18236567}
... not so bad.