ref: a17c2948a0ea0a310511f65ec0c81d907dfdc15d
dir: /dnn/training_tf2/pade.py/
# Optimizing a rational function to optimize a tanh() approximation
import numpy as np
import tensorflow as tf
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Input, GRU, Dense, Embedding, Reshape, Concatenate, Lambda, Conv1D, Multiply, Add, Bidirectional, MaxPooling1D, Activation
import tensorflow.keras.backend as K
from tensorflow.keras.optimizers import Adam, SGD
def my_loss1(y_true, y_pred):
return 1*K.mean(K.square(y_true-y_pred)) + 1*K.max(K.square(y_true-y_pred), axis=1)
def my_loss2(y_true, y_pred):
return .1*K.mean(K.square(y_true-y_pred)) + 1*K.max(K.square(y_true-y_pred), axis=1)
def my_loss3(y_true, y_pred):
return .01*K.mean(K.square(y_true-y_pred)) + 1*K.max(K.square(y_true-y_pred), axis=1)
# Using these initializers to seed the approximation
# with a reasonable starting point
def num_init(shape, dtype=None):
rr = tf.constant([[945], [105], [1]], dtype=dtype)
#rr = tf.constant([[946.56757], [98.01368], [0.66841]], dtype=dtype)
print(rr)
return rr
def den_init(shape, dtype=None):
rr = tf.constant([[945], [420], [15]], dtype=dtype)
#rr = tf.constant([[946.604], [413.342], [12.465]], dtype=dtype)
print(rr)
return rr
x = np.arange(-10, 10, .01)
N = len(x)
x = np.reshape(x, (1, -1, 1))
x2 = x*x
x2in = np.concatenate([x2*0 + 1, x2, x2*x2], axis=2)
yout = np.tanh(x)
model_x = Input(shape=(None, 1,))
model_x2 = Input(shape=(None, 3,))
num = Dense(1, name='num', use_bias=False, kernel_initializer=num_init)
den = Dense(1, name='den', use_bias=False, kernel_initializer=den_init)
def ratio(x):
return tf.minimum(1., tf.maximum(-1., x[0]*x[1]/x[2]))
out_layer = Lambda(ratio)
output = out_layer([model_x, num(model_x2), den(model_x2)])
model = Model([model_x, model_x2], output)
model.summary()
model.compile(Adam(0.05, beta_1=0.9, beta_2=0.9, decay=2e-5), loss='mean_squared_error')
model.fit([x, x2in], yout, batch_size=1, epochs=500000, validation_split=0.0)
model.compile(Adam(0.001, beta_2=0.9, decay=1e-4), loss=my_loss1)
model.fit([x, x2in], yout, batch_size=1, epochs=50000, validation_split=0.0)
model.compile(Adam(0.0001, beta_2=0.9, decay=1e-4), loss=my_loss2)
model.fit([x, x2in], yout, batch_size=1, epochs=50000, validation_split=0.0)
model.compile(Adam(0.00001, beta_2=0.9, decay=1e-4), loss=my_loss3)
model.fit([x, x2in], yout, batch_size=1, epochs=50000, validation_split=0.0)
model.save_weights('tanh.h5')