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Bir onceki egitim kitapciginda 'Tensor'lari ve onlar ustunde kullanabileceginiz operasyonlari tanittik. Bu kitapcikta ise makine ogrenmesi modellerinin eniyilenmesinde onemli bir teknik olan otomatik degisimi ogrenecegiz.
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import tensorflow.compat.v1 as tf
TensorFlow'un tf.GradientTape API'si otomatik degisim yani girdi degiskenlerine bagli olarak hesaplanan egimin hesaplanisini hali hazirda bize saglar. Tensorflow tf.GradientTape kapsaminda yapilan butun operasyonlari bir "tape(bant)"e "kaydeder". Tensorflow daha sonra "kaydedilmis" egimleri, bu bant ve her bir kayitla iliskili egim verilerini ters mod degisimi kullanarak hesaplar.
Ornegin:
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x = tf.ones((2, 2))
with tf.GradientTape() as t:
t.watch(x)
y = tf.reduce_sum(x)
z = tf.multiply(y, y)
# Orjinal girdi tensoru x'e gore z'nin turevi
dz_dx = t.gradient(z, x)
for i in [0, 1]:
for j in [0, 1]:
assert dz_dx[i][j].numpy() == 8.0
Ayrica "kaydedilmis" 'tf.GradientTape' kapsaminda hesaplanan ara degerlere gore ciktilari egimini de isteyebilirsiniz.
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x = tf.ones((2, 2))
with tf.GradientTape() as t:
t.watch(x)
y = tf.reduce_sum(x)
z = tf.multiply(y, y)
# Banti kullanarak ara deger y'ye gore z'nin turevini hesaplayabiliriz.
dz_dy = t.gradient(z, y)
assert dz_dy.numpy() == 8.0
GradientTape.gradient() yontemini cagirdimizda GradientTape tarafindan tutulan kaynaklar serbest birakilir. Ayni degerleri kullanarak birden fazla egim hesaplamak istiyorsaniz 'persistent(kalici)' egim banti olusturmalisiniz. Bu sayede bant nesnesi cop toplayicisi tarafindan toplanip kaynaklar serbest birakildikca 'gradient()' yontemini bircok kere cagirmamiza izin verir. Ornegin:
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x = tf.constant(3.0)
with tf.GradientTape(persistent=True) as t:
t.watch(x)
y = x * x
z = y * y
dz_dx = t.gradient(z, x) # 108.0 (4*x^3 at x = 3)
dy_dx = t.gradient(y, x) # 6.0
del t # Referansi banta indirgeyelim
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def f(x, y):
output = 1.0
for i in range(y):
if i > 1 and i < 5:
output = tf.multiply(output, x)
return output
def grad(x, y):
with tf.GradientTape() as t:
t.watch(x)
out = f(x, y)
return t.gradient(out, x)
x = tf.convert_to_tensor(2.0)
assert grad(x, 6).numpy() == 12.0
assert grad(x, 5).numpy() == 12.0
assert grad(x, 4).numpy() == 4.0
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x = tf.Variable(1.0) # 1.0 degerine ilklenmis bir Tensorflow degiskeni olusturalim
with tf.GradientTape() as t:
with tf.GradientTape() as t2:
y = x * x * x
# 't' kapsam yoneticisi icerisinde egimi hesaplayalim
# ki bu egim hesaplanmasinin turevlenebilir oldugu anlamina gelir.
dy_dx = t2.gradient(y, x)
d2y_dx2 = t.gradient(dy_dx, x)
assert dy_dx.numpy() == 3.0
assert d2y_dx2.numpy() == 6.0