函数式自动微分
环境配置
# 实验环境已经预装了mindspore==2.2.14，如需更换mindspore版本，可更改下面mindspore的版本号
!pip uninstall mindspore -y
!pip install -i https://pypi.mirrors.ustc.edu.cn/simple mindspore==2.2.14
import numpy as np
import mindspore
from mindspore import nn
from mindspore import ops
from mindspore import Tensor, Parameter
函数与计算图
-
w x + b = z wx + b = z wx+b=z
-> A c t i v a t i o n − F u n c t i o n ( z ) Activation - Function(z) Activation−Function(z)
-> y p r e d y_{pred} ypred
-> C r o s s − E n t r o p y ( y , y p r e d ) Cross - Entropy(y , y_{pred}) Cross−Entropy(y,ypred) -
w , b 为需要优化的参数 w,b为需要优化的参数 w,b为需要优化的参数
x = ops.ones(5, mindspore.float32) # input tensor y = ops.zones(3, mindspore.float32) # expected output w = Parameter(Tensor(np.random.randn(5, 3), mindspore.float32), name = 'w') b = Parameter(Tensor(np.random.randn(3,), mindspore.float32), name='b') # bias def function(x, y, w, b): z = ops.matmul(x, w) + b loss = ops.binary_cross_entropy_with_logits(z, y, ops.ones_like(z), ops.ones_like(z)) return loss loss = function(x, y, w, b) print(loss) #output Tensor(shape=[], dtype=Float32, value= 0.914285)
微分函数与梯度计算
- 为优化模型需要求参数对loss的导数 ∂ l o s s ∂ w \frac{\partial loss}{\partial w} ∂w∂loss, ∂ l o s s ∂ b \frac{\partial loss}{\partial b} ∂b∂loss
- 调用
mindspore.grad函数获取function的微分函数 fn:待求导函数grad_position:指定求导输入位置索引- 使用
grad获得微分函数是一种函数变换，即输入为函数，输出也为函数
grad_fn = mindspore.grad(function, (2, 3))
grads = grad_fn(x, y, w, b)
print(grads)
#Output (Tensor(shape=[5, 3], dtype=Float32, value= [[ 6.56869709e-02, 5.37334494e-02, 3.01467031e-01], [ 6.56869709e-02, 5.37334494e-02, 3.01467031e-01], [ 6.56869709e-02, 5.37334494e-02, 3.01467031e-01], [ 6.56869709e-02, 5.37334494e-02, 3.01467031e-01], [ 6.56869709e-02, 5.37334494e-02, 3.01467031e-01]]), Tensor(shape=[3], dtype=Float32, value= [ 6.56869709e-02, 5.37334494e-02, 3.01467031e-01]))
Stop Gradient
- 实现对某个输出项的梯度截断，或消除某个Tensor对梯度的影响
def function_with_logits(x, y, w, b):
z = ops.matmul(x, w) + b
loss = ops.binary_cross_entropy_with_logits(z, y, ops.ones_like(z), ops.ones_like(z))
return loss, z
grad_fn = mindspore.grad(function_with_logits, (2, 3))
grads = grad_fn(x, y, w, b)
# 若想屏蔽掉z对梯度的影响，使用ops.stop_gradient接口, 将梯度在此截断
def function_stop_gradient(x, y, w, b):
z = ops.matmul(x, w) + b
loss = ops.binary_cross_entropy_with_logits(z, y, ops.ones_like(z), ops.ones_like(z))
return loss, ops.stop_gradient(z)
grad_fn = mindspore.grad(function_stop_gradient, (2, 3))
grads = grad_fn(x, y, w, b)
Auxiliary data
- Auxiliary data为辅助数据，是函数除第一个输出项外的其他输出。
grad和value_and_grad提供has_aux参数，当其设置为True时，可以自动实现前文手动添加stop_gradient的功能。
grad_fn = mindspore.grad(function_with_logits, (2, 3), has_aux=True)
grads, (z,) = grad_fn(x, y, w, b)
神经网络梯度计算
#定义模型
class Network(nn.Cell):
def __init__(self):
super().__init__()
self.w = w
self.b = b
def construct(self, x):
z = ops.matmul(x, self.w) + self.b
return z
# 实例化模型
model = Network()
# 实例化损失函数
loss_fn = nn.BCEWithLogitsLoss()
# 定义正向传播
def forward_fn(x, y):
z = model(x)
loss = loss_fn(z, y)
return loss
grad_fn = mindspore.value_and_grad(forward_fn, None, weights=model.trainable_params())
loss, grads = grad_fn(x, y)
