clip_by_norm

這裡的clip_by_norm是指對梯度進行裁剪，通過控制梯度的最大正規化，防止梯度爆炸的問題，是一種比較常用的梯度規約的方式。

tensorflow中的clip_by_norm

示例

optimizer = tf.train.AdamOptimizer(learning_rate, beta1=0.5)
grads = optimizer.compute_gradients(cost)
for i, (g, v) in enumerate(grads):
    if g is not None:
        grads[i] = (tf.clip_by_norm(g, 5
 
), v)  # clip gradients
train_op = optimizer.apply_gradients(grads)

上面是一段比較通用的定義梯度計算公式的程式碼，其中用到了tf.clip_by_norm這個方法，下面是該函式的原始碼：

def clip_by_norm(t, clip_norm, axes=None, name=None):
  """Clips tensor values to a maximum L2-norm.

  Given a tensor `t`, and a maximum clip value `clip_norm`, this operation
  normalizes `t` so that its L2-norm is less than or equal to `clip_norm`,
  along the dimensions given in `axes`. Specifically, in the default case
  where all dimensions are used for calculation, if the L2-norm of `t` is
  already less than or equal to `clip_norm`, then `t` is not modified. If
  the L2-norm is greater than `clip_norm`, then this operation returns a
  tensor of the same type and shape as `t` with its values set to:

  `t * clip_norm / l2norm(t)`

  In this case, the L2-norm of the output tensor is `clip_norm`.

  As another example, if `t` is a matrix and `axes == [1]`, then each row
  of the output will have L2-norm equal to `clip_norm`. If `axes == [0]`
  instead, each column of the output will be clipped.

  This operation is typically used to clip gradients before applying them with
  an optimizer.

  Args:
    t: A `Tensor`.
    clip_norm: A 0-D (scalar) `Tensor` > 0. A maximum clipping value.
    axes: A 1-D (vector) `Tensor` of type int32 containing the dimensions
      to use for computing the L2-norm. If `None` (the default), uses all
      dimensions.
    name: A name for the operation (optional).

  Returns:
    A clipped `Tensor`.
  """
 

  with ops.name_scope(name, "clip_by_norm", [t, clip_norm]) as name:
    t = ops.convert_to_tensor(t, name="t")

    # Calculate L2-norm, clip elements by ratio of clip_norm to L2-norm
    l2norm_inv = math_ops.rsqrt(
        math_ops.reduce_sum(t * t, axes, keep_dims=True))
    tclip = array_ops.identity(t * clip_norm * math_ops.minimum(
        l2norm_inv, constant_op.constant(1.0
 
, dtype=t.dtype) / clip_norm),
                               name=name)

  return tclip

通過註解可以清晰的明白其作用在於將傳入的梯度張量t的L2範數進行了上限約束，約束值即為clip_norm，如果t的L2範數超過了clip_norm，則變換為t * clip_norm / l2norm(t)，如此一來，變換後的t的L2範數便小於等於clip_norm了。

示例

下面我們通過一段程式碼來直觀地展示該函式的作用。

生成隨機數

import numpy as np
t = np.random.randint(low=0,high=5,size=10)
t

array([1, 1, 3, 4, 2, 2, 1, 4, 2, 3])

計算L2範數

l2norm4t = np.linalg.norm(t)
l2norm4t

8.0622577482985491

隨機數規約

clip_norm = 5
transformed_t = t *clip_norm/l2norm4t
transformed_t

array([ 0.62017367,  0.62017367,  1.86052102,  2.48069469,  1.24034735,
        1.24034735,  0.62017367,  2.48069469,  1.24034735,  1.86052102])

驗證

np.linalg.norm(transformed_t)

5.0

可以看出，該隨機數序列的L2範數已經被規約為clip_norm的值。