Question

我想在我的TensorFlow图中为几个权重矩阵添加最大范数约束，ala Torch的{{3}}方法。

如果任何神经元的权重矩阵的L2范数超过max_norm，我想缩减其权重，使其L2范数正好为max_norm。

使用TensorFlow表达此信息的最佳方式是什么？

Answer 1

这是一个可能的实现：

import tensorflow as tf

def maxnorm_regularizer(threshold, axes=1, name="maxnorm", collection="maxnorm"):
    def maxnorm(weights):
        clipped = tf.clip_by_norm(weights, clip_norm=threshold, axes=axes)
        clip_weights = tf.assign(weights, clipped, name=name)
        tf.add_to_collection(collection, clip_weights)
        return None # there is no regularization loss term
    return maxnorm

以下是您将如何使用它：

from tensorflow.contrib.layers import fully_connected
from tensorflow.contrib.framework import arg_scope

with arg_scope(
        [fully_connected],
        weights_regularizer=max_norm_regularizer(1.5)):
    hidden1 = fully_connected(X, 200, scope="hidden1")
    hidden2 = fully_connected(hidden1, 100, scope="hidden2")
    outputs = fully_connected(hidden2, 5, activation_fn=None, scope="outs")

max_norm_ops = tf.get_collection("max_norm")

[...]

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(n_epochs):
        for X_batch, y_batch in load_next_batch():
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
            sess.run(max_norm_ops)

这创建了一个3层神经网络，并在每一层（阈值为1.5）进行最大范数正则化训练。我只是尝试过，似乎工作。希望这可以帮助！欢迎提出改进建议。：）

备注

此代码基于tf.clip_by_norm()：

>>> x = tf.constant([0., 0., 3., 4., 30., 40., 300., 400.], shape=(4, 2)) >>> print(x.eval()) [[ 0. 0.] [ 3. 4.] [ 30. 40.] [ 300. 400.]] >>> clip_rows = tf.clip_by_norm(x, clip_norm=10, axes=1) >>> print(clip_rows.eval()) [[ 0. 0. ] [ 3. 4. ] [ 6. 8. ] # clipped! [ 6.00000048 8. ]] # clipped!

如果需要，您还可以剪辑列：

>>> clip_cols = tf.clip_by_norm(x, clip_norm=350, axes=0) >>> print(clip_cols.eval()) [[ 0. 0. ] [ 3. 3.48245788] [ 30. 34.82457733] [ 300. 348.24578857]] # clipped!

Answer 2

使用Rafał的建议和TensorFlow的clip_by_norm def renorm(x, axis, max_norm): '''Renormalizes the sub-tensors along axis such that they do not exceed norm max_norm.''' # This elaborate dance avoids empty slices, which TF dislikes. rank = tf.rank(x) bigrange = tf.range(-1, rank + 1) dims = tf.slice( tf.concat(0, [tf.slice(bigrange, [0], [1 + axis]), tf.slice(bigrange, [axis + 2], [-1])]), [1], rank - [1]) # Determine which columns need to be renormalized. l2norm_inv = tf.rsqrt(tf.reduce_sum(x * x, dims, keep_dims=True)) scale = max_norm * tf.minimum(l2norm_inv, tf.constant(1.0 / max_norm)) # Broadcast the scalings return tf.mul(scale, x)，这是我想出的：

> x = tf.constant([0., 0., 3., 4., 30., 40., 300., 400.], shape=(4, 2))
> print x.eval()
[[   0.    0.]  # rows have norms of 0, 5, 50, 500
 [   3.    4.]  # cols have norms of ~302, ~402
 [  30.   40.]
 [ 300.  400.]]
> print renorm(x, 0, 10).eval()
[[ 0.          0.        ]  # unaffected
 [ 3.          4.        ]  # unaffected
 [ 5.99999952  7.99999952]  # rescaled
 [ 6.00000048  8.00000095]] # rescaled
> print renorm(x, 1, 350).eval()
[[   0.            0.        ]  # col 0 is unaffected
 [   3.            3.48245788]  # col 1 is rescaled
 [  30.           34.82457733]
 [ 300.          348.24578857]]

它似乎具有二维矩阵所需的行为，应该如此概括为张量：

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Answer 3

查看clip_by_norm函数，它正是这样做的。它需要一个张量作为输入并返回按比例缩小的张量。

使用TensorFlow重整化权重矩阵

3 个答案: