Broadcasting

目录

* Broadcasting
<https://www.cnblogs.com/nickchen121/p/10849477.html#broadcasting>
* Key idea <https://www.cnblogs.com/nickchen121/p/10849477.html#key-idea>
* How to understand?
<https://www.cnblogs.com/nickchen121/p/10849477.html#how-to-understand>
* Why broadcasting？
<https://www.cnblogs.com/nickchen121/p/10849477.html#why-broadcasting>
* Broadcastable?
<https://www.cnblogs.com/nickchen121/p/10849477.html#broadcastable>
* Broadcast VS Tile
<https://www.cnblogs.com/nickchen121/p/10849477.html#broadcast-vs-tile>
Broadcasting

* expand（扩展数据）
* without copying data（不复制数据）
* tf.broadcast_to
Key idea

* Insert 1 dim ahead if needed
* Expand dims with size 1 to same size
* example:
* [4,16,16,32]
* [32]
* [4,16,16,32]
*
[1,1,1,32]

* [4,16,16,32]
*
[4,16,16,32]



How to understand?

* When it has no axis
* Create a new concepy
* [classes, students, scores] + [scores]
* When it has dim of size 1
* Treat it shared by all
* [classes,students,scores] + [students,1]
Broadcasting可以理解成把维度分成大维度和小维度，小维度较为具体，大维度更加抽象。也就是小维度针对某个示例，然后让这个示例通用语大维度。

Why broadcasting？

* for real demanding
* [classes, students, scores]
* Add bias for every student: +5 score
* [4,32,8] + [4,32,8]
* [4,32,8] + [5.0]
* memory consumption
* [4,32,8] -> 1024
* bias = [8]: [5.0,5.0,5.0,...] -> 8
Broadcastable?

* Match from Last dim!
* if current dim=1, expand to same
* if either has no dim, insert one dim and expand to same
* otherwise, Not Broadcastable
* [4,32,14,14]
* [1,32,1,1] -> [4,32,14,14] √
* [14,14] -> [1,1,14,14] -> [4,32,14,14] √
* [2,32,14,14] ×
* [3] √
* [32,32,1] √
* [4,1,1,1] √ import tensorflow as tf x = tf.random.normal([4,32,32,3])
x.shape TensorShape([4, 32, 32, 3]) (x+tf.random.normal([3])).shape
TensorShape([4, 32, 32, 3]) (x+tf.random.normal([32,32,1])).shape
TensorShape([4, 32, 32, 3]) (x+tf.random.normal([4,1,1,1])).shape
TensorShape([4, 32, 32, 3]) try: (x+tf.random.normal([1,4,1,1])).shape except
Exception as e: print(e) Incompatible shapes: [4,32,32,3] vs. [1,4,1,1]
[Op:Add] name: add/ (x+tf.random.normal([4,1,1,1])).shape TensorShape([4, 32,
32, 3]) b = tf.broadcast_to(tf.random.normal([4,1,1,1]),[4,32,32,3]) b.shape
TensorShape([4, 32, 32, 3])
Broadcast VS Tile
a = tf.ones([3,4]) a.shape TensorShape([3, 4]) a1 = tf.broadcast_to(a,[2,3,4])
a1.shape TensorShape([2, 3, 4]) a2 = tf.expand_dims(a,axis=0) # 0前插入一维 a2.shape
TensorShape([1, 3, 4]) a2 = tf.tile(a2,[2,1,1]) # 复制一维2次，复制二、三维1次 a2.shape
TensorShape([2, 3, 4])

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