Attention in Neural Networks and How to Use It
http://akosiorek.github.io/ml/2017/10/14/visual-attention.html
这篇博文主要介绍神经网络中的注意力机制，代码实现了两个 soft visual attention
What is Attention? 首先来看看 注意力机制是什么？
Informally, a neural attention mechanism equips a neural network with the ability to focus on a subset of its inputs (or features): it selects specific inputs.
注意力机制可以让一个神经网络能够只关注其输入的一部分信息，它能够选择特定的输入。
attention is implemented as 
f 是一个 attention network，其生成一个 attention vector a, 再讲 a 与输入 x 的 特征向量 z 相乘，这个 a 取值范围是 【0,1】，当我们说 soft attention 时，其取值是 0 到 1，当我们说 hard attention 其取值就只有 0 或 1。
为什么 attention 是重要的了？我们还有从 neural network 的本质说起， neural network 本质上就是一个 函数拟合器 function approximator，它的结构决定其可以拟合什么类型的函数，通常情况下输入向量彼此的作用方式只能是相加 A typical neural net is implemented as a chain of matrix multiplications and element-wise non-linearities, where elements of the input or feature vectors interact with each other only by addition
但是 注意力机制可以让输入向量之间的作用方式是相乘
Attention mechanisms compute a mask which is used to multiply features
neural networks are universal function approximators and can approximate an arbitrary function to arbitrary precision, but only in the limit of an infinite number of hidden units. In any practical setting, that is not the case: we are limited by the number of hidden units we can use.
神经网络可以拟合任意函数，但是受限于神经单元的数量，我们拟合的函数是有限制的。
The above definition of attention as multiplicative interactions allow us to consider a broader class of models if we relax the constrains on the values of the attention mask
注意力引入的 multiplicative interactions 可以让我们拟合更复杂的函数模型
Visual Attention
Attention 可以被应用到任意类型的输入，不管其形状如何，对于矩阵形式的输入 如 图像，我们可以探讨 visual attention，
Hard Attention
对于图像的 Hard Attention 就是 image cropping ： g = I[y:y+h, x:x+w]， 这个 hard attention 的问题是 non-differentiable，可以通过 score-function estimator 来解决
Soft Attention
文献 Show, Attend and Tell 中使用这种类型的 attention， 
The model learns to attend to specific parts of the image while generating the word describing that part
Closing Thoughts
Attention mechanisms expand capabilities of neural networks: they allow approximating more complicated functions, or in more intuitive terms, they enable focusing on specific parts of the input.
Attention mechanisms 应该可以发挥更大的作用！
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