课程地址：https://www.coursera.org/learn/neural-networks

老师主页：http://www.cs.toronto.edu/~hinton

备注：笔记内容和图片均参考老师课件。

这周介绍了pre-train，这里主要回顾下选择题。

#### 选择题 1

The objective function of an autoencoder is to reconstruct its input, i.e., it is trying to learn a function $f$, such that $f(x) = x$ for all points $x$ in the dataset.It makes sense to learn a mapping from $x$ to some target $t$ for solving a classification or regression problem, but why do we want to learn a mapping that takes $x$ to $x$ ? It seems like a silly thing to do!

- While the objective is to learn $f$ such that $f(x)=x$, we might end up learning a mapping to a totally different space in which $f(x)$ might be a much better representation of the input.
- Due to the constraints in the network, $x$ will never be mapped exactly to $x$ but to something close-by, say $\hat{x}$. We can then use $\hat{x}$ as a better representation of $x$.
- We want to have a decoder network, so that it is easy to get a reconstruction of the data.
- While the objective is to reconstruct $x$, what we really care about is learning good representations in the hidden layers which come as a by-product of doing this.

学习autoencoder最主要的原因是学习中间的隐藏层，第四项正确。

#### 选择题 2

The process of autoencoding a vector seems to lose some information since the autoencoder cannot reconstruct the input exactly (as seen by the blurring of reconstructed images reconstructed from 256-bit codes). In other words, the intermediate representation appears to have less information than the input representation. In that case, why is this intermediate representation more useful than the input representation ?

- The intermediate representation actually has more information than the inputs.
- The intermediate representation is more compressible than the input representation.
- The intermediate representation has more noise.
- The intermediate representation may take much less memory to store and much less time to do comparisons with compared to the input. That makes matching queries to a database faster.

学习autoencoder的最主要原因是减少数据的维度，方便比较，第四项正确。

#### 选择题 3

Why is it harder to train deep autoencoders compared to shallow ones ?

- The objective function is intractable for deep autoencoders.
- Starting with small initial weights, backpropagated gradients become very small going down through the network, so the bottom layers do not get much gradient.
- Backpropagation is not exact for deep autoencoders.
- The Markov chain involved in estimate negative phase sufficient statistics does not mix well.

deep autoencoders最主要的问题是反向传播的梯度会越来越小，第二项正确。

#### 选择题 4

In all the autoencoders discussed in the lecture, the decoder network has the same number of layers and hidden units as the encoder network, but arranged in reverse order. Brian feels that this is not a strict requirement for building an autoencoder. He insists that we can build an autoencoder which has a very different decoder network than the encoder network. Which of the following statements is correct?

- Brian is correct. We can indeed have any decoder network, as long as it produces output of the same shape as the data, so that we can compare the output to the original data and tell the network where it’s making mistakes.
- Brian is correct, as long as the decoder network has
**at least**as many parameters as the encoder network. - Brian is correct, as long as the decoder network has the same number of parameters as the encoder network.
- Brian is mistaken. The decoder network must have the same architecture. Otherwise backpropagation will not work.

autoencoder最主目的是重建数据，第一项正确。

#### 选择题 5

Another way of extracting short codes for images is to hash them using standard hash functions. These functions are very fast to compute, require no training and transform inputs into fixed length representations. Why is it more useful to learn an autoencoder to do this ?

- Autoencoders have smooth objective functions whereas standard hash functions have no concept of an objective function.
- For an autoencoder, it is possible to invert the mapping from the hashed value to the reconstruct the original input using the decoder, while this is not true for most hash functions.
- Autoencoders have several hidden units, unlike hash functions.
- Autoencoders are smooth functions and map nearby points in input space to nearby points in code space. They are also invariant to small fluctuations in the input. In this sense, this hashing is locality-sensitive, whereas general hash functions are not locality-sensitive.

Semantic hashing可以将内容相近的输入映射到附近的位置，所以Autoencoder一个光滑的函数，第四项正确。

#### 选择题 6

RBMs and single-hidden layer autoencoders can both be seen as different ways of extracting one layer of hidden variables from the inputs. In what sense are they different ?

- The objective function and its gradients are intractable to compute exactly for RBMs but can be computed efficiently exactly for autoencoders.
- RBMs work only with binary inputs but autoencoders work with all kinds of inputs.
- RBMs define a probability distribution over the hidden variables conditioned on the visible units while autoencoders define a deterministic mapping from inputs to hidden variables.
- RBMs are undirected graphical models, but autoencoders are feed-forward neural nets.

RBM的目标函数是对数似然，它的梯度难以计算，并且计算它们大致需要CD或其他MCMC方法。 autoencoder通常具有易处理的目标，例如平方损耗或交叉熵，易于计算和区分，所以第一项正确。RBM定义一个概率分布，第三项正确。RBM是无向图模型，autoencoder是前馈神经网络，第四项正确。

#### 选择题 7

Autoencoders seem like a very powerful and flexible way of learning hidden representations. You just need to get lots of data and ask the neural network to reconstruct it. Gradients and objective functions can be exactly computed. Any kind of data can be plugged in. What might be a limitation of these models ?

- Autoencoders cannot work with discrete-valued inputs.
- If the input data comes with a lot of noise, the autoencoder is being forced to reconstruct noisy input data. Being a deterministic mapping, it has to spend a lot of capacity in modelling the noise in order to reconstruct correctly. That capacity is not being used for anything semantically valuable, which is a waste.
- The inference process for finding states of hidden units given the input is intractable for autoencoders.
- The hidden representations are noisy.

第二项正确。