Feed forward neural networks (FF or FFNN) and perceptrons (P) are very straight forward, they feed information from the front to the back (input and output, respectively). Neural networks are often described as having layers, where each layer consists of either input, hidden or output cells in parallel. A layer alone never has connections and in general two adjacent layers are fully connected (every neuron form one layer to every neuron to another layer). The simplest somewhat practical network has two input cells and one output cell, which can be used to model logic gates. One usually trains FFNNs through back-propagation, giving the network paired datasets of “what goes in” and “what we want to have coming out”. This is called supervised learning, as opposed to unsupervised learning where we only give it input and let the network fill in the blanks. The error being back-propagated is often some variation of the difference between the input and the output (like MSE or just the linear difference). Given that the network has enough hidden neurons, it can theoretically always model the relationship between the input and output. Practically their use is a lot more limited but they are popularly combined with other networks to form new networks.
前馈神经网络(FF或FFNN)和感知器(P)是非常直接的，它们将信息从前面反馈到后面(分别是输入和输出)。神经网络通常被描述为具有多个层，其中每个层由并行的输入、隐藏或输出单元组成。单独的一层永远不会有连接，通常相邻的两层是完全连接的(每个神经元从一层到另一层)。
最简单而实用的网络有两个输入单元和一个输出单元，可以用它们来建模逻辑门。人们通常通过反向传播来训练FFNNs，给网络配对的数据集“输入什么”和“输出什么”。这叫做监督学习，而不是我们只给它输入，让网络来填补空白的非监督学习。
反向传播的错误通常是输入和输出之间的差异的一些变化(如MSE或只是线性差异)。假设网络有足够多的隐藏神经元，理论上它总是可以模拟输入和输出之间的关系。实际上，它们的使用非常有限，但是它们通常与其他网络结合在一起形成新的网络。
Rosenblatt, Frank. “The perceptron: a probabilistic model for information storage and organization in the brain.” Psychological review 65.6 (1958): 386.
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RBF
Radial basis function (RBF) networks are FFNNs with radial basis functions as activation functions. There’s nothing more to it. Doesn’t mean they don’t have their uses, but most FFNNs with other activation functions don’t get their own name. This mostly has to do with inventing them at the right time.
径向基函数网络是以径向基函数为激活函数的神经网络。没有别的了。这并不意味着它们没有自己的用途，但是大多数带有其他激活函数的FFNNs都没有自己的名称。这主要与在正确的时间发明它们有关。
Broomhead, David S., and David Lowe. Radial basis functions, multi-variable functional interpolation and adaptive networks. No. RSRE-MEMO-4148. ROYAL SIGNALS AND RADAR ESTABLISHMENT MALVERN (UNITED KINGDOM), 1988.
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RNN
Recurrent neural networks (RNN) are FFNNs with a time twist: they are not stateless; they have connections between passes, connections through time. Neurons are fed information not just from the previous layer but also from themselves from the previous pass. This means that the order in which you feed the input and train the network matters: feeding it “milk” and then “cookies” may yield different results compared to feeding it “cookies” and then “milk”. One big problem with RNNs is the vanishing (or exploding) gradient problem where, depending on the activation functions used, information rapidly gets lost over time, just like very deep FFNNs lose information in depth. Intuitively this wouldn’t be much of a problem because these are just weights and not neuron states, but the weights through time is actually where the information from the past is stored; if the weight reaches a value of 0 or 1 000 000, the previous state won’t be very informative. RNNs can in principle be used in many fields as most forms of data that don’t actually have a timeline (i.e. unlike sound or video) can be represented as a sequence. A picture or a string of text can be fed one pixel or character at a time, so the time dependent weights are used for what came before in the sequence, not actually from what happened x seconds before. In general, recurrent networks are a good choice for advancing or completing information, such as autocompletion.
递归神经网络(RNN)是具有时间扭曲的FFNNs:它们不是无状态的;它们之间有联系，时间上的联系。神经元不仅接受来自前一层的信息，还接受来自前一层的自身信息。这意味着输入和训练网络的顺序很重要:先给它“牛奶”，然后再给它“饼干”，与先给它“饼干”，然后再给它“牛奶”相比，可能会产生不同的结果。
RNNs的一个大问题是消失(或爆炸)梯度问题，根据使用的激活函数，随着时间的推移，信息迅速丢失，就像非常深的FFNNs在深度上丢失信息一样。直觉上这不会是个大问题因为这些只是权重而不是神经元的状态，但是时间的权重实际上是储存过去信息的地方;如果权重达到0或1,000 000，则前面的状态不会提供太多信息。
RNNs原则上可以在许多领域中使用，因为大多数没有时间轴的数据形式(与声音或视频不同)都可以表示为序列。一张图片或一串文本可以一次输入一个像素或字符，所以时间相关的权重用于序列中之前发生的内容，而不是x秒之前发生的内容。一般来说，递归网络是一个很好的选择，用于推进或完成信息，如自动完成。
Elman, Jeffrey L. “Finding structure in time.” Cognitive science 14.2 (1990): 179-211.
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LSTM
Long / short term memory (LSTM) networks try to combat the vanishing / exploding gradient problem by introducing gates and an explicitly defined memory cell. These are inspired mostly by circuitry, not so much biology. Each neuron has a memory cell and three gates: input, output and forget. The function of these gates is to safeguard the information by stopping or allowing the flow of it. The input gate determines how much of the information from the previous layer gets stored in the cell. The output layer takes the job on the other end and determines how much of the next layer gets to know about the state of this cell. The forget gate seems like an odd inclusion at first but sometimes it’s good to forget: if it’s learning a book and a new chapter begins, it may be necessary for the network to forget some characters from the previous chapter. LSTMs have been shown to be able to learn complex sequences, such as writing like Shakespeare or composing primitive music. Note that each of these gates has a weight to a cell in the previous neuron, so they typically require more resources to run.
长/短期内存(LSTM)网络试图通过引入门和显式定义的内存单元来解决渐变消失/爆炸的问题。这些灵感主要来自电路，而不是生物学。
每个神经元都有一个记忆细胞和三个门:输入、输出和遗忘。这些门的功能是通过阻止或允许信息流动来保护信息。输入门决定前一层的信息有多少存储在单元格中。输出层接受另一端的任务，并确定下一层对这个单元格的状态了解多少。“忘记门”一开始看起来很奇怪，但有时候忘记也是有好处的:如果你正在学习一本书，并且翻开了新的一章，那么网络可能有必要忘记前一章中的一些字符。
LSTMs已经被证明能够学习复杂的序列，比如像莎士比亚那样的写作或者创作原始音乐。注意，这些门中的每一个都对前一个神经元中的一个细胞有一个权重，因此它们通常需要更多的资源来运行。
Hochreiter, Sepp, and Jürgen Schmidhuber. “Long short-term memory.” Neural computation 9.8 (1997): 1735-1780.
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GRU
Gated recurrent units (GRU) are a slight variation on LSTMs. They have one less gate and are wired slightly differently: instead of an input, output and a forget gate, they have an update gate. This update gate determines both how much information to keep from the last state and how much information to let in from the previous layer. The reset gate functions much like the forget gate of an LSTM but it’s located slightly differently. They always send out their full state, they don’t have an output gate. In most cases, they function very similarly to LSTMs, with the biggest difference being that GRUs are slightly faster and easier to run (but also slightly less expressive). In practice these tend to cancel each other out, as you need a bigger network to regain some expressiveness which then in turn cancels out the performance benefits. In some cases where the extra expressiveness is not needed, GRUs can outperform LSTMs.
门控循环单位（GRU）是LSTM的一个微小变化。它们少了一个门，接线方式略有不同：它们没有输入、输出和忘记门，而是有一个更新门。这个更新门决定了与上一个状态保持多少信息，以及从上一层允许多少信息。
重置门的功能与LSTM的忘记门非常相似，但其位置略有不同。它们总是发送它们的完整状态，它们没有输出门。在大多数情况下，它们的功能与lstms非常相似，最大的区别在于grus的速度稍快，运行起来也更容易（但表达能力也稍差）。在实践中，它们往往会相互抵消，因为您需要一个更大的网络来重新获得一些表现力，而这反过来又会抵消性能优势。在一些不需要额外表现力的情况下，GRUS可以优于LSTM。
Chung, Junyoung, et al. “Empirical evaluation of gated recurrent neural networks on sequence modeling.” arXiv preprint arXiv:1412.3555 (2014).
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BiRNN, BiLSTM and BiGRU
Bidirectional recurrent neural networks, bidirectional long / short term memory networks and bidirectional gated recurrent units (BiRNN, BiLSTM and BiGRU respectively) are not shown on the chart because they look exactly the same as their unidirectional counterparts. The difference is that these networks are not just connected to the past, but also to the future. As an example, unidirectional LSTMs might be trained to predict the word “fish” by being fed the letters one by one, where the recurrent connections through time remember the last value. A BiLSTM would also be fed the next letter in the sequence on the backward pass, giving it access to future information. This trains the network to fill in gaps instead of advancing information, so instead of expanding an image on the edge, it could fill a hole in the middle of an image.
图中没有显示双向递归神经网络、双向长/短期记忆网络和双向门控递归单元(BiRNN、BiLSTM和BiGRU)，因为它们看起来与单向递归单元完全相同。不同之处在于，这些网络不仅与过去相连，而且与未来相连。例如，单向LSTMs可以通过逐个输入字母来训练预测单词“fish”，其中通过时间的重复连接记住最后一个值。BiLSTM还将在向后传递时按顺序输入下一个字母，让它访问未来的信息。这就训练了网络来填补空白，而不是推进信息，因此它可以填补图像中间的一个洞，而不是在边缘扩展图像。
Schuster, Mike, and Kuldip K. Paliwal. “Bidirectional recurrent neural networks.” IEEE Transactions on Signal Processing 45.11 (1997): 2673-2681.
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