一步一步分析讲解神经网络基础-Feedforward Neural Network

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A feedforward neural network is an artificial neural network wherein connections between the units do not form a cycle. As such, it is different from recurrent neural networks.
The feedforward neural network was the first and simplest type of artificial neural network devised.[citation needed] In this network, the information moves in only one direction, forward, from the input nodes, through the hidden nodes (if any) and to the output nodes. There are no cycles or loops in the network.

前馈神经网络是一个人工神经网络，并且没有循环，单向传播，是最简单的人工神经网络。
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A similar neuron was described by Warren McCulloch and Walter Pitts in the 1940s.
Warren McCulloch and Walter Pitts在1940年左右，提出前馈神经网络。
This result can be found in Peter Auer, Harald Burgsteiner and Wolfgang Maass “A learning rule for very simple universal approximators consisting of a single layer of perceptrons”.
Peter Auer, Harald Burgsteiner and Wolfgang Maass 描述这是一种简单的万能逼近器。
这里写图片描述
A two-layer neural network capable of calculating XOR. The numbers within the neurons represent each neuron’s explicit threshold (which can be factored out so that all neurons have the same threshold, usually 1). The numbers that annotate arrows represent the weight of the inputs. This net assumes that if the threshold is not reached, zero (not -1) is output. Note that the bottom layer of inputs is not always considered a real neural network layer.
计算XOR的两层神经网络。神经元内的数字表示每个神经元（Perceptron层）的显式阈值（可以将其分解，以便所有神经元具有相同的阈值，通常为1）。注释箭头的数字代表输入的权重。该网络假定如果未达到阈值，则输出零。请注意，最后一层（Output层）的输入并不是一个真正的神经网络层。

References

1， Zell, Andreas (1994). Simulation Neuronaler Netze [Simulation of Neural Networks] (in German) (1st ed.). Addison-Wesley. p. 73. ISBN 3-89319-554-8.
2，Jump up ^ Auer, Peter; Harald Burgsteiner; Wolfgang Maass (2008). “A learning rule for very simple universal approximators consisting of a single layer of perceptrons” (PDF). Neural Networks. 21 (5): 786–795. doi:10.1016/j.neunet.2007.12.036. PMID 18249524.
3，Jump up ^ Roman M. Balabin; Ravilya Z. Safieva; Ekaterina I. Lomakina (2007). “Comparison of linear and nonlinear calibration models based on near infrared (NIR) spectroscopy data for gasoline properties prediction”. Chemometr Intell Lab. 88 (2): 183–188. doi:10.1016/j.chemolab.2007.04.006.
4，Jump up ^ Tahmasebi, Pejman; Hezarkhani, Ardeshir (21 January 2011). “Application of a Modular Feedforward Neural Network for Grade Estimation”. Natural Resources Research. 20 (1): 25–32. doi:10.1007/s11053-011-9135-3.

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