前馈神经网络

前馈神经网络（英文：Feedforward Neural Network），是指神经网络的识别-推理架构。人工神经网络架构是以输入乘上权重来获得输出（输入对输出）：前馈。^[1]循环神经网络或有循环的神经网络允许后处理阶段的资讯回馈到前处理阶段进行序列处理。^[2]然而，在推论的每个阶段，前馈乘法仍然是核心，对于反向传播或透过时间的反向传播来说是不可或缺的。^[3]^[4]^[5]^[6]^[7]因此，神经网络不能包含负反馈或正反馈等回馈，在负反馈或正反馈中，输出会回馈到相同的输入并对其进行修改，因为这会形成一个无限循环，不可能通过反向传播在时间上倒退以产生错误信号。这个问题和命名似乎是一些计算机科学家和其他研究脑部网络领域的科学家之间的混淆点。^[8]

前馈神经网络为人工智能领域中，最早发明的简单人工神经网络类型。在它内部，参数从输入层向输出层单向传播。有异于循环神经网络，它的内部不会构成有向环。^[9]

单层感知机

多层感知机

参考

^ Zell, Andreas. Simulation Neuronaler Netze [Simulation of Neural Networks] 1st. Addison-Wesley. 1994: 73. ISBN 3-89319-554-8 （German）.
^ Schmidhuber, Jürgen. Deep learning in neural networks: An overview. Neural Networks. 2015-01-01, 61: 85–117. ISSN 0893-6080. PMID 25462637. S2CID 11715509. arXiv:1404.7828  . doi:10.1016/j.neunet.2014.09.003 （英语）.
^ Linnainmaa, Seppo. The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors (学位论文). University of Helsinki: 6–7. 1970 （芬兰语）.
^ Kelley, Henry J. Gradient theory of optimal flight paths. ARS Journal. 1960, 30 (10): 947–954. doi:10.2514/8.5282.
^ Rosenblatt, Frank. x. Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms. Spartan Books, Washington DC, 1961
^ Werbos, Paul. Applications of advances in nonlinear sensitivity analysis (PDF). System modeling and optimization. Springer. 1982: 762–770 [2 July 2017]. （原始内容存档 (PDF)于14 April 2016）.
^ Rumelhart, David E., Geoffrey E. Hinton, and R. J. Williams. "Learning Internal Representations by Error Propagation". David E. Rumelhart, James L. McClelland, and the PDP research group. (editors), Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundation. MIT Press, 1986.
^ Achler, T. What AI, Neuroscience, and Cognitive Science Can Learn from Each Other: An Embedded Perspective. Cognitive Computation. 2023 （英语）.
^ 戴葵. 译.（机械工业出版社）《神经网络设计》

[Zell1994p73-1] Zell, Andreas. Simulation Neuronaler Netze [Simulation of Neural Networks] 1st. Addison-Wesley. 1994: 73. ISBN 3-89319-554-8 （German）.

[2] Schmidhuber, Jürgen. Deep learning in neural networks: An overview. Neural Networks. 2015-01-01, 61: 85–117. ISSN 0893-6080. PMID 25462637. S2CID 11715509. arXiv:1404.7828  . doi:10.1016/j.neunet.2014.09.003 （英语）.

[lin1970-3] Linnainmaa, Seppo. The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors (学位论文). University of Helsinki: 6–7. 1970 （芬兰语）.

[kelley1960-4] Kelley, Henry J. Gradient theory of optimal flight paths. ARS Journal. 1960, 30 (10): 947–954. doi:10.2514/8.5282.

[5] Rosenblatt, Frank. x. Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms. Spartan Books, Washington DC, 1961

[werbos1982-6] Werbos, Paul. Applications of advances in nonlinear sensitivity analysis (PDF). System modeling and optimization. Springer. 1982: 762–770 [2 July 2017]. （原始内容存档 (PDF)于14 April 2016）.

[rumelhart1986-7] Rumelhart, David E., Geoffrey E. Hinton, and R. J. Williams. "Learning Internal Representations by Error Propagation". David E. Rumelhart, James L. McClelland, and the PDP research group. (editors), Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundation. MIT Press, 1986.

[AINeuroCog-8] Achler, T. What AI, Neuroscience, and Cognitive Science Can Learn from Each Other: An Embedded Perspective. Cognitive Computation. 2023 （英语）.

[9] 戴葵. 译.（机械工业出版社）《神经网络设计》

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