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The nonlinear model introduced in the previous chapter consists of applying a sigmoid function to a linear combination of the input data. This model can successfully approximate several logic gates, including the AND, OR, NAND, and NOR gates. However, it fails to represent more complex gates such as the XOR gate (as well as the XAND gate). In this chapter, we introduce intermediate variables and employ composite functions to approximate the XOR gate. These composite functions can be interpreted as a network of interconnected neural nodes, and the intermediate variables correspond to the hidden layers of the network.

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Shallow Neural Network

  • 章节

  • 发表日期：

    2026年

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  • Xiang-Sheng Wang,
  • Chisheng Wang

摘要

The nonlinear model introduced in the previous chapter consists of applying a sigmoid function to a linear combination of the input data. This model can successfully approximate several logic gates, including the AND, OR, NAND, and NOR gates. However, it fails to represent more complex gates such as the XOR gate (as well as the XAND gate). In this chapter, we introduce intermediate variables and employ composite functions to approximate the XOR gate. These composite functions can be interpreted as a network of interconnected neural nodes, and the intermediate variables correspond to the hidden layers of the network.