# Integrated Photonic Neural Networks for Equalizing Optical Communication Signals: A Review
## 4 Building Blocks of Photonic Neural Networks
Figure 5: MNIST classification performance with the MXene saturable absorber acting as a nonlinear activation function. (**a**) Structure of the fully connected network. (**b**) Different MXene-based activation functions. (**c**) Prediction accuracy of the photonic neural network. (**d**) Convolutional neural network with all-optical nonlinear activation function operations. (**e**) Model accuracy comparison. (**f**) Experimental confusion matrices. Reproduced without modification from [PERSON] et al. [103], © 2023, licensed under an Attribution-Noncommercial-Noderivs International License 4.0 (CC BY-NC-ND 4.0). Figure 6: Matrix multiplication computation methods. Reproduced without modification from [PERSON] et al. [107], © 2022, licensed under a Creative Commons Attribution International License 4.0 (CC BY 4.0). Other recent investigations that combine multiplication matrices, activation functions, and training stages to process optical signals from the front door to the output port can further be highlighted in the direction of building all-optical photonic neural networks. For example, [PERSON] et al. demonstrated an all-photonic accelerator using a single-ring resonator to store information encoded in the amplitude of frequency modes [110]. Nonlinear optical processes enable interaction among these modes. The matrix multiplication and the activation functions on these modes in this work are performed coherently, allowing a direct representation of negative and complex numbers without passing through digital electronics. Thus, this architecture enables on-chip analog Hamiltonian-echo backpropagation for gradient descent and other self-learning tasks [110]. [PERSON] et al. presented a study on an optical authentication system based on a diffractive deep neural network [111]. A unique and secure image representation at a precise distance is generated by manipulating a light beam with a public and private key. The certification system possesses inherent concealment characteristics and enhanced security by leveraging invisible terahertz light. Specifically, a diffractive deep neural network with diffraction lay  
Figure 7: (**a**–**c**) Matrix multiplication. (**d**) Electro-optic blocks. (**e**) Hardware implementation of a neuron in three phases. (**f**) Matrix–vector multiplication process. (**g**) The time–division multiplexing scheme followed during the tiled matrix–vector multiplication process of (**f**). Reproduced without modification from [PERSON]. [PERSON] et al. [109], © 2023, licensed under a Creative Commons Attribution International License 4.0 (CC BY 4.0). ers is designed following this scheme, and a THz beam for illumination is employed [111]. The side length of each diffracted neuron, the scale of each network layer, and the interval between two adjacent layers are determined, in which in each diffraction layer there are \(200\times 200\) neurons. Thus, every neuron on the adjacent diffraction layer is connected to each other through the diffraction layer, generating 6.4 billion neural connections from the input layer to the output layer. This entire certification process proposed by these authors operates solely through the manipulation of the light beam, eliminating the need for electronic calculations [111]. Furthermore, [PERSON] et al. recently presented a reconfigurable optical activation function based on adding or subtracting the outputs of two saturable absorbers [112]. This approach can provide bounded and unbounded outputs by facilitating an electrically programmable adder/subtractor design. Furthermore, by investigating the multiplication noise and the loss function, a vector-matrix multiplication that was six times more parallel than the conventional optical vector-matrix multiplication method was obtained [112]. Integrating on-chip nonlinear activation functions, multiplication operations, and training mechanisms in the optical domain is essential for efficiently processing optical signals from input to output.