A method to improve the computational performance of nonlinear all—optical diffractive deep neural network model

Figures & data

Figure 1. Schematic diagram of ReLU phase-limit N-D²NN structure. (a) Using MNIST as a dataset to train the model. (b) Using Fashion-MNIST as a dataset to train the model.

Figure 2. Mathematical models of various activation functions. (a) Sigmoid, Tanh, Softsign, Softplus, Swish and Mish. (b) ReLU, Leaky- ReLU, PReLU, RReLU, eLU, SeLU and ReLU6.

Table 1. The confusion matrix of ten classifiers.

		Predictive value
		0	1	2	…	8	9
True value	0	${\chi }_{00}$	${\chi }_{01}$	${\chi }_{02}$	…	${\chi }_{08}$	${\chi }_{09}$
	1	${\chi }_{10}$	${\chi }_{11}$	${\chi }_{12}$		${\chi }_{18}$	${\chi }_{19}$
	2	${\chi }_{20}$	${\chi }_{21}$	${\chi }_{22}$		${\chi }_{28}$	${\chi }_{29}$
		…			…	…
	8	${\chi }_{80}$	${\chi }_{81}$	${\chi }_{82}$	…	${\chi }_{88}$	${\chi }_{89}$
	9	${\chi }_{90}$	${\chi }_{91}$	${\chi }_{92}$		${\chi }_{98}$	${\chi }_{99}$

Table 2. Physical parameters of grating in ReLU phase-limit N-D2NN.

Grating parameters	Numerical
Wavelength $\lambda$	10.6 µm
Pixel size	5 µm
Spacing of diffraction grating	$30\lambda$

Table 3. Training parameters in ReLU phase-limit N-D²NN.

Training parameters	Numerical
Diffraction grating layers	6
Number of neurons in each hidden layer	100 × 100
Batch size	100
Epoch	50
Learning rate	5 × 10^−2

Figure 3. Correspondence between epoch and accuracy at training time for different ReLU phase-limit N-D²NN models. (a) Using MNIST as a dataset to train the model. (b) Using Fashion-MNIST as a dataset to train the model.

Figure 4. Classification performance obtained by different the ReLU phase-limit N-D²NN on the the MNIST and Fashion-MNIST datasets.

Figure 5. Two kinds of functions are used to limit the classification accuracy of N-D²NN with phase on datasets. (a) MNIST. (b) Fashion-MNIST.

Table 4. Computational performance of different D²NN models.

Model	Accuracy (%)
	MNIST dataset	Fashion-MNIST dataset
ReLU phase-limit N-D^2NN	98.38	90.14
F-D^2NN^[^7^]	98.1	/
In situ optical training of DONN^[^8^]	97.48	/
N-D^2NN (Sigmoid phase-limit)^[^9^]	97.86	89.28
DNN-NOM^[^12^]	97.00	88.26
Nonlinear-TAPLM1^[^13^]	94.64	/
Nonlinear-TAPLM2^[^13^]	95.82	/
Nonlinear-OASLM^[^13^]	94.85	/
D^2NN reduces the influence of gradient Vanishing (complex-valued)^[^15^]	97.81	89.32
D^2NN reduces the influence of gradient Vanishing (phase-only)^[^15^]	97.18	89.13
Res-D^2NN^[^16^]	98.4	88.4
D^2NN with OReLU function based on genetic algorithm^[^26^]	97.97	87.85
Visible light D^2NN^[^39^]	91.57	/

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Data availability statement

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.