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Ensemble learning of diffractive optical networks
Md Sadman Sakib Rahman, Jingxi Li, Deniz Mengu, Yair Rivenson, Aydogan Ozcan
TL;DR
Despite progress in diffractive optical processing, significant room remains for improvement. The study diversifies D2NN inputs with passive filters, then prunes 1,252 independently trained networks into ensembles. On CIFAR-10, ensembles of 14 and 30 achieve the highest D2NN inference accuracies reported to date on that dataset.
Problem
Despite reported progress, significant room remains for improving diffractive processing of optical information.
Source: Introduction · p. 2Method
The authors engineered D2NN inputs with passive filters, independently trained 1,252 networks, and used iterative pruning to select ensembles.
Source: Introduction · pp. 2–3Results
61.14±0.23% for N=14 and 62.13±0.05% for N=30 are the blind testing accuracies on CIFAR-10, the highest achieved to date by D2NN designs on this dataset.
Source: Discussion · p. 8Takeaways & Limitations
The pruned ensemble performs significantly better than any individual diffractive network within it, demonstrating a “wisdom of the crowd.”
Source: Results · p. 6Larger ensembles increase optical setup complexity and illumination-power demand, while building the initial pool of 1,252 networks substantially raises training time.
Source: Discussion · pp. 7–8
Abstract
from arXiv · showhide
A plethora of research advances have emerged in the fields of optics and photonics that benefit from harnessing the power of machine learning. Specifically, there has been a revival of interest in optical computing hardware, due to its potential advantages for machine learning tasks in terms of parallelization, power efficiency and computation speed. Diffractive Deep Neural Networks (D2NNs) form such an optical computing framework, which benefits from deep learning-based design of successive diffractive layers to all-optically process information as the input light diffracts through these passive layers. D2NNs have demonstrated success in various tasks, including e.g., object classification, spectral-encoding of information, optical pulse shaping and imaging, among others. Here, we significantly improve the inference performance of diffractive optical networks using feature engineering and ensemble learning. After independently training a total of 1252 D2NNs that were diversely engineered with a variety of passive input filters, we applied a pruning algorithm to select an optimized ensemble of D2NNs that collectively improve their image classification accuracy. Through this pruning, we numerically demonstrated that ensembles of N=14 and N=30 D2NNs achieve blind testing accuracies of 61.14% and 62.13%, respectively, on the classification of CIFAR-10 test images, providing an inference improvement of >16% compared to the average performance of the individual D2NNs within each ensemble. These results constitute the highest inference accuracies achieved to date by any diffractive optical neural network design on the same dataset and might provide a significant leapfrog to extend the application space of diffractive optical image classification and machine vision systems.
Introduction
This work explores improving CIFAR-10 inference with diffractive optical networks by diversifying D2NN inputs and pruning an ensemble of independently trained networks. It also describes grayscale-image training with data augmentation, validation-based model selection, and reported training and pruning runtimes.
Introduction
- Ensembles of N=14 and N=30 D2NNs achieved 61.14±0.23% and 62.13±0.05% blind CIFAR-10 test accuracy, respectively—the highest reported for a diffractive optical network on that dataset and >16% above the constituent-model average.The study selected these ensembles by pruning a pool of 1252 independently trained D2NNs.Source: Introduction · p. 3, Discussion · p. 8
Results
- The initial pool comprised 1252 D2NNs diversified by object-plane or Fourier-plane passive filters and amplitude- or phase-encoded inputs.Of the pool, 340 used amplitude encoding and 912 used phase encoding; the networks processed the filtered image in the spatial domain.Source: Introduction · p. 3, Results · p. 4
- Pruning optimized class-specific weights on validation data, ranked networks by their weight L1 norms, and iteratively removed members, sometimes at random.The final ensemble was chosen by validation accuracy under a size limit, without using the test set during pruning.Source: Results · pp. 4–5, Discussion · p. 11
- With N=77, blind CIFAR-10 accuracy reached 62.56%, while gains diminished as ensemble size increased; the N=14 ensemble reached 61.14±0.23%.For Nmax=14, periodic random elimination yielded better accuracy than pruning without random elimination; the best average was 61.14±0.23%.Source: Results · p. 5
- The N=14 ensemble outperformed every constituent classifier, with class-specific true-positive-rate gains of 13.47% to 19.98% over the individual-model mean.The top 10 individual D2NNs in the initial pool were not selected, and some selected models had <40% accuracy despite unselected models exceeding 50%.Source: Results · p. 6
- Combining phase- and amplitude-encoded models improved inference over phase-only ensembles, whose best Nmax=14 result was 60.74±0.17% with N=14.The median phase-only ensemble achieved 60.65% blind test accuracy.Source: Results · p. 6
Discussion
- The N=30 ensemble’s 62.13±0.05% accuracy approached LeNet’s 66.43% on grayscale CIFAR-10 but remained below AlexNet’s 72.64% and ResNet’s 87.54%.The authors identify broader feature engineering and larger, more diverse D2NN pools as potential routes to narrowing this gap.Source: Discussion · p. 7
- Larger ensembles increase optical hardware and illumination-power requirements, but parallel passive operation preserves inference latency; replacing optimized weights with equal sums reduced the N=14 result only from 61.21% to 61.08%.Training also grows with the 1252-model initial pool, though it is a one-time effort; the authors note that fabrication advances may ease hardware size and complexity.Source: Discussion · pp. 7–8
- Each D2NN used softmax-cross-entropy training and was selected by validation performance after 50 epochs with batches of 8.Training used Adam with an initial learning rate of 0.001, decayed by 0.7 every 8 epochs; images were converted to grayscale and randomly flipped left-to-right with probability 0.5.Source: Discussion · p. 11
- A typical D2NN took about 4.5 hours to train, while iterative ensemble pruning took 0.75–7.5 hours depending on its hyperparameters.The computations ran on a GTX 1080 Ti GPU, an Intel Core i7-8700 CPU, and 64 GB of RAM under Windows 10.Source: Discussion · p. 11
Figures and Tables
The figures and table depict feature-filtered D2NN ensembles, weighted combination of their class scores, and iterative pruning. They report CIFAR-10 blind-test results and show how accuracy relates to ensemble size and pruning settings.
Fig. 1 and Table 1
- 62.13±0.05% for N=30, 61.14±0.23% for N=14, and 60.35±0.39% for N=12 are reported on CIFAR-10; Table 1 marks N=14 best for average accuracy and N=12 best per network.The reported standard deviations are calculated over three repeats with the same hyperparameters.Source: Figure 1 · p. 17, Table 1 · p. 22
Fig. 1
- Base networks filter inputs on either the object plane or the Fourier plane of a 4-f system, and the ensemble combines their differential detector signals by weighted summation.The illustrated object-plane filter uses a passive transmission window; the Fourier-plane example is a bandpass filter.Source: Figure 1 · p. 17
Fig. 2
- Fig. 2 tracks blind testing accuracy against Nmax and N, and relates those ensemble sizes across different pruning parameters.Nmax is the maximum allowed ensemble size during pruning.Source: Figure 2 · p. 18
Fig. 3
- 61.08% without class-specific weights is below the reported 61.21%; the ensemble improves test accuracy by about 16.6% over the mean individual-network performance.The figure also compares classwise true-positive rates and individual-network test accuracy with the ensemble.Source: Figure 3 · p. 19, Figures and Tables · p. 20
- Networks 1–4 use amplitude inputs and 5–14 phase inputs; border colors encode phase ranges from 0–π/2 through 0–2π.The phase-encoding dynamic range is represented by the border color.Source: Figures and Tables · p. 20
Fig. 4
- Pruning produces successively smaller ensembles; after T iterations, removals switch from weight ranking to random selection restricted to the bottom two-thirds.The flow chart identifies i as the iteration number.Source: Figures and Tables · p. 21, Figure 4 · p. 21