Generalized Training for Neural Network Learnability: a Spectral Methods Approach

TL;DR

The paper tackles the data- and compute-hungry bottlenecks of training neural systems by introducing a spectral-methods framework that generates synthetic, spectrally parameterized training data for HONNs. It leverages a dual-vortex encoder to enable fast, linear phase reconstruction in the Fourier domain and uses dataset metrics $H_{ m SVD}$ and $\Omega_k$ to control learnability and reconstruction fidelity. A key finding is that higher $H_{ m SVD}$ increases learning time, but matching spectral content between training and test data (SAD parity) improves reconstruction; speckle-pretrained reconstructions can also serve as effective preprocessors for downstream classification. The approach suggests a pathway to reduce computational overhead in vision tasks by designing training data with targeted spectral properties while preserving meaningful downstream performance.

Abstract

Hybrid optical neural networks (HONNs) offload some electronic computation to optical preprocessors to achieve low-power and fast training and inference phases in machine learning tasks. Our contribution to the development of HONNs is a spectral-methods paradigm for building synthetic training data for machine-learned models. Here, our synthetic training image data does not resemble the image test data. As a result, the neural network focuses on learning specific features parameterized by the synthetic training data. Within this paradigm, a dataset's singular value decomposition entropy indicates {\it learnability}, i.e., how rapidly a model converges. Subsequently, we train a neural network model to rapidly learn specific features for further downstream analyses.

Figures (5)

• Figure 1: Schematic for a dual vortex, optically encoded and electronically decoded system. A set of spectral correlations of some source image, $\psi(x,y)$, are produced in the sensor plane, $\psi'(x,y)$ (top). The resulting data has some of the original image's phase information. This system is analogous to an autoencoder, machine-learned architecture that distills features and denoises images (below).
• Figure 2: (A) Representative speckle images from 100 training sets and models, which are parameterized with Singular Value Decomposition Entropy ($H_{\rm SVD}$) and Speckle Analogue Density (SAD, $\Omega_k$). The diagonal, blue-highlighted images represent the primary dataset from which the other 90 are formed. (B) Representative vortex-encoded sensor patterns applied in parallel with topological charges $m$ = 1, 3 for the primary dataset. (C) Images from the MNIST fashion and CIFAR-100 datasets and their vortex-encoded, sensor patterns for $m=1,3$. (D) Representative reconstructed images using the pre-trained models from the primary datasets.
• Figure 3: (A) Several machine learning convergence plots are shown on a log-scale. Each of these convergence curves correspond to a model trained on a dataset with a different $H_{SVD}$. (B) Those same plots are extended to reflect the average $H_{SVD}$ of the images used to train the models. Given this view, it is clear that models with lower $H_{SVD}$ train faster--reach training loss-convergence.
• Figure 4: The LPIPS of models trained on the synthetic training datasets as described earlier in this text is plotted against the average SAD ($\Omega_k$) and $H_{SVD}$. Lower (darker) LPIPS refers to greater fidelity to the original image. Underneath is a density map of the CIFAR10 dataset also parameterized by SAD and $H_{SVD}$. The lowest LPIPS value (the highest fidelity) coincides with the height of CIFAR10 density.
• Figure 5: (A) A previously untrained 2-layer dense neural network is used to classify CIFAR-10. Predictably, the classification accuracy of the model is 10%, which is no better than random chance. (B) Whereas, the same original information can be first preprocessed by a neural network to create images that, when used to train a classification neural network, yield upwards of 90% accuracy. (C) Compressed representations of the overall landscape of the performance of test data 'distilled' with models of varying $H_{SVD}$ and $\Omega_k$. For the most part, high entropy/high SAD data result in better classification performance, regardless of initial reconstruction accuracy.