Lagrange Oscillatory Neural Networks for Constraint Satisfaction and Optimization

Physics-inspired computing paradigms are receiving renewed attention to enhance efficiency in compute-intensive tasks such as artificial intelligence and optimization. Similar to Hopfield neural networks, oscillatory neural networks (ONNs) minimize an Ising energy function that embeds the solutions of hard combinatorial optimization problems. Despite their success in solving unconstrained optimization problems, Ising machines still face challenges with constrained problems as they can get stuck at infeasible local minima. In this paper, we introduce a Lagrange ONN (LagONN) designed to escape infeasible states based on the theory of Lagrange multipliers. Unlike existing oscillatory Ising machines, LagONN employs additional Lagrange oscillators to guide the system towards feasible states in an augmented energy landscape and settles only when constraints are met. Taking the maximum satisfiability problem with three literals as a use case (Max-3-SAT), we harness LagONN's constraint satisfaction mechanism to find optimal solutions for random SATlib instances with up to 200 variables and 860 clauses, which provides a deterministic alternative to simulated annealing for coupled oscillators. We further discuss the potential of Lagrange oscillators to address other constraints, such as phase copying, which is useful in oscillatory Ising machines with limited connectivity.

Oscillatory Neural Network as Hetero-Associative Memory for Image Edge Detection

The increasing amount of data to be processed on edge devices, such as cameras, has motivated Artificial Intelligence (AI) integration at the edge. Typical image processing methods performed at the edge, such as feature extraction or edge detection, use convolutional filters that are energy, computation, and memory hungry algorithms. But edge devices and cameras have scarce computational resources, bandwidth, and power and are limited due to privacy constraints to send data over to the cloud. Thus, there is a need to process image data at the edge. Over the years, this need has incited a lot of interest in implementing neuromorphic computing at the edge. Neuromorphic systems aim to emulate the biological neural functions to achieve energy-efficient computing. Recently, Oscillatory Neural Networks (ONN) present a novel brain-inspired computing approach by emulating brain oscillations to perform autoassociative memory types of applications. To speed up image edge detection and reduce its power consumption, we perform an in-depth investigation with ONNs. We propose a novel image processing method by using ONNs as a hetero-associative memory (HAM) for image edge detection. We simulate our ONN-HAM solution using first, a Matlab emulator, and then a fully digital ONN design. We show results on gray scale square evaluation maps, also on black and white and gray scale 28x28 MNIST images and finally on black and white 512x512 standard test images. We compare our solution with standard edge detection filters such as Sobel and Canny. Finally, using the fully digital design simulation results, we report on timing and resource characteristics, and evaluate its feasibility for real-time image processing applications. Our digital ONN-HAM solution can process images with up to 120x120 pixels (166 MHz system frequency) respecting real-time camera constraints. This work is the first to explore ONNs as hetero-associative memory for image processing applications.