Recurrent correlation associative memories

A model for a class of high-capacity associative memories is presented. Since they are based on two-layer recurrent neural networks and their operations depend on the correlation measure, these associative memories are called recurrent correlation associative memories (RCAMs). The RCAMs are shown to be asymptotically stable in both synchronous and asynchronous (sequential) update modes as long as their weighting functions are continuous and monotone nondecreasing. In particular, a high-capacity RCAM named the exponential correlation associative memory (ECAM) is proposed. The asymptotic storage capacity of the ECAM scales exponentially with the length of memory patterns, and it meets the ultimate upper bound for the capacity of associative memories. The asymptotic storage capacity of the ECAM with limited dynamic range in its exponentiation nodes is found to be proportional to that dynamic range. Design and fabrication of a 3-mm CMOS ECAM chip is reported. The prototype chip can store 32 24-bit memory patterns, and its speed is higher than one associative recall operation every 3 µs. An application of the ECAM chip to vector quantization is also described

How important are activation functions in regression and classification? A survey, performance comparison, and future directions

Inspired by biological neurons, the activation functions play an essential part in the learning process of any artificial neural network commonly used in many real-world problems. Various activation functions have been proposed in the literature for classification as well as regression tasks. In this work, we survey the activation functions that have been employed in the past as well as the current state-of-the-art. In particular, we present various developments in activation functions over the years and the advantages as well as disadvantages or limitations of these activation functions. We also discuss classical (fixed) activation functions, including rectifier units, and adaptive activation functions. In addition to discussing the taxonomy of activation functions based on characterization, a taxonomy of activation functions based on applications is presented. To this end, the systematic comparison of various fixed and adaptive activation functions is performed for classification data sets such as the MNIST, CIFAR-10, and CIFAR- 100. In recent years, a physics-informed machine learning framework has emerged for solving problems related to scientific computations. For this purpose, we also discuss various requirements for activation functions that have been used in the physics-informed machine learning framework. Furthermore, various comparisons are made among different fixed and adaptive activation functions using various machine learning libraries such as TensorFlow, Pytorch, and JAX.Comment: 28 pages, 15 figure

Recurrent correlation associative memories

A model for a class of high-capacity associative memories is presented. Since they are based on two-layer recurrent neural networks and their operations depend on the correlation measure, these associative memories are called recurrent correlation associative memories (RCAMs). The RCAMs are shown to be asymptotically stable in both synchronous and asynchronous (sequential) update modes as long as their weighting functions are continuous and monotone nondecreasing. In particular, a high-capacity RCAM named the exponential correlation associative memory (ECAM) is proposed. The asymptotic storage capacity of the ECAM scales exponentially with the length of memory patterns, and it meets the ultimate upper bound for the capacity of associative memories. The asymptotic storage capacity of the ECAM with limited dynamic range in its exponentiation nodes is found to be proportional to that dynamic range. Design and fabrication of a 3-mm CMOS ECAM chip is reported. The prototype chip can store 32 24-bit memory patterns, and its speed is higher than one associative recall operation every 3 µs. An application of the ECAM chip to vector quantization is also described

Analog Photonics Computing for Information Processing, Inference and Optimisation

This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.Comment: Invited submission by Journal of Advanced Quantum Technologies; accepted version 5/06/202

A Decade of Neural Networks: Practical Applications and Prospects

The Jet Propulsion Laboratory Neural Network Workshop, sponsored by NASA and DOD, brings together sponsoring agencies, active researchers, and the user community to formulate a vision for the next decade of neural network research and application prospects. While the speed and computing power of microprocessors continue to grow at an ever-increasing pace, the demand to intelligently and adaptively deal with the complex, fuzzy, and often ill-defined world around us remains to a large extent unaddressed. Powerful, highly parallel computing paradigms such as neural networks promise to have a major impact in addressing these needs. Papers in the workshop proceedings highlight benefits of neural networks in real-world applications compared to conventional computing techniques. Topics include fault diagnosis, pattern recognition, and multiparameter optimization

Unconventional computing platforms and nature-inspired methods for solving hard optimisation problems

The search for novel hardware beyond the traditional von Neumann architecture has given rise to a modern area of unconventional computing requiring the efforts of mathematicians, physicists and engineers. Many analogue physical systems, including networks of nonlinear oscillators, lasers, condensates, and superconducting qubits, are proposed and realised to address challenging computational problems from various areas of social and physical sciences and technology. Understanding the underlying physical process by which the system finds the solutions to such problems often leads to new optimisation algorithms. This thesis focuses on studying gain-dissipative systems and nature-inspired algorithms that form a hybrid architecture that may soon rival classical hardware. Chapter 1 lays the necessary foundation and explains various interdisciplinary terms that are used throughout the dissertation. In particular, connections between the optimisation problems and spin Hamiltonians are established, their computational complexity classes are explained, and the most prominent physical platforms for spin Hamiltonian implementation are reviewed. Chapter 2 demonstrates a large variety of behaviours encapsulated in networks of polariton condensates, which are a vivid example of a gain-dissipative system we use throughout the thesis. We explain how the variations of experimentally tunable parameters allow the networks of polariton condensates to represent different oscillator models. We derive analytic expressions for the interactions between two spatially separated polariton condensates and show various synchronisation regimes for periodic chains of condensates. An odd number of condensates at the vertices of a regular polygon leads to a spontaneous formation of a giant multiply-quantised vortex at the centre of a polygon. Numerical simulations of all studied configurations of polariton condensates are performed with a mean-field approach with some theoretically proposed physical phenomena supported by the relevant experiments. Chapter 3 examines the potential of polariton graphs to find the low-energy minima of the spin Hamiltonians. By associating a spin with a condensate phase, the minima of the XY model are achieved for simple configurations of spatially-interacting polariton condensates. We argue that such implementation of gain-dissipative simulators limits their applicability to the classes of easily solvable problems since the parameters of a particular Hamiltonian depend on the node occupancies that are not known a priori. To overcome this difficulty, we propose to adjust pumping intensities and coupling strengths dynamically. We further theoretically suggest how the discrete Ising and $n$-state planar Potts models with or without external fields can be simulated using gain-dissipative platforms. The underlying operational principle originates from a combination of resonant and non-resonant pumping. Spatial anisotropy of pump and dissipation profiles enables an effective control of the sign and intensity of the coupling strength between any two neighbouring sites, which we demonstrate with a two dimensional square lattice of polariton condensates. For an accurate minimisation of discrete and continuous spin Hamiltonians, we propose a fully controllable polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates. In Chapter 4, we look at classical computing rivals and study nature-inspired methods for optimising spin Hamiltonians. Based on the operational principles of gain-dissipative machines, we develop a novel class of gain-dissipative algorithms for the optimisation of discrete and continuous problems and show its performance in comparison with traditional optimisation techniques. Besides looking at traditional heuristic methods for Ising minimisation, such as the Hopfield-Tank neural networks and parallel tempering, we consider a recent physics-inspired algorithm, namely chaotic amplitude control, and exact commercial solver, Gurobi. For a proper evaluation of physical simulators, we further discuss the importance of detecting easy instances of hard combinatorial optimisation problems. The Ising model for certain interaction matrices, that are commonly used for evaluating the performance of unconventional computing machines and assumed to be exponentially hard, is shown to be solvable in polynomial time including the Mobius ladder graphs and Mattis spin glasses. In Chapter 5 we discuss possible future applications of unconventional computing platforms including emulation of search algorithms such as PageRank, realisation of a proof-of-work protocol for blockchain technology, and reservoir computing

Proposal for an analog CMOS median filter system based on neural network architectural principles

This thesis summarizes the investigation of a proposed analog electronic CMOS system for performing median filtering. A description of the problem and rational for investigating neural networks are given followed by a review of recent efforts toward solving the median filtering problem in hardware. A review of the major developments in hardware neural networks is also presented followed by the system proposal. A comparator design intended to function as a major building block is presented and analyzed. A description of efforts to accurately model the comparator follows. A Spice macro model simulation was assembled as well as a dedicated Runge-Kutta system level simulation. The two models were used to evaluate the system's performance when asked to perform median filtering on a number of different types of input data sets. Methods for predicting the behavior of the system are proposed and compared to simulation results. Finally, conclusions and suggestions for future investigations are offered based on the reported simulation results. A large amount of time was spent on putting the necessary software in place to do the work that this thesis summarizes. Difficulties with incompatible spice models, curve fitters. pre-production software versions, and communication links between computers abounded. In spite of all these obstacles, some meaningful data was finally generated allowing the conclusion of this effort.Electrical Engineerin