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Abstract Phase-encoded oscillating neural networks offer compelling advantages over metal-oxide-semiconductor-based technology for tackling complex optimization problems, with promising potential for ultralow power consumption and exceptionally rapid computational performance. In this work, we investigate the ability of these networks to solve optimization problems belonging to the nondeterministic polynomial time complexity class using nanoscale vanadium-dioxide-based oscillators integrated onto a Silicon platform. Specifically, we demonstrate how the dynamic behavior of coupled vanadium dioxide devices can effectively solve combinatorial optimization problems, including Graph Coloring, Max-cut, and Max-3SAT problems. The electrical mappings of these problems are derived from the equivalent Ising Hamiltonian formulation to design circuits with up to nine crossbar vanadium dioxide oscillators. Using sub-harmonic injection locking techniques, we binarize the solution space provided by the oscillators and demonstrate that graphs with high connection density (η > 0.4) converge more easily towards the optimal solution due to the small spectral radius of the problem’s equivalent adjacency matrix. Our findings indicate that these systems achieve stability within 25 oscillation cycles and exhibit power efficiency and potential for scaling that surpasses available commercial options and other technologies under study. These results pave the way for accelerated parallel computing enabled by large-scale networks of interconnected oscillators.

Oscillatory neural networks (ONNs) exhibit a high potential for energy-efficient computing. In ONNs, neurons are implemented with oscillators and synapses with resistive and/or capacitive coupling between pairs of oscillators. Computing is carried out on the basis of the rich, complex, non-linear synchronization dynamics of a system of coupled oscillators. The exploited synchronization phenomena in ONNs are an example of fully parallel collective computing. A fast system’s convergence to stable states, which correspond to the desired processed information, enables an energy-efficient solution if small area and low-power oscillators are used, specifically when they are built on the basis of the hysteresis exhibited by phase-transition materials such as VO2. In recent years, there have been numerous studies on ONNs using VO2. Most of them report simulation results. Although in some cases experimental results are also shown, they do not implement the design techniques that other works on electrical simulations report that allow to improve the behavior of the ONNs. Experimental validation of these approaches is necessary. Therefore, in this study, we describe an ONN realized in a commercial CMOS technology in which the oscillators are built using a circuit that we have developed to emulate the VO2 device. The purpose is to be able to study in-depth the synchronization dynamics of relaxation oscillators similar to those that can be performed with VO2 devices. The fabricated circuit is very flexible. It allows programming the synapses to implement different ONNs, calibrating the frequency of the oscillators, or controlling their initialization. It uses differential oscillators and resistive synapses, equivalent to the use of memristors. In this article, the designed and fabricated circuits are described in detail, and experimental results are shown. Specifically, its satisfactory operation as an associative memory is demonstrated. The experiments carried out allow us to conclude that the ONN must be operated according to the type of computational task to be solved, and guidelines are extracted in this regard.

Alternative paradigms to the von Neumann computing scheme are currently arousing huge interest. Oscillatory neural networks (ONNs) using emerging phase-change materials like VO2 constitute an energy-efficient, massively parallel, brain-inspired, in-memory computing approach. The encoding of information in the phase pattern of frequency-locked, weakly coupled oscillators makes it possible to exploit their rich non-linear dynamics and their synchronization phenomena for computing. A single fully connected ONN layer can implement an auto-associative memory comparable to that of a Hopfield network, hence Hebbian learning rule is the most widely adopted method for configuring ONNs for such applications, despite its well-known limitations. An extensive amount of literature is available about learning in Hopfield networks, with information regarding many different learning algorithms that perform better than the Hebbian rule. However, not all of these algorithms are useful for ONN training due to the constraints imposed by their physical implementation. This paper evaluates different learning methods with respect to their suitability for ONNs. It proposes a new approach, which is compared against previous works. The proposed method has been shown to produce competitive results in terms of pattern recognition accuracy with reduced precision in synaptic weights, and to be suitable for online learning.

Liquid State Machines (LSMs) are computing reservoirs composed of recurrently connected Spiking Neural Networks which have attracted research interest for their modeling capacity of biological structures and as promising pattern recognition tools suitable for their implementation in neuromorphic processors, benefited from the modest use of computing resources in their training process. However, it has been difficult to optimize LSMs for solving complex tasks such as event-based computer vision and few implementations in large-scale neuromorphic processors have been attempted. In this work, we show that offline-trained LSMs implemented in the SpiNNaker neuromorphic processor are able to classify visual events, achieving state-of-the-art performance in the event-based N-MNIST dataset. The training of the readout layer is performed using a recent adaptation of back-propagation-through-time (BPTT) for SNNs, while the internal weights of the reservoir are kept static. Results show that mapping our LSM from a Deep Learning framework to SpiNNaker does not affect the performance of the classification task. Additionally, we show that weight quantization, which substantially reduces the memory footprint of the LSM, has a small impact on its performance.

Computing paradigm based on von Neuman architectures cannot keep up with the ever-increasing data growth (also called “data deluge gap”). This has resulted in investigating novel computing paradigms and design approaches at all levels from materials to system-level implementations and applications. An alternative computing approach based on artificial neural networks uses oscillators to compute or Oscillatory Neural Networks (ONNs). ONNs can perform computations efficiently and can be used to build a more extensive neuromorphic system. Here, we address a fundamental problem: can we efficiently perform artificial intelligence applications with ONNs? We present a digital ONN implementation to show a proof-of-concept of the ONN approach of “computing-in-phase” for pattern recognition applications. To the best of our knowledge, this is the first attempt to implement an FPGA-based fully-digital ONN. We report ONN accuracy, training, inference, memory capacity, operating frequency, hardware resources based on simulations and implementations of 5 × 3 and 10 × 6 ONNs. We present the digital ONN implementation on FPGA for pattern recognition applications such as performing digits recognition from a camera stream. We discuss practical challenges and future directions in implementing digital ONN.

Oscillatory Neural Networks (ONNs) are currently arousing interest in the research community for their potential to implement very fast, ultra-low-power computing tasks by exploiting specific emerging technologies. From the architectural point of view, ONNs are based on the synchronization of oscillatory neurons in cognitive processing, as occurs in the human brain. As emerging technologies, VO2 and memristive devices show promising potential for the efficient implementation of ONNs. Abundant literature is now becoming available pertaining to the study and building of ONNs based on VO2 devices and resistive coupling, such as memristors. One drawback of direct resistive coupling is that physical resistances cannot be negative, but from the architectural and computational perspective this would be a powerful advantage when interconnecting weights in ONNs. Here we solve the problem by proposing a hardware implementation technique based on differential oscillatory neurons for ONNs (DONNs) with VO2-based oscillators and memristor-bridge circuits. Each differential oscillatory neuron is made of a pair of VO2 oscillators operating in anti-phase. This way, the neurons provide a pair of differential output signals in opposite phase. The memristor-bridge circuit is used as an adjustable coupling function that is compatible with differential structures and capable of providing both positive and negative weights. By combining differential oscillatory neurons and memristor-bridge circuits, we propose the hardware implementation of a fully connected differential ONN (DONN) and use it as an associative memory. The standard Hebbian rule is used for training, and the weights are then mapped to the memristor-bridge circuit through a proposed mapping rule. The paper also introduces some functional and hardware specifications to evaluate the design. Evaluation is performed by circuit-level electrical simulations and shows that the retrieval accuracy of the proposed design is comparable to that of classic Hopfield Neural Networks.

Nano-oscillators based on phase-transition materials are being explored for the implementation of different non-conventional computing paradigms. In particular, vanadium dioxide (VO2) devices are used to design autonomous non-linear oscillators from which oscillatory neural networks (ONNs) can be developed. In this work, we propose a new architecture for ONNs in which sub-harmonic injection locking (SHIL) is exploited to ensure that the phase information encoded in each neuron can only take two values. In this sense, the implementation of ONNs from neurons that inherently encode information with two-phase values has advantages in terms of robustness and tolerance to variability present in VO2 devices. Unlike conventional interconnection schemes, in which the sign of the weights is coded in the value of the resistances, in our proposal the negative (positive) weights are coded using static inverting (non-inverting) logic at the output of the oscillator. The operation of the proposed architecture is shown for pattern recognition applications.

Neurophysiological observations are clarifying how astrocytes can actively participate in information processing and how they can encode information through frequency and amplitude modulation of intracellular Ca2+ signals. Consequently, hardware realization of astrocytes is important for developing the next generation of bio-inspired computing systems. In this paper, astrocytic calcium oscillations and neuronal firing dynamics are presented by De Pittà and IF (Integrated & Fire) models, respectively. Considering highly nonlinear equations of the astrocyte model, linear approximation and single constant multiplication (SCM) techniques are employed for efficient hardware execution while maintaining the dynamic of the original models. This low-cost hardware architecture for the astrocyte model is able to show the essential features of different types of Ca2+ modulation such as amplitude modulation (AM), frequency modulation (FM), or both modes (AFM). To show good agreement between the results of original models simulated in MATLAB and the proposed digital circuits executed on FPGA, quantitative, and qualitative analyses including phase plane are done. This new neuromorphic circuit of astrocyte is able to successfully demonstrate AM/FM/AFM calcium signaling in its real operation on FPGA and has applications in self-repairing systems. It also can be employed as a subsystem for linking biological cells to artificial neuronal networks using astrocytic calcium oscillations in future research.

In computational neuroscience, synaptic plasticity learning rules are typically studied using the full 64-bit floating point precision computers provide. However, for dedicated hardware implementations, the precision used not only penalizes directly the required memory resources, but also the computing, communication, and energy resources. When it comes to hardware engineering, a key question is always to find the minimum number of necessary bits to keep the neurocomputational system working satisfactorily. Here we present some techniques and results obtained when limiting synaptic weights to 1-bit precision, applied to a Spike-Timing-Dependent-Plasticity (STDP) learning rule in Spiking Neural Networks (SNN). We first illustrate the 1-bit synapses STDP operation by replicating a classical biological experiment on visual orientation tuning, using a simple four neuron setup. After this, we apply 1-bit STDP learning to the hidden feature extraction layer of a 2-layer system, where for the second (and output) layer we use already reported SNN classifiers. The systems are tested on two spiking datasets: a Dynamic Vision Sensor (DVS) recorded poker card symbols dataset and a Poisson-distributed spike representation MNIST dataset version. Tests are performed using the in-house MegaSim event-driven behavioral simulator and by implementing the systems on FPGA (Field Programmable Gate Array) hardware.

Convolutional Neural Networks (ConvNets) are a particular type of neural network often used for many applications like image recognition, video analysis or natural language processing. They are inspired by the human brain, following a specific organization of the connectivity pattern between layers of neurons known as receptive field. These networks have been traditionally implemented in software, but they are becoming more computationally expensive as they scale up, having limitations for real-time processing of high-speed stimuli. On the other hand, hardware implementations show difficulties to be used for different applications, due to their reduced flexibility. In this paper, we propose a fully configurable event-driven convolutional node with rate saturation mechanism that can be used to implement arbitrary ConvNets on FPGAs. This node includes a convolutional processing unit and a routing element which allows to build large 2D arrays where any multilayer structure can be implemented. The rate saturation mechanism emulates the refractory behavior in biological neurons, guaranteeing a minimum separation in time between consecutive events. A 4-layer ConvNet with 22 convolutional nodes trained for poker card symbol recognition has been implemented in a Spartan6 FPGA. This network has been tested with a stimulus where 40 poker cards were observed by a Dynamic Vision Sensor (DVS) in 1 s time. Different slow-down factors were applied to characterize the behavior of the system for high speed processing. For slow stimulus play-back, a 96% recognition rate is obtained with a power consumption of 0.85 mW. At maximum play-back speed, a traffic control mechanism downsamples the input stimulus, obtaining a recognition rate above 63% when less than 20% of the input events are processed, demonstrating the robustness of the network.

This paper introduces a novel methodology for training an event-driven classifier within a Spiking Neural Network (SNN) System capable of yielding good classification results when using both synthetic input data and real data captured from Dynamic Vision Sensor (DVS) chips. The proposed supervised method uses the spiking activity provided by an arbitrary topology of prior SNN layers to build histograms and train the classifier in the frame domain using the stochastic gradient descent algorithm. In addition, this approach can cope with leaky integrate-and-fire neuron models within the SNN, a desirable feature for real-world SNN applications, where neural activation must fade away after some time in the absence of inputs. Consequently, this way of building histograms captures the dynamics of spikes immediately before the classifier. We tested our method on the MNIST data set using different synthetic encodings and real DVS sensory data sets such as N-MNIST, MNIST-DVS, and Poker-DVS using the same network topology and feature maps. We demonstrate the effectiveness of our approach by achieving the highest classification accuracy reported on the N-MNIST (97.77%) and Poker-DVS (100%) real DVS data sets to date with a spiking convolutional network. Moreover, by using the proposed method we were able to retrain the output layer of a previously reported spiking neural network and increase its performance by 2%, suggesting that the proposed classifier can be used as the output layer in works where features are extracted using unsupervised spike-based learning methods. In addition, we also analyze SNN performance figures such as total event activity and network latencies, which are relevant for eventual hardware implementations. In summary, the paper aggregates unsupervised-trained SNNs with a supervised-trained SNN classifier, combining and applying them to heterogeneous sets of benchmarks, both synthetic and from real DVS chips.