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Computational Complexity of Neuromorphic Algorithms

Neuromorphic computing has several characteristics that make it an extremely compelling computing paradigm for post Moore computation. Some of these characteristics include intrinsic parallelism, inherent scalability, collocated processing and memory, and event-driven computation. While these characteristics impart energy efficiency to neuromorphic systems, they do come with their own set of challenges. One of the biggest challenges in neuromorphic computing is to establish the theoretical underpinnings of the computational complexity of neuromorphic algorithms. In this paper, we take the first steps towards defining the space and time complexity of neuromorphic algorithms. Specifically, we describe a model of neuromorphic computation and state the assumptions that govern the computational complexity of neuromorphic algorithms. Next, we present a theoretical framework to define the computational complexity of a neuromorphic algorithm. We explicitly define what space and time complexities mean in the context of neuromorphic algorithms based on our model of neuromorphic computation. Finally, we leverage our approach and define the computational complexities of six neuromorphic algorithms: constant function, successor function, predecessor function, projection function, neuromorphic sorting algorithm and neighborhood subgraph extraction algorithm.

Date, Prasanna↗

Revolutionizing Neuromorphic Computing for Science (Brochure on the 2024 ASCR Workshop on Neuromorphic Computing for Science)

The ASCR basic research needs for Neuromorphic Computing for Science workshop was held in September 2024. The workshop brochure and report aim to inform and draft a set of grand challenges for advancing the field of neuromorphic computing and developing proof of principle neuromorphic circuits applicable for High Performance Computer (HPC) acceleration for scientific discovery, and brainstorm ideas needed for a successful, robust, and world leading basic research program. The resulting priority research directions are: (1) Neuromorphic computing circuit primitives; (2) Connectivity, communication, and hardware integration; (3) Neuroscience-derived dynamics and algorithms; and (4) Ecosystem for scalable neuromorphic co-design. Breakthroughs in understanding, designing, and prototyping the circuitry and simulation capabilities for a truly neuromorphic computer are essential to enable progress in the field.

97 MATHEMATICS AND COMPUTING↗

Revolutionizing Neuromorphic Computing for Science (Report for the 2024 ASCR Workshop on Neuromorphic Computing for Science)

The ASCR basic research needs for Neuromorphic Computing for Science workshop was held in September 2024. The workshop brochure and report aim to inform and draft a set of grand challenges for advancing the field of neuromorphic computing and developing proof of principle neuromorphic circuits applicable for High Performance Computer (HPC) acceleration for scientific discovery, and brainstorm ideas needed for a successful, robust, and world leading basic research program. The resulting priority research directions are: (1) Neuromorphic computing circuit primitives; (2) Connectivity, communication, and hardware integration; (3) Neuroscience-derived dynamics and algorithms; and (4) Ecosystem for scalable neuromorphic co-design. Breakthroughs in understanding, designing, and prototyping the circuitry and simulation capabilities for a truly neuromorphic computer are essential to enable progress in the field.

97 MATHEMATICS AND COMPUTING↗

Uncontrolled Learning: Codesign of Neuromorphic Hardware Topology for Neuromorphic Algorithms

Neuromorphic computing has the potential to revolutionize future technologies and our understanding of intelligence, yet it remains challenging to realize in practice. The learning-from-mistakes algorithm, inspired by the brain's simple learning rules of inhibition and pruning, is one of the few brain-like training methods. This algorithm is implemented in neuromorphic memristive hardware through a codesign process that evaluates essential hardware trade-offs. While the algorithm effectively trains small networks as binary classifiers and perceptrons, performance declines significantly with increasing network size unless the hardware is tailored to the algorithm. This work investigates the trade-offs between depth, controllability, and capacity—the number of learnable patterns—in neuromorphic hardware. This highlights the importance of topology and governing equations, providing theoretical tools to evaluate a device's computational capacity based on its measurements and circuit structure. The findings show that breaking neural network symmetry enhances both controllability and capacity. Additionally, by pruning the circuit, neuromorphic algorithms in all-memristive circuits can utilize stochastic resources to create local contrasts in network weights. Through combined experimental and simulation efforts, the parameters are identified that enable networks to exhibit emergent intelligence from simple rules, advancing the potential of neuromorphic computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On-Sensor Data Filtering using Neuromorphic Computing for High Energy Physics Experiments

This work describes the investigation of neuromorphic computing-based spiking neural network (SNN) models used to filter data from sensor electronics in high energy physics experiments conducted at the High Luminosity Large Hadron Collider. We present our approach for developing a compact neuromorphic model that filters out the sensor data based on the particle's transverse momentum with the goal of reducing the amount of data being sent to the downstream electronics. The incoming charge waveforms are converted to streams of binary-valued events, which are then processed by the SNN. We present our insights on the various system design choices - from data encoding to optimal hyperparameters of the training algorithm - for an accurate and compact SNN optimized for hardware deployment. Our results show that an SNN trained with an evolutionary algorithm and an optimized set of hyperparameters obtains a signal efficiency of about 91% with nearly half as many parameters as a deep neural network.

R. Kulkarni, Shruti↗

Advanced Functional Materials ZnO@ZIF-8 Heterostructures for Neuromorphic Synaptic Devices

Metal-Organic Frameworks have shown great promise for memristive synaptic devices because of their adaptable electrical properties and inherent porosity, which help in efficient ion transport and storage of functional molecules. However, the limited conductivity and sensitivity to moisture associated with most MOF materials hinder their use in electronic applications. In this study, MOFs derived from metabolites have been synthesized, using ZnO as a self-sacrificial metallic source to grow Zeolitic Imidazolate Framework-8 (ZIF-8), forming ZnO@ZIF-8 heteronanostructures for neuromorphic applications. These hybrids ZnO@ZIF-8 act as promising candidates for advanced electronic applications. Through systematic investigations, including a comparison of ZnO@ZIF-8 bilayer devices with ZnO single-layer counterparts, a significant discovery emerged. The bilayer synaptic devices outperformed their single layer counterparts in electrical characteristics, as evidenced by Current-Voltage curve analysis and Long-Term Potentiation/Long Term Depression (LTP/LTD) measurements. Additionally, the ZnO layer thickness (10, 30, 50 nm) has been emphasized and the effects of annealing at 300°C in a vacuum were carefully studied for Neuromorphic Synaptic Devices. Remarkably, the 10 nm ZnO layer exhibited the lowest set voltage and a consistent On/Off ratio. This work marks a significant advancement in understanding bilayer synaptic devices, highlighting the crucial role of ZIF-8 in shaping the future of neuromorphic systems

Kolleboyina, Jayaramulu↗

Hyperparameter Optimization in Binary Communication Networks for Neuromorphic Deployment

Training neural networks for neuromorphic deployment is non-trivial. There have been a variety of approaches proposed to adapt back-propagation or back-propagation-like algorithms appropriate for training. Considering that these networks often have very different performance characteristics than traditional neural networks, it is often unclear how to set either the network topology or the hyperparameters to achieve optimal performance. In this work, we introduce a Bayesian approach for optimizing the hyperparameters of an algorithm for training binary communication networks that can be deployed to neuromorphic hardware. We show that by optimizing the hyperparameters on this algorithm for each dataset, we can achieve improvements in accuracy over the previous state-of-the-art for this algorithm on each dataset (by up to 15 percent). This jump in performance continues to emphasize the potential when converting traditional neural networks to binary communication applicable to neuromorphic hardware.

Parsa, Maryam↗

Physics for neuromorphic computing

Neuromorphic computing takes inspiration from the brain to create energy-efficient hardware for information processing, capable of highly sophisticated tasks. Systems built with standard electronics achieve gains in speed and energy by mimicking the distributed topology of the brain. Scaling-up such systems and improving their energy usage, speed and performance by several orders of magnitude requires a revolution in hardware. Here, we discuss how including more physics in the algorithms and nanoscale materials used for data processing could have a major impact in the field of neuromorphic computing. We review striking results that leverage physics to enhance the computing capabilities of artificial neural networks, using resistive switching materials, photonics, spintronics and other technologies. We discuss the paths that could lead these approaches to maturity, towards low-power, miniaturized chips that could infer and learn in real time.

device physics↗

Knowledge gaps for neuromorphic ionic computing

BACKGROUND Neuromorphic computing, inspired by the human brain’s ability to process information efficiently, represents a transformative approach to computation. In this Review, we explore the emerging field of neuromorphic ionic computing, which leverages ionic conduction and coupling to mimic neural processes, and identify critical knowledge gaps that must be addressed to realize its full potential. A central theme of the discussion is energy efficiency, a challenge that is both a limitation and an opportunity for this technology. Although complementary metal-oxide semiconductor (CMOS)–based neuromorphic technologies have made strides in scaling to billions of neurons and are increasingly applied in artificial intelligence and numerical computing, they remain orders of magnitude behind the human brain in terms of connectivity and energy efficiency. Neuromorphic ionic computing promises to overcome these limitations by leveraging the distinct architectural and operational principles of the brain. Our brains achieve this energy efficiency by combining several key features: using the same network elements to store and process information; using an incredibly complex and massively interconnected three-dimensional (3D) network of locally active elements that enables sparsity, robustness in the presence of noise, adaptation, and life-long learning; computing at comparatively low voltage and frequency; and last, taking advantage of a plethora of ions and small molecules as information carriers. Here, we propose that ionic computing systems can take advantage of similar features to achieve substantial gains in energy efficiency. ADVANCES Since the first reports of neuromorphic ionic behavior in nanofluidic channels, we have witnessed an explosion of reports that used ionic devices to produce synaptomimetic behaviors. However, achieving the goals of ionic computing requires not only implementation of much more sophisticated device functionality but also overcoming fundamental barriers in materials science, device architecture, and system integration. Current ionic devices, even those incorporating state-of-the-art materials, still suffer from limited functionality and stability, which restrict their performance and increase energy demands. Developing new materials with enhanced ionic properties is essential to overcome these limitations. Similarly, the design of neuromorphic devices must evolve to leverage the particular advantages of ionic processes. Existing architectures often follow a single-information-carrier logic of conventional electronics or are constructed of mesoscale fluidics, failing to capitalize on the energy-efficient mechanisms inherent to ionic systems or implement the multiple-information-carrier paradigm. Current neuromorphic chips focus on large-scale networks of analog memory elements based on mechanisms such as charge trap (flash), filamentary, phase change, or spin, which are built on top of a network of artificial CMOS neurons. Although such prototype networks have achieved impressive performance, it is difficult to envision how they can implement the key features such as massive connectivity, sophisticated plasticity, adaptability, sparsity, and “multichromatic” computing. Although small-scale devices have demonstrated promising results, integrating them, maintaining energy efficiency, and implementing temperature control as systems grow in complexity and size to computationally relevant scale remain major hurdles. Furthermore, interfacing neuromorphic ionic devices with existing computing technologies presents technical and conceptual challenges that will require innovative approaches that combine insights from neuroscience, materials science, and engineering. OUTLOOK Despite these challenges, the potential impact of neuromorphic ionic computing is profound with potential applications ranging from artificial intelligence to robotics and beyond. We also argue that neuromorphic ionic computing systems should not, at least in the beginning, compete with CMOS technologies but rather should focus on applications that require extreme energy efficiency with chemical and/or biological compatibility, such as biomedical applications (for example, brain-computer interfaces), environmental monitoring, and agricultural and food applications. Ultimately, this Review highlights the crucial role of interdisciplinary collaboration in advancing the field. Neuromorphic ionic computing is not merely a technological innovation; it represents a substantial step toward sustainable computation, aligning with the growing demand for energy-conscious solutions in a world that is increasingly reliant on data and computation.

Neuromorphic↗

Scaled-up Neuromorphic Array Communications Controller (SNACC) for Large-scale Neural Networks

Neuromorphic computing is one promising post-Moore’s law era technology, which takes inspiration from biological brains to perform computing tasks. The human brain contains billions of neurons with trillions of synapses and as neuromorphic hardware systems scale to larger and larger sizes, the communication system used to transfer information between neuromorphic elements and traditional computers must scale to keep up. In prior work, we describe the use of a separate neuromorphic array communications controller to support low-latency, high-throughput communication between our neuromorphic systems and a traditional computer. In this work, the neuromorphic array communications controller is used to support the scaling of a neuromorphic development system which uses multiple neuromorphic processors arranged in a two-dimensional array. The neuromorphic array communications controller, along with scalable local connections, is used to create a scalable neuromorphic platform to enable the development and testing of large neuromorphic network arrays.

Young, Aaron↗

Virtual Neuron: A Neuromorphic Approach for Encoding Numbers

Neuromorphic computers perform computations by emulating the human brain and are expected to be indispensable for energy-efficient computing in the future. They are primarily used in spiking neural network-based machine learning applications. However, neuromorphic computers are unable to preprocess data for these applications. Currently, data is preprocessed on a CPU or a GPU-this incurs a significant cost of transferring data from the CPU/GPU to the neuromorphic processor and vice versa. This cost can be avoided if preprocessing is done on the neuromorphic processor. To efficiently preprocess data on a neuromorphic processor, we first need an efficient mechanism for encoding data that can lend itself to all general-purpose preprocessing operations. Current encoding approaches have limited applicability and may not be suitable for all preprocessing operations. In this paper, we present the virtual neuron as a mechanism for encoding integers and rational numbers on neuromorphic processors. We evaluate the performance of the virtual neuron on physical and simulated neuromorphic hardware and show that it can perform an addition operation using 23 nJ of energy on average using a mixed-signal, memristor-based neuromorphic processor. The virtual neuron encoding approach is the first step in preprocessing data on a neuromorphic processor.

Date, Prasanna↗

Neuromorphic Computing is Turing-Complete

Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and GPUs. They have the potential to drive critical use cases such as autonomous vehicles, edge computing and internet of things in the future. For this reason, they are sought to be an indispensable part of the future computing landscape. Neuromorphic systems are mainly used for spike-based machine learning applications, although there are some non-machine learning applications in graph theory, differential equations, and spike-based simulations. These applications suggest that neuromorphic computing might be capable of general-purpose computing. However, general-purpose computability of neuromorphic computing has not been established yet. In this work, we prove that neuromorphic computing is Turing-complete and therefore capable of general-purpose computing. Specifically, we present a model of neuromorphic computing, with just two neuron parameters (threshold and leak), and two synaptic parameters (weight and delay). We devise neuromorphic circuits for computing all the μ-recursive functions (i.e., constant, successor and projection functions) and all the μ-recursive operators (i.e., composition, primitive recursion and minimization operators). Given that the μ-recursive functions and operators are precisely the ones that can be computed using a Turing machine, this work establishes the Turing-completeness of neuromorphic computing.

Date, Prasanna↗

An introduction to neuromorphic computing and its potential impact for unattended ground sensors

Neuromorphic computers are hardware systems that mimic the brain’s computational process phenomenology. This is in contrast to neural network accelerators, such as the Google TPU or the Intel Neural Compute Stick, which seek to accelerate the fundamental computation and data flows of neural network models used in the field of machine learning. Neuromorphic computers emulate the integrate and fire neuron dynamics of the brain to achieve a spiking communication architecture for computation. While neural networks are brain-inspired, they drastically oversimplify the brain’s computation model. Neuromorphic architectures are closer to the true computation model of the brain (albeit, still simplified). Neuromorphic computing models herald a 1000x power improvement over conventional CPU architectures. Sandia National Labs is a major contributor to the research community on neuromorphic systems by performing design analysis, evaluation, and algorithm development for neuromorphic computers. Space-based remote sensing development has been a focused target of funding for exploratory research into neuromorphic systems for their potential advantage in that program area; SNL has led some of these efforts. Recently, neuromorphic application evaluation has reached the NA-22 program area. This same exploratory research and algorithm development should penetrate the unattended ground sensor space for SNL’s mission partners and program areas. Neuromorphic computing paradigms offer a distinct advantage for the SWaP-constrained embedded systems of our diverse sponsor-driven program areas.

97 MATHEMATICS AND COMPUTING↗

Neuromorphic Graph Algorithms: Cycle Detection, Odd Cycle Detection, and Max Flow

Neuromorphic computing is poised to become a promising computing paradigm in the post Moore’s law era due to its extremely low power usage and inherent parallelism. Spiking neural networks are the traditional use case for neuromorphic systems, and have proven to be highly effective at machine learning tasks such as control problems. More recently, neuromorphic systems have been applied outside of the arena of machine learning, primarily in the field of graph algorithms. Neuromorphic systems have been shown to perform graph algorithms faster and with lower power consumption than their traditional (GPU/CPU) counterparts, and are hence an attractive option for a co-processing unit in future high performance computing systems, where graph algorithms play a critical role. In this paper, we present a neuromorphic implementation of cycle detection, odd cycle detection, and the Ford-Fulkerson max-flow algorithm. We further evaluate the performance of these implementations using the NEST neuromorphic simulator by using spike counts and simulation time as proxies for energy consumption and run time. In addition to gains inherent in neuromorphic systems, we show that within the neuromorphic implementations early stopping criteria can be implemented to further improve performance.

Kay, Bill↗

Introduction: Neuromorphic Materials

The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.

Circuits↗

Neuromorphic intermediate representation: A unified instruction set for interoperable brain-inspired computing

Abstract Spiking neural networks and neuromorphic hardware platforms that simulate neuronal dynamics are getting wide attention and are being applied to many relevant problems using Machine Learning. Despite a well-established mathematical foundation for neural dynamics, there exists numerous software and hardware solutions and stacks whose variability makes it difficult to reproduce findings. Here, we establish a common reference frame for computations in digital neuromorphic systems, titled Neuromorphic Intermediate Representation (NIR). NIR defines a set of computational and composable model primitives as hybrid systems combining continuous-time dynamics and discrete events. By abstracting away assumptions around discretization and hardware constraints, NIR faithfully captures the computational model, while bridging differences between the evaluated implementation and the underlying mathematical formalism. NIR supports an unprecedented number of neuromorphic systems, which we demonstrate by reproducing three spiking neural network models of different complexity across 7 neuromorphic simulators and 4 digital hardware platforms. NIR decouples the development of neuromorphic hardware and software, enabling interoperability between platforms and improving accessibility to multiple neuromorphic technologies. We believe that NIR is a key next step in brain-inspired hardware-software co-evolution, enabling research towards the implementation of energy efficient computational principles of nervous systems. NIR is available atneuroir.org

Science & Technology - Other Topics↗