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We introduce NeuroSA, a neuromorphic architecture specifically designed to ensure asymptotic convergence to the ground state of an Ising problem using an annealing process that is governed by the physics of quantum mechanical tunneling using Fowler-Nordheim (FN). The core component of NeuroSA consists of a pair of asynchronous ON-OFF neurons, which effectively map classical simulated annealing (SA) dynamics onto a network of integrate-and-fire (IF) neurons. The threshold of each ON-OFF neuron pair is adaptively adjusted by an FN annealer which replicates the optimal escape mechanism and convergence of SA, particularly at low temperatures. To validate the effectiveness of our neuromorphic Ising machine, we systematically solved various benchmark MAX-CUT combinatorial optimization problems. Across multiple runs, NeuroSA consistently generates solutions that approach the state-of-the-art level with high accuracy (greater than 99%), and without any graph-specific hyperparameter tuning. For practical illustration, we present results from an implementation of NeuroSA on the SpiNNaker2 platform, highlighting the feasibility of mapping our proposed architecture onto a standard neuromorphic accelerator platform., Comment: 36 pages, 8 figures

Matrix multiplication (MatMul) typically dominates the overall computational cost of large language models (LLMs). This cost only grows as LLMs scale to larger embedding dimensions and context lengths. In this work, we show that MatMul operations can be completely eliminated from LLMs while maintaining strong performance at billion-parameter scales. Our experiments show that our proposed MatMul-free models achieve performance on-par with state-of-the-art Transformers that require far more memory during inference at a scale up to at least 2.7B parameters. We investigate the scaling laws and find that the performance gap between our MatMul-free models and full precision Transformers narrows as the model size increases. We also provide a GPU-efficient implementation of this model which reduces memory usage by up to 61% over an unoptimized baseline during training. By utilizing an optimized kernel during inference, our model's memory consumption can be reduced by more than 10x compared to unoptimized models. To properly quantify the efficiency of our architecture, we build a custom hardware solution on an FPGA which exploits lightweight operations beyond what GPUs are capable of. We processed billion-parameter scale models at 13W beyond human readable throughput, moving LLMs closer to brain-like efficiency. This work not only shows how far LLMs can be stripped back while still performing effectively, but also points at the types of operations future accelerators should be optimized for in processing the next generation of lightweight LLMs. Our code implementation is available at https://github.com/ridgerchu/matmulfreellm.

Autonomous driving demands an integrated approach that encompasses perception, prediction, and planning, all while operating under strict energy constraints to enhance scalability and environmental sustainability. We present Spiking Autonomous Driving (SAD), the first unified Spiking Neural Network (SNN) to address the energy challenges faced by autonomous driving systems through its event-driven and energy-efficient nature. SAD is trained end-to-end and consists of three main modules: perception, which processes inputs from multi-view cameras to construct a spatiotemporal bird's eye view; prediction, which utilizes a novel dual-pathway with spiking neurons to forecast future states; and planning, which generates safe trajectories considering predicted occupancy, traffic rules, and ride comfort. Evaluated on the nuScenes dataset, SAD achieves competitive performance in perception, prediction, and planning tasks, while drawing upon the energy efficiency of SNNs. This work highlights the potential of neuromorphic computing to be applied to energy-efficient autonomous driving, a critical step toward sustainable and safety-critical automotive technology. Our code is available at \url{https://github.com/ridgerchu/SAD}.

Recent advancements in neuroscience research have propelled the development of Spiking Neural Networks (SNNs), which not only have the potential to further advance neuroscience research but also serve as an energy-efficient alternative to Artificial Neural Networks (ANNs) due to their spike-driven characteristics. However, previous studies often neglected the multiscale information and its spatiotemporal correlation between event data, leading SNN models to approximate each frame of input events as static images. We hypothesize that this oversimplification significantly contributes to the performance gap between SNNs and traditional ANNs. To address this issue, we have designed a Spiking Multiscale Attention (SMA) module that captures multiscale spatiotemporal interaction information. Furthermore, we developed a regularization method named Attention ZoneOut (AZO), which utilizes spatiotemporal attention weights to reduce the model's generalization error through pseudo-ensemble training. Our approach has achieved state-of-the-art results on mainstream neural morphology datasets. Additionally, we have reached a performance of 77.1% on the Imagenet-1K dataset using a 104-layer ResNet architecture enhanced with SMA and AZO. This achievement confirms the state-of-the-art performance of SNNs with non-transformer architectures and underscores the effectiveness of our method in bridging the performance gap between SNN models and traditional ANN models.

Weight quantization is used to deploy high-performance deep learning models on resource-limited hardware, enabling the use of low-precision integers for storage and computation. Spiking neural networks (SNNs) share the goal of enhancing efficiency, but adopt an 'event-driven' approach to reduce the power consumption of neural network inference. While extensive research has focused on weight quantization, quantization-aware training (QAT), and their application to SNNs, the precision reduction of state variables during training has been largely overlooked, potentially diminishing inference performance. This paper introduces two QAT schemes for stateful neurons: (i) a uniform quantization strategy, an established method for weight quantization, and (ii) threshold-centered quantization, which allocates exponentially more quantization levels near the firing threshold. Our results show that increasing the density of quantization levels around the firing threshold improves accuracy across several benchmark datasets. We provide an ablation analysis of the effects of weight and state quantization, both individually and combined, and how they impact models. Our comprehensive empirical evaluation includes full precision, 8-bit, 4-bit, and 2-bit quantized SNNs, using QAT, stateful QAT (SQUAT), and post-training quantization methods. The findings indicate that the combination of QAT and SQUAT enhance performance the most, but given the choice of one or the other, QAT improves performance by the larger degree. These trends are consistent all datasets. Our methods have been made available in our Python library snnTorch: https://github.com/jeshraghian/snntorch., Comment: 10 pages, 4 figures, accepted at NICE 2024

There is increasing interest in the application large language models (LLMs) to the medical field, in part because of their impressive performance on medical exam questions. While promising, exam questions do not reflect the complexity of real patient-doctor interactions. In reality, physicians' decisions are shaped by many complex factors, such as patient compliance, personal experience, ethical beliefs, and cognitive bias. Taking a step toward understanding this, our hypothesis posits that when LLMs are confronted with clinical questions containing cognitive biases, they will yield significantly less accurate responses compared to the same questions presented without such biases. In this study, we developed BiasMedQA, a benchmark for evaluating cognitive biases in LLMs applied to medical tasks. Using BiasMedQA we evaluated six LLMs, namely GPT-4, Mixtral-8x70B, GPT-3.5, PaLM-2, Llama 2 70B-chat, and the medically specialized PMC Llama 13B. We tested these models on 1,273 questions from the US Medical Licensing Exam (USMLE) Steps 1, 2, and 3, modified to replicate common clinically-relevant cognitive biases. Our analysis revealed varying effects for biases on these LLMs, with GPT-4 standing out for its resilience to bias, in contrast to Llama 2 70B-chat and PMC Llama 13B, which were disproportionately affected by cognitive bias. Our findings highlight the critical need for bias mitigation in the development of medical LLMs, pointing towards safer and more reliable applications in healthcare.

Spiking neural networks and neuromorphic hardware platforms that emulate neural dynamics are slowly gaining momentum and entering main-stream usage. Despite a well-established mathematical foundation for neural dynamics, the implementation details vary greatly across different platforms. Correspondingly, there are a plethora of software and hardware implementations with their own unique technology stacks. Consequently, neuromorphic systems typically diverge from the expected computational model, which challenges the reproducibility and reliability across platforms. Additionally, most neuromorphic hardware is limited by its access via a single software frameworks with a limited set of training procedures. Here, we establish a common reference-frame for computations in neuromorphic systems, dubbed the Neuromorphic Intermediate Representation (NIR). NIR defines a set of computational primitives as idealized continuous-time hybrid systems that can be composed into graphs and mapped to and from various neuromorphic technology stacks. By abstracting away assumptions around discretization and hardware constraints, NIR faithfully captures the fundamental computation, while simultaneously exposing the exact differences between the evaluated implementation and the idealized mathematical formalism. We reproduce three NIR graphs across 7 neuromorphic simulators and 4 hardware platforms, demonstrating support for an unprecedented number of neuromorphic systems. With NIR, we decouple the evolution of neuromorphic hardware and software, ultimately increasing the interoperability between platforms and improving accessibility to neuromorphic technologies. We believe that NIR is an important step towards the continued study of brain-inspired hardware and bottom-up approaches aimed at an improved understanding of the computational underpinnings of nervous systems., Comment: NIR is available at https://github.com/neuromorphs/NIR

Spiking Neural Networks (SNNs) have garnered substantial attention in brain-like computing for their biological fidelity and the capacity to execute energy-efficient spike-driven operations. As the demand for heightened performance in SNNs surges, the trend towards training deeper networks becomes imperative, while residual learning stands as a pivotal method for training deep neural networks. In our investigation, we identified that the SEW-ResNet, a prominent representative of deep residual spiking neural networks, incorporates non-event-driven operations. To rectify this, we propose a novel training paradigm that first accumulates a large amount of redundant information through OR Residual Connection (ORRC), and then filters out the redundant information using the Synergistic Attention (SynA) module, which promotes feature extraction in the backbone while suppressing the influence of noise and useless features in the shortcuts. When integrating SynA into the network, we observed the phenomenon of "natural pruning", where after training, some or all of the shortcuts in the network naturally drop out without affecting the model's classification accuracy. This significantly reduces computational overhead and makes it more suitable for deployment on edge devices. Experimental results on various public datasets confirmed that the SynA-ResNet achieved single-sample classification with as little as 0.8 spikes per neuron. Moreover, when compared to other residual SNN models, it exhibited higher accuracy and up to a 28-fold reduction in energy consumption., Comment: 12 pages, 5 figures and 10 tables

Recent advances in robot-assisted surgery have resulted in progressively more precise, efficient, and minimally invasive procedures, sparking a new era of robotic surgical intervention. This enables doctors, in collaborative interaction with robots, to perform traditional or minimally invasive surgeries with improved outcomes through smaller incisions. Recent efforts are working toward making robotic surgery more autonomous which has the potential to reduce variability of surgical outcomes and reduce complication rates. Deep reinforcement learning methodologies offer scalable solutions for surgical automation, but their effectiveness relies on extensive data acquisition due to the absence of prior knowledge in successfully accomplishing tasks. Due to the intensive nature of simulated data collection, previous works have focused on making existing algorithms more efficient. In this work, we focus on making the simulator more efficient, making training data much more accessible than previously possible. We introduce Surgical Gym, an open-source high performance platform for surgical robot learning where both the physics simulation and reinforcement learning occur directly on the GPU. We demonstrate between 100-5000x faster training times compared with previous surgical learning platforms. The code is available at: https://github.com/SamuelSchmidgall/SurgicalGym.

Diagnostic investigation has an important role in risk stratification and clinical decision making of patients with suspected and documented Coronary Artery Disease (CAD). However, the majority of existing tools are primarily focused on the selection of gatekeeper tests, whereas only a handful of systems contain information regarding the downstream testing or treatment. We propose a multi-task deep learning model to support risk stratification and down-stream test selection for patients undergoing Coronary Computed Tomography Angiography (CCTA). The analysis included 14,021 patients who underwent CCTA between 2006 and 2017. Our novel multitask deep learning framework extends the state-of-the art Perceiver model to deal with real-world CCTA report data. Our model achieved an Area Under the receiver operating characteristic Curve (AUC) of 0.76 in CAD risk stratification, and 0.72 AUC in predicting downstream tests. Our proposed deep learning model can accurately estimate the likelihood of CAD and provide recommended downstream tests based on prior CCTA data. In clinical practice, the utilization of such an approach could bring a paradigm shift in risk stratification and downstream management. Despite significant progress using deep learning models for tabular data, they do not outperform gradient boosting decision trees, and further research is required in this area. However, neural networks appear to benefit more readily from multi-task learning than tree-based models. This could offset the shortcomings of using single task learning approach when working with tabular data.

Neuromodulation techniques have emerged as promising approaches for treating a wide range of neurological disorders, precisely delivering electrical stimulation to modulate abnormal neuronal activity. While leveraging the unique capabilities of artificial intelligence (AI) holds immense potential for responsive neurostimulation, it appears as an extremely challenging proposition where real-time (low-latency) processing, low power consumption, and heat constraints are limiting factors. The use of sophisticated AI-driven models for personalized neurostimulation depends on back-telemetry of data to external systems (e.g. cloud-based medical mesosystems and ecosystems). While this can be a solution, integrating continuous learning within implantable neuromodulation devices for several applications, such as seizure prediction in epilepsy, is an open question. We believe neuromorphic architectures hold an outstanding potential to open new avenues for sophisticated on-chip analysis of neural signals and AI-driven personalized treatments. With more than three orders of magnitude reduction in the total data required for data processing and feature extraction, the high power- and memory-efficiency of neuromorphic computing to hardware-firmware co-design can be considered as the solution-in-the-making to resource-constraint implantable neuromodulation systems. This perspective introduces the concept of Neuromorphic Neuromodulation, a new breed of closed-loop responsive feedback system. It highlights its potential to revolutionize implantable brain-machine microsystems for patient-specific treatment

As deep learning models scale, they become increasingly competitive from domains spanning from computer vision to natural language processing; however, this happens at the expense of efficiency since they require increasingly more memory and computing power. The power efficiency of the biological brain outperforms any large-scale deep learning ( DL ) model; thus, neuromorphic computing tries to mimic the brain operations, such as spike-based information processing, to improve the efficiency of DL models. Despite the benefits of the brain, such as efficient information transmission, dense neuronal interconnects, and the co-location of computation and memory, the available biological substrate has severely constrained the evolution of biological brains. Electronic hardware does not have the same constraints; therefore, while modeling spiking neural networks ( SNNs) might uncover one piece of the puzzle, the design of efficient hardware backends for SNN s needs further investigation, potentially taking inspiration from the available work done on the artificial neural networks ( ANNs) side. As such, when is it wise to look at the brain while designing new hardware, and when should it be ignored? To answer this question, we quantitatively compare the digital hardware acceleration techniques and platforms of ANNs and SNN s. As a result, we provide the following insights: (i) ANNs currently process static data more efficiently, (ii) applications targeting data produced by neuromorphic sensors, such as event-based cameras and silicon cochleas, need more investigation since the behavior of these sensors might naturally fit the SNN paradigm, and (iii) hybrid approaches combining SNN s and ANNs might lead to the best solutions and should be investigated further at the hardware level, accounting for both efficiency and loss optimization., Comment: Fixed error in bio

Memristive reservoirs draw inspiration from a novel class of neuromorphic hardware known as nanowire networks. These systems display emergent brain-like dynamics, with optimal performance demonstrated at dynamical phase transitions. In these networks, a limited number of electrodes are available to modulate system dynamics, in contrast to the global controllability offered by neuromorphic hardware through random access memories. We demonstrate that the learn-to-learn framework can effectively address this challenge in the context of optimization. Using the framework, we successfully identify the optimal hyperparameters for the reservoir. This finding aligns with previous research, which suggests that the optimal performance of a memristive reservoir occurs at the `edge of formation' of a conductive pathway. Furthermore, our results show that these systems can mimic membrane potential behavior observed in spiking neurons, and may serve as an interface between spike-based and continuous processes., Comment: 7 pages, 6 figures, ICONS 2023, accepted

Artificial neural networks (ANNs) have emerged as an essential tool in machine learning, achieving remarkable success across diverse domains, including image and speech generation, game playing, and robotics. However, there exist fundamental differences between ANNs' operating mechanisms and those of the biological brain, particularly concerning learning processes. This paper presents a comprehensive review of current brain-inspired learning representations in artificial neural networks. We investigate the integration of more biologically plausible mechanisms, such as synaptic plasticity, to enhance these networks' capabilities. Moreover, we delve into the potential advantages and challenges accompanying this approach. Ultimately, we pinpoint promising avenues for future research in this rapidly advancing field, which could bring us closer to understanding the essence of intelligence.

Analog compute-in-memory (CIM) systems are promising for deep neural network (DNN) inference acceleration due to their energy efficiency and high throughput. However, as the use of DNNs expands, protecting user input privacy has become increasingly important. In this paper, we identify a potential security vulnerability wherein an adversary can reconstruct the user's private input data from a power side-channel attack, under proper data acquisition and pre-processing, even without knowledge of the DNN model. We further demonstrate a machine learning-based attack approach using a generative adversarial network (GAN) to enhance the data reconstruction. Our results show that the attack methodology is effective in reconstructing user inputs from analog CIM accelerator power leakage, even at large noise levels and after countermeasures are applied. Specifically, we demonstrate the efficacy of our approach on an example of U-Net inference chip for brain tumor detection, and show the original magnetic resonance imaging (MRI) medical images can be successfully reconstructed even at a noise-level of 20% standard deviation of the maximum power signal value. Our study highlights a potential security vulnerability in analog CIM accelerators and raises awareness of using GAN to breach user privacy in such systems.

Neuromorphic computing shows promise for advancing computing efficiency and capabilities of AI applications using brain-inspired principles. However, the neuromorphic research field currently lacks standardized benchmarks, making it difficult to accurately measure technological advancements, compare performance with conventional methods, and identify promising future research directions. Prior neuromorphic computing benchmark efforts have not seen widespread adoption due to a lack of inclusive, actionable, and iterative benchmark design and guidelines. To address these shortcomings, we present NeuroBench: a benchmark framework for neuromorphic computing algorithms and systems. NeuroBench is a collaboratively-designed effort from an open community of nearly 100 co-authors across over 50 institutions in industry and academia, aiming to provide a representative structure for standardizing the evaluation of neuromorphic approaches. The NeuroBench framework introduces a common set of tools and systematic methodology for inclusive benchmark measurement, delivering an objective reference framework for quantifying neuromorphic approaches in both hardware-independent (algorithm track) and hardware-dependent (system track) settings. In this article, we present initial performance baselines across various model architectures on the algorithm track and outline the system track benchmark tasks and guidelines. NeuroBench is intended to continually expand its benchmarks and features to foster and track the progress made by the research community., Comment: Updated from whitepaper to full perspective article preprint

As the size of large language models continue to scale, so does the computational resources required to run it. Spiking Neural Networks (SNNs) have emerged as an energy-efficient approach to deep learning that leverage sparse and event-driven activations to reduce the computational overhead associated with model inference. While they have become competitive with non-spiking models on many computer vision tasks, SNNs have also proven to be more challenging to train. As a result, their performance lags behind modern deep learning, and we are yet to see the effectiveness of SNNs in language generation. In this paper, inspired by the Receptance Weighted Key Value (RWKV) language model, we successfully implement `SpikeGPT', a generative language model with binary, event-driven spiking activation units. We train the proposed model on two model variants: 45M and 216M parameters. To the best of our knowledge, SpikeGPT is the largest backpropagation-trained SNN model to date, rendering it suitable for both the generation and comprehension of natural language. We achieve this by modifying the transformer block to replace multi-head self attention to reduce quadratic computational complexity O(N^2) to linear complexity O(N) with increasing sequence length. Input tokens are instead streamed in sequentially to our attention mechanism (as with typical SNNs). Our preliminary experiments show that SpikeGPT remains competitive with non-spiking models on tested benchmarks, while maintaining 20x fewer operations when processed on neuromorphic hardware that can leverage sparse, event-driven activations. Our code implementation is available at https://github.com/ridgerchu/SpikeGPT., Comment: Accepted by TMLR

This paper presents a spiking neural network (SNN) accelerator made using fully open-source EDA tools, process design kit (PDK), and memory macros synthesized using OpenRAM. The chip is taped out in the 130 nm SkyWater process and integrates over 1 million synaptic weights, and offers a reprogrammable architecture. It operates at a clock speed of 40 MHz, a supply of 1.8 V, uses a PicoRV32 core for control, and occupies an area of 33.3 mm^2. The throughput of the accelerator is 48,262 images per second with a wallclock time of 20.72 us, at 56.8 GOPS/W. The spiking neurons use hysteresis to provide an adaptive threshold (i.e., a Schmitt trigger) which can reduce state instability. This results in high performing SNNs across a range of benchmarks that remain competitive with state-of-the-art, full precision SNNs. The design is open sourced and available online: https://github.com/sfmth/OpenSpike, Comment: The design is open sourced and available online: https://github.com/sfmth/OpenSpike

Spiking neural networks (SNNs) have achieved orders of magnitude improvement in terms of energy consumption and latency when performing inference with deep learning workloads. Error backpropagation is presently regarded as the most effective method for training SNNs, but in a twist of irony, when training on modern graphics processing units (GPUs) this becomes more expensive than non-spiking networks. The emergence of Graphcore's Intelligence Processing Units (IPUs) balances the parallelized nature of deep learning workloads with the sequential, reusable, and sparsified nature of operations prevalent when training SNNs. IPUs adopt multi-instruction multi-data (MIMD) parallelism by running individual processing threads on smaller data blocks, which is a natural fit for the sequential, non-vectorized steps required to solve spiking neuron dynamical state equations. We present an IPU-optimized release of our custom SNN Python package, snnTorch, which exploits fine-grained parallelism by utilizing low-level, pre-compiled custom operations to accelerate irregular and sparse data access patterns that are characteristic of training SNN workloads. We provide a rigorous performance assessment across a suite of commonly used spiking neuron models, and propose methods to further reduce training run-time via half-precision training. By amortizing the cost of sequential processing into vectorizable population codes, we ultimately demonstrate the potential for integrating domain-specific accelerators with the next generation of neural networks., Comment: 10 pages, 9 figures, journal

Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the undisputed efficiency of the human brain, they introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. To open the pathway toward engineering applications, we introduce this exciting technology in the context of continuum mechanics. However, the nature of spiking neural networks poses a challenge for regression problems, which frequently arise in the modeling of engineering sciences. To overcome this problem, a framework for regression using spiking neural networks is proposed. In particular, a network topology for decoding binary spike trains to real numbers is introduced, utilizing the membrane potential of spiking neurons. As the aim of this contribution is a concise introduction to this new methodology, several different spiking neural architectures, ranging from simple spiking feed-forward to complex spiking long short-term memory neural networks, are derived. Several numerical experiments directed towards regression of linear and nonlinear, history-dependent material models are carried out. A direct comparison with counterparts of traditional neural networks shows that the proposed framework is much more efficient while retaining precision and generalizability. All code has been made publicly available in the interest of reproducibility and to promote continued enhancement in this new domain.

In-memory computing (IMC) systems have great potential for accelerating data-intensive tasks such as deep neural networks (DNNs). As DNN models are generally highly proprietary, the neural network architectures become valuable targets for attacks. In IMC systems, since the whole model is mapped on chip and weight memory read can be restricted, the pre-mapped DNN model acts as a ``black box'' for users. However, the localized and stationary weight and data patterns may subject IMC systems to other attacks. In this paper, we propose a side-channel attack methodology on IMC architectures. We show that it is possible to extract model architectural information from power trace measurements without any prior knowledge of the neural network. We first developed a simulation framework that can emulate the dynamic power traces of the IMC macros. We then performed side-channel leakage analysis to reverse engineer model information such as the stored layer type, layer sequence, output channel/feature size and convolution kernel size from power traces of the IMC macros. Based on the extracted information, full networks can potentially be reconstructed without any knowledge of the neural network. Finally, we discuss potential countermeasures for building IMC systems that offer resistance to these model extraction attack.

We present MEMprop, the adoption of gradient-based learning to train fully memristive spiking neural networks (MSNNs). Our approach harnesses intrinsic device dynamics to trigger naturally arising voltage spikes. These spikes emitted by memristive dynamics are analog in nature, and thus fully differentiable, which eliminates the need for surrogate gradient methods that are prevalent in the spiking neural network (SNN) literature. Memristive neural networks typically either integrate memristors as synapses that map offline-trained networks, or otherwise rely on associative learning mechanisms to train networks of memristive neurons. We instead apply the backpropagation through time (BPTT) training algorithm directly on analog SPICE models of memristive neurons and synapses. Our implementation is fully memristive, in that synaptic weights and spiking neurons are both integrated on resistive RAM (RRAM) arrays without the need for additional circuits to implement spiking dynamics, e.g., analog-to-digital converters (ADCs) or thresholded comparators. As a result, higher-order electrophysical effects are fully exploited to use the state-driven dynamics of memristive neurons at run time. By moving towards non-approximate gradient-based learning, we obtain highly competitive accuracy amongst previously reported lightweight dense fully MSNNs on several benchmarks.

Spiking neural networks have shown much promise as an energy-efficient alternative to artificial neural networks. However, understanding the impacts of sensor noises and input encodings on the network activity and performance remains difficult with common neuromorphic vision baselines like classification. Therefore, we propose a spiking neural network approach for single object localization trained using surrogate gradient descent, for frame- and event-based sensors. We compare our method with similar artificial neural networks and show that our model has competitive/better performance in accuracy, robustness against various corruptions, and has lower energy consumption. Moreover, we study the impact of neural coding schemes for static images in accuracy, robustness, and energy efficiency. Our observations differ importantly from previous studies on bio-plausible learning rules, which helps in the design of surrogate gradient trained architectures, and offers insight to design priorities in future neuromorphic technologies in terms of noise characteristics and data encoding methods., Comment: 21 pages, 12 figures

We present a fully memristive spiking neural network (MSNN) consisting of novel memristive neurons trained using the backpropagation through time (BPTT) learning rule. Gradient descent is applied directly to the memristive integrated-and-fire (MIF) neuron designed using analog SPICE circuit models, which generates distinct depolarization, hyperpolarization, and repolarization voltage waveforms. Synaptic weights are trained by BPTT using the membrane potential of the MIF neuron model and can be processed on memristive crossbars. The natural spiking dynamics of the MIF neuron model are fully differentiable, eliminating the need for gradient approximations that are prevalent in the spiking neural network literature. Despite the added complexity of training directly on SPICE circuit models, we achieve 97.58% accuracy on the MNIST testing dataset and 75.26% on the Fashion-MNIST testing dataset, the highest accuracies among all fully MSNNs.

We present a fully memristive spiking neural network (MSNN) consisting of physically-realizable memristive neurons and memristive synapses to implement an unsupervised Spiking Time Dependent Plasticity (STDP) learning rule. The system is fully memristive in that both neuronal and synaptic dynamics can be realized by using memristors. The neuron is implemented using the SPICE-level memristive integrate-and-fire (MIF) model, which consists of a minimal number of circuit elements necessary to achieve distinct depolarization, hyperpolarization, and repolarization voltage waveforms. The proposed MSNN uniquely implements STDP learning by using cumulative weight changes in memristive synapses from the voltage waveform changes across the synapses, which arise from the presynaptic and postsynaptic spiking voltage signals during the training process. Two types of MSNN architectures are investigated: 1) a biologically plausible memory retrieval system, and 2) a multi-class classification system. Our circuit simulation results verify the MSNN's unsupervised learning efficacy by replicating biological memory retrieval mechanisms, and achieving 97.5% accuracy in a 4-pattern recognition problem in a large scale discriminative MSNN.

Spiking and Quantized Neural Networks (NNs) are becoming exceedingly important for hyper-efficient implementations of Deep Learning (DL) algorithms. However, these networks face challenges when trained using error backpropagation, due to the absence of gradient signals when applying hard thresholds. The broadly accepted trick to overcoming this is through the use of biased gradient estimators: surrogate gradients which approximate thresholding in Spiking Neural Networks (SNNs), and Straight-Through Estimators (STEs), which completely bypass thresholding in Quantized Neural Networks (QNNs). While noisy gradient feedback has enabled reasonable performance on simple supervised learning tasks, it is thought that such noise increases the difficulty of finding optima in loss landscapes, especially during the later stages of optimization. By periodically boosting the Learning Rate (LR) during training, we expect the network can navigate unexplored solution spaces that would otherwise be difficult to reach due to local minima, barriers, or flat surfaces. This paper presents a systematic evaluation of a cosine-annealed LR schedule coupled with weight-independent adaptive moment estimation as applied to Quantized SNNs (QSNNs). We provide a rigorous empirical evaluation of this technique on high precision and 4-bit quantized SNNs across three datasets, demonstrating (close to) state-of-the-art performance on the more complex datasets. Our source code is available at this link: https://github.com/jeshraghian/QSNNs.

Spiking neural networks can compensate for quantization error by encoding information either in the temporal domain, or by processing discretized quantities in hidden states of higher precision. In theory, a wide dynamic range state-space enables multiple binarized inputs to be accumulated together, thus improving the representational capacity of individual neurons. This may be achieved by increasing the firing threshold, but make it too high and sparse spike activity turns into no spike emission. In this paper, we propose the use of `threshold annealing' as a warm-up method for firing thresholds. We show it enables the propagation of spikes across multiple layers where neurons would otherwise cease to fire, and in doing so, achieve highly competitive results on four diverse datasets, despite using binarized weights. Source code is available at https://github.com/jeshraghian/snn-tha/

The impact of device and circuit-level effects in mixed-signal Resistive Random Access Memory (RRAM) accelerators typically manifest as performance degradation of Deep Learning (DL) algorithms, but the degree of impact varies based on algorithmic features. These include network architecture, capacity, weight distribution, and the type of inter-layer connections. Techniques are continuously emerging to efficiently train sparse neural networks, which may have activation sparsity, quantization, and memristive noise. In this paper, we present an extended Design Space Exploration (DSE) methodology to quantify the benefits and limitations of dense and sparse mapping schemes for a variety of network architectures. While sparsity of connectivity promotes less power consumption and is often optimized for extracting localized features, its performance on tiled RRAM arrays may be more susceptible to noise due to under-parameterization, when compared to dense mapping schemes. Moreover, we present a case study quantifying and formalizing the trade-offs of typical non-idealities introduced into 1-Transistor-1-Resistor (1T1R) tiled memristive architectures and the size of modular crossbar tiles using the CIFAR-10 dataset., Comment: Accepted at 2022 IEEE International Symposium on Circuits and Systems (ISCAS). [v2] Fixed incorrectly labeled author affiliations for Chenqi Li, Amirali Amirsoleimani, and Roman Genov

The brain is the perfect place to look for inspiration to develop more efficient neural networks. The inner workings of our synapses and neurons provide a glimpse at what the future of deep learning might look like. This paper serves as a tutorial and perspective showing how to apply the lessons learnt from several decades of research in deep learning, gradient descent, backpropagation and neuroscience to biologically plausible spiking neural neural networks. We also explore the delicate interplay between encoding data as spikes and the learning process; the challenges and solutions of applying gradient-based learning to spiking neural networks (SNNs); the subtle link between temporal backpropagation and spike timing dependent plasticity, and how deep learning might move towards biologically plausible online learning. Some ideas are well accepted and commonly used amongst the neuromorphic engineering community, while others are presented or justified for the first time here. The fields of deep learning and spiking neural networks evolve very rapidly. We endeavour to treat this document as a 'dynamic' manuscript that will continue to be updated as the common practices in training SNNs also change. A series of companion interactive tutorials complementary to this paper using our Python package, snnTorch, are also made available. See https://snntorch.readthedocs.io/en/latest/tutorials/index.html .

The problem of worst case edge deletion from a network is considered. Suppose that you have a communication network and you can delete a single edge. Which edge deletion causes the largest disruption? More formally, given a graph, which edge after deletion disconnects the maximum number of pairs of vertices, where ties for number of pairs disconnected are broken by finding an edge that increases the average shortest path length the maximum amount. This problem is interesting both practically and theoretically. We call it the \emph{single edge deletion problem}. Our contributions include formally defining the single edge deletion problem and providing motivations from network analysis. Also, we give an algorithm that solves the problem much faster than a naive solution. The algorithm incorporates sophisticated and novel techniques, and generalises to the problem of computing the all-pairs shortest paths table after deleting each edge individually. This means the algorithm has deep theoretical interest as well as the potential for even wider applications than those we present here., Comment: Found previous published results with similar findings