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Spiking Neural Networks (SNNs) simulators are essential tools to prototype biologically inspired models and neuromorphic hardware architectures and predict their performance. For such a tool, ease of use and flexibility are critical, but so is simulation speed especially given the complexity inherent to simulating SNN. Here, we present SNNAX, a JAX-based framework for simulating and training such models with PyTorch-like intuitiveness and JAX-like execution speed. SNNAX models are easily extended and customized to fit the desired model specifications and target neuromorphic hardware. Additionally, SNNAX offers key features for optimizing the training and deployment of SNNs such as flexible automatic differentiation and just-in-time compilation. We evaluate and compare SNNAX to other commonly used machine learning (ML) frameworks used for programming SNNs. We provide key performance metrics, best practices, documented examples for simulating SNNs in SNNAX, and implement several benchmarks used in the literature.

Achieving personalized intelligence at the edge with real-time learning capabilities holds enormous promise in enhancing our daily experiences and helping decision making, planning, and sensing. However, efficient and reliable edge learning remains difficult with current technology due to the lack of personalized data, insufficient hardware capabilities, and inherent challenges posed by online learning. Over time and across multiple developmental stages, the brain has evolved to efficiently incorporate new knowledge by gradually building on previous knowledge. In this work, we emulate the multiple stages of learning with digital neuromorphic technology that simulates the neural and synaptic processes of the brain using two stages of learning. First, a meta-training stage trains the hyperparameters of synaptic plasticity for one-shot learning using a differentiable simulation of the neuromorphic hardware. This meta-training process refines a hardware local three-factor synaptic plasticity rule and its associated hyperparameters to align with the trained task domain. In a subsequent deployment stage, these optimized hyperparameters enable fast, data-efficient, and accurate learning of new classes. We demonstrate our approach using event-driven vision sensor data and the Intel Loihi neuromorphic processor with its plasticity dynamics, achieving real-time one-shot learning of new classes that is vastly improved over transfer learning. Our methodology can be deployed with arbitrary plasticity models and can be applied to situations demanding quick learning and adaptation at the edge, such as navigating unfamiliar environments or learning unexpected categories of data through user engagement., Comment: 17 page journal article. Submitted to IOP NCE

Computing Jacobians with automatic differentiation is ubiquitous in many scientific domains such as machine learning, computational fluid dynamics, robotics and finance. Even small savings in the number of computations or memory usage in Jacobian computations can already incur massive savings in energy consumption and runtime. While there exist many methods that allow for such savings, they generally trade computational efficiency for approximations of the exact Jacobian. In this paper, we present a novel method to optimize the number of necessary multiplications for Jacobian computation by leveraging deep reinforcement learning (RL) and a concept called cross-country elimination while still computing the exact Jacobian. Cross-country elimination is a framework for automatic differentiation that phrases Jacobian accumulation as ordered elimination of all vertices on the computational graph where every elimination incurs a certain computational cost. We formulate the search for the optimal elimination order that minimizes the number of necessary multiplications as a single player game which is played by an RL agent. We demonstrate that this method achieves up to 33% improvements over state-of-the-art methods on several relevant tasks taken from diverse domains. Furthermore, we show that these theoretical gains translate into actual runtime improvements by providing a cross-country elimination interpreter in JAX that can efficiently execute the obtained elimination orders.

Programming recurrent spiking neural networks (RSNNs) to robustly perform multi-timescale computation remains a difficult challenge. To address this, we describe a single-shot weight learning scheme to embed robust multi-timescale dynamics into attractor-based RSNNs, by exploiting the properties of high-dimensional distributed representations. We embed finite state machines into the RSNN dynamics by superimposing a symmetric autoassociative weight matrix and asymmetric transition terms, which are each formed by the vector binding of an input and heteroassociative outer-products between states. Our approach is validated through simulations with highly non-ideal weights; an experimental closed-loop memristive hardware setup; and on Loihi 2, where it scales seamlessly to large state machines. This work introduces a scalable approach to embed robust symbolic computation through recurrent dynamics into neuromorphic hardware, without requiring parameter fine-tuning or significant platform-specific optimisation. Moreover, it demonstrates that distributed symbolic representations serve as a highly capable representation-invariant language for cognitive algorithms in neuromorphic hardware., Comment: 15 pages, 6 figures. Supplementary material: 7 pages, 6 figures

Event cameras offer high temporal resolution and dynamic range with minimal motion blur, making them promising for object detection tasks. While Spiking Neural Networks (SNNs) are a natural match for event-based sensory data and enable ultra-energy efficient and low latency inference on neuromorphic hardware, Artificial Neural Networks (ANNs) tend to display more stable training dynamics and faster convergence resulting in greater task performance. Hybrid SNN-ANN approaches are a promising alternative, enabling to leverage the strengths of both SNN and ANN architectures. In this work, we introduce the first Hybrid Attention-based SNN-ANN backbone for object detection using event cameras. We propose a novel Attention-based SNN-ANN bridge module to capture sparse spatial and temporal relations from the SNN layer and convert them into dense feature maps for the ANN part of the backbone. Experimental results demonstrate that our proposed method surpasses baseline hybrid and SNN-based approaches by significant margins, with results comparable to existing ANN-based methods. Extensive ablation studies confirm the effectiveness of our proposed modules and architectural choices. These results pave the way toward a hybrid SNN-ANN architecture that achieves ANN like performance at a drastically reduced parameter budget. We implemented the SNN blocks on digital neuromorphic hardware to investigate latency and power consumption and demonstrate the feasibility of our approach.

Simulation frameworks such MemTorch, DNN+NeuroSim, and aihwkit are commonly used to facilitate the end-to-end co-design of memristive machine learning (ML) accelerators. These simulators can take device nonidealities into account and are integrated with modern ML frameworks. However, memristors in these simulators are modeled with either lookup tables or simple analytic models with basic nonlinearities. These simple models are unable to capture certain performance-critical aspects of device nonidealities. For example, they ignore the physical cause of switching, which induces errors in switching timings and thus incorrect estimations of conductance states. This work aims at bringing physical dynamics into consideration to model nonidealities while being compatible with GPU accelerators. We focus on Valence Change Memory (VCM) cells, where the switching nonlinearity and SET/RESET asymmetry relate tightly with the thermal resistance, ion mobility, Schottky barrier height, parasitic resistance, and other effects. The resulting dynamics require solving an ODE that captures changes in oxygen vacancies. We modified a physics-derived SPICE-level VCM model, integrated it with the aihwkit simulator and tested the performance with the MNIST dataset. Results show that noise that disrupts the SET/RESET matching affects network performance the most. This work serves as a tool for evaluating how physical dynamics in memristive devices affect neural network accuracy and can be used to guide the development of future integrated devices., Comment: This work is published at the 2022 56th Asilomar Conference

Memristive devices hold promise to improve the scale and efficiency of machine learning and neuromorphic hardware, thanks to their compact size, low power consumption, and the ability to perform matrix multiplications in constant time. However, on-chip training with memristor arrays still faces challenges, including device-to-device and cycle-to-cycle variations, switching non-linearity, and especially SET and RESET asymmetry. To combat device non-linearity and asymmetry, we propose to program memristors by harnessing neural networks that map desired conductance updates to the required pulse times. With our method, approximately 95% of devices can be programmed within a relative percentage difference of +-50% from the target conductance after just one attempt. Our approach substantially reduces memristor programming delays compared to traditional write-and-verify methods, presenting an advantageous solution for on-chip training scenarios. Furthermore, our proposed neural network can be accelerated by memristor arrays upon deployment, providing assistance while reducing hardware overhead compared with previous works. This work contributes significantly to the practical application of memristors, particularly in reducing delays in memristor programming. It also envisions the future development of memristor-based machine learning accelerators., Comment: This work is accepted at the 2024 IEEE AICAS

Current AI training infrastructure is dominated by single instruction multiple data (SIMD) and systolic array architectures, such as Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs), that excel at accelerating parallel workloads and dense vector matrix multiplications. Potentially more efficient neural network models utilizing sparsity and recurrence cannot leverage the full power of SIMD processor and are thus at a severe disadvantage compared to today's prominent parallel architectures like Transformers and CNNs, thereby hindering the path towards more sustainable AI. To overcome this limitation, we explore sparse and recurrent model training on a massively parallel multiple instruction multiple data (MIMD) architecture with distributed local memory. We implement a training routine based on backpropagation through time (BPTT) for the brain-inspired class of Spiking Neural Networks (SNNs) that feature binary sparse activations. We observe a massive advantage in using sparse activation tensors with a MIMD processor, the Intelligence Processing Unit (IPU) compared to GPUs. On training workloads, our results demonstrate 5-10x throughput gains compared to A100 GPUs and up to 38x gains for higher levels of activation sparsity, without a significant slowdown in training convergence or reduction in final model performance. Furthermore, our results show highly promising trends for both single and multi IPU configurations as we scale up to larger model sizes. Our work paves the way towards more efficient, non-standard models via AI training hardware beyond GPUs, and competitive large scale SNN models.

Lifelong learning - an agent's ability to learn throughout its lifetime - is a hallmark of biological learning systems and a central challenge for artificial intelligence (AI). The development of lifelong learning algorithms could lead to a range of novel AI applications, but this will also require the development of appropriate hardware accelerators, particularly if the models are to be deployed on edge platforms, which have strict size, weight, and power constraints. Here, we explore the design of lifelong learning AI accelerators that are intended for deployment in untethered environments. We identify key desirable capabilities for lifelong learning accelerators and highlight metrics to evaluate such accelerators. We then discuss current edge AI accelerators and explore the future design of lifelong learning accelerators, considering the role that different emerging technologies could play.

Backpropagation (BP), the standard learning algorithm for artificial neural networks, is often considered biologically implausible. In contrast, the standard learning algorithm for predictive coding (PC) models in neuroscience, known as the inference learning algorithm (IL), is a promising, bio-plausible alternative. However, several challenges and questions hinder IL's application to real-world problems. For example, IL is computationally demanding, and without memory-intensive optimizers like Adam, IL may converge to poor local minima. Moreover, although IL can reduce loss more quickly than BP, the reasons for these speedups or their robustness remains unclear. In this paper, we tackle these challenges by 1) altering the standard implementation of PC circuits to substantially reduce computation, 2) developing a novel optimizer that improves the convergence of IL without increasing memory usage, and 3) establishing theoretical results that help elucidate the conditions under which IL is sensitive to second and higher-order information.

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

Transformers are state-of-the-art networks for most sequence processing tasks. However, the self-attention mechanism often used in Transformers requires large time windows for each computation step and thus makes them less suitable for online signal processing compared to Recurrent Neural Networks (RNNs). In this paper, instead of the self-attention mechanism, we use a sliding window attention mechanism. We show that this mechanism is more efficient for continuous signals with finite-range dependencies between input and target, and that we can use it to process sequences element-by-element, this making it compatible with online processing. We test our model on a finger position regression dataset (NinaproDB8) with Surface Electromyographic (sEMG) signals measured on the forearm skin to estimate muscle activities. Our approach sets the new state-of-the-art in terms of accuracy on this dataset while requiring only very short time windows of 3.5 ms at each inference step. Moreover, we increase the sparsity of the network using Leaky-Integrate and Fire (LIF) units, a bio-inspired neuron model that activates sparsely in time solely when crossing a threshold. We thus reduce the number of synaptic operations up to a factor of $\times5.3$ without loss of accuracy. Our results hold great promises for accurate and fast online processing of sEMG signals for smooth prosthetic hand control and is a step towards Transformers and Spiking Neural Networks (SNNs) co-integration for energy efficient temporal signal processing., Comment: Preprint of 9 pages, 4 figures

Neuromorphic perception with event-based sensors, asynchronous hardware and spiking neurons is showing promising results for real-time and energy-efficient inference in embedded systems. The next promise of brain-inspired computing is to enable adaptation to changes at the edge with online learning. However, the parallel and distributed architectures of neuromorphic hardware based on co-localized compute and memory imposes locality constraints to the on-chip learning rules. We propose in this work the Event-based Three-factor Local Plasticity (ETLP) rule that uses (1) the pre-synaptic spike trace, (2) the post-synaptic membrane voltage and (3) a third factor in the form of projected labels with no error calculation, that also serve as update triggers. We apply ETLP with feedforward and recurrent spiking neural networks on visual and auditory event-based pattern recognition, and compare it to Back-Propagation Through Time (BPTT) and eProp. We show a competitive performance in accuracy with a clear advantage in the computational complexity for ETLP. We also show that when using local plasticity, threshold adaptation in spiking neurons and a recurrent topology are necessary to learn spatio-temporal patterns with a rich temporal structure. Finally, we provide a proof of concept hardware implementation of ETLP on FPGA to highlight the simplicity of its computational primitives and how they can be mapped into neuromorphic hardware for online learning with low-energy consumption and real-time interaction.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Although deep Reinforcement Learning (RL) has proven successful in a wide range of tasks, one challenge it faces is interpretability when applied to real-world problems. Saliency maps are frequently used to provide interpretability for deep neural networks. However, in the RL domain, existing saliency map approaches are either computationally expensive and thus cannot satisfy the real-time requirement of real-world scenarios or cannot produce interpretable saliency maps for RL policies. In this work, we propose an approach of Distillation with selective Input Gradient Regularization (DIGR) which uses policy distillation and input gradient regularization to produce new policies that achieve both high interpretability and computation efficiency in generating saliency maps. Our approach is also found to improve the robustness of RL policies to multiple adversarial attacks. We conduct experiments on three tasks, MiniGrid (Fetch Object), Atari (Breakout) and CARLA Autonomous Driving, to demonstrate the importance and effectiveness of our approach.

Adaptive "life-long" learning at the edge and during online task performance is an aspirational goal of AI research. Neuromorphic hardware implementing Spiking Neural Networks (SNNs) are particularly attractive in this regard, as their real-time, event-based, local computing paradigm makes them suitable for edge implementations and fast learning. However, the long and iterative learning that characterizes state-of-the-art SNN training is incompatible with the physical nature and real-time operation of neuromorphic hardware. Bi-level learning, such as meta-learning is increasingly used in deep learning to overcome these limitations. In this work, we demonstrate gradient-based meta-learning in SNNs using the surrogate gradient method that approximates the spiking threshold function for gradient estimations. Because surrogate gradients can be made twice differentiable, well-established, and effective second-order gradient meta-learning methods such as Model Agnostic Meta Learning (MAML) can be used. We show that SNNs meta-trained using MAML match or exceed the performance of conventional ANNs meta-trained with MAML on event-based meta-datasets. Furthermore, we demonstrate the specific advantages that accrue from meta-learning: fast learning without the requirement of high precision weights or gradients. Our results emphasize how meta-learning techniques can become instrumental for deploying neuromorphic learning technologies on real-world problems., Comment: Submitted to IOP Neuromorphic Computing and Engineering for peer review

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 .

Modern computation based on the von Neumann architecture is today a mature cutting-edge science. In the Von Neumann architecture, processing and memory units are implemented as separate blocks interchanging data intensively and continuously. This data transfer is responsible for a large part of the power consumption. The next generation computer technology is expected to solve problems at the exascale with 1018 calculations each second. Even though these future computers will be incredibly powerful, if they are based on von Neumann type architectures, they will consume between 20 and 30 megawatts of power and will not have intrinsic physically built-in capabilities to learn or deal with complex data as our brain does. These needs can be addressed by neuromorphic computing systems which are inspired by the biological concepts of the human brain. This new generation of computers has the potential to be used for the storage and processing of large amounts of digital information with much lower power consumption than conventional processors. Among their potential future applications, an important niche is moving the control from data centers to edge devices. The aim of this Roadmap is to present a snapshot of the present state of neuromorphic technology and provide an opinion on the challenges and opportunities that the future holds in the major areas of neuromorphic technology, namely materials, devices, neuromorphic circuits, neuromorphic algorithms, applications, and ethics. The Roadmap is a collection of perspectives where leading researchers in the neuromorphic community provide their own view about the current state and the future challenges. We hope that this Roadmap will be a useful resource to readers outside this field, for those who are just entering the field, and for those who are well established in the neuromorphic community. https://doi.org/10.1088/2634-4386/ac4a83

Predictive coding (PC) is a general theory of cortical function. The local, gradient-based learning rules found in one kind of PC model have recently been shown to closely approximate backpropagation. This finding suggests that this gradient-based PC model may be useful for understanding how the brain solves the credit assignment problem. The model may also be useful for developing local learning algorithms that are compatible with neuromorphic hardware. In this paper, we modify this PC model so that it better fits biological constraints, including the constraints that neurons can only have positive firing rates and the constraint that synapses only flow in one direction. We also compute the gradient-based weight and activity updates given the modified activity values. We show that, under certain conditions, these modified PC networks perform as well or nearly as well on MNIST data as the unmodified PC model and networks trained with backpropagation., Comment: This is a preprint of a published article. For final, published version see https://doi.org/10.1145/3477145.3477148

To achieve the low latency, high throughput, and energy efficiency benefits of Spiking Neural Networks (SNNs), reducing the memory and compute requirements when running on a neuromorphic hardware is an important step. Neuromorphic architecture allows massively parallel computation with variable and local bit-precisions. However, how different bit-precisions should be allocated to different layers or connections of the network is not trivial. In this work, we demonstrate how a layer-wise Hessian trace analysis can measure the sensitivity of the loss to any perturbation of the layer's weights, and this can be used to guide the allocation of a layer-specific bit-precision when quantizing an SNN. In addition, current gradient based methods of SNN training use a complex neuron model with multiple state variables, which is not ideal for compute and memory efficiency. To address this challenge, we present a simplified neuron model that reduces the number of state variables by 4-fold while still being compatible with gradient based training. We find that the impact on model accuracy when using a layer-wise bit-precision correlated well with that layer's Hessian trace. The accuracy of the optimal quantized network only dropped by 0.2%, yet the network size was reduced by 58%. This reduces memory usage and allows fixed-point arithmetic with simpler digital circuits to be used, increasing the overall throughput and energy efficiency.

Neuromorphic hardware equipped with learning capabilities can adapt to new, real-time data. While models of Spiking Neural Networks (SNNs) can now be trained using gradient descent to reach an accuracy comparable to equivalent conventional neural networks, such learning often relies on external labels. However, real-world data is unlabeled which can make supervised methods inapplicable. To solve this problem, we propose a Hybrid Guided Variational Autoencoder (VAE) which encodes event based data sensed by a Dynamic Vision Sensor (DVS) into a latent space representation using an SNN. These representations can be used as an embedding to measure data similarity and predict labels in real-world data. We show that the Hybrid Guided-VAE achieves 87% classification accuracy on the DVSGesture dataset and it can encode the sparse, noisy inputs into an interpretable latent space representation, visualized through T-SNE plots. We also implement the encoder component of the model on neuromorphic hardware and discuss the potential for our algorithm to enable real-time learning from real-world event data., Comment: Published in NICE 2022

Many real-world mission-critical applications require continual online learning from noisy data and real-time decision making with a defined confidence level. Probabilistic models and stochastic neural networks can explicitly handle uncertainty in data and allow adaptive learning-on-the-fly, but their implementation in a low-power substrate remains a challenge. Here, we introduce a novel hardware fabric that implements a new class of stochastic NN called Neural-Sampling-Machine that exploits stochasticity in synaptic connections for approximate Bayesian inference. Harnessing the inherent non-linearities and stochasticity occurring at the atomic level in emerging materials and devices allows us to capture the synaptic stochasticity occurring at the molecular level in biological synapses. We experimentally demonstrate in-silico hybrid stochastic synapse by pairing a ferroelectric field-effect transistor -based analog weight cell with a two-terminal stochastic selector element. Such a stochastic synapse can be integrated within the well-established crossbar array architecture for compute-in-memory. We experimentally show that the inherent stochastic switching of the selector element between the insulator and metallic state introduces a multiplicative stochastic noise within the synapses of NSM that samples the conductance states of the FeFET, both during learning and inference. We perform network-level simulations to highlight the salient automatic weight normalization feature introduced by the stochastic synapses of the NSM that paves the way for continual online learning without any offline Batch Normalization. We also showcase the Bayesian inferencing capability introduced by the stochastic synapse during inference mode, thus accounting for uncertainty in data. We report 98.25%accuracy on standard image classification task as well as estimation of data uncertainty in rotated samples.

Despite the recent success of deep reinforcement learning (RL), domain adaptation remains an open problem. Although the generalization ability of RL agents is critical for the real-world applicability of Deep RL, zero-shot policy transfer is still a challenging problem since even minor visual changes could make the trained agent completely fail in the new task. To address this issue, we propose a two-stage RL agent that first learns a latent unified state representation (LUSR) which is consistent across multiple domains in the first stage, and then do RL training in one source domain based on LUSR in the second stage. The cross-domain consistency of LUSR allows the policy acquired from the source domain to generalize to other target domains without extra training. We first demonstrate our approach in variants of CarRacing games with customized manipulations, and then verify it in CARLA, an autonomous driving simulator with more complex and realistic visual observations. Our results show that this approach can achieve state-of-the-art domain adaptation performance in related RL tasks and outperforms prior approaches based on latent-representation based RL and image-to-image translation., Comment: Accepted by AAAI 2021; Fixed a typo in equation 3

Recent breakthroughs in neuromorphic computing show that local forms of gradient descent learning are compatible with Spiking Neural Networks (SNNs) and synaptic plasticity. Although SNNs can be scalably implemented using neuromorphic VLSI, an architecture that can learn using gradient-descent in situ is still missing. In this paper, we propose a local, gradient-based, error-triggered learning algorithm with online ternary weight updates. The proposed algorithm enables online training of multi-layer SNNs with memristive neuromorphic hardware showing a small loss in the performance compared with the state of the art. We also propose a hardware architecture based on memristive crossbar arrays to perform the required vector-matrix multiplications. The necessary peripheral circuitry including pre-synaptic, post-synaptic and write circuits required for online training, have been designed in the sub-threshold regime for power saving with a standard 180 nm CMOS process., Comment: 15 pages, 11 figures, Journal of Emerging Technology in Circuits and Systems (JETCAS)

Neuromorphic hardware strives to emulate brain-like neural networks and thus holds the promise for scalable, low-power information processing on temporal data streams. Yet, to solve real-world problems, these networks need to be trained. However, training on neuromorphic substrates creates significant challenges due to the offline character and the required non-local computations of gradient-based learning algorithms. This article provides a mathematical framework for the design of practical online learning algorithms for neuromorphic substrates. Specifically, we show a direct connection between Real-Time Recurrent Learning (RTRL), an online algorithm for computing gradients in conventional Recurrent Neural Networks (RNNs), and biologically plausible learning rules for training Spiking Neural Networks (SNNs). Further, we motivate a sparse approximation based on block-diagonal Jacobians, which reduces the algorithm's computational complexity, diminishes the non-local information requirements, and empirically leads to good learning performance, thereby improving its applicability to neuromorphic substrates. In summary, our framework bridges the gap between synaptic plasticity and gradient-based approaches from deep learning and lays the foundations for powerful information processing on future neuromorphic hardware systems., Comment: All authors contributed equally

We present the Surrogate-gradient Online Error-triggered Learning (SOEL) system for online few-shot learning on neuromorphic processors. The SOEL learning system uses a combination of transfer learning and principles of computational neuroscience and deep learning. We show that partially trained deep Spiking Neural Networks (SNNs) implemented on neuromorphic hardware can rapidly adapt online to new classes of data within a domain. SOEL updates trigger when an error occurs, enabling faster learning with fewer updates. Using gesture recognition as a case study, we show SOEL can be used for online few-shot learning of new classes of pre-recorded gesture data and rapid online learning of new gestures from data streamed live from a Dynamic Active-pixel Vision Sensor to an Intel Loihi neuromorphic research processor., Comment: 10 pages, accepted by IEEE JETCAS

The energy efficiency of neuromorphic hardware is greatly affected by the energy of storing, accessing, and updating synaptic parameters. Various methods of memory organisation targeting energy-efficient digital accelerators have been investigated in the past, however, they do not completely encapsulate the energy costs at a system level. To address this shortcoming and to account for various overheads, we synthesize the controller and memory for different encoding schemes and extract the energy costs from these synthesized blocks. Additionally, we introduce functional encoding for structured connectivity such as the connectivity in convolutional layers. Functional encoding offers a 58% reduction in the energy to implement a backward pass and weight update in such layers compared to existing index-based solutions. We show that for a 2 layer spiking neural network trained to retain a spatio-temporal pattern, bitmap (PB-BMP) based organization can encode the sparser networks more efficiently. This form of encoding delivers a 1.37x improvement in energy efficiency coming at the cost of a 4% degradation in network retention accuracy as measured by the van Rossum distance., Comment: submitted to ISCAS2020

Multiplicative stochasticity such as Dropout improves the robustness and generalizability of deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons are sufficient operations for deep neural networks. We call such models Neural Sampling Machines (NSM). We find that the probability of activation of the NSM exhibits a self-normalizing property that mirrors Weight Normalization, a previously studied mechanism that fulfills many of the features of Batch Normalization in an online fashion. The normalization of activities during training speeds up convergence by preventing internal covariate shift caused by changes in the input distribution. The always-on stochasticity of the NSM confers the following advantages: the network is identical in the inference and learning phases, making the NSM suitable for online learning, it can exploit stochasticity inherent to a physical substrate such as analog non-volatile memories for in-memory computing, and it is suitable for Monte Carlo sampling, while requiring almost exclusively addition and comparison operations. We demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and event-based classification benchmarks (N-MNIST and DVS Gestures). Our results show that NSMs perform comparably or better than conventional artificial neural networks with the same architecture.

Recent breakthroughs suggest that local, approximate gradient descent learning is compatible with Spiking Neural Networks (SNNs). Although SNNs can be scalably implemented using neuromorphic VLSI, an architecture that can learn in-situ as accurately as conventional processors is still missing. Here, we propose a subthreshold circuit architecture designed through insights obtained from machine learning and computational neuroscience that could achieve such accuracy. Using a surrogate gradient learning framework, we derive local, error-triggered learning dynamics compatible with crossbar arrays and the temporal dynamics of SNNs. The derivation reveals that circuits used for inference and training dynamics can be shared, which simplifies the circuit and suppresses the effects of fabrication mismatch. We present SPICE simulations on XFAB 180nm process, as well as large-scale simulations of the spiking neural networks on event-based benchmarks, including a gesture recognition task. Our results show that the number of updates can be reduced hundred-fold compared to the standard rule while achieving performances that are on par with the state-of-the-art.

Recent work suggests that synaptic plasticity dynamics in biological models of neurons and neuromorphic hardware are compatible with gradient-based learning (Neftci et al., 2019). Gradient-based learning requires iterating several times over a dataset, which is both time-consuming and constrains the training samples to be independently and identically distributed. This is incompatible with learning systems that do not have boundaries between training and inference, such as in neuromorphic hardware. One approach to overcome these constraints is transfer learning, where a portion of the network is pre-trained and mapped into hardware and the remaining portion is trained online. Transfer learning has the advantage that pre-training can be accelerated offline if the task domain is known, and few samples of each class are sufficient for learning the target task at reasonable accuracies. Here, we demonstrate on-line surrogate gradient few-shot learning on Intel's Loihi neuromorphic research processor using features pre-trained with spike-based gradient backpropagation-through-time. Our experimental results show that the Loihi chip can learn gestures online using a small number of shots and achieve results that are comparable to the models simulated on a conventional processor., Comment: Preprint, work in progress. Submitted to AICAS 2020 for review

Spike-based communication between biological neurons is sparse and unreliable. This enables the brain to process visual information from the eyes efficiently. Taking inspiration from biology, artificial spiking neural networks coupled with silicon retinas attempt to model these computations. Recent findings in machine learning allowed the derivation of a family of powerful synaptic plasticity rules approximating backpropagation for spiking networks. Are these rules capable of processing real-world visual sensory data? In this paper, we evaluate the performance of Event-Driven Random Back-Propagation (eRBP) at learning representations from event streams provided by a Dynamic Vision Sensor (DVS). First, we show that eRBP matches state-of-the-art performance on the DvsGesture dataset with the addition of a simple covert attention mechanism. By remapping visual receptive fields relatively to the center of the motion, this attention mechanism provides translation invariance at low computational cost compared to convolutions. Second, we successfully integrate eRBP in a real robotic setup, where a robotic arm grasps objects according to detected visual affordances. In this setup, visual information is actively sensed by a DVS mounted on a robotic head performing microsaccadic eye movements. We show that our method classifies affordances within 100ms after microsaccade onset, which is comparable to human performance reported in behavioral study. Our results suggest that advances in neuromorphic technology and plasticity rules enable the development of autonomous robots operating at high speed and low energy consumption., Comment: v2: title update, better plots and wordings. 8 pages, 9 figures, 1 table, video: https://neurorobotics-files.net/index.php/s/sBQzWFrBPoH9Dx7

Spiking neural networks are nature's versatile solution to fault-tolerant and energy efficient signal processing. To translate these benefits into hardware, a growing number of neuromorphic spiking neural network processors attempt to emulate biological neural networks. These developments have created an imminent need for methods and tools to enable such systems to solve real-world signal processing problems. Like conventional neural networks, spiking neural networks can be trained on real, domain specific data. However, their training requires overcoming a number of challenges linked to their binary and dynamical nature. This article elucidates step-by-step the problems typically encountered when training spiking neural networks, and guides the reader through the key concepts of synaptic plasticity and data-driven learning in the spiking setting. To that end, it gives an overview of existing approaches and provides an introduction to surrogate gradient methods, specifically, as a particularly flexible and efficient method to overcome the aforementioned challenges.

A growing body of work underlines striking similarities between biological neural networks and recurrent, binary neural networks. A relatively smaller body of work, however, discusses similarities between learning dynamics employed in deep artificial neural networks and synaptic plasticity in spiking neural networks. The challenge preventing this is largely caused by the discrepancy between the dynamical properties of synaptic plasticity and the requirements for gradient backpropagation. Learning algorithms that approximate gradient backpropagation using locally synthesized gradients can overcome this challenge. Here, we show that synthetic gradients enable the derivation of Deep Continuous Local Learning (DECOLLE) in spiking neural networks. DECOLLE is capable of learning deep spatio-temporal representations from spikes relying solely on local information. Synaptic plasticity rules are derived systematically from user-defined cost functions and neural dynamics by leveraging existing autodifferentiation methods of machine learning frameworks. We benchmark our approach on the MNIST and the event-based neuromorphic DvsGesture dataset, on which DECOLLE performs comparably to the state-of-the-art. DECOLLE networks provide continuously learning machines that are relevant to biology and supportive of event-based, low-power computer vision architectures matching the accuracies of conventional computers on tasks where temporal precision and speed are essential., Comment: Published in Frontiers in Neuroscience - Neuromorphic Engineering

Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb's rule and the contrastive divergence algorithm. It operates in two phases, the forward (or free) phase, where the data are fed to the network, and a backward (or clamped) phase, where the target signals are clamped to the output layer of the network and the feedback signals are transformed through the transpose synaptic weight matrices. This implies symmetries at the synaptic level, for which there is no evidence in the brain. In this work, we propose a new variant of the algorithm, called random contrastive Hebbian learning, which does not rely on any synaptic weights symmetries. Instead, it uses random matrices to transform the feedback signals during the clamped phase, and the neural dynamics are described by first order non-linear differential equations. The algorithm is experimentally verified by solving a Boolean logic task, classification tasks (handwritten digits and letters), and an autoencoding task. This article also shows how the parameters affect learning, especially the random matrices. We use the pseudospectra analysis to investigate further how random matrices impact the learning process. Finally, we discuss the biological plausibility of the proposed algorithm, and how it can give rise to better computational models for learning.

Embedded, continual learning for autonomous and adaptive behavior is a key application of neuromorphic hardware. However, neuromorphic implementations of embedded learning at large scales that are both flexible and efficient have been hindered by a lack of a suitable algorithmic framework. As a result, the most neuromorphic hardware is trained off-line on large clusters of dedicated processors or GPUs and transferred post hoc to the device. We address this by introducing the neural and synaptic array transceiver (NSAT), a neuromorphic computational framework facilitating flexible and efficient embedded learning by matching algorithmic requirements and neural and synaptic dynamics. NSAT supports event-driven supervised, unsupervised and reinforcement learning algorithms including deep learning. We demonstrate the NSAT in a wide range of tasks, including the simulation of Mihalas-Niebur neuron, dynamic neural fields, event-driven random back-propagation for event-based deep learning, event-based contrastive divergence for unsupervised learning, and voltage-based learning rules for sequence learning. We anticipate that this contribution will establish the foundation for a new generation of devices enabling adaptive mobile systems, wearable devices, and robots with data-driven autonomy.

An ongoing challenge in neuromorphic computing is to devise general and computationally efficient models of inference and learning which are compatible with the spatial and temporal constraints of the brain. One increasingly popular and successful approach is to take inspiration from inference and learning algorithms used in deep neural networks. However, the workhorse of deep learning, the gradient descent Back Propagation (BP) rule, often relies on the immediate availability of network-wide information stored with high-precision memory, and precise operations that are difficult to realize in neuromorphic hardware. Remarkably, recent work showed that exact backpropagated weights are not essential for learning deep representations. Random BP replaces feedback weights with random ones and encourages the network to adjust its feed-forward weights to learn pseudo-inverses of the (random) feedback weights. Building on these results, we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware. The rule requires only one addition and two comparisons for each synaptic weight using a two-compartment leaky Integrate & Fire (I&F) neuron, making it very suitable for implementation in digital or mixed-signal neuromorphic hardware. Our results show that using eRBP, deep representations are rapidly learned, achieving nearly identical classification accuracies compared to artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.

Current large scale implementations of deep learning and data mining require thousands of processors, massive amounts of off-chip memory, and consume gigajoules of energy. Emerging memory technologies such as nanoscale two-terminal resistive switching memory devices offer a compact, scalable and low power alternative that permits on-chip co-located processing and memory in fine-grain distributed parallel architecture. Here we report first use of resistive switching memory devices for implementing and training a Restricted Boltzmann Machine (RBM), a generative probabilistic graphical model as a key component for unsupervised learning in deep networks. We experimentally demonstrate a 45-synapse RBM realized with 90 resistive switching phase change memory (PCM) elements trained with a bio-inspired variant of the Contrastive Divergence (CD) algorithm, implementing Hebbian and anti-Hebbian weight updates. The resistive PCM devices show a two-fold to ten-fold reduction in error rate in a missing pixel pattern completion task trained over 30 epochs, compared to untrained case. Measured programming energy consumption is 6.1 nJ per epoch with the resistive switching PCM devices, a factor of ~150 times lower than conventional processor-memory systems. We analyze and discuss the dependence of learning performance on cycle-to-cycle variations as well as number of gradual levels in the PCM analog memory devices., Comment: Accepted for publication in IEEE Transactions on Electron Devices. This version is the submitted version

Spike-timing-dependent plasticity (STDP) incurs both causal and acausal synaptic weight updates, for negative and positive time differences between pre-synaptic and post-synaptic spike events. For realizing such updates in neuromorphic hardware, current implementations either require forward and reverse lookup access to the synaptic connectivity table, or rely on memory-intensive architectures such as crossbar arrays. We present a novel method for realizing both causal and acausal weight updates using only forward lookup access of the synaptic connectivity table, permitting memory-efficient implementation. A simplified implementation in FPGA, using a single timer variable for each neuron, closely approximates exact STDP cumulative weight updates for neuron refractory periods greater than 10 ms, and reduces to exact STDP for refractory periods greater than the STDP time window. Compared to conventional crossbar implementation, the forward table-based implementation leads to substantial memory savings for sparsely connected networks supporting scalable neuromorphic systems with fully reconfigurable synaptic connectivity and plasticity., Comment: Submitted to BioCAS 2016

In recent years the field of neuromorphic low-power systems that consume orders of magnitude less power gained significant momentum. However, their wider use is still hindered by the lack of algorithms that can harness the strengths of such architectures. While neuromorphic adaptations of representation learning algorithms are now emerging, efficient processing of temporal sequences or variable length-inputs remain difficult. Recurrent neural networks (RNN) are widely used in machine learning to solve a variety of sequence learning tasks. In this work we present a train-and-constrain methodology that enables the mapping of machine learned (Elman) RNNs on a substrate of spiking neurons, while being compatible with the capabilities of current and near-future neuromorphic systems. This "train-and-constrain" method consists of first training RNNs using backpropagation through time, then discretizing the weights and finally converting them to spiking RNNs by matching the responses of artificial neurons with those of the spiking neurons. We demonstrate our approach by mapping a natural language processing task (question classification), where we demonstrate the entire mapping process of the recurrent layer of the network on IBM's Neurosynaptic System "TrueNorth", a spike-based digital neuromorphic hardware architecture. TrueNorth imposes specific constraints on connectivity, neural and synaptic parameters. To satisfy these constraints, it was necessary to discretize the synaptic weights and neural activities to 16 levels, and to limit fan-in to 64 inputs. We find that short synaptic delays are sufficient to implement the dynamical (temporal) aspect of the RNN in the question classification task. The hardware-constrained model achieved 74% accuracy in question classification while using less than 0.025% of the cores on one TrueNorth chip, resulting in an estimated power consumption of ~17 uW.

We present an approach to constructing a neuromorphic device that responds to language input by producing neuron spikes in proportion to the strength of the appropriate positive or negative emotional response. Specifically, we perform a fine-grained sentiment analysis task with implementations on two different systems: one using conventional spiking neural network (SNN) simulators and the other one using IBM's Neurosynaptic System TrueNorth. Input words are projected into a high-dimensional semantic space and processed through a fully-connected neural network (FCNN) containing rectified linear units trained via backpropagation. After training, this FCNN is converted to a SNN by substituting the ReLUs with integrate-and-fire neurons. We show that there is practically no performance loss due to conversion to a spiking network on a sentiment analysis test set, i.e. correlations between predictions and human annotations differ by less than 0.02 comparing the original DNN and its spiking equivalent. Additionally, we show that the SNN generated with this technique can be mapped to existing neuromorphic hardware -- in our case, the TrueNorth chip. Mapping to the chip involves 4-bit synaptic weight discretization and adjustment of the neuron thresholds. The resulting end-to-end system can take a user input, i.e. a word in a vocabulary of over 300,000 words, and estimate its sentiment on TrueNorth with a power consumption of approximately 50 uW.

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

The goal of a generative model is to capture the distribution underlying the data, typically through latent variables. After training, these variables are often used as a new representation, more effective than the original features in a variety of learning tasks. However, the representations constructed by contemporary generative models are usually point-wise deterministic mappings from the original feature space. Thus, even with representations robust to class-specific transformations, statistically driven models trained on them would not be able to generalize when the labeled data is scarce. Inspired by the stochasticity of the synaptic connections in the brain, we introduce Energy-based Stochastic Ensembles. These ensembles can learn non-deterministic representations, i.e., mappings from the feature space to a family of distributions in the latent space. These mappings are encoded in a distribution over a (possibly infinite) collection of models. By conditionally sampling models from the ensemble, we obtain multiple representations for every input example and effectively augment the data. We propose an algorithm similar to contrastive divergence for training restricted Boltzmann stochastic ensembles. Finally, we demonstrate the concept of the stochastic representations on a synthetic dataset as well as test them in the one-shot learning scenario on MNIST., Comment: 9 pages, 3 figures, ICLR-15 workshop contribution

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality., Comment: (Under review)