Neuromorphic hardware implementations of Spiking Neural Networks (SNNs) promise energy-efficient, low-latency AI through sparse, event-driven computation. Yet, training SNNs under fine temporal discretization remains a major challenge, hindering both low-latency responsiveness and the mapping of software-trained SNNs to efficient hardware. In current approaches, spiking neurons are modeled as self-recurrent units, embedded into recurrent networks to maintain state over time, and trained with BPTT or RTRL variants based on surrogate gradients. These methods scale poorly with temporal resolution, while online approximations often exhibit instability for long sequences and tend to fail at capturing temporal patterns precisely. To address these limitations, we develop spiking neurons with internal recursive memory structures that we combine with sigma-delta spike-coding. We show that this SpikingGamma model supports direct error backpropagation without surrogate gradients, can learn fine temporal patterns with minimal spiking in an online manner, and scale feedforward SNNs to complex tasks and benchmarks with competitive accuracy, all while being insensitive to the temporal resolution of the model. Our approach offers both an alternative to current recurrent SNNs trained with surrogate gradients, and a direct route for mapping SNNs to neuromorphic hardware.

Vision is an essential part of attitude control for many flying animals, some of which have no dedicated sense of gravity. Flying robots, on the other hand, typically depend heavily on accelerometers and gyroscopes for attitude stabilization. In this work, we present the first vision-only approach to flight control for use in generic environments. We show that a quadrotor drone equipped with a downward-facing event camera can estimate its attitude and rotation rate from just the event stream, enabling flight control without inertial sensors. Our approach uses a small recurrent convolutional neural network trained through supervised learning. Real-world flight tests demonstrate that our combination of event camera and low-latency neural network is capable of replacing the inertial measurement unit in a traditional flight control loop. Furthermore, we investigate the network's generalization across different environments, and the impact of memory and different fields of view. While networks with memory and access to horizon-like visual cues achieve best performance, variants with a narrower field of view achieve better relative generalization. Our work showcases vision-only flight control as a promising candidate for enabling autonomous, insect-scale flying robots.

Real-world sequential signals, such as audio or video, contain critical information that is often embedded within long periods of silence or noise. While recurrent neural networks (RNNs) are designed to process such data efficiently, they often suffer from “memory decay” due to a rigid update schedule: they typically update their internal state at every time step, even when the input is static. This constant activity forces the model to overwrite its own memory and makes it hard for the learning signal to reach back to distant past events. Here we show that we can overcome this limitation using Selective-Update RNNs (suRNNs), a non-linear architecture that learns to preserve its memory when the input is redundant. By using a neuron-level binary switch that only opens for informative events, suRNNs decouple the recurrent updates from the raw sequence length. This mechanism allows the model to maintain an exact, unchanged memory of the past during low-information intervals, creating a direct path for gradients to flow across time. Our experiments on the Long Range Arena, WikiText, and other synthetic benchmarks show that suRNNs match or exceed the accuracy of much more complex models such as Transformers, while remaining significantly more efficient for long-term storage. By allowing each neuron to learn its own update timescale, our approach resolves the mismatch between how long a sequence is and how much information it actually contains. By providing a principled approach to managing temporal information density, this work establishes a new direction for achieving Transformer-level performance within the highly efficient framework of recurrent modeling.

Uncertainty estimation is a key component for quantifying the reliability of modern deep learning models, and is crucial for many real-world applications. However, efficient methods for uncertainty estimation in spiking neural networks (SNNs), particularly for regression tasks, remain underexplored. In this work, we demonstrate that uncertainty estimation in SNNbased regression tasks can be effectively achieved using recent frameworks originally developed for classification. Specifically, we adapt these frameworks to regression with two uncertaintyaware approaches: (1) a heteroscedastic Gaussian method, in which the SNN predicts both the mean and variance of the target variable; and (2) a Regression-as-Classification (RAC) method, which reformulates regression as a classification task to enable probabilistic modeling. We evaluate our approaches on a toy dataset and several benchmark regression datasets, showing that these approaches deliver efficient and high-quality uncertainty estimates, comparable to or surpassing state-of-theart deep neural network baselines. Our findings underscore the potential of SNNs for uncertainty estimation in regression tasks, offering a biologically inspired and energy-efficient solution for applications requiring both accuracy and robustness, while also paving the way for broader adoption of SNNs in sequential and event-driven domains.

Predictive coding is a prominent theoretical framework for understanding hierarchical sensory processing in the brain, yet how it could be implemented in networks of cortical neurons is still unclear. While most existing studies have taken a hand-wiring approach to creating microcircuits that match experimental results, recent work in rate-based artificial neural networks revealed that suitable cortical connectivity might result from self-organisation given some fundamental computational principle, such as energy efficiency. As no corresponding approach has studied this in more plausible networks of spiking neurons, we here investigate whether predictive coding properties in a multi-compartment spiking neural network can emerge from energy optimisation. We find that a model trained with an energy objective in addition to a task-relevant objective is able to reconstruct internal representations given top-down expectation signals alone. Additionally, neurons in the energy-optimised model show differential responses to expected versus unexpected stimuli, qualitatively similar to experimental evidence for predictive coding. These findings indicate that predictive-coding-like behaviour might be an emergent property of energy optimisation, providing a new perspective on how predictive coding could be achieved in the cortex.

The endeavor to emulate the extraordinary efficiency and adaptability inherent in the human brain via spike-based neuromorphic computing presents significant potential across a diverse array of applications. The attainment of this objective necessitates the translation of biological principles into artificial systems, a task that continues to pose a complex challenge requiring a profound comprehension of the mechanisms by which neural systems produce robust computational outcomes. This tutorial paper provides a comprehensive overview of the foundational concepts and emerging design trends in spike-based neuromorphic computing, covering advances from materials and circuits to hardware architectures and learning mechanisms. It begins with an examination of key aspects of brain biology and their influence on neuromorphic design, followed by a brief discussion of biologically plausible neuron and synapse models. The paper then defines the core principles and defining attributes of neuromorphic computing, highlighting the trade-offs and design choices underlying current implementations. Building on these foundations, it explores the critical properties of neuromorphic systems, surveys a variety of learning algorithms, and reviews hardware-level realizations of bioinspired neurons and synapses. Subsequent sections discuss state-of-the-art spiking neural network architectures, mapping and compilation strategies, and representative application domains. By providing this end-to-end perspective, the article aims to guide the development of future neuromorphic systems that more closely emulate brain efficiency, scalability, and resilience.

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 researchers across 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 outline tasks and guidelines for benchmarks across multiple application domains, and present initial performance baselines across neuromorphic and conventional approaches for both benchmark tracks. NeuroBench is intended to continually expand its benchmarks and features to foster and track the progress made by the research community.

In data assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is computationally expensive and infeasible to run in real-time for complex systems. Here, we present a novel particle filter methodology, the Deep Latent Space Particle filter or D-LSPF, that uses neural network-based surrogate models to overcome this computational challenge. The D-LSPF enables filtering in the low-dimensional latent space obtained using Wasserstein AEs with modified vision transformer layers for dimensionality reduction and transformers for parameterized latent space time stepping. As we demonstrate on three test cases, including leak localization in multi-phase pipe flow and seabed identification for fully nonlinear water waves, the D-LSPF runs orders of magnitude faster than a high-fidelity particle filter and 3-5 times faster than alternative methods while being up to an order of magnitude more accurate. The D-LSPF thus enables real-time data assimilation with uncertainty quantification for the test cases demonstrated in this paper.

To make sense of their surroundings, intelligent systems must transform complex sensory inputs to structured codes that are reduced to task-relevant information such as object category. Biological agents achieve this in a largely autonomous manner, presumably via self-supervised learning. Whereas previous attempts to model the underlying mechanisms were largely discriminative in nature, there is ample evidence that the brain employs a generative model of the world. Here, we propose that eye movements, in combination with the focused nature of primate vision, constitute a generative, self-supervised task of predicting and revealing visual information. We construct a proof-of-principle model starting from the framework of masked image modeling (MIM), a common approach in deep representation learning. To do so, we analyze how core components of MIM such as masking technique and data augmentation influence the formation of category-specific representations. This allows us not only to better understand the principles behind MIM, but to then reassemble a MIM more in line with the focused nature of biological perception. We find that MIM disentangles neurons in latent space without explicit regularization, a property that has been suggested to structure visual representations in primates. Together with previous findings of invariance learning, this highlights an interesting connection of MIM to latent regularization approaches for self-supervised learning. The source code is available under https://github.com/RobinWeiler/FocusMIM.

Speech enhancement improves communication in noisy environments, affecting areas such as automatic speech recognition (ASR), hearing aids, and telecommunications. With these domains typically being power-constrained and event-based, and often requiring low latency, neuromorphic algorithms-particularly spiking neural networks (SNNs)-hold significant potential. However, current effective SNN solutions require a long temporal window to calculate Short Time Fourier Transforms (STFTs) and thus impose substantial latency, typically around 32 ms, which is too long for applications such as hearing aids. Inspired by the Dual-Path Recurrent Neural Network (DPRNN) in deep neural networks (DNNs), we develop a two-phase time-domain streaming SNN fframework for speech enhancement, named Dual-Path Spiking Neural Network (DPSNN). DPSNNs achieve low latency by replacing the STFT and inverse STFT (iSTFT) in traditional frequency-domain models with a learned convolutional encoder and decoder. In the DPSNN, the first phase uses Spiking Convolutional Neural Networks (SCNNs) to capture temporal contextual information, while the second phase uses Spiking Recurrent Neural Networks (SRNNs) to focus on frequency-related features. In addition, threshold-based activation suppression, along with L1 regularization loss, is applied to specific non-spiking layers in DPSNNs to further improve their energy efficiency. Evaluating on the Voice Cloning Toolkit (VCTK) Corpus and Intel N-DNS Challenge dataset, our approach demonstrates excellent performance in speech objective metrics, along with the very low latency (approximately 5 ms) required for applications like hearing aids.

Uncertainty estimation is a standard tool to quantify the reliability of modern deep learning models, and crucial for many real-world applications. However, efficient uncertainty estimation methods for spiking neural networks, particularly for regression models, have been lacking. Here, we introduce two methods that adapt the Average-Over-Time Spiking Neural Network (AOT-SNN) framework to regression tasks, enhancing uncertainty estimation in event-driven models. The first method uses the heteroscedastic Gaussian approach, where SNNs predict both the mean and variance at each time step, thereby generating a conditional probability distribution of the target variable. The second method leverages the Regression-as-Classification (RAC) approach, reformulating regression as a classification problem to facilitate uncertainty estimation. We evaluate our approaches on both a toy dataset and several benchmark datasets, demonstrating that the proposed AOT-SNN models achieve performance comparable to or better than state-of-the-art deep neural network methods, particularly in uncertainty estimation. Our findings highlight the potential of SNNs for uncertainty estimation in regression tasks, providing an efficient and biologically inspired alternative for applications requiring both accuracy and energy efficiency.

Many cognitive problems can be decomposed into series of subproblems that are solved sequentially by the brain. When subproblems are solved, relevant intermediate results need to be stored by neurons and propagated to the next subproblem, until the overarching goal has been completed. We will here consider visual tasks, which can be decomposed into sequences of elemental visual operations. Experimental evidence suggests that intermediate results of the elemental operations are stored in working memory as an enhancement of neural activity in the visual cortex. The focus of enhanced activity is then available for subsequent operations to act upon. The main question at stake is how the elemental operations and their sequencing can emerge in neural networks that are trained with only rewards, in a reinforcement learning setting. We here propose a new recurrent neural network architecture that can learn composite visual tasks that require the application of successive elemental operations. Specifically, we selected three tasks for which electrophysiological recordings of monkeys’ visual cortex are available. To train the networks, we used RELEARNN, a biologically plausible four-factor Hebbian learning rule, which is local both in time and space. We report that networks learn elemental operations, such as contour grouping and visual search, and execute sequences of operations, solely based on the characteristics of the visual stimuli and the reward structure of a task. After training was completed, the activity of the units of the neural network elicited by behaviorally relevant image items was stronger than that elicited by irrelevant ones, just as has been observed in the visual cortex of monkeys solving the same tasks. Relevant information that needed to be exchanged between subroutines was maintained as a focus of enhanced activity and passed on to the subsequent subroutines. Our results demonstrate how a biologically plausible learning rule can train a recurrent neural network on multistep visual tasks.

Predictive coding is a prominent theoretical framework for understanding the hierarchical sensory processing in the brain, yet how it could be implemented in networks of cortical neurons is still unclear. While most existing works have taken a hand-wiring approach to creating microcircuits that match experimental results, recent work in applying an optimisation approach to rate-based artificial neural networks revealed that cortical connectivity might result from self-organisation given some fundamental computational principle, such as energy efficiency. As no corresponding approach has studied this in more plausible networks of spiking neurons, we here investigate whether predictive coding properties in a multi-compartment spiking neural network can emerge from energy optimisation. We find that a model trained with an energy objective in addition to a task-relevant objective is able to reconstruct internal representations given top-down expectation signals alone. Additionally, neurons in the energy-optimised model also show differential responses to expected versus unexpected stimuli, qualitatively similar to experimental evidence for predictive coding. These findings indicate that predictive-coding-like behaviour might be an emergent property of energy optimisation, providing a new perspective on how predictive coding could be achieved in the cortex.### Competing Interest StatementThe authors have declared no competing interest.

Predictive coding (PC) is an influential theory in neuroscience, which suggests the existence of a cortical architecture that is constantly generating and updating predictive representations of sensory inputs. Owing to its hierarchical and generative nature, PC has inspired many computational models of perception in the literature. However, the biological plausibility of existing models has not been sufficiently explored due to their use of artificial neurons that approximate neural activity with firing rates in the continuous time domain and propagate signals synchronously. Therefore, we developed a spiking neural network for predictive coding (SNN-PC), in which neurons communicate using event-driven and asynchronous spikes. Adopting the hierarchical structure and Hebbian learning algorithms from previous PC neural network models, SNN-PC introduces two novel features: (1) a fast feedforward sweep from the input to higher areas, which generates a spatially reduced and abstract representation of input (i.e., a neural code for the gist of a scene) and provides a neurobiological alternative to an arbitrary choice of priors; and (2) a separation of positive and negative error-computing neurons, which counters the biological implausibility of a bi-directional error neuron with a very high baseline firing rate. After training with the MNIST handwritten digit dataset, SNN-PC developed hierarchical internal representations and was able to reconstruct samples it had not seen during training. SNN-PC suggests biologically plausible mechanisms by which the brain may perform perceptual inference and learning in an unsupervised manner. In addition, it may be used in neuromorphic applications that can utilize its energy-efficient, event-driven, local learning, and parallel information processing nature.

The resonate-and-fire (RF) neuron, introduced over two decades ago, is a simple, efficient, yet biologically plausible spiking neuron model, which can extract frequency patterns within the time domain due to its resonating membrane dynamics. However, previous RF formulations suffer from intrinsic shortcomings that limit effective learning and prevent exploiting the principled advantage of RF neurons. Here, we introduce the balanced RF (BRF) neuron, which alleviates some of the intrinsic limitations of vanilla RF neurons and demonstrates its effectiveness within recurrent spiking neural networks (RSNNs) on various sequence learning tasks. We show that networks of BRF neurons achieve overall higher task performance, produce only a fraction of the spikes, and require significantly fewer parameters as compared to modern RSNNs. Moreover, BRF-RSNN consistently provide much faster and more stable training convergence, even when bridging many hundreds of time steps during backpropagation through time (BPTT). These results underscore that our BRF-RSNN is a strong candidate for future large-scale RSNN architectures, further lines of research in SNN methodology, and more efficient hardware implementations.

The acquisition of knowledge and skills does not occur in isolation but learning experiences amalgamate within and across domains. The process through which learning can accelerate over time is referred to as learning-to-learn or meta-learning. While meta-learning can be implemented in recurrent neural networks, these networks tend to be trained with architectures that are not easily interpretable or mappable to the brain and with learning rules that are biologically implausible. Specifically, these rules have often employed backpropagation-through-time, which relies on information that is unavailable at synapses that are undergoing plasticity in the brain. Previous studies that exclusively used local information for their weight updates had a limited capacity to integrate information over long timespans and could not easily learn-to-learn. Here, we propose a novel gated memory network named RECOLLECT, which can flexibly retain or forget information by means of a single memory gate and is trained with a biologically plausible trial-and-error-learning that requires only local information. We demonstrate that RECOLLECT successfully learns to represent task-relevant information over increasingly long memory delays in a pro-/anti-saccade task, and that it learns to flush its memory at the end of a trial. Moreover, we show that RECOLLECT can learn-to-learn an effective policy on a reversal bandit task. Finally, we show that the solutions acquired by RECOLLECT resemble how animals learn similar tasks.

This paper presents the development of a Digital Twin (DTwin) to detect and localize the leaks in water distribution networks (WDNs), using single-stage and two-stage data-driven models. In the single-stage model, we test the anomalies in the dataset using Logistic Regression and Random Forest. In the two-stage model, a linear regression model predicts pressure differences between sensor pairs in the first stage. Based on this, we compute the distribution of residuals. In the second stage, changes in the residual distribution are classified using Multinomial Logistic Regression and Random Forest models to compute possible leak locations’ posterior probabilities. We have tested these models on a real-time dataset.

Natural scenes usually contain a vast number of objects that need to be segmented and segregated from each other and from the background to guide behaviour. In the visual brain, object-based attention is the process by which image fragments belonging to the same objects are grouped together. The curve-tracing task is a special case of a perceptual grouping task that tests our ability to group image elements of an elongated curve. The task consists in determining which image elements belong to the same curve, and in the brain, neurons spread an enhanced activity level over the representation of the relevant curve. A previous “growth-cone model of attention” accounted for the scale invariance of tracing by proposing that the enhanced activity propagates at multiple levels of the visual cortical hierarchy. However, the precise neuronal circuitry for learning and implementing scale-invariant tracing remains unknown. We propose a new recurrent architecture for the scale-invariant labelling of curves and objects. The architecture is composed of a feedforward pathway that dynamically selects the right scale and prevents the spilling over of the enhanced activity to other curves, and a recurrent pathway for tag spreading that involves horizontal and feedback interactions, mediated by a disinhibitory loop involving VIP and SOM interneurons. We trained the network with curves up to seven pixels long using reinforcement learning and a learning rule local in time and space and we found that it generalized to curves of any length and to spatially extended objects. The network chose the appropriate scale and switched to higher or lower scales as dictated by the distance between curves, just has as been observed in human psychophysics and in the visual cortex of monkeys. Our work provide a mechanistic account of the learning of scale-invariant perceptual grouping in the brain. Significance Statement Objects are labelled and grouped in the visual cortex via a tag of enhanced activity. If the scale-invariant dynamics of propagations of this tag are well characterised, it remains unknown what neural architectures and learning rules can produce those dynamics. This work is the first to propose a neural architecture trained with reward that give rises to the same dynamics observed in monkeys’ visual cortex or human reaction times, shedding light on the mechanisms of multiscale object-based attention in the visual cortex. ### Competing Interest Statement The authors have declared no competing interest.