Sander M. Bohté

Jason Yik, Korneel Van den Berghe, Douwe den Blanken et al. · eth-zurich

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.

Tao Sun, Bojian Yin, Sander Bohte

Spiking neural networks (SNNs) have gained attention as models of sparse and event-driven communication of biological neurons, and as such have shown increasing promise for energy-efficient applications in neuromorphic hardware. As with classical artificial neural networks (ANNs), predictive uncertainties are important for decision making in high-stakes applications, such as autonomous vehicles, medical diagnosis, and high frequency trading. Yet, discussion of uncertainty estimation in SNNs is limited, and approaches for uncertainty estimation in artificial neural networks (ANNs) are not directly applicable to SNNs. Here, we propose an efficient Monte Carlo(MC)-dropout based approach for uncertainty estimation in SNNs. Our approach exploits the time-step mechanism of SNNs to enable MC-dropout in a computationally efficient manner, without introducing significant overheads during training and inference while demonstrating high accuracy and uncertainty quality.

Guillermo Martín-Sánchez, Sander Bohté, Sebastian Otte

Backpropagation through time (BPTT) is the de facto standard for training recurrent neural networks (RNNs), but it is non-causal and non-local. Real-time recurrent learning is a causal alternative, but it is highly inefficient. Recently, e-prop was proposed as a causal, local, and efficient practical alternative to these algorithms, providing an approximation of the exact gradient by radically pruning the recurrent dependencies carried over time. Here, we derive RTRL from BPTT using a detailed notation bringing intuition and clarification to how they are connected. Furthermore, we frame e-prop within in the picture, formalising what it approximates. Finally, we derive a family of algorithms of which e-prop is a special case.

Tao Sun, Sander Bohté

Speech enhancement (SE) improves communication in noisy environments, affecting areas such as automatic speech recognition, hearing aids, and telecommunications. With these domains typically being power-constrained and event-based while requiring low latency, neuromorphic algorithms in the form of spiking neural networks (SNNs) have great potential. Yet, current effective SNN solutions require a contextual sampling window imposing substantial latency, typically around 32ms, too long for many applications. Inspired by Dual-Path Spiking Neural Networks (DPSNNs) in classical neural networks, we develop a two-phase time-domain streaming SNN framework -- the Dual-Path Spiking Neural Network (DPSNN). In the DPSNN, the first phase uses Spiking Convolutional Neural Networks (SCNNs) to capture global contextual information, while the second phase uses Spiking Recurrent Neural Networks (SRNNs) to focus on frequency-related features. In addition, the regularizer suppresses activation to further enhance energy efficiency of our DPSNNs. Evaluating on the VCTK and Intel DNS Datasets, we demonstrate that our approach achieves the very low latency (approximately 5ms) required for applications like hearing aids, while demonstrating excellent signal-to-noise ratio (SNR), perceptual quality, and energy efficiency.

Robin Weiler, Matthias Brucklacher, Cyriel M. A. Pennartz et al.

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

Saya Higuchi, Sebastian Kairat, Sander M. Bohte et al.

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.

Jesse J. Hagenaars, Stein Stroobants, Sander M. Bohte et al.

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.

Tao Sun, Sander Bohté

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.

Nikolaj T. Mücke, Sander M. Bohté, Cornelis W. Oosterlee

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 physical systems.

Saya Higuchi, Sander M. Bohte, Sebastian Otte

Resonate-and-Fire (RF) neurons are an interesting complementary model for integrator neurons in spiking neural networks (SNNs). Due to their resonating membrane dynamics they can extract frequency patterns within the time domain. While established RF variants suffer from intrinsic shortcomings, the recently proposed balanced resonate-and-fire (BRF) neuron marked a significant methodological advance in terms of task performance, spiking and parameter efficiency, as well as, general stability and robustness, demonstrated for recurrent SNNs in various sequence learning tasks. One of the most intriguing result, however, was an immense improvement in training convergence speed and smoothness, overcoming the typical convergence dilemma in backprop-based SNN training. This paper aims at providing further intuitions about how and why these convergence advantages emerge. We show that BRF neurons, in contrast to well-established ALIF neurons, span a very clean and smooth - almost convex - error landscape. Furthermore, empirical results reveal that the convergence benefits are predominantly coupled with a divergence boundary-aware optimization, a major component of the BRF formulation that addresses the numerical stability of the time-discrete resonator approximation. These results are supported by a formal investigation of the membrane dynamics indicating that the gradient is transferred back through time without loss of magnitude.

Bojian Yin, Federico Corradi, Sander M. Bohte

The event-driven and sparse nature of communication between spiking neurons in the brain holds great promise for flexible and energy-efficient AI. Recent advances in learning algorithms have demonstrated that recurrent networks of spiking neurons can be effectively trained to achieve competitive performance compared to standard recurrent neural networks. Still, as these learning algorithms use error-backpropagation through time (BPTT), they suffer from high memory requirements, are slow to train, and are incompatible with online learning. This limits the application of these learning algorithms to relatively small networks and to limited temporal sequence lengths. Online approximations to BPTT with lower computational and memory complexity have been proposed (e-prop, OSTL), but in practice also suffer from memory limitations and, as approximations, do not outperform standard BPTT training. Here, we show how a recently developed alternative to BPTT, Forward Propagation Through Time (FPTT) can be applied in spiking neural networks. Different from BPTT, FPTT attempts to minimize an ongoing dynamically regularized risk on the loss. As a result, FPTT can be computed in an online fashion and has fixed complexity with respect to the sequence length. When combined with a novel dynamic spiking neuron model, the Liquid-Time-Constant neuron, we show that SNNs trained with FPTT outperform online BPTT approximations, and approach or exceed offline BPTT accuracy on temporal classification tasks. This approach thus makes it feasible to train SNNs in a memory-friendly online fashion on long sequences and scale up SNNs to novel and complex neural architectures.

Bojian Yin, Federico Corradi, Sander M. Bohte

Inspired by more detailed modeling of biological neurons, Spiking neural networks (SNNs) have been investigated both as more biologically plausible and potentially more powerful models of neural computation, and also with the aim of extracting biological neurons' energy efficiency; the performance of such networks however has remained lacking compared to classical artificial neural networks (ANNs). Here, we demonstrate how a novel surrogate gradient combined with recurrent networks of tunable and adaptive spiking neurons yields state-of-the-art for SNNs on challenging benchmarks in the time-domain, like speech and gesture recognition. This also exceeds the performance of standard classical recurrent neural networks (RNNs) and approaches that of the best modern ANNs. As these SNNs exhibit sparse spiking, we show that they theoretically are one to three orders of magnitude more computationally efficient compared to RNNs with comparable performance. Together, this positions SNNs as an attractive solution for AI hardware implementations.

Bojian Yin, Federico Corradi, Sander M. Bohté

The emergence of brain-inspired neuromorphic computing as a paradigm for edge AI is motivating the search for high-performance and efficient spiking neural networks to run on this hardware. However, compared to classical neural networks in deep learning, current spiking neural networks lack competitive performance in compelling areas. Here, for sequential and streaming tasks, we demonstrate how a novel type of adaptive spiking recurrent neural network (SRNN) is able to achieve state-of-the-art performance compared to other spiking neural networks and almost reach or exceed the performance of classical recurrent neural networks (RNNs) while exhibiting sparse activity. From this, we calculate a $>$100x energy improvement for our SRNNs over classical RNNs on the harder tasks. To achieve this, we model standard and adaptive multiple-timescale spiking neurons as self-recurrent neural units, and leverage surrogate gradients and auto-differentiation in the PyTorch Deep Learning framework to efficiently implement backpropagation-through-time, including learning of the important spiking neuron parameters to adapt our spiking neurons to the tasks.

Oliver Struckmeier, Kshitij Tiwari, Shirin Dora et al.

Extracting and binding salient information from different sensory modalities to determine common features in the environment is a significant challenge in robotics. Here we present MuPNet (Multi-modal Predictive Coding Network), a biologically plausible network architecture for extracting joint latent features from visuo-tactile sensory data gathered from a biomimetic mobile robot. In this study we evaluate MuPNet applied to place recognition as a simulated biomimetic robot platform explores visually aliased environments. The F1 scores demonstrate that its performance over prior hand-crafted sensory feature extraction techniques is equivalent under controlled conditions, with significant improvement when operating in novel environments.

Bojian Yin, Siebren Schaafsma, Henk Corporaal et al.

While modern convolutional neural networks achieve outstanding accuracy on many image classification tasks, they are, compared to humans, much more sensitive to image degradation. Here, we describe a variant of Batch Normalization, LocalNorm, that regularizes the normalization layer in the spirit of Dropout while dynamically adapting to the local image intensity and contrast at test-time. We show that the resulting deep neural networks are much more resistant to noise-induced image degradation, improving accuracy by up to three times, while achieving the same or slightly better accuracy on non-degraded classical benchmarks. In computational terms, LocalNorm adds negligible training cost and little or no cost at inference time, and can be applied to already-trained networks in a straightforward manner.

Anastasia Borovykh, Cornelis W. Oosterlee, Sander M. Bohte

In this paper we study the generalization capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being i.i.d. samples from some data-generating distribution. We use the input and weight Hessians, that is the smoothness of the learned function with respect to the input and the width of the minimum in weight space, to quantify a network's ability to generalize to unseen data. While such generalization metrics have been studied extensively in the i.i.d. setting of for example image recognition, here we empirically validate their use in the task of time series forecasting. Furthermore we discuss how one can control the generalization capability of the network by means of the training process using the learning rate, batch size and the number of training iterations as controls. Using these hyperparameters one can efficiently control the complexity of the output function without imposing explicit constraints.

Shuaiqiang Liu, Cornelis W. Oosterlee, Sander M. Bohte

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

Isabella Pozzi, Sander Bohté, Pieter Roelfsema

Researchers have proposed that deep learning, which is providing important progress in a wide range of high complexity tasks, might inspire new insights into learning in the brain. However, the methods used for deep learning by artificial neural networks are biologically unrealistic and would need to be replaced by biologically realistic counterparts. Previous biologically plausible reinforcement learning rules, like AGREL and AuGMEnT, showed promising results but focused on shallow networks with three layers. Will these learning rules also generalize to networks with more layers and can they handle tasks of higher complexity? We demonstrate the learning scheme on classical and hard image-classification benchmarks, namely MNIST, CIFAR10 and CIFAR100, cast as direct reward tasks, both for fully connected, convolutional and locally connected architectures. We show that our learning rule - Q-AGREL - performs comparably to supervised learning via error-backpropagation, with this type of trial-and-error reinforcement learning requiring only 1.5-2.5 times more epochs, even when classifying 100 different classes as in CIFAR100. Our results provide new insights into how deep learning may be implemented in the brain.

Bojian Yin, Marleen Balvert, Davide Zambrano et al.

The folding structure of the DNA molecule combined with helper molecules, also referred to as the chromatin, is highly relevant for the functional properties of DNA. The chromatin structure is largely determined by the underlying primary DNA sequence, though the interaction is not yet fully understood. In this paper we develop a convolutional neural network that takes an image-representation of primary DNA sequence as its input, and predicts key determinants of chromatin structure. The method is developed such that it is capable of detecting interactions between distal elements in the DNA sequence, which are known to be highly relevant. Our experiments show that the method outperforms several existing methods both in terms of prediction accuracy and training time.

Davide Zambrano, Roeland Nusselder, H. Steven Scholte et al.

Artificial Neural Networks (ANNs) are bio-inspired models of neural computation that have proven highly effective. Still, ANNs lack a natural notion of time, and neural units in ANNs exchange analog values in a frame-based manner, a computationally and energetically inefficient form of communication. This contrasts sharply with biological neurons that communicate sparingly and efficiently using binary spikes. While artificial Spiking Neural Networks (SNNs) can be constructed by replacing the units of an ANN with spiking neurons, the current performance is far from that of deep ANNs on hard benchmarks and these SNNs use much higher firing rates compared to their biological counterparts, limiting their efficiency. Here we show how spiking neurons that employ an efficient form of neural coding can be used to construct SNNs that match high-performance ANNs and exceed state-of-the-art in SNNs on important benchmarks, while requiring much lower average firing rates. For this, we use spike-time coding based on the firing rate limiting adaptation phenomenon observed in biological spiking neurons. This phenomenon can be captured in adapting spiking neuron models, for which we derive the effective transfer function. Neural units in ANNs trained with this transfer function can be substituted directly with adaptive spiking neurons, and the resulting Adaptive SNNs (AdSNNs) can carry out inference in deep neural networks using up to an order of magnitude fewer spikes compared to previous SNNs. Adaptive spike-time coding additionally allows for the dynamic control of neural coding precision: we show how a simple model of arousal in AdSNNs further halves the average required firing rate and this notion naturally extends to other forms of attention. AdSNNs thus hold promise as a novel and efficient model for neural computation that naturally fits to temporally continuous and asynchronous applications.

Anastasia Borovykh, Sander Bohte, Cornelis W. Oosterlee

We present a method for conditional time series forecasting based on an adaptation of the recent deep convolutional WaveNet architecture. The proposed network contains stacks of dilated convolutions that allow it to access a broad range of history when forecasting, a ReLU activation function and conditioning is performed by applying multiple convolutional filters in parallel to separate time series which allows for the fast processing of data and the exploitation of the correlation structure between the multivariate time series. We test and analyze the performance of the convolutional network both unconditionally as well as conditionally for financial time series forecasting using the S&P500, the volatility index, the CBOE interest rate and several exchange rates and extensively compare it to the performance of the well-known autoregressive model and a long-short term memory network. We show that a convolutional network is well-suited for regression-type problems and is able to effectively learn dependencies in and between the series without the need for long historical time series, is a time-efficient and easy to implement alternative to recurrent-type networks and tends to outperform linear and recurrent models.

Davide Zambrano, Sander M. Bohte

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so very few spikes to communicate. Building on recent insights in neuroscience, we present an Adapting Spiking Neural Network (ASNN) based on adaptive spiking neurons. These spiking neurons efficiently encode information in spike-trains using a form of Asynchronous Pulsed Sigma-Delta coding while homeostatically optimizing their firing rate. In the proposed paradigm of spiking neuron computation, neural adaptation is tightly coupled to synaptic plasticity, to ensure that downstream neurons can correctly decode upstream spiking neurons. We show that this type of network is inherently able to carry out asynchronous and event-driven neural computation, while performing identical to corresponding artificial neural networks (ANNs). In particular, we show that these adaptive spiking neurons can be drop in replacements for ReLU neurons in standard feedforward ANNs comprised of such units. We demonstrate that this can also be successfully applied to a ReLU based deep convolutional neural network for classifying the MNIST dataset. The ASNN thus outperforms current Spiking Neural Networks (SNNs) implementations, while responding (up to) an order of magnitude faster and using an order of magnitude fewer spikes. Additionally, in a streaming setting where frames are continuously classified, we show that the ASNN requires substantially fewer network updates as compared to the corresponding ANN.

Koen Groenland, Sander Bohte

When a Convolutional Neural Network is used for on-the-fly evaluation of continuously updating time-sequences, many redundant convolution operations are performed. We propose the method of Deep Shifting, which remembers previously calculated results of convolution operations in order to minimize the number of calculations. The reduction in complexity is at least a constant and in the best case quadratic. We demonstrate that this method does indeed save significant computation time in a practical implementation, especially when the networks receives a large number of time-frames.