Robert Legenstein

Ozan Özdenizci, Robert Legenstein

Image restoration under adverse weather conditions has been of significant interest for various computer vision applications. Recent successful methods rely on the current progress in deep neural network architectural designs (e.g., with vision transformers). Motivated by the recent progress achieved with state-of-the-art conditional generative models, we present a novel patch-based image restoration algorithm based on denoising diffusion probabilistic models. Our patch-based diffusion modeling approach enables size-agnostic image restoration by using a guided denoising process with smoothed noise estimates across overlapping patches during inference. We empirically evaluate our model on benchmark datasets for image desnowing, combined deraining and dehazing, and raindrop removal. We demonstrate our approach to achieve state-of-the-art performances on both weather-specific and multi-weather image restoration, and experimentally show strong generalization to real-world test images.

Ozan Özdenizci, Robert Legenstein

Spiking neural networks (SNNs) provide an energy-efficient alternative to a variety of artificial neural network (ANN) based AI applications. As the progress in neuromorphic computing with SNNs expands their use in applications, the problem of adversarial robustness of SNNs becomes more pronounced. To the contrary of the widely explored end-to-end adversarial training based solutions, we address the limited progress in scalable robust SNN training methods by proposing an adversarially robust ANN-to-SNN conversion algorithm. Our method provides an efficient approach to embrace various computationally demanding robust learning objectives that have been proposed for ANNs. During a post-conversion robust finetuning phase, our method adversarially optimizes both layer-wise firing thresholds and synaptic connectivity weights of the SNN to maintain transferred robustness gains from the pre-trained ANN. We perform experimental evaluations in a novel setting proposed to rigorously assess the robustness of SNNs, where numerous adaptive adversarial attacks that account for the spike-based operation dynamics are considered. Results show that our approach yields a scalable state-of-the-art solution for adversarially robust deep SNNs with low-latency.

Thomas Limbacher, Ozan Özdenizci, Robert Legenstein

Memory is a key component of biological neural systems that enables the retention of information over a huge range of temporal scales, ranging from hundreds of milliseconds up to years. While Hebbian plasticity is believed to play a pivotal role in biological memory, it has so far been analyzed mostly in the context of pattern completion and unsupervised learning. Here, we propose that Hebbian plasticity is fundamental for computations in biological neural systems. We introduce a novel spiking neural network architecture that is enriched by Hebbian synaptic plasticity. We show that Hebbian enrichment renders spiking neural networks surprisingly versatile in terms of their computational as well as learning capabilities. It improves their abilities for out-of-distribution generalization, one-shot learning, cross-modal generative association, language processing, and reward-based learning. As spiking neural networks are the basis for energy-efficient neuromorphic hardware, this also suggests that powerful cognitive neuromorphic systems can be build based on this principle.

Julian Gutheil, Simon Hitzginger, Robert Legenstein

Winner-take-all (WTA) networks constitute a central circuit motif in cortical networks of the brain. In addition, WTA-like activations are abundant in modern deep learning models in the form of the softmax activation for example in attention layers of transformers. While their role in the extraction of latent factors has been studied for relatively simple generative models, their role in the context of highly non-linearly entangled latent factors has remained elusive. In this article, we show that a WTA bottleneck within a deep neural network can enforce under certain well-defined conditions the extraction of categorical latent factors of the data in a multi-task learning setup. In particular, we prove that the representation that emerges in the WTA bottleneck is highly symbolic, where a single neuron or a population of neurons encodes the presence of a single abstract feature such as a specific object, color, or position. We furthermore show empirically on two datasets, that this also holds for architectures and setups that do not fully comply with the assumptions of our theorem and demonstrate the advantages of the acquired symbolic representation for generalization. Our proposed model provides insights into the generalization capabilities of deep neural networks with WTA-like components and may serve as an interface between symbolic and subsymbolic AI systems.

Jacques Kaiser, Michael Hoff, Andreas Konle et al.

The endeavor to understand the brain involves multiple collaborating research fields. Classically, synaptic plasticity rules derived by theoretical neuroscientists are evaluated in isolation on pattern classification tasks. This contrasts with the biological brain which purpose is to control a body in closed-loop. This paper contributes to bringing the fields of computational neuroscience and robotics closer together by integrating open-source software components from these two fields. The resulting framework allows to evaluate the validity of biologically-plausibe plasticity models in closed-loop robotics environments. We demonstrate this framework to evaluate Synaptic Plasticity with Online REinforcement learning (SPORE), a reward-learning rule based on synaptic sampling, on two visuomotor tasks: reaching and lane following. We show that SPORE is capable of learning to perform policies within the course of simulated hours for both tasks. Provisional parameter explorations indicate that the learning rate and the temperature driving the stochastic processes that govern synaptic learning dynamics need to be regulated for performance improvements to be retained. We conclude by discussing the recent deep reinforcement learning techniques which would be beneficial to increase the functionality of SPORE on visuomotor tasks.

Maximilian Baronig, Yeganeh Bahariasl, Ozan Özdenizci et al.

Recurrent spiking neural networks (RSNNs) can be implemented very efficiently in neuromorphic systems. Nevertheless, training of these models with powerful gradient-based learning algorithms is mostly performed on standard digital hardware using Backpropagation through time (BPTT). However, BPTT has substantial limitations. It does not permit online training and its memory consumption scales linearly with the number of computation steps. In contrast, learning methods using forward propagation of gradients operate in an online manner with a memory consumption independent of the number of time steps. These methods enable SNNs to learn from continuous, infinite-length input sequences. Yet, slow execution speed on conventional hardware as well as inferior performance has hindered their widespread application. In this work, we introduce HYbrid PRopagation (HYPR) that combines the efficiency of parallelization with approximate online forward learning. Our algorithm yields high-throughput online learning through parallelization, paired with constant, i.e., sequence length independent, memory demands. HYPR enables parallelization of parameter update computation over the sub sequences for RSNNs consisting of almost arbitrary non-linear spiking neuron models. We apply HYPR to networks of spiking neurons with oscillatory subthreshold dynamics. We find that this type of neuron model is particularly well trainable by HYPR, resulting in an unprecedentedly low task performance gap between approximate forward gradient learning and BPTT.

Thomas Ortner, Horst Petschenig, Athanasios Vasilopoulos et al.

There is a growing demand for low-power, autonomously learning artificial intelligence (AI) systems that can be applied at the edge and rapidly adapt to the specific situation at deployment site. However, current AI models struggle in such scenarios, often requiring extensive fine-tuning, computational resources, and data. In contrast, humans can effortlessly adjust to new tasks by transferring knowledge from related ones. The concept of learning-to-learn (L2L) mimics this process and enables AI models to rapidly adapt with only little computational effort and data. In-memory computing neuromorphic hardware (NMHW) is inspired by the brain's operating principles and mimics its physical co-location of memory and compute. In this work, we pair L2L with in-memory computing NMHW based on phase-change memory devices to build efficient AI models that can rapidly adapt to new tasks. We demonstrate the versatility of our approach in two scenarios: a convolutional neural network performing image classification and a biologically-inspired spiking neural network generating motor commands for a real robotic arm. Both models rapidly learn with few parameter updates. Deployed on the NMHW, they perform on-par with their software equivalents. Moreover, meta-training of these models can be performed in software with high-precision, alleviating the need for accurate hardware models.

Manuel Traub, Robert Legenstein, Sebastian Otte

In the paper, we show how scalable, low-cost trunk-like robotic arms can be constructed using only basic 3D-printing equipment and simple electronics. The design is based on uniform, stackable joint modules with three degrees of freedom each. Moreover, we present an approach for controlling these robots with recurrent spiking neural networks. At first, a spiking forward model learns motor-pose correlations from movement observations. After training, intentions can be projected back through unrolled spike trains of the forward model essentially routing the intention-driven motor gradients towards the respective joints, which unfolds goal-direction navigation. We demonstrate that spiking neural networks can thus effectively control trunk-like robotic arms with up to 75 articulated degrees of freedom with near millimeter accuracy.

Agnes Korcsak-Gorzo, Michael G. Müller, Andreas Baumbach et al.

Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering.

Yexin Yan, David Kappel, Felix Neumaerker et al.

Advances in neuroscience uncover the mechanisms employed by the brain to efficiently solve complex learning tasks with very limited resources. However, the efficiency is often lost when one tries to port these findings to a silicon substrate, since brain-inspired algorithms often make extensive use of complex functions such as random number generators, that are expensive to compute on standard general purpose hardware. The prototype chip of the 2nd generation SpiNNaker system is designed to overcome this problem. Low-power ARM processors equipped with a random number generator and an exponential function accelerator enable the efficient execution of brain-inspired algorithms. We implement the recently introduced reward-based synaptic sampling model that employs structural plasticity to learn a function or task. The numerical simulation of the model requires to update the synapse variables in each time step including an explorative random term. To the best of our knowledge, this is the most complex synapse model implemented so far on the SpiNNaker system. By making efficient use of the hardware accelerators and numerical optimizations the computation time of one plasticity update is reduced by a factor of 2. This, combined with fitting the model into to the local SRAM, leads to 62% energy reduction compared to the case without accelerators and the use of external DRAM. The model implementation is integrated into the SpiNNaker software framework allowing for scalability onto larger systems. The hardware-software system presented in this work paves the way for power-efficient mobile and biomedical applications with biologically plausible brain-inspired algorithms.

Guillaume Bellec, Franz Scherr, Elias Hajek et al.

The way how recurrently connected networks of spiking neurons in the brain acquire powerful information processing capabilities through learning has remained a mystery. This lack of understanding is linked to a lack of learning algorithms for recurrent networks of spiking neurons (RSNNs) that are both functionally powerful and can be implemented by known biological mechanisms. Since RSNNs are simultaneously a primary target for implementations of brain-inspired circuits in neuromorphic hardware, this lack of algorithmic insight also hinders technological progress in that area. The gold standard for learning in recurrent neural networks in machine learning is back-propagation through time (BPTT), which implements stochastic gradient descent with regard to a given loss function. But BPTT is unrealistic from a biological perspective, since it requires a transmission of error signals backwards in time and in space, i.e., from post- to presynaptic neurons. We show that an online merging of locally available information during a computation with suitable top-down learning signals in real-time provides highly capable approximations to BPTT. For tasks where information on errors arises only late during a network computation, we enrich locally available information through feedforward eligibility traces of synapses that can easily be computed in an online manner. The resulting new generation of learning algorithms for recurrent neural networks provides a new understanding of network learning in the brain that can be tested experimentally. In addition, these algorithms provide efficient methods for on-chip training of RSNNs in neuromorphic hardware.

Guillaume Bellec, Darjan Salaj, Anand Subramoney et al.

Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with artificial neural networks (ANNs). We address two possible reasons for that. One is that RSNNs in the brain are not randomly connected or designed according to simple rules, and they do not start learning as a tabula rasa network. Rather, RSNNs in the brain were optimized for their tasks through evolution, development, and prior experience. Details of these optimization processes are largely unknown. But their functional contribution can be approximated through powerful optimization methods, such as backpropagation through time (BPTT). A second major mismatch between RSNNs in the brain and models is that the latter only show a small fraction of the dynamics of neurons and synapses in the brain. We include neurons in our RSNN model that reproduce one prominent dynamical process of biological neurons that takes place at the behaviourally relevant time scale of seconds: neuronal adaptation. We denote these networks as LSNNs because of their Long short-term memory. The inclusion of adapting neurons drastically increases the computing and learning capability of RSNNs if they are trained and configured by deep learning (BPTT combined with a rewiring algorithm that optimizes the network architecture). In fact, the computational performance of these RSNNs approaches for the first time that of LSTM networks. In addition RSNNs with adapting neurons can acquire abstract knowledge from prior learning in a Learning-to-Learn (L2L) scheme, and transfer that knowledge in order to learn new but related tasks from very few examples. We demonstrate this for supervised learning and reinforcement learning.

Guillaume Bellec, David Kappel, Wolfgang Maass et al.

Neuromorphic hardware tends to pose limits on the connectivity of deep networks that one can run on them. But also generic hardware and software implementations of deep learning run more efficiently for sparse networks. Several methods exist for pruning connections of a neural network after it was trained without connectivity constraints. We present an algorithm, DEEP R, that enables us to train directly a sparsely connected neural network. DEEP R automatically rewires the network during supervised training so that connections are there where they are most needed for the task, while its total number is all the time strictly bounded. We demonstrate that DEEP R can be used to train very sparse feedforward and recurrent neural networks on standard benchmark tasks with just a minor loss in performance. DEEP R is based on a rigorous theoretical foundation that views rewiring as stochastic sampling of network configurations from a posterior.

David Kappel, Robert Legenstein, Stefan Habenschuss et al.

Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine dynamics is at least as large as the component that depends on the history of pre- and postsynaptic neural activity. These data are inconsistent with common models for network plasticity, and raise the questions how neural circuits can maintain a stable computational function in spite of these continuously ongoing processes, and what functional uses these ongoing processes might have. Here, we present a rigorous theoretical framework for these seemingly stochastic spine dynamics and rewiring processes in the context of reward-based learning tasks. We show that spontaneous synapse-autonomous processes, in combination with reward signals such as dopamine, can explain the capability of networks of neurons in the brain to configure themselves for specific computational tasks, and to compensate automatically for later changes in the network or task. Furthermore we show theoretically and through computer simulations that stable computational performance is compatible with continuously ongoing synapse-autonomous changes. After reaching good computational performance it causes primarily a slow drift of network architecture and dynamics in task-irrelevant dimensions, as observed for neural activity in motor cortex and other areas. On the more abstract level of reinforcement learning the resulting model gives rise to an understanding of reward-driven network plasticity as continuous sampling of network configurations.

Mihai A. Petrovici, Sebastian Schmitt, Johann Klähn et al.

Despite being originally inspired by the central nervous system, artificial neural networks have diverged from their biological archetypes as they have been remodeled to fit particular tasks. In this paper, we review several possibilites to reverse map these architectures to biologically more realistic spiking networks with the aim of emulating them on fast, low-power neuromorphic hardware. Since many of these devices employ analog components, which cannot be perfectly controlled, finding ways to compensate for the resulting effects represents a key challenge. Here, we discuss three different strategies to address this problem: the addition of auxiliary network components for stabilizing activity, the utilization of inherently robust architectures and a training method for hardware-emulated networks that functions without perfect knowledge of the system's dynamics and parameters. For all three scenarios, we corroborate our theoretical considerations with experimental results on accelerated analog neuromorphic platforms.

Sebastian Schmitt, Johann Klaehn, Guillaume Bellec et al.

Emulating spiking neural networks on analog neuromorphic hardware offers several advantages over simulating them on conventional computers, particularly in terms of speed and energy consumption. However, this usually comes at the cost of reduced control over the dynamics of the emulated networks. In this paper, we demonstrate how iterative training of a hardware-emulated network can compensate for anomalies induced by the analog substrate. We first convert a deep neural network trained in software to a spiking network on the BrainScaleS wafer-scale neuromorphic system, thereby enabling an acceleration factor of 10 000 compared to the biological time domain. This mapping is followed by the in-the-loop training, where in each training step, the network activity is first recorded in hardware and then used to compute the parameter updates in software via backpropagation. An essential finding is that the parameter updates do not have to be precise, but only need to approximately follow the correct gradient, which simplifies the computation of updates. Using this approach, after only several tens of iterations, the spiking network shows an accuracy close to the ideal software-emulated prototype. The presented techniques show that deep spiking networks emulated on analog neuromorphic devices can attain good computational performance despite the inherent variations of the analog substrate.

Zhaofei Yu, David Kappel, Robert Legenstein et al.

Synaptic plasticity is implemented and controlled through over thousand different types of molecules in the postsynaptic density and presynaptic boutons that assume a staggering array of different states through phosporylation and other mechanisms. One of the most prominent molecule in the postsynaptic density is CaMKII, that is described in molecular biology as a "memory molecule" that can integrate through auto-phosporylation Ca-influx signals on a relatively large time scale of dozens of seconds. The functional impact of this memory mechanism is largely unknown. We show that the experimental data on the specific role of CaMKII activation in dopamine-gated spine consolidation suggest a general functional role in speeding up reward-guided search for network configurations that maximize reward expectation. Our theoretical analysis shows that stochastic search could in principle even attain optimal network configurations by emulating one of the most well-known nonlinear optimization methods, simulated annealing. But this optimization is usually impeded by slowness of stochastic search at a given temperature. We propose that CaMKII contributes a momentum term that substantially speeds up this search. In particular, it allows the network to overcome saddle points of the fitness function. The resulting improved stochastic policy search can be understood on a more abstract level as Hamiltonian sampling, which is known to be one of the most efficient stochastic search methods.

David Kappel, Stefan Habenschuss, Robert Legenstein et al.

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.