Dominik Dold

Dario Izzo, Alexander Hadjiivanov, Dominik Dold et al.

The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain, or sensors that get inspiration from, e.g., the visual or olfactory systems in insects and mammals to acquire information about the environment. This approach is not without ambition as it promises to enable engineered devices able to reproduce the level of performance observed in biological organisms -- the main immediate advantage being the efficient use of scarce resources, which translates into low power requirements. The emphasis on low power and energy efficiency of neuromorphic devices is a perfect match for space applications. Spacecraft -- especially miniaturized ones -- have strict energy constraints as they need to operate in an environment which is scarce with resources and extremely hostile. In this work we present an overview of early attempts made to study a neuromorphic approach in a space context at the European Space Agency's (ESA) Advanced Concepts Team (ACT).

Dario Izzo, Gabriele Meoni, Pablo Gómez et al.

The development and adoption of artificial intelligence (AI) technologies in space applications is growing quickly as the consensus increases on the potential benefits introduced. As more and more aerospace engineers are becoming aware of new trends in AI, traditional approaches are revisited to consider the applications of emerging AI technologies. Already at the time of writing, the scope of AI-related activities across academia, the aerospace industry and space agencies is so wide that an in-depth review would not fit in these pages. In this chapter we focus instead on two main emerging trends we believe capture the most relevant and exciting activities in the field: differentiable intelligence and on-board machine learning. Differentiable intelligence, in a nutshell, refers to works making extensive use of automatic differentiation frameworks to learn the parameters of machine learning or related models. Onboard machine learning considers the problem of moving inference, as well as learning, onboard. Within these fields, we discuss a few selected projects originating from the European Space Agency's (ESA) Advanced Concepts Team (ACT), giving priority to advanced topics going beyond the transposition of established AI techniques and practices to the space domain.

Anna Himmelhuber, Dominik Dold, Stephan Grimm et al.

Machine learning (ML) on graph-structured data has recently received deepened interest in the context of intrusion detection in the cybersecurity domain. Due to the increasing amounts of data generated by monitoring tools as well as more and more sophisticated attacks, these ML methods are gaining traction. Knowledge graphs and their corresponding learning techniques such as Graph Neural Networks (GNNs) with their ability to seamlessly integrate data from multiple domains using human-understandable vocabularies, are finding application in the cybersecurity domain. However, similar to other connectionist models, GNNs are lacking transparency in their decision making. This is especially important as there tend to be a high number of false positive alerts in the cybersecurity domain, such that triage needs to be done by domain experts, requiring a lot of man power. Therefore, we are addressing Explainable AI (XAI) for GNNs to enhance trust management by exploring combining symbolic and sub-symbolic methods in the area of cybersecurity that incorporate domain knowledge. We experimented with this approach by generating explanations in an industrial demonstrator system. The proposed method is shown to produce intuitive explanations for alerts for a diverse range of scenarios. Not only do the explanations provide deeper insights into the alerts, but they also lead to a reduction of false positive alerts by 66% and by 93% when including the fidelity metric.

Dominik Dold, Josep Soler Garrido, Victor Caceres Chian et al.

Knowledge graphs are an expressive and widely used data structure due to their ability to integrate data from different domains in a sensible and machine-readable way. Thus, they can be used to model a variety of systems such as molecules and social networks. However, it still remains an open question how symbolic reasoning could be realized in spiking systems and, therefore, how spiking neural networks could be applied to such graph data. Here, we extend previous work on spike-based graph algorithms by demonstrating how symbolic and multi-relational information can be encoded using spiking neurons, allowing reasoning over symbolic structures like knowledge graphs with spiking neural networks. The introduced framework is enabled by combining the graph embedding paradigm and the recent progress in training spiking neural networks using error backpropagation. The presented methods are applicable to a variety of spiking neuron models and can be trained end-to-end in combination with other differentiable network architectures, which we demonstrate by implementing a spiking relational graph neural network.

Dominik Dold, Derek Aranguren van Egmond

Architected materials possessing physico-chemical properties adaptable to disparate environmental conditions embody a disruptive new domain of materials science. Fueled by advances in digital design and fabrication, materials shaped into lattice topologies enable a degree of property customization not afforded to bulk materials. A promising venue for inspiration toward their design is in the irregular micro-architectures of nature. However, the immense design variability unlocked by such irregularity is challenging to probe analytically. Here, we propose a new computational approach using graph-based representation for regular and irregular lattice materials. Our method uses differentiable message passing algorithms to calculate mechanical properties, therefore allowing automatic differentiation with surrogate derivatives to adjust both geometric structure and local attributes of individual lattice elements to achieve inversely designed materials with desired properties. We further introduce a graph neural network surrogate model for structural analysis at scale. The methodology is generalizable to any system representable as heterogeneous graphs.

Dominik Dold

Relational representation learning has lately received an increase in interest due to its flexibility in modeling a variety of systems like interacting particles, materials and industrial projects for, e.g., the design of spacecraft. A prominent method for dealing with relational data are knowledge graph embedding algorithms, where entities and relations of a knowledge graph are mapped to a low-dimensional vector space while preserving its semantic structure. Recently, a graph embedding method has been proposed that maps graph elements to the temporal domain of spiking neural networks. However, it relies on encoding graph elements through populations of neurons that only spike once. Here, we present a model that allows us to learn spike train-based embeddings of knowledge graphs, requiring only one neuron per graph element by fully utilizing the temporal domain of spike patterns. This coding scheme can be implemented with arbitrary spiking neuron models as long as gradients with respect to spike times can be calculated, which we demonstrate for the integrate-and-fire neuron model. In general, the presented results show how relational knowledge can be integrated into spike-based systems, opening up the possibility of merging event-based computing and relational data to build powerful and energy efficient artificial intelligence applications and reasoning systems.

Dominik Dold, Philipp Christian Petersen

In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results are only valid for neurons that spike at most once, which is commonly thought to be a strong limitation. Here, we show that the opposite is true for a large class of spiking neuron models, including the commonly used leaky integrate-and-fire model with subtractive reset: for every approximation bound that is valid for a set of multi-spike neural networks, there is an equivalent set of single-spike neural networks with only linearly more neurons (in the maximum number of spikes) for which the bound holds. The same is true for the reverse direction too, showing that regarding their approximation capabilities in general machine learning tasks, single-spike and multi-spike neural networks are equivalent. Consequently, many approximation results in the literature for single-spike neural networks also hold for the multi-spike case.

A. Martina Neuman, Dominik Dold, Philipp Christian Petersen

We study the learning problem associated with spiking neural networks. Specifically, we focus on spiking neural networks composed of simple spiking neurons having only positive synaptic weights, equipped with an affine encoder and decoder; we refer to these as affine spiking neural networks. These neural networks are shown to depend continuously on their parameters, which facilitates classical covering number-based generalization statements and supports stable gradient-based training. We demonstrate that the positivity of the weights enables a wide range of expressivity results, including rate-optimal approximation of smooth functions and dimension-independent approximation of Barron regular functions. In particular, we show in theory and simulations that affine spiking neural networks are capable of approximating shallow ReLU neural networks. Furthermore, we apply these affine spiking neural networks to standard machine learning benchmarks and reach competitive results. Finally, we observe that from a generalization perspective, contrary to feedforward neural networks or previous results for general spiking neural networks, the depth has little to no adverse effect on the generalization capabilities.

Zacharia A. Rudge, Dario Izzo, Moritz Fieback et al.

In recent years, the space community has been exploring the possibilities of Artificial Intelligence (AI), specifically Artificial Neural Networks (ANNs), for a variety of on board applications. However, this development is limited by the restricted energy budget of smallsats and cubesats as well as radiation concerns plaguing modern chips. This necessitates research into neural network accelerators capable of meeting these requirements whilst satisfying the compute and performance needs of the application. This paper explores the use of Phase-Change Memory (PCM) and Resistive Random-Access Memory (RRAM) memristors for on-board in-memory computing AI acceleration in space applications. A guidance and control neural network (G\&CNET) accelerated using memristors is simulated in a variety of scenarios and with both device types to evaluate the performance of memristor-based accelerators, considering device non-idealities such as noise and conductance drift. We show that the memristive accelerator is able to learn the expert actions, though challenges remain with the impact of noise on accuracy. We also show that re-training after degradation is able to restore performance to nominal levels. This study provides a foundation for future research into memristor-based AI accelerators for space, highlighting their potential and the need for further investigation.

Dominik Dold, Philipp Christian Petersen

We introduce a novel concept for spiking neural networks (SNNs) derived from the idea of "linear pieces" used to analyse the expressiveness and trainability of artificial neural networks (ANNs). We prove that the input domain of SNNs decomposes into distinct causal regions where its output spike times are locally Lipschitz continuous with respect to the input spike times and network parameters. The number of such regions - which we call "causal pieces" - is a measure of the approximation capabilities of SNNs. In particular, we demonstrate in simulation that parameter initialisations which yield a high number of causal pieces on the training set strongly correlate with SNN training success. Moreover, we find that feedforward SNNs with purely positive weights exhibit a surprisingly high number of causal pieces, allowing them to achieve competitive performance levels on benchmark tasks. We believe that causal pieces are not only a powerful and principled tool for improving SNNs, but might also open up new ways of comparing SNNs and ANNs in the future.

Dominik Dold, Amy Thomas, Nicole Rosi et al.

Recently, a class of mechanical lattices with reconfigurable, zero-stiffness structures has been proposed, called Totimorphic lattices. In this work, we introduce a computational framework that enables continuous reprogramming of a Totimorphic lattice's effective properties, such as mechanical and optical behaviour, through geometric changes alone, demonstrated using computer simulations. Our approach is differentiable and guarantees valid Totimorphic configurations throughout the optimisation process, providing not only target states with desired properties but also continuous trajectories in configuration space that connect them. This enables reprogrammable structures in which actuators are controlled via automatic differentiation on an objective-dependent cost function, continuously adapting the lattice to achieve a given goal. We focus on deep space applications, where harsh and resource-constrained environments demand solutions that combine flexibility, efficiency, and autonomy. As proof of concept, we present two scenarios: a reprogrammable disordered lattice material and a space telescope mirror with adjustable focal length. The introduced framework is adaptable to a wide range of Totimorphic designs and objectives, providing a lightweight model for endowing physical systems with autonomous self-configuration and self-repair capabilities.

Nadezhda Dobreva, Emmanuel Blazquez, Jai Grover et al.

We present a decentralized model for autonomous reconfiguration of homogeneous pivoting cube modular robots in two dimensions. Each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its local neighborhood, trained using reinforcement learning. Furthermore, using geometric deep learning, we include the grid symmetries of the cube ensemble in the neural network architecture. We find that even the most localized versions succeed in reconfiguring to the target shape, although reconfiguration happens faster the more information about the whole ensemble is available to individual cubes. Near-optimal reconfiguration is achieved with only nearest neighbor interactions by using multiple information passing between cubes, allowing them to accumulate more global information about the ensemble. Compared to standard neural network architectures, using geometric deep learning approaches provided only minor benefits. Overall, we successfully demonstrate mostly local control of a modular self-assembling system, which is transferable to other space-relevant systems with different action spaces, such as sliding cube modular robots and CubeSat swarms.

Zacharia A. Rudge, Dominik Dold, Moritz Fieback et al.

Memristors are an emerging technology that enables artificial intelligence (AI) accelerators with high energy efficiency and radiation robustness -- properties that are vital for the deployment of AI on-board spacecraft. However, space applications require reliable and precise computations, while memristive devices suffer from non-idealities, such as device variability, conductance drifts, and device faults. Thus, porting neural networks (NNs) to memristive devices often faces the challenge of severe performance degradation. In this work, we show in simulations that memristor-based NNs achieve competitive performance levels on on-board tasks, such as navigation \& control and geodesy of asteroids. Through bit-slicing, temporal averaging of NN layers, and periodic activation functions, we improve initial results from around $0.07$ to $0.01$ and $0.3$ to $0.007$ for both tasks using RRAM devices, coming close to state-of-the-art levels ($0.003-0.005$ and $0.003$, respectively). Our results demonstrate the potential of memristors for on-board space applications, and we are convinced that future technology and NN improvements will further close the performance gap to fully unlock the benefits of memristors.

Dominik Dold, Josep Soler Garrido

Machine learning on graph-structured data has recently become a major topic in industry and research, finding many exciting applications such as recommender systems and automated theorem proving. We propose an energy-based graph embedding algorithm to characterize industrial automation systems, integrating knowledge from different domains like industrial automation, communications and cybersecurity. By combining knowledge from multiple domains, the learned model is capable of making context-aware predictions regarding novel system events and can be used to evaluate the severity of anomalies that might be indicative of, e.g., cybersecurity breaches. The presented model is mappable to a biologically-inspired neural architecture, serving as a first bridge between graph embedding methods and neuromorphic computing - uncovering a promising edge application for this upcoming technology.

Victor Caceres Chian, Marcel Hildebrandt, Thomas Runkler et al.

Computing latent representations for graph-structured data is an ubiquitous learning task in many industrial and academic applications ranging from molecule synthetization to social network analysis and recommender systems. Knowledge graphs are among the most popular and widely used data representations related to the Semantic Web. Next to structuring factual knowledge in a machine-readable format, knowledge graphs serve as the backbone of many artificial intelligence applications and allow the ingestion of context information into various learning algorithms. Graph neural networks attempt to encode graph structures in low-dimensional vector spaces via a message passing heuristic between neighboring nodes. Over the recent years, a multitude of different graph neural network architectures demonstrated ground-breaking performances in many learning tasks. In this work, we propose a strategy to map deep graph learning architectures for knowledge graph reasoning to neuromorphic architectures. Based on the insight that randomly initialized and untrained (i.e., frozen) graph neural networks are able to preserve local graph structures, we compose a frozen neural network with shallow knowledge graph embedding models. We experimentally show that already on conventional computing hardware, this leads to a significant speedup and memory reduction while maintaining a competitive performance level. Moreover, we extend the frozen architecture to spiking neural networks, introducing a novel, event-based and highly sparse knowledge graph embedding algorithm that is suitable for implementation in neuromorphic hardware.

Josep Soler Garrido, Dominik Dold, Johannes Frank

Machine learning techniques are gaining attention in the context of intrusion detection due to the increasing amounts of data generated by monitoring tools, as well as the sophistication displayed by attackers in hiding their activity. However, existing methods often exhibit important limitations in terms of the quantity and relevance of the generated alerts. Recently, knowledge graphs are finding application in the cybersecurity domain, showing the potential to alleviate some of these drawbacks thanks to their ability to seamlessly integrate data from multiple domains using human-understandable vocabularies. We discuss the application of machine learning on knowledge graphs for intrusion detection and experimentally evaluate a link-prediction method for scoring anomalous activity in industrial systems. After initial unsupervised training, the proposed method is shown to produce intuitively well-calibrated and interpretable alerts in a diverse range of scenarios, hinting at the potential benefits of relational machine learning on knowledge graphs for intrusion detection purposes.

Dominik Dold, Josep Soler Garrido

Despite the recent success of reconciling spike-based coding with the error backpropagation algorithm, spiking neural networks are still mostly applied to tasks stemming from sensory processing, operating on traditional data structures like visual or auditory data. A rich data representation that finds wide application in industry and research is the so-called knowledge graph - a graph-based structure where entities are depicted as nodes and relations between them as edges. Complex systems like molecules, social networks and industrial factory systems can be described using the common language of knowledge graphs, allowing the usage of graph embedding algorithms to make context-aware predictions in these information-packed environments. We propose a spike-based algorithm where nodes in a graph are represented by single spike times of neuron populations and relations as spike time differences between populations. Learning such spike-based embeddings only requires knowledge about spike times and spike time differences, compatible with recently proposed frameworks for training spiking neural networks. The presented model is easily mapped to current neuromorphic hardware systems and thereby moves inference on knowledge graphs into a domain where these architectures thrive, unlocking a promising industrial application area for this technology.

Sebastian Billaudelle, Yannik Stradmann, Korbinian Schreiber et al.

We present first experimental results on the novel BrainScaleS-2 neuromorphic architecture based on an analog neuro-synaptic core and augmented by embedded microprocessors for complex plasticity and experiment control. The high acceleration factor of 1000 compared to biological dynamics enables the execution of computationally expensive tasks, by allowing the fast emulation of long-duration experiments or rapid iteration over many consecutive trials. The flexibility of our architecture is demonstrated in a suite of five distinct experiments, which emphasize different aspects of the BrainScaleS-2 system.

Julian Göltz, Laura Kriener, Andreas Baumbach et al.

For a biological agent operating under environmental pressure, energy consumption and reaction times are of critical importance. Similarly, engineered systems are optimized for short time-to-solution and low energy-to-solution characteristics. At the level of neuronal implementation, this implies achieving the desired results with as few and as early spikes as possible. With time-to-first-spike coding both of these goals are inherently emerging features of learning. Here, we describe a rigorous derivation of a learning rule for such first-spike times in networks of leaky integrate-and-fire neurons, relying solely on input and output spike times, and show how this mechanism can implement error backpropagation in hierarchical spiking networks. Furthermore, we emulate our framework on the BrainScaleS-2 neuromorphic system and demonstrate its capability of harnessing the system's speed and energy characteristics. Finally, we examine how our approach generalizes to other neuromorphic platforms by studying how its performance is affected by typical distortive effects induced by neuromorphic substrates.

Dominik Dold, Ilja Bytschok, Akos F. Kungl et al.

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may, in fact, have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functionally Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.

Akos F. Kungl, Sebastian Schmitt, Johann Klähn et al.

The massively parallel nature of biological information processing plays an important role for its superiority to human-engineered computing devices. In particular, it may hold the key to overcoming the von Neumann bottleneck that limits contemporary computer architectures. Physical-model neuromorphic devices seek to replicate not only this inherent parallelism, but also aspects of its microscopic dynamics in analog circuits emulating neurons and synapses. However, these machines require network models that are not only adept at solving particular tasks, but that can also cope with the inherent imperfections of analog substrates. We present a spiking network model that performs Bayesian inference through sampling on the BrainScaleS neuromorphic platform, where we use it for generative and discriminative computations on visual data. By illustrating its functionality on this platform, we implicitly demonstrate its robustness to various substrate-specific distortive effects, as well as its accelerated capability for computation. These results showcase the advantages of brain-inspired physical computation and provide important building blocks for large-scale neuromorphic applications.