Hyperdimensional Computing (HDC) has shown promise in time series classification by enhancing MiniROCKET, forming HDC-MiniROCKET. However, the impact of choosing a specific HDC implementation, referred to as a Vector Symbolic Architecture (VSA), within this framework is so far unexplored. This paper systematically evaluates different VSAs within HDC-MiniROCKET, analyzing their impact on classification performance, hyperparameter sensitivity, and computational efficiency. Our findings reveal that certain VSAs require a significantly broader range of hyperparameter values to achieve optimal accuracy despite similar properties. We demonstrate this effect on a synthetic dataset and validate it across a subset of the real-world benchmark UCR, showing that VSA performance varies depending on the dataset characteristics. Additionally, we investigate the trade-off between computational complexity and classification accuracy. We find that computationally efficient VSAs not only reduce processing time but also achieve comparable or superior accuracy to more complex alternatives. These insights help to select VSAs in HDC-based time series classification.

Abstract Time series classification poses significant challenges due to the inherent temporal order of the data points and the existence of sequential dependencies between them. The ROCKET family, featuring methods like MiniROCKET, MultiROCKET, and HYDRA, is currently a leading approach in this domain, leveraging convolution kernels to aggregate temporal features into encodings for linear classifiers. However, these models encode temporal features over short temporal windows and then aggregate them as an unordered set of encodings over the longer temporal window of the entire data sequence. This prevents these models from capturing any longer sequence structure. To address this design drawback, we propose integrating hyperdimensional computing into ROCKET methods to explicitly incorporate temporal order of the short-term features within the entire time series. This approach enhances the discriminative power of encodings generated by MiniROCKET, MultiROCKET, and HYDRA where longer-term structure exists in the data, leading to increased classification performance with minimal computational overhead. More specifically, we introduce a method to represent time series as high-dimensional vectors through multiplicative binding of ROCKET encodings with encodings representing temporal order, applying this approach across various ROCKET methods. Additionally, we explore different high-dimensional vector representations of temporal order, yielding diverse similarity kernels that enhance classification accuracy. Through experiments on synthetic datasets, we highlight the limitations of ROCKET methods in handling temporal dependencies and show how the methods based on hyperdimensional computing overcome these limitations. Furthermore, our extensive experimental evaluation with real-world datasets included in the recent UCR archive, validates the advantages of our approach, consistently achieving classification improvements across all ROCKET methods that integrate hyperdimensional computing. Notably, our best model achieves a relative error rate reduction of over 50% compared to the best ROCKET model on several UCR datasets.

The vector superposition operation plays a central role in Hyperdimensional Computing (HDC), enabling compositionality of hypervectors without expanding the dimensionality, unlike concatenation. However, a problem arises when the quantity of superimposed vectors surpasses a certain threshold, which is determined by the hypervector’s information capacity relative to its dimensionality. Beyond this point, cross-talk noise incrementally obscures the distinctiveness of individual hypervectors and information is lost. To solve this challenge, we introduce a novel method for weighting individual hypervectors within the superposition, ensuring that only those hypervectors crucial for a given task are prioritized. The weights are learned end-to-end using the backpropagation algorithm in a neural network. Our method is characterized by two key features: (1) The resultant weighting model is exceptionally compact, as the number of trainable weights is equal to the total number of hypervectors in the superposition; (2) The model offers enhanced explainability due to the compositional nature of its encoding. These features collectively contribute to the efficiency and effectiveness of our proposed classification approach using hyperdimensional computing. We illustrate our approach through the multi-channel time series classification task. In this framework, each channel is encoded as a hypervector-descriptor, and those are subsequently composed into a single hypervector via superposition. This superimposed vector forms the basis for training the classification model based on the neural network. Applying our approach of weighted superposition on this task improved the classification performance compared to standard superposition or concatenation of feature vectors, especially for larger numbers of channels.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence at about the same computational effort for inference.

Visual place recognition is the task of recognizing same places of query images in a set of database images, despite potential condition changes due to time of day, weather or seasons. It is important for loop closure detection in SLAM and candidate selection for global localization. Many approaches in the literature perform computationally inefficient full image comparisons between queries and all database images. There is still a lack of suited methods for efficient place recognition that allow a fast, sparse comparison of only the most promising image pairs without any loss in performance. While this is partially given by ANN-based methods, they trade speed for precision and additional memory consumption, and many cannot find arbitrary numbers of matching database images in case of loops in the database. In this paper, we propose a novel fast sequence-based method for efficient place recognition that can be applied online. It uses relocalization to recover from sequence losses, and exploits usually available but often unused intra-database similarities for a potential detection of all matching database images for each query in case of loops or stops in the database. We performed extensive experimental evaluations over five datasets and 21 sequence combinations, and show that our method outperforms two state-of-the-art approaches and even full image comparisons in many cases, while providing a good tradeoff between performance and percentage of evaluated image pairs. Source code for Matlab will be provided with publication of this paper.

Visual place recognition is the task of finding matchings of images that show the same place in the world. Combinations of appearance changes (e.g. changing illumination or weather) and geometric changes (e.g. viewpoint changes or occlusions) challenge existing approaches. Learning-based local image feature pipelines are a promising approach to this type of problem. We present a novel attentive feature pooling method that can be used to train a CNN to jointly detect and describe local image features. It can be trained on small or moderately sized datasets with weak supervision in a classification training setup (e.g. we use a set of 24k images of publicly available web-camera images in our experiments). We propose to use a joint loss function that combines the cross-entropy loss for the classification task with a mean squared error in order to increase the repeatability of feature detections. We show how the approach can be integrated in a place recognition pipeline and run experiments on several standard place recognition datasets. Despite the small training dataset, we demonstrate a 15% improvement in the average performance compared to the best of a number of compared state-of-the-art approaches, and, probably more importantly, a 3x improvement in the worst-case performance. Open source code is available.

Robust and reliable online 3D multi-object tracking is an essential component of autonomous driving. Recent research follows the tracking-by-detection paradigm and focuses mainly on lidar sensors, due to their superior range, resolution and depth accuracy compared to other automotive sensors. This simplifies the challenging data association in crowded urban road scenes, resulting in a predominant status of laser based methods. In contrast, we propose an online 3D multi-object tracker based solely on mono camera images and radar data to promote non-lidar based tracking research. By representing all detections of one frame as a Gaussian mixture model (GMM), we are able to avoid a fixed data association, which may include wrong assumptions. Instead, we assign the GMM to each tracked object and solve the data association implicitly and jointly by estimating the full 3D object tracks in our factor graph based optimization back end. By including all available information from the object detector, our algorithm achieves accurate, robust and reliable tracking results. We conduct real world experiments on the nuScenes tracking data set improving the state-of-the-art for non-lidar based methods from 17.7% to 34.1 % AMOTA.

In this paper, we present a novel approach for driving style classification based on time series data. Instead of automatically learning the embedding vector for temporal representation of the input data with Recurrent Neural Networks, we propose a combination of Hyperdimensional Computing (HDC) for data representation in high-dimensional vectors and much simpler feed-forward neural networks. This approach provides three key advantages: first, instead of having a “black box” of Recurrent Neural Networks learning the temporal representation of the data, our approach allows to encode this temporal structure in high-dimensional vectors in a human-comprehensible way using the algebraic operations of HDC while only relying on feed-forward neural networks for the classification task. Second, we show that this combination is able to achieve at least similar and even slightly superior classification accuracy compared to state-of-the-art Long Short-Term Memory (LSTM)-based networks while significantly reducing training time and the necessary amount of data for successful learning. Third, our HDC-based data representation as well as the feed-forward neural network, allow implementation in the substrate of Spiking Neural Networks (SNNs). SNNs show promise to be orders of magnitude more energy-efficient than their rate-based counterparts while maintaining comparable prediction accuracy when being deployed on dedicated neuromorphic computing hardware, which could be an energy-efficient addition in future intelligent vehicles with tight restrictions regarding on-board computing and energy resources. We present a thorough analysis of our approach on a publicly available data set including a comparison with state-of-the-art reference models.

Visual place recognition in changing environments is the problem of finding matchings between two sets of observations, a query set and a reference set, despite severe appearance changes. Recently, image comparison using CNNbased descriptors showed very promising results. However, the experiments in the literature typically assume a single distinctive condition within each set (e.g., reference images are captured at daytime and the query sequence is at night). In this paper, we will demonstrate that as soon as the conditions change within one set (e.g., reference is daytime and now the query is a traversal daytime-dusk-night-dawn), different places under the same condition can suddenly look more similar than same places under different conditions. As a consequence, state-of-the-art approaches like CNN-based descriptors fail. This paper discusses this practically very important problem of in-sequence condition changes and defines a hierarchy of problem setups from (1) no in-sequence changes, (2) discrete in-sequence changes, to (3) continuous in-sequence changes. We will experimentally evaluate the effect of in-sequence condition changes on two state-of-the-art CNN-descriptors and investigate unsupervised methods to improve their performance. This includes an evaluation of the importance of statistical normalization (standardization) of descriptors, which is often omitted in existing approaches but can considerably improve results for problems up to discrete in-sequence changes. To address the practical most relevant setup of continuous changes, we investigate the application of unsupervised learning methods using two PCA-based approaches from the literature and propose a novel clustering-based extension of the statistical normalization. We experimentally demonstrate that these approaches can significantly improve place recognition performance in case of continuous in-sequence condition changes. Matlab implementations of the presented approaches are available online: www.tu-chemnitz.de/etit/proaut/cont_changing_envs.

Accurate and reliable tracking of multiple moving objects in 3D space is an essential component of urban scene understanding. This is a challenging task because it requires the assignment of detections in the current frame to the predicted objects from the previous one. Existing filter-based approaches tend to struggle if this initial assignment is not correct, which can happen easily.We propose a novel optimization-based approach that does not rely on explicit and fixed assignments. Instead, we represent the result of an off-the-shelf 3D object detector as Gaussian mixture model, which is incorporated in a factor graph framework. This gives us the flexibility to assign all detections to all objects simultaneously. As a result, the assignment problem is solved implicitly and jointly with the 3D spatial multi-object state estimation using non-linear least squares optimization.Despite its simplicity, the proposed algorithm achieves robust and reliable tracking results and can be applied for offline as well as online tracking. We demonstrate its performance on the real world KITTI tracking dataset and achieve better results than many state-of-the-art algorithms. Especially the consistency of the estimated tracks is superior offline as well as online.

Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their robustness depends on a close approximation of the real error distribution, their parametrization is crucial. We propose a novel approach that allows to adapt a multi-modal Gaussian mixture model to the error distribution of a sensor fusion problem. By combining expectation-maximization and non-linear least squares optimization, we are able to provide a computationally efficient solution with well-behaved convergence properties. We demonstrate the performance of these algorithms on several real-world GNSS and indoor localization datasets. The proposed adaptive mixture algorithm outperforms state-of-the-art approaches with static parametrization. Source code and datasets are available under https://mytuc.org/libRSF.

GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding distributions in the sensor fusion algorithm. However, these approaches require prior knowledge about the sensor's distribution, which is often not available. We introduce a novel sensor fusion algorithm based on variational Bayesian inference, that is able to approximate the true distribution with a Gaussian mixture model and to learn its parametrization online. The proposed Incremental Variational Mixture algorithm automatically adapts the number of mixture components to the complexity of the measurement's error distribution. We compare the proposed algorithm against current state-of-the-art approaches using a collection of open access real world datasets and demonstrate its superior localization accuracy.

Circular Convolutional Neural Networks (CCNN) are an easy to use alternative to CNNs for input data with wrap-around structure like 360° images and multi-layer laserscans. Although circular convolutions have been used in neural networks before, a detailed description and analysis is still missing. This paper closes this gap by defining circular convolutional and circular transposed convolutional layers as the replacement of their linear counterparts, and by identifying pros and cons of applying CCNNs. We experimentally evaluate their properties using a circular MNIST classification and a Velodyne laserscanner segmentation dataset. For the latter, we replace the convolutional layers in two state-of-the-art networks with the proposed circular convolutional layers. Compared to the standard CNNs, the resulting CCNNs show improved recognition rates in image border areas. This is essential to prevent blind spots in the environmental perception. Further, we present and evaluate how weight transfer can be used to obtain a CCNN from an available, readily trained CNN. Compared to alternative approaches (e.g. input padding), our experiments show benefits of CCNNs and transferred CCNNs regarding simplicity of usage (once the layer implementations are available), performance and runtime for training and inference. Implementations for Keras with Tensorflow are provided online2.

A fundamental problem of non-linear state estimation in robotics is the violation of assumptions about the sensors' error distribution. State of the art approaches reduce the impact of these violations with robust cost functions or predefined non-Gaussian error models. Both require extensive parameter tuning and fail if the sensors' error characteristic changes over time, due to environmental changes, ageing or sensor malfunctions. We demonstrate how the error distribution itself can be part of the state estimation process. Based on an efficient approximation of a Gaussian mixture, we optimize the sensor model simultaneously during the standard state estimation. Due to an implicit expectation-maximization approach, we achieve a fast convergence without prior knowledge of the true distribution parameters. We implement this self-tuning algorithm in a least-squares optimization framework and demonstrate its real time capability on a real world dataset for satellite localization of a driving vehicle. The resulting estimation quality is superior to previous robust algorithms.

Camera-based navigation within a given three-dimensional map enables heterogeneous robotic systems to share maps and use more abstract environment models like floor plans. This paper builds upon our previous work, and addresses the problem of how to combine 3D distance information from the map and the current visual image from the robot's camera in order to navigate within this map. The underlying assumption is that features which cause depth changes are also likely to create visual gradients. Based on this assumption, the similarity of visual image and depth images that are synthesized from the 3D map can be used to evaluate pose hypothesis. This paper integrates this idea into a Monte Carlo localization approach and additionally presents its application to path following. The presented approach is evaluated on a synthetic datasets that provides perfect knowledge of the ground truth, as well as two real-world datasets acquired by a heterogeneous robotic team: a proof-of-concept dataset in a scattered indoor environment, and a challenging corridor dataset.

While many applications of sensor fusion suffer from the occurrence of outliers, a broad range of outlier robust graph optimization techniques has been developed for simultaneous localization and mapping. In this paper we investigate the performance of some of the most advanced algorithms for a simulated wireless localization setting affected by non-Gaussian errors. With this first analysis we can show some of the advantages and disadvantages that are connected with the different concepts behind Max-Mixture, Generalized iSAM, Switchable Constraints and Dynamic Covariance Scaling.

A major insight from our previous work on extensive comparison of super pixel segmentation algorithms is the existence of several trade-offs for such algorithms. The most intuitive is the trade-off between segmentation quality and runtime. However, there exist many more between these two and a multitude of other performance measures. In this work, we present two new super pixel segmentation algorithms, based on existing algorithms, that provide better balanced trade-offs. Better balanced means, that we increase one performance measure by a large amount at the cost of slightly decreasing another. The proposed new algorithms are expected to be more appropriate for many real time computer vision tasks. The first proposed algorithm, Preemptive SLIC, is a faster version of SLIC, running at frame-rate (30 Hz for image size 481x321) on a standard desktop CPU. The speed-up comes at the cost of slightly worse segmentation quality. The second proposed algorithm is Compact Watershed. It is based on Seeded Watershed segmentation, but creates uniformly shaped super pixels similar to SLIC in about 10 ms per image. We extensively evaluate the influence of the proposed algorithmic changes on the trade-offs between various performance measures.

There exist almost as many superpixel segmentation algorithms as applications they can be used for. So far, the choice of the right superpixel algorithm for the task at hand is based on their ability to resemble human-made ground truth segmentations (besides runtime and availability). We investigate the equally important question of how stable the segmentations are under image changes as they appear in video data. Further we propose a new quality measure that evaluates how well the segmentation algorithms cover relevant image boundaries. Instead of relying on human-made annotations, that may be biased by semantic knowledge, we present a completely data-driven measure that inherently emphasizes the importance of image boundaries. Our evaluation is based on two recently published datasets coming with ground truth optical flow fields. We discuss how these ground optical truth fields can be used to evaluate segmentation algorithms and compare several existing superpixel algorithms.

Our paper explores the performance of a recently proposed incremental smoother in the context of nonlinear sensor fusion for a real-world UAV. This efficient factor graph based smoothing approach has a number of advantages compared to conventional filtering techniques like the EKF or its variants. It can more easily incorporate asynchronous and delayed measurements from sensors operating at different rates and is supposed to be less error-prone in highly nonlinear settings. We compare the novel incremental smoothing approach based on iSAM2 against our conventional EKF based sensor fusion framework. Unlike previously presented work, the experiments are not only performed in simulation, but also on a real-world quadrotor UAV system using IMU, optical flow and altitude measurements.

SLAM algorithms that can infer a correct map despite the presence of outliers have recently attracted increasing attention. In the context of SLAM, outlier constraints are typically caused by a failed place recognition due to perceptional aliasing. If not handled correctly, they can have catastrophic effects on the inferred map. Since robust robotic mapping and SLAM are among the key requirements for autonomous long-term operation, inference methods that can cope with such data association failures are a hot topic in current research. Our paper compares three very recently published approaches to robust pose graph SLAM, namely switchable constraints, max-mixture models and the RRR algorithm. All three methods were developed as extensions to existing factor graph-based SLAM back-ends and aim at improving the overall system's robustness to false positive loop closure constraints. Due to the novelty of the three proposed algorithms, no direct comparison has been conducted so far.

Reliable vehicle positioning is a crucial requirement for many applications of advanced driver assistance systems. While satellite navigation provides a reasonable performance in general, it often suffers from multipath and non-line-of-sight errors when it is applied in urban areas and therefore does not guarantee consistent results anymore. Our paper proposes a novel online method that identifies and excludes the affected pseudorange measurements. Our approach does not depend on additional sensors, maps, or environmental models. We rather formulate the positioning problem as a Bayesian inference problem in a factor graph and combine the recently developed concept of switchable constraints with an algorithm for efficient incremental inference in such graphs. We furthermore introduce the concepts of auxiliary updates and factor graph pruning in order to accelerate convergence while keeping the graph size and required runtime bounded. A real-world experiment demonstrates that the resulting algorithm is able to successfully localize despite a large number of satellite observations are influenced by NLOS or multipath effects.

Current state of the art solutions of the SLAM problem are based on efficient sparse optimization techniques and represent the problem as probabilistic constraint graphs. For example in pose graphs the nodes represent poses and the edges between them express spatial information (e.g. obtained from odometry) and information on loop closures. The task of constructing the graph is delegated to a front-end that has access to the available sensor information. The optimizer, the so called back-end of the system, relies heavily on the topological correctness of the graph structure and is not robust against misplaced constraint edges. Especially edges representing false positive loop closures will lead to the divergence of current solvers. We propose a novel formulation that allows the back-end to change parts of the topological structure of the graph during the optimization process. The back-end can thereby discard loop closures and converge towards correct solutions even in the presence of false positive loop closures. This largely increases the overall robustness of the SLAM system and closes a gap between the sensor-driven front-end and the back-end optimizers. We demonstrate the approach and present results both on large scale synthetic and real-world datasets.

Current SLAM back-ends are based on least squares optimization and thus are not robust against outliers like data association errors and false positive loop closure detections. Our paper presents and evaluates a robust back-end formulation for SLAM using switchable constraints. Instead of proposing yet another appearance-based data association technique, our system is able to recognize and reject outliers during the optimization. This is achieved by making the topology of the underlying factor graph representation subject to the optimization instead of keeping it fixed. The evaluation shows that the approach can deal with up to 1000 false positive loop closure constraints on various datasets. This largely increases the robustness of the overall SLAM system and closes a gap between the sensor-driven front-end and the back-end optimizers.

Our paper adapts recent advances in the SLAM (Simultaneous Localization and Mapping) literature to the problem of multipath mitigation and proposes a novel approach to successfully localize a vehicle despite a significant number of multipath observations. We show that GNSS-based localization problems can be modelled as factor graphs and solved using efficient nonlinear least squares methods that exploit the sparsity inherent in the problem formulation. Using a recently developed novel approach for robust optimization, satellite observations that are subject to multipath errors can be successfully identified and rejected during the optimization process. We demonstrate the feasibility of the proposed approach on a real-world urban dataset and compare it to an existing method of multipath detection.

The ability to recognize known places is an essential competence of any intelligent system that operates autonomously over longer periods of time. Approaches that rely on the visual appearance of distinct scenes have recently been developed and applied to large scale SLAM scenarios. FAB-Map is maybe the most successful of these systems. Our paper proposes BRIEF-Gist, a very simplistic appearance-based place recognition system based on the BRIEF descriptor. BRIEF-Gist is much more easy to implement and more efficient compared to recent approaches like FAB-Map. Despite its simplicity, we can show that it performs comparably well as a front-end for large scale SLAM. We benchmark our approach using two standard datasets and perform SLAM on the 66 km long urban St. Lucia dataset.

A SLAM algorithm inspired by biological principles has been recently proposed and shown to perform well in a large and demanding scenario. We analyse and compare this system (RatSLAM) and the established Bayesian SLAM methods and identify the key difference to be an additive update step. Using this insight, we derive a novel filter scheme and successfully show that it can entirely replace the core of the RatSLAM system while maintaining its desirable robustness. This leads to a massive speedup, as the novel filter can be calculated very efficiently. We successfully applied the new algorithm to the same 66 km long dataset that was used with the original algorithm.

Recently a SLAM algorithm based on biological principles (RatSLAM) has been proposed. It was proven to perform well in large and demanding scenarios. In this paper we establish a comparison of the principles underlying this algorithm with standard probabilistic SLAM approaches and identify the key difference to be an additive update step. Using this insight, we derive the novel, non-Bayesian Causal Update filter that is suitable for application in appearance-based SLAM. We successfully apply this new filter to two demanding vision-only urban SLAM problems of 5 and 66 km length. We show that it can functionally replace the core of RatSLAM, gaining a massive speed-up.

We present a fast line segment tracker which does not require any knowledge about the motion of the camera nor the structure of the observed scene. It runs on 320 times 240 pixel images at 30 Hz. We adapted the RAPiD tracker with a new way of handling multiple line hypotheses to deal with the simple model of a single line segment. We discuss the difficulty of using a chi2-test as merging criterion and also present a new approach to overcome it. Furthermore, instead of making assumptions about the camera motion, a constant velocity motion model to predict the line segment position in the following frame is used. We explain how to deal with the instability of the endpoint extraction in this motion model to avoid unintentional motion along the line. Finally, we present results on real world indoor and urban outdoor image sequences.

In this paper, we present our threefold concept of "bringing robotics closer to students". Our efforts begin with motivating high-school students to study engineering sciences by increasing their interest in technical issues. This is achieved by a national robotics contest. Besides our work with high-school students, we also focus on projects for undergraduate university students. Several robotics projects and competitions are included into the curriculum of electrical and mechanical engineering and computer science. These projects offer chances to do special assignments and student research projects. It may be important to point out that most of the work described in this paper, including inventing and specifying the projects and organizing the events, has been done by undergraduate and graduate students

In this paper, we introduce RoboKing, a national contest of mobile autonomous robots, dedicated to teams of high school students. RoboKing differs from similar contests by supporting the participating teams with a 250 Euro voucher and by not restricting the kind of materials the robots can be build with. Its task is manageable for students without previous knowledge in robotics but offers enough complexity to be challenging for advanced participants. The first RoboKing contest with 12 participating teams from different parts of Germany took place at the Hannover Messe in 2004. Because of its great success, RoboKing will be held annually. RoboKing 2005 has been extended to 20 teams of pupils and offers a new challenging task. More pictures and video files can be found under www. roboking. de .

The fault-tolerance characteristics of time-continuous, recurrent artificial neural networks (ANNs) that can be used to solve optimization problems are investigated. The performance of these networks is illustrated by using well-known model problems like the traveling salesman problem and the assignment problem. The ANNs are then subjected to up to 13 simultaneous stuck-at-1 or stuck-at-0 faults for network sizes of up to 900 neurons. The effect of these faults on the performance is demonstrated, and the cause for the observed fault-tolerance is discussed. An application is presented in which a network performs a critical task for a real-time distributed processing system by generating new task allocations during the reconfiguration of the system. The performance degradation of the ANN under the presence of faults is investigated by large-scale simulations and the potential benefits of delegating a critical task to a fault-tolerant network are discussed.