Spatio-temporal models analyze spatial structures and temporal dynamics, which makes them prone to information degeneration among space and time.Prior literature has demonstrated that over-squashing in causal attention or temporal convolutions creates a bias on the first tokens.To analyze whether such a bias is present in temporal attention mechanisms, we derive sensitivity bounds on the expected value of the Jacobian of a temporal attention layer.We theoretically show how off-diagonal attention scores depend on the sequence length, and that temporal attention matrices suffer a diagonal attention sink.We suggest regularization methods, and experimentally demonstrate their effectiveness.

Developments in Deep Learning have significantly improved time series forecasting by enabling more accurate modeling of complex temporal dependencies inherent in sequential data. The effectiveness of such models is often demonstrated on limited sets of specific real-world data. Although this allows for comparative analysis, it still does not demonstrate how specific data characteristics align with the architectural strengths of individual models. Our research aims at uncovering clear connections between time series characteristics and particular models. We introduce a novel dataset generated using Gaussian Processes, specifically designed to display distinct, known characteristics for targeted evaluations of model adaptability to them. Furthermore, we present TimeFlex, a new model that incorporates a modular architecture tailored to handle diverse temporal dynamics, including trends and periodic patterns. This model is compared to current state-of-the-art models, offering a deeper understanding of how models perform under varied time series conditions.

Graph neural networks based on message-passing rely on the principle of neighborhood aggregation which has shown to work well for many graph tasks. In other cases these approaches appear insufficient, for example, when graphs are heterophilic. In such cases, it can help to modulate the aggregation method depending on the characteristic of the current neighborhood. Furthermore, when considering higher-order relations, heterophilic settings become even more important. In this work, we investigate a sparse version of message-passing that allows selective neighbor integration and aims for learning to identify most salient nodes that are then integrated over. In our approach, information on individual nodes is encoded by generating distinct walks. Because these walks follow distinct trajectories, the higher-order neighborhood grows only linearly which mitigates information bottlenecks. Overall, we aim to find the most salient substructures by deploying a learnable sampling strategy. We validate our method on commonly used graph benchmarks and show the effectiveness especially in heterophilic graphs. We finally discuss possible extensions to the framework.

Decentralized control has been established as a key control principle in insect walking and has been successfully leveraged to account for a wide range of walking behaviors in the proposed neuroWalknet architecture. This controller allows for walking patterns at different velocities in both, forward and backward direction-quite similar to the behavior shown in stick insects-, for negotiation of curves, and for robustly dealing with various disturbances. While these simulations focus on the cooperation of different, decentrally controlled legs, here we consider a set of biological experiments not yet been tested by neuroWalknet, that focus on the function of the individual leg and are context dependent. These intraleg studies deal with four groups of interjoint reflexes. The reflexes are elicited by stimulation of the femoral chordotonal organ (fCO) or groups of campaniform sensilla (CS). Motor output signals are recorded from the alpha-joint, the beta-joint or the gamma-joint of the leg. Furthermore, the influence of these sensory inputs to artificially induced oscillations by application of pilocarpine has been studied. Although these biological data represent results obtained from different local reflexes in different contexts, they fit with and are embedded into the behavior shown by the global structure of neuroWalknet. In particular, a specific and intensively studied behavior, active reaction, has since long been assumed to represent a separate behavioral element, from which it is not clear why it occurs in some situations, but not in others. This question could now be explained as an emergent property of the holistic structure of neuroWalknet which has shown to be able to produce artificially elicited pilocarpine-driven oscillation that can be controlled by sensory input without the need of explicit innate CPG structures. As the simulation data result from a holistic system, further results were obtained that could be used as predictions to be tested in further biological experiments.

Accurate traffic prediction is a key ingredient to enable traffic management like rerouting cars to reduce road congestion or regulating traffic via dynamic speed limits to maintain a steady flow. One way to represent traffic data is as temporally changing heatmaps visualizing attributes of traffic, such as speed and volume. In recent approaches, U-Net models have shown state of the art performance on traffic forecasting from such heatmaps. We propose to combine the U-Net architecture with graph layers which improves spatial generalization to unseen road networks compared to a Vanilla U-Net. In particular, we specialize existing graph operations to be sensitive to geographical topology and generalize pooling and upsampling operations to be applicable to graphs.

Locomotion in animals provides a model for adaptive behavior as it is able to deal with various kinds of perturbations. Work in insects suggests that this evolved flexibility results from a modular architecture, which can be characterized by a recurrent neural network allowing for various emerging attractor states. Whereas a lower control-level coordinates joint movements on a short timescale, a higher-level handles action selection on longer timescales. Implementation of such a control system on a walking hexapod robot was able to deal with various walking patterns including disturbances such as uneven terrain or loss of a leg. Here, we propose a cognitive expansion to the adaptive control system that allows dealing with novel challenging situations. This approach makes use of an internal simulation-based planner that is triggered when the model-free controller fails to recover from an unstable pose. Using a grounded internal body model, the planner then tries, in internal simulation, different solutions out of context, and thus, proposes a new plan to be executed on the real robot. We demonstrate the feasibility of this control approach for walking over terrain with uncertain footholds in three scenarios.

Prediction of movements is essential for successful cooperation with intelligent systems.We propose a model that integrates organized spatial information as given through the moving body's skeletal structure.This inherent structure is exploited in our model through application of Graph Convolutions and we demonstrate how this allows leveraging the structured spatial information into competitive predictions that are based on a lightweight model that requires a comparatively small number of parameters.* This research was supported by the research training group "Dataninja" (Trustworthy AI for Seamless Problem Solving: Next Generation Intelligence Joins Robust Data Analysis) funded by the German federal state of North Rhine-Westphalia.1 https://github.com/LucaHermes

Decentralization is a central characteristic of biological motor control that allows for fast responses relying on local sensory information. In contrast, the current trend of Deep Reinforcement Learning (DRL) based approaches to motor control follows a centralized paradigm using a single, holistic controller that has to untangle the whole input information space. This motivates to ask whether decentralization as seen in biological control architectures might also be beneficial for embodied sensori-motor control systems when using DRL. To answer this question, we provide an analysis and comparison of eight control architectures for adaptive locomotion that were derived for a four-legged agent, but with their degree of decentralization varying systematically between the extremes of fully centralized and fully decentralized. Our comparison shows that learning speed is significantly enhanced in distributed architectures-while still reaching the same high performance level of centralized architectures-due to smaller search spaces and local costs providing more focused information for learning. Second, we find an increased robustness of the learning process in the decentralized cases-it is less demanding to hyperparameter selection and less prone to becoming trapped in poor local minima. Finally, when examining generalization to uneven terrains-not used during training-we find best performance for an intermediate architecture that is decentralized, but integrates only local information from both neighboring legs. Together, these findings demonstrate beneficial effects of distributing control into decentralized units and relying on local information. This appears as a promising approach towards more robust DRL and better generalization towards adaptive behavior.

Locomotion is a prime example for adaptive behavior in animals and biological control principles have inspired control architectures for legged robots. While machine learning has been successfully applied to many tasks in recent years, Deep Reinforcement Learning approaches still appear to struggle when applied to real world robots in continuous control tasks and in particular do not appear as robust solutions that can handle uncertainties well. Therefore, there is a new interest in incorporating biological principles into such learning architectures. While inducing a hierarchical organization as found in motor control has shown already some success, we here propose a decentralized organization as found in insect motor control for coordination of different legs. A decentralized and distributed architecture is introduced on a simulated hexapod robot and the details of the controller are learned through Deep Reinforcement Learning. We first show that such a concurrent local structure is able to learn better walking behavior. Secondly, that the simpler organization is learned faster compared to holistic approaches.

Controlling the six legs of an insect walking in an unpredictable environment is a challenging task, as many degrees of freedom have to be coordinated. Solutions proposed to deal with this task are usually based on the highly influential concept that (sensory-modulated) central pattern generators (CPG) are required to control the rhythmic movements of walking legs. Here, we investigate a different view. To this end, we introduce a sensor based controller operating on artificial neurons, being applied to a (simulated) insectoid robot required to exploit the "loop through the world" allowing for simplification of neural computation. We show that such a decentralized solution leads to adaptive behavior when facing uncertain environments which we demonstrate for a broad range of behaviors never dealt with in a single system by earlier approaches. This includes the ability to produce footfall patterns such as velocity dependent "tripod", "tetrapod", "pentapod" as well as various stable intermediate patterns as observed in stick insects and in Drosophila. These patterns are found to be stable against disturbances and when starting from various leg configurations. Our neuronal architecture easily allows for starting or interrupting a walk, all being difficult for CPG controlled solutions. Furthermore, negotiation of curves and walking on a treadmill with various treatments of individual legs is possible as well as backward walking and performing short steps. This approach can as well account for the neurophysiological results usually interpreted to support the idea that CPGs form the basis of walking, although our approach is not relying on explicit CPG-like structures. Application of CPGs may however be required for very fast walking. Our neuronal structure allows to pinpoint specific neurons known from various insect studies. Interestingly, specific common properties observed in both insects and crustaceans suggest a significance of our controller beyond the realm of insects.

An internal model of the own body can be assumed a fundamental and evolutionary-early representation as it is present throughout the animal kingdom. Such functional models are, on the one hand, required in motor control, for example solving the inverse kinematic or dynamic task in goal-directed movements or a forward task in ballistic movements. On the other hand, such models are recruited in cognitive tasks as are planning ahead or observation of actions of a conspecific. Here, we present a functional internal body model that is based on the Mean of Multiple ss principle. For the first time such a model is completely realized in a recurrent neural network as necessary normalization steps are integrated into the neural model itself. Secondly, a dynamic extension is applied to the model. It is shown how the neural network solves a series of inverse tasks. Furthermore, emerging representation in transformational layers are analyzed that show a form of prototypical population-coding as found in place or direction cells.

Internal models of the body are assumed to serve a multitude of different functions. Forward and inverse models are important concepts in motor control. Usually, it is distinguished between these function and there are different models for each individual function or there are even models that are specific to individual behaviors. Here, we present a concept of a core internal model of the body which can act both as an inverse and forward model. In addition, it provides a mechanism for integration of sensory data and can be in this way grounded in the continuous interaction with the environment. In this article, a hierarchical Mean of Multiple Computations neural network is presented that is based on an axis-angle representation of joint movements using dual quaternions. It is shown in detail how the network provides a solution for the forward kinematic problem applied for the case of a seven degrees of freedom robotic arm. Furthermore, it is used in a complex scenario of a bimanual movement task. This demonstrates how the MMC approach can be easily scaled up from a representation of a single arm to a complex model of a complete body.

Recent developments in machine-learning algorithms have led to impressive performance increases in many traditional application scenarios of artificial intelligence research. In the area of deep reinforcement learning, deep learning functional architectures are combined with incremental learning schemes for sequential tasks that include interaction-based, but often delayed feedback. Despite their impressive successes, modern machine-learning approaches, including deep reinforcement learning, still perform weakly when compared to flexibly adaptive biological systems in certain naturally occurring scenarios. Such scenarios include transfers to environments different than the ones in which the training took place or environments that dynamically change, both of which are often mastered by biological systems through a capability that we here term “fluid adaptivity” to contrast it from the much slower adaptivity (“crystallized adaptivity”) of the prior learning from which the behavior emerged. In this article, we derive and discuss research strategies, based on analyzes of fluid adaptivity in biological systems and its neuronal modeling, that might aid in equipping future artificially intelligent systems with capabilities of fluid adaptivity more similar to those seen in some biologically intelligent systems. A key component of this research strategy is the dynamization of the problem space itself and the implementation of this dynamization by suitably designed flexibly interacting modules.

The main advantage of multi-legged robots is the ability to traverse uneven terrain and to overcome obstacles that would impede the movement of a wheeled robot. Compliant joint drives can further improve the performance of legged robot systems by considerably reducing the problems associated with uneven or slippery footholds. Small changes of the foot position in uneven terrain are compensated by the passive joint compliance without the need for fast contact detection and controller responses while the mechanical tension is reduced. On rougher terrain with bigger elevations/depressions of the surface structure, however, a reliable ground contact detection and stance height regulation for each leg is required to distribute the weight of the robot evenly among the legs on ground during stance phase. This work presents a concept that allows the inherently compliant hexapod robot HECTOR to walk on uneven terrain and to overcome moderate obstacles by means of a decentralized walking controller. An important prerequisite is the availability of inherently compliant joint drives with an increased power/weight-ratio.

Population based encodings allow to represent probabilistic and fuzzy state estimates. Such a representation will be introduced and applied for the case of a redundant manipulator. Following the Mean of Multiple Computations principle, a neural network model (PbMMC) is presented in which the overall complexity is divided into multiple local relationships. This allows to solve inverse, forward and mixed kinematic problems. The local transformations in between the kinematic variables can be sufficiently well learned by small single MLP layers. The population codes of the kinematic variables are based on nested periodic receptive fields which allow to express multiple weighted state estimates. Therefore, the model as such is quite flexible as it can keep track of multiple possible solutions at the same time.

While internal models are recruited in many tasks and can subserve in this way perception and cognition, it is important that they are grounded and embodied in sensorimotor representation. In this paper we analyze an internal model of the body and show how it can be used for motor control. We extend the Mean of Multiple Computation principle to a dual quaternion representation of transformation and show how this can be directly applied to the control of a simulated robot leg. The model is encoded as a recurrent neural network acting as an autoassociator that is able to solve any kinematic problem in an iterative fashion. We will analyze the convergence properties, especially when additional constraints (acting on the joint level) are introduced that restrict the attractor space.

While internal models are a prerequisite for higher-level function, they have to be grounded in lower-level function serving sensorimotor control. In this paper we introduce an internal body model for the control of a hexapod walker. The internal model deals with a highly complex robotic structure of 22 degrees of freedom and coordinates the single joint movements to achieve an overall stable and adaptive walking behavior. It is implemented as a hierarchical recurrent neural network consisting of different levels of abstraction which are tightly intertwined. We demonstrate the feasibility of the concept by applying the model to a simulated robot and show how the different levels of the body model interact and how this allows to scale the model even further. While the internal model is used in this context explicitly for motor control, it is also a predictive model and can be applied for sensor fusion. We discuss how in this way such an internal model offers the flexibility to be utilized in motor control and to be used for planning ahead by a cognitive expansion of the movement controller.

An internal model of the own body can be assumed to be a central and early representation as such a model is already required in simple behavioural tasks. More and more evidence is showing that such grounded internal models are applied in higher level tasks. Internal models appear to be recruited in service for cognitive function. Understanding what another person is doing seems to rely on the ability to step into the shoes of the other person and map the observed action onto ones own action system. This rules out dedicated and highly specialized models, but presupposes a flexible internal model which can be applied in different context and fulfilling different functions. Here, we are going to present a recurrent neural network approach of an internal body model. The model can be used in the context of movement control, e.g. in reaching tasks, but can also be employed as a predictor, e.g. for planning ahead. The introduced extension allows to integrate visual features into the kinematic model. Simulation results show how in this way the model can be to utilised in perception.

How is it possible for an autonomous agent to learn and retrieve hierarchically organized information? The question is particularly interesting if there is not a simple, tree-like hierarchy, but when low-level items may belong to several superordinate elements. In this article we propose a solution for this problem following the ideas of O'Connor et al., which are guided by the observation that children learn superordinate concepts from implicitly given information. For the simulation, we use a simple, one-layered RNN consisting of IC units and a very simple learning rule based on teacher forcing. We assume the capability of figure-ground separation as being given. Furthermore, the agent is assumed to owe sensory systems. There are, however, no explicit, preformulated concepts given like `Red'. Further, the agent is assumed to be able to record words. Each object presented to the agent is separately and individually learned and represented in the RNN forming an episodic memory. We show that, using this simple approach, learning and retrieval of hierarchically organized information is possible, although this information is not given explicitly and no hierarchical structure can be found in the network. Learning is very fast. The net shows top-down generalisation and bottom-up activation. Furthermore, asymmetric priming effects can be observed similar to those fond in human subjects. The agent is able to chunk different sensory inputs to represent the same object in memory, but nevertheless being able to distinguish between the different stimuli if, during learning, a supervisor labels the different stimuli with the same name.

Internal models are assumed to be a prerequisite for getting cognitive. In this article, I introduce a neural network approach for a model representing the kinematics of a complex manipulator which at the same time can be used for solving inverse and forward kinematic function. The Mean of Multiple Computation principle applied to a dual quaternion representation of transformations describing the manipulator is extendable to integrate into the model additional sensory information or information concerning the environment. It will be discussed how the body model presented may serve functions related to specific behaviours like targeted movements. But the model is suited to be applied in a more universal way. It can be used for planning ahead in a form of mental simulation for predictive purposes. The principle proposed can be applied to arbitrarily complex geometrical structures.

Walknet, a biological inspired neural network, has been proposed to control walking of a 6-legged; 18 DoF walker. Control of stance movement is difficult because all legs in stance are mechanically coupled. Based on the idea of velocity feedback, recently a specific revision, local positive velocity feedback, has been proposed to solve this problem using an extremely decentralised architecture. In this control scheme the locally measured joint velocity of an elastic joint is fed into the same joint in the next time step to maintain the movement. At the same time an additional part of the same joint controller observes the mechanical joint power to confine the positive feedback. In this paper, we show that this principle can actually be successfully applied to move a complete 6-legged system. This is tested using a dynamic simulation.

A cognitive control system for a walking robot should be able to solve from simple reactive tasks up to complex tasks, including tasks which need cognitive capabilities and setting up plans. Planning ahead involves some kind of internal representation: most important a model of the own body. Considering planning as mental simulation, this model must be fully functional: it is constrained in the same way as the body itself and it can move and be used in the same way as the body. This model can then be used to try out movements mentally without doing the action in reality. For this purpose it must be possible to decouple the body itself from the action controlling modules to use the original controllers for control of the internal representations. In this publication we introduce a hierarchical model, implemented as an recurrent neural network based on the MMC principle.

Advanced VR simulation systems are composed of several components with independent and heterogeneously structured databases. To guarantee a closed and consistent world simulation, flexible and robust data exchange between these components has to be realized. This multiple database problem is well known in many distributed application domains, but it is central for VR setups composed of diverse simulation components. Particularly complicated is the exchange between object-centered and graph-based representation formats, where entity attributes may be distributed over the graph structure. This article presents an abstract declarative attribute representation concept, which handles different representation formats uniformly and enables automatic data exchange and synchronization between them. This mechanism is tailored to support the integration of a central knowledge component, which provides a uniform representation of the accumulated knowledge of the several simulation components involved. This component handles the incoming-possibly conflicting-world changes propagated by the diverse components. It becomes the central instance for process flow synchronization of several autonomous evaluation loops.