Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of arbitrary strings. However, there is a mismatch between context-free grammars required to express the set of syntactically correct equations, missing closure properties of the former, and a tree structure of the latter. Our contributions are to (i) compactly express experts' prior beliefs about which equations are more likely to be expected by probabilistic Regular Tree Expressions (pRTE), and (ii) adapt Bayesian inference to make such priors efficiently available for symbolic regression encoded as finite state machines. Our scientific case studies show its effectiveness in soil science to find sorption isotherms and for modeling hyper-elastic materials.

Link prediction on knowledge graphs (KGs) has been extensively studied on binary relational KGs, wherein each fact is represented by a triple. A significant amount of important knowledge, however, is represented by hyper-relational facts where each fact is composed of a primal triple and a set of qualifiers comprising a key-value pair that allows for expressing more complicated semantics. Although some recent works have proposed to embed hyper-relational KGs, these methods fail to capture essential inference patterns of hyper-relational facts such as qualifier monotonicity, qualifier implication, and qualifier mutual exclusion, limiting their generalization capability. To unlock this, we present \emph{ShrinkE}, a geometric hyper-relational KG embedding method aiming to explicitly model these patterns. ShrinkE models the primal triple as a spatial-functional transformation from the head into a relation-specific box. Each qualifier ``shrinks'' the box to narrow down the possible answer set and, thus, realizes qualifier monotonicity. The spatial relationships between the qualifier boxes allow for modeling core inference patterns of qualifiers such as implication and mutual exclusion. Experimental results demonstrate ShrinkE's superiority on three benchmarks of hyper-relational KGs.

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions. Their preservation of relational structures and their appealing properties and interpretability have led to their uptake for tasks such as knowledge graph completion, ontology and hierarchy reasoning, logical query answering, and hierarchical multi-label classification. We survey methods that underly geometric relational embeddings and categorize them based on (i) the embedding geometries that are used to represent the data; and (ii) the relational reasoning tasks that they aim to improve. We identify the desired properties (i.e., inductive biases) of each kind of embedding and discuss some potential future work.

Medical decision-making processes can be enhanced by comprehensive biomedical knowledge bases, which require fusing knowledge graphs constructed from different sources via a uniform index system. The index system often organizes biomedical terms in a hierarchy to provide the aligned entities with fine-grained granularity. To address the challenge of scarce supervision in the biomedical knowledge fusion (BKF) task, researchers have proposed various unsupervised methods. However, these methods heavily rely on ad-hoc lexical and structural matching algorithms, which fail to capture the rich semantics conveyed by biomedical entities and terms. Recently, neural embedding models have proved effective in semantic-rich tasks, but they rely on sufficient labeled data to be adequately trained. To bridge the gap between the scarce-labeled BKF and neural embedding models, we propose HiPrompt, a supervision-efficient knowledge fusion framework that elicits the few-shot reasoning ability of large language models through hierarchy-oriented prompts. Empirical results on the collected KG-Hi-BKF benchmark datasets demonstrate the effectiveness of HiPrompt.

Answering first-order logical (FOL) queries over knowledge graphs (KG) remains a challenging task mainly due to KG incompleteness. Query embedding approaches this problem by computing the low-dimensional vector representations of entities, relations, and logical queries. KGs exhibit relational patterns such as symmetry and composition and modeling the patterns can further enhance the performance of query embedding models. However, the role of such patterns in answering FOL queries by query embedding models has not been yet studied in the literature. In this paper, we fill in this research gap and empower FOL queries reasoning with pattern inference by introducing an inductive bias that allows for learning relation patterns. To this end, we develop a novel query embedding method, RoConE, that defines query regions as geometric cones and algebraic query operators by rotations in complex space. RoConE combines the advantages of Cone as a well-specified geometric representation for query embedding, and also the rotation operator as a powerful algebraic operation for pattern inference. Our experimental results on several benchmark datasets confirm the advantage of relational patterns for enhancing logical query answering task.

Predicting missing links between entities in a knowledge graph is a fundamental task to deal with the incompleteness of data on the Web. Knowledge graph embeddings map nodes into a vector space to predict new links, scoring them according to geometric criteria. Relations in the graph may follow patterns that can be learned, e.g., some relations might be symmetric and others might be hierarchical. However, the learning capability of different embedding models varies for each pattern and, so far, no single model can learn all patterns equally well. In this paper, we combine the query representations from several models in a unified one to incorporate patterns that are independently captured by each model. Our combination uses attention to select the most suitable model to answer each query. The models are also mapped onto a non-Euclidean manifold, the Poincar\'e ball, to capture structural patterns, such as hierarchies, besides relational patterns, such as symmetry. We prove that our combination provides a higher expressiveness and inference power than each model on its own. As a result, the combined model can learn relational and structural patterns. We conduct extensive experimental analysis with various link prediction benchmarks showing that the combined model outperforms individual models, including state-of-the-art approaches.

Abstract--Understanding traffic scenes requires considering heterogeneous information about dynamic agents and the static infrastructure. Task-specific decoders can be applied to predict desired attributes of the scene. To this end, the vehicle needs to correctly estimate which sensory information is reliable I. NDERSTANDING traffic scenes is important for an autonomous vehicle such that it may develop a safe, agents is conveyed by the perception systems of autonomous effective and efficient plan of how to move forward. We raise the hypothesis that considering additional instance, whether a stationary car is parked or just temporarily heterogeneous entities in a traffic scene might add valuable stopped determines whether the autonomous vehicle should information. In particular, reasoning should also involve wait or overtake. Understanding of traffic scenes requires knowledge about static infrastructure, which may either be reasoning about dynamic agents and static infrastructure in perceived or in our case is provided by a High Definition order to predict the intents of nearby dynamic agents (e.g., (HD) map.

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this work, we represent a recurrent neural network as a linear time-invariant system with nonlinear disturbances. By introducing constraints on the parameters, we can guarantee finite gain stability and incremental finite gain stability. We apply this identification method to learn the motion of a four-degrees-of-freedom ship that is moving in open water and compare it against other purely learning-based approaches with unconstrained parameters. Our analysis shows that the constrained recurrent neural network has a lower prediction accuracy on the test set, but it achieves comparable results on an out-of-distribution set and respects stability conditions.

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds provide specific inductive biases for embedding hierarchical or spherical data. However, they cannot align well with data of mixed graph topologies. We consider a larger class of pseudo-Riemannian manifolds that generalize hyperboloid and sphere. We develop new geodesic tools that allow for extending neural network operations into geodesically disconnected pseudo-Riemannian manifolds. As a consequence, we derive a pseudo-Riemannian GCN that models data in pseudo-Riemannian manifolds of constant nonzero curvature in the context of graph neural networks. Our method provides a geometric inductive bias that is sufficiently flexible to model mixed heterogeneous topologies like hierarchical graphs with cycles. We demonstrate the representational capabilities of this method by applying it to the tasks of graph reconstruction, node classification and link prediction on a series of standard graphs with mixed topologies. Empirical results demonstrate that our method outperforms Riemannian counterparts when embedding graphs of complex topologies.

Physical motion models offer interpretable predictions for the motion of vehicles. However, some model parameters, such as those related to aero- and hydrodynamics, are expensive to measure and are often only roughly approximated reducing prediction accuracy. Recurrent neural networks achieve high prediction accuracy at low cost, as they can use cheap measurements collected during routine operation of the vehicle, but their results are hard to interpret. To precisely predict vehicle states without expensive measurements of physical parameters, we propose a hybrid approach combining deep learning and physical motion models including a novel two-phase training procedure. We achieve interpretability by restricting the output range of the deep neural network as part of the hybrid model, which limits the uncertainty introduced by the neural network to a known quantity. We have evaluated our approach for the use case of ship and quadcopter motion. The results show that our hybrid model can improve model interpretability with no decrease in accuracy compared to existing deep learning approaches.