Steffen Staab

Carlos Mougan, Klaus Broelemann, David Masip et al.

As input data distributions evolve, the predictive performance of machine learning models tends to deteriorate. In practice, new input data tend to come without target labels. Then, state-of-the-art techniques model input data distributions or model prediction distributions and try to understand issues regarding the interactions between learned models and shifting distributions. We suggest a novel approach that models how explanation characteristics shift when affected by distribution shifts. We find that the modeling of explanation shifts can be a better indicator for detecting out-of-distribution model behaviour than state-of-the-art techniques. We analyze different types of distribution shifts using synthetic examples and real-world data sets. We provide an algorithmic method that allows us to inspect the interaction between data set features and learned models and compare them to the state-of-the-art. We release our methods in an open-source Python package, as well as the code used to reproduce our experiments.

Jiaying Lu, Jiaming Shen, Bo Xiong et al. · deepmind

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.

Ratan Bahadur Thapa, Ali Darijani, Jürgen Beyerer et al.

Distributed uncertainty-management systems often combine local probabilistic models along aggregation trees chosen by communication, privacy, or scheduling constraints. The final density should depend on the weighted sources, not on the particular order in which intermediate nodes combine them. We study this requirement as an algebraic compositionality problem for binary fusion of weighted probability densities. The central question is when a local fusion rule can be executed hierarchically while remaining order-invariant. We establish a compositional boundary for local segment-valued fusion rules. Within the class of continuous binary rules with additive output weights and weight-only coefficients, order-invariant hierarchical execution characterizes normalized weighted linear pooling; norm-induced segment balancing realizes the corresponding coefficient. Smooth endpoint-to-candidate $f$-divergence balancing has a different local geometry: its quadratic expansion induces square-root effective weights, showing why pairwise solvability alone is insufficient for schedule-independent fusion. We show that this obstruction is local to endpoint-to-candidate binary balancing, whereas global divergence barycenters retain additive-weight local limits. Finally, Gaussian mixtures show how the same issue appears in finite model classes: exact fusion is compositional, whereas stepwise compression is compositional only under a congruence condition on unnormalized component measures. These results distinguish exact schedule-independent fusion from global aggregation objectives and local approximation heuristics.

Bo Xiong, Shichao Zhu, Mojtaba Nayyeri et al.

Recent knowledge graph (KG) embeddings have been advanced by hyperbolic geometry due to its superior capability for representing hierarchies. The topological structures of real-world KGs, however, are rather heterogeneous, i.e., a KG is composed of multiple distinct hierarchies and non-hierarchical graph structures. Therefore, a homogeneous (either Euclidean or hyperbolic) geometry is not sufficient for fairly representing such heterogeneous structures. To capture the topological heterogeneity of KGs, we present an ultrahyperbolic KG embedding (UltraE) in an ultrahyperbolic (or pseudo-Riemannian) manifold that seamlessly interleaves hyperbolic and spherical manifolds. In particular, we model each relation as a pseudo-orthogonal transformation that preserves the pseudo-Riemannian bilinear form. The pseudo-orthogonal transformation is decomposed into various operators (i.e., circular rotations, reflections and hyperbolic rotations), allowing for simultaneously modeling heterogeneous structures as well as complex relational patterns. Experimental results on three standard KGs show that UltraE outperforms previous Euclidean- and hyperbolic-based approaches.

Thomas Monninger, Julian Schmidt, Jan Rupprecht et al.

Understanding traffic scenes requires considering heterogeneous information about dynamic agents and the static infrastructure. In this work we propose SCENE, a methodology to encode diverse traffic scenes in heterogeneous graphs and to reason about these graphs using a heterogeneous Graph Neural Network encoder and task-specific decoders. The heterogeneous graphs, whose structures are defined by an ontology, consist of different nodes with type-specific node features and different relations with type-specific edge features. In order to exploit all the information given by these graphs, we propose to use cascaded layers of graph convolution. The result is an encoding of the scene. Task-specific decoders can be applied to predict desired attributes of the scene. Extensive evaluation on two diverse binary node classification tasks show the main strength of this methodology: despite being generic, it even manages to outperform task-specific baselines. The further application of our methodology to the task of node classification in various knowledge graphs shows its transferability to other domains.

Bo Xiong, Mojtaba Nayyer, Shirui Pan et al.

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.

Bo Xiong, Mojtaba Nayyeri, Ming Jin et al.

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.

Thomas Monninger, Andreas Weber, Steffen Staab

Understanding which traffic light controls which lane is crucial to navigate intersections safely. Autonomous vehicles commonly rely on High Definition (HD) maps that contain information about the assignment of traffic lights to lanes. The manual provisioning of this information is tedious, expensive, and not scalable. To remedy these issues, our novel approach derives the assignments from traffic light states and the corresponding motion patterns of vehicle traffic. This works in an automated way and independently of the geometric arrangement. We show the effectiveness of basic statistical approaches for this task by implementing and evaluating a pattern-based contribution method. In addition, our novel rejection method includes accompanying safety considerations by leveraging statistical hypothesis testing. Finally, we propose a dataset transformation to re-purpose available motion prediction datasets for semantic map learning. Our publicly available API for the Lyft Level 5 dataset enables researchers to develop and evaluate their own approaches.

Carlos Mougan, Klaus Broelemann, Gjergji Kasneci et al.

As input data distributions evolve, the predictive performance of machine learning models tends to deteriorate. In the past, predictive performance was considered the key indicator to monitor. However, explanation aspects have come to attention within the last years. In this work, we investigate how model predictive performance and model explanation characteristics are affected under distribution shifts and how these key indicators are related to each other for tabular data. We find that the modeling of explanation shifts can be a better indicator for the detection of predictive performance changes than state-of-the-art techniques based on representations of distribution shifts. We provide a mathematical analysis of different types of distribution shifts as well as synthetic experimental examples.

Carlos Mougan, Laura State, Antonio Ferrara et al.

Liberalism-oriented political philosophy reasons that all individuals should be treated equally independently of their protected characteristics. Related work in machine learning has translated the concept of \emph{equal treatment} into terms of \emph{equal outcome} and measured it as \emph{demographic parity} (also called \emph{statistical parity}). Our analysis reveals that the two concepts of equal outcome and equal treatment diverge; therefore, demographic parity does not faithfully represent the notion of \emph{equal treatment}. We propose a new formalization for equal treatment by (i) considering the influence of feature values on predictions, such as computed by Shapley values decomposing predictions across its features, (ii) defining distributions of explanations, and (iii) comparing explanation distributions between populations with different protected characteristics. We show the theoretical properties of our notion of equal treatment and devise a classifier two-sample test based on the AUC of an equal treatment inspector. We study our formalization of equal treatment on synthetic and natural data. We release \texttt{explanationspace}, an open-source Python package with methods and tutorials.

Cosimo Gregucci, Mojtaba Nayyeri, Daniel Hernández et al.

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 Poincaré 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.

Yunjie He, Mojtaba Nayyeri, Bo Xiong et al.

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.

Xuan Zhao, Simone Fabbrizzi, Paula Reyero Lobo et al.

The unequal representation of different groups in a sample population can lead to discrimination of minority groups when machine learning models make automated decisions. To address these issues, fairness-aware machine learning jointly optimizes two (or more) metrics aiming at predictive effectiveness and low unfairness. However, the inherent under-representation of minorities in the data makes the disparate treatment of subpopulations less noticeable and difficult to deal with during learning. In this paper, we propose a novel adversarial reweighting method to address such \emph{representation bias}. To balance the data distribution between the majority and the minority groups, our approach deemphasizes samples from the majority group. To minimize empirical risk, our method prefers samples from the majority group that are close to the minority group as evaluated by the Wasserstein distance. Our theoretical analysis shows the effectiveness of our adversarial reweighting approach. Experiments demonstrate that our approach mitigates bias without sacrificing classification accuracy, outperforming related state-of-the-art methods on image and tabular benchmark datasets.

Tim Schneider, Amin Totounferoush, Wolfgang Nowak et al.

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.

Thomas Monninger, Zihan Zhang, Steffen Staab et al.

Accurate environmental representations are essential for autonomous driving, providing the foundation for safe and efficient navigation. Traditionally, high-definition (HD) maps are providing this representation of the static road infrastructure to the autonomous system a priori. However, because the real world is constantly changing, such maps must be constructed online from on-board sensor data. Navigation-grade standard-definition (SD) maps are widely available, but their resolution is insufficient for direct deployment. Instead, they can be used as coarse prior to guide the online map construction process. We propose NavMapFusion, a diffusion-based framework that performs iterative denoising conditioned on high-fidelity sensor data and on low-fidelity navigation maps. This paper strives to answer: (1) How can coarse, potentially outdated navigation maps guide online map construction? (2) What advantages do diffusion models offer for map fusion? We demonstrate that diffusion-based map construction provides a robust framework for map fusion. Our key insight is that discrepancies between the prior map and online perception naturally correspond to noise within the diffusion process; consistent regions reinforce the map construction, whereas outdated segments are suppressed. On the nuScenes benchmark, NavMapFusion conditioned on coarse road lines from OpenStreetMap data reaches a 21.4% relative improvement on 100 m, and even stronger improvements on larger perception ranges, while maintaining real-time capabilities. By fusing low-fidelity priors with high-fidelity sensor data, the proposed method generates accurate and up-to-date environment representations, guiding towards safer and more reliable autonomous driving. The code is available at https://github.com/tmonnin/navmapfusion

Mojtaba Nayyeri, Zihao Wang, Mst. Mahfuja Akter et al.

Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for predicting novel structural knowledge. Few approaches have integrated learning and inference with both modalities and these existing ones could only partially exploit the interaction of structural and textual knowledge. In our approach, we build on existing strong representations of single modalities and we use hypercomplex algebra to represent both, (i), single-modality embedding as well as, (ii), the interaction between different modalities and their complementary means of knowledge representation. More specifically, we suggest Dihedron and Quaternion representations of 4D hypercomplex numbers to integrate four modalities namely structural knowledge graph embedding, word-level representations (e.g.\ Word2vec, Fasttext), sentence-level representations (Sentence transformer), and document-level representations (sentence transformer, Doc2vec). Our unified vector representation scores the plausibility of labelled edges via Hamilton and Dihedron products, thus modeling pairwise interactions between different modalities. Extensive experimental evaluation on standard benchmark datasets shows the superiority of our two new models using abundant textual information besides sparse structural knowledge to enhance performance in link prediction tasks.

Yuqicheng Zhu, Nico Potyka, Mojtaba Nayyeri et al.

Knowledge graph embedding (KGE) models are often used to predict missing links for knowledge graphs (KGs). However, multiple KG embeddings can perform almost equally well for link prediction yet give conflicting predictions for unseen queries. This phenomenon is termed \textit{predictive multiplicity} in the literature. It poses substantial risks for KGE-based applications in high-stake domains but has been overlooked in KGE research. We define predictive multiplicity in link prediction, introduce evaluation metrics and measure predictive multiplicity for representative KGE methods on commonly used benchmark datasets. Our empirical study reveals significant predictive multiplicity in link prediction, with $8\%$ to $39\%$ testing queries exhibiting conflicting predictions. We address this issue by leveraging voting methods from social choice theory, significantly mitigating conflicts by $66\%$ to $78\%$ in our experiments.

Dongzhuoran Zhou, Yuqicheng Zhu, Xiaxia Wang et al. · oxford

Large language models (LLMs) achieve strong results on knowledge graph question answering (KGQA), but most benchmarks assume complete knowledge graphs (KGs) where direct supporting triples exist. This reduces evaluation to shallow retrieval and overlooks the reality of incomplete KGs, where many facts are missing and answers must be inferred from existing facts. We bridge this gap by proposing a methodology for constructing benchmarks under KG incompleteness, which removes direct supporting triples while ensuring that alternative reasoning paths required to infer the answer remain. Experiments on benchmarks constructed using our methodology show that existing methods suffer consistent performance degradation under incompleteness, highlighting their limited reasoning ability. To overcome this limitation, we present the Adaptive Graph Reasoning Agent (GR-Agent). It first constructs an interactive environment from the KG, and then formalizes KGQA as agent environment interaction within this environment. GR-Agent operates over an action space comprising graph reasoning tools and maintains a memory of potential supporting reasoning evidence, including relevant relations and reasoning paths. Extensive experiments demonstrate that GR-Agent outperforms non-training baselines and performs comparably to training-based methods under both complete and incomplete settings.

Yunjie He, Daniel Hernandez, Mojtaba Nayyeri et al.

Query embedding approaches answer complex logical queries over incomplete knowledge graphs (KGs) by computing and operating on low-dimensional vector representations of entities, relations, and queries. However, current query embedding models heavily rely on excessively parameterized neural networks and cannot explain the knowledge learned from the graph. We propose a novel query embedding method, AConE, which explains the knowledge learned from the graph in the form of $SROI^-$ description logic axioms while being more parameter-efficient than most existing approaches. AConE associates queries to a $SROI^-$ description logic concept. Every $SROI^-$ concept is embedded as a cone in complex vector space, and each $SROI^-$ relation is embedded as a transformation that rotates and scales cones. We show theoretically that AConE can learn $SROI^-$ axioms, and defines an algebra whose operations correspond one to one to $SROI^-$ description logic concept constructs. Our empirical study on multiple query datasets shows that AConE achieves superior results over previous baselines with fewer parameters. Notably on the WN18RR dataset, AConE achieves significant improvement over baseline models. We provide comprehensive analyses showing that the capability to represent axioms positively impacts the results of query answering.

Yuqicheng Zhu, Nico Potyka, Bo Xiong et al.

Statistical information is ubiquitous but drawing valid conclusions from it is prohibitively hard. We explain how knowledge graph embeddings can be used to approximate probabilistic inference efficiently using the example of Statistical EL (SEL), a statistical extension of the lightweight Description Logic EL. We provide proofs for runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.

Daniel Frank, Decky Aspandi Latif, Michael Muehlebach et al.

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.

Yuqicheng Zhu, Nico Potyka, Jiarong Pan et al.

Knowledge graph embeddings (KGE) apply machine learning methods on knowledge graphs (KGs) to provide non-classical reasoning capabilities based on similarities and analogies. The learned KG embeddings are typically used to answer queries by ranking all potential answers, but rankings often lack a meaningful probabilistic interpretation - lower-ranked answers do not necessarily have a lower probability of being true. This limitation makes it difficult to quantify uncertainty of model's predictions, posing challenges for the application of KGE methods in high-stakes domains like medicine. We address this issue by applying the theory of conformal prediction that allows generating answer sets, which contain the correct answer with probabilistic guarantees. We explain how conformal prediction can be used to generate such answer sets for link prediction tasks. Our empirical evaluation on four benchmark datasets using six representative KGE methods validates that the generated answer sets satisfy the probabilistic guarantees given by the theory of conformal prediction. We also demonstrate that the generated answer sets often have a sensible size and that the size adapts well with respect to the difficulty of the query.

Anna-Maria Halacheva, Mojtaba Nayyeri, Steffen Staab

Attention mechanisms and Transformer architectures have revolutionized Natural Language Processing (NLP) by enabling exceptional modeling of long-range dependencies and capturing intricate linguistic patterns. However, their inherent reliance on linear operations in the form of matrix multiplications limits their ability to fully capture inter-token relationships on their own. We propose MöbiusAttention, a novel approach that integrates Möbius transformations within the attention mechanism of Transformer-based models. Möbius transformations are non-linear operations in spaces over complex numbers with the ability to map between various geometries. By incorporating these properties, MöbiusAttention empowers models to learn more intricate geometric relationships between tokens and capture a wider range of information through complex-valued weight vectors. We build and pre-train a BERT and a RoFormer version enhanced with MöbiusAttention, which we then finetune on the GLUE benchmark. We evaluate empirically our approach against the baseline BERT and RoFormer models on a range of downstream tasks. Our approach compares favorably against the baseline models, even with smaller number of parameters suggesting the enhanced expressivity of MöbiusAttention. This research paves the way for exploring the potential of Möbius transformations in the complex projective space to enhance the expressivity and performance of foundation models.

Yoav Kor Sade, Arvindh Arun, Rishi Puri et al.

GraphRAG conditions language models on subgraphs retrieved from knowledge graphs, encoded via message-passing GNNs. Because these encoders entangle node contributions through iterated neighborhood aggregation, there is no closed-form way to determine how much each retrieved entity influenced the encoder's output, and therefore no way to faithfully audit what structural evidence actually reached the model. We introduce Ex-GraphRAG, which replaces the GNN encoder with a Multivariate Graph Neural Additive Network (M-GNAN), an extension of additive graph models to high-dimensional embedding spaces that yields an exact decomposition of the encoder's output across individual nodes and feature groups, without post-hoc approximation. On STaRK-Prime, this auditable encoder matches black-box performance. Using it to audit evidence routing, we uncover a semantic-structural mismatch: the nodes that dominate the encoder's output are structurally disconnected in the retrieved subgraph, held together by low-attribution intermediaries whose removal degrades multi-hop QA by up to 28%. This mismatch, invisible to any opaque encoder, reveals that semantic importance and structural connectivity are governed by disjoint sets of nodes, with direct implications for retrieval pruning, context construction, and failure diagnosis in graph-augmented LLMs.

Etienne Hoffmann, Jan-Felix Klein, Sören Weindel et al.

While linear manufacturing relies on homogeneous materials and predefined process sequences, circular manufacturing reintroduces used products with heterogeneous and uncertain conditions. This shift demands manufacturing systems capable of handling variable product states, dynamically reconfigurable processes, and the integration of human and machine knowledge. Conventional manufacturing IT architectures, designed for stable structures and deterministic execution, are unable to meet these requirements, as they cannot adequately represent and manage the uniqueness of individual components at runtime. Following a design science methodology for developing a Cyber Physical Production System for circular manufacturing, we derive 14 requirements from five complementary perspectives. Based on these requirements, we design KAPPS, a knowledge-based architecture that uses an ontology-grounded knowledge graph as a unifying data backbone, combined with a semantic interface layer to enable consistent data and information integration, reasoning, and communication across heterogeneous systems and services, turning the knowledge graph from an integration layer into the factories authoritative write-time state. KAPPS incorporates modules for constraint enforcement and event-driven planning, enabling incremental adaptation of execution plans under uncertainty and human-machine knowledge exchange. The applicability of KAPPS is demonstrated through two implemented use cases: (i) Anomaly detection and learning through knowledge graph mediated services and (ii) runtime constraint enforcement in a modular conveyor system. Subsequently, the architecture is evaluated against the 14 requirements (ed. abstract shortened)

Ling Xin, Mojtaba Nayyeri, Zahra Makki Nayeri et al.

Structural knowledge graph foundation models aim to generalize reasoning to completely new graphs with unseen entities and relations. A key limitation of existing approaches like Ultra is their reliance on a single relational transformation (e.g., element-wise multiplication) in message passing, which can constrain expressiveness and fail to capture diverse relational and structural patterns exhibited on diverse graphs. In this paper, we propose Gamma, a novel foundation model that introduces multi-head geometric attention to knowledge graph reasoning. Gamma replaces the single relational transformation with multiple parallel ones, including real, complex, split-complex, and dual number based transformations, each designed to model different relational structures. A relational conditioned attention fusion mechanism then adaptively fuses them at link level via a lightweight gating with entropy regularization, allowing the model to robustly emphasize the most appropriate relational bias for each triple pattern. We present a full formalization of these algebraic message functions and discuss how their combination increases expressiveness beyond any single space. Comprehensive experiments on 56 diverse knowledge graphs demonstrate that Gamma consistently outperforms Ultra in zero-shot inductive link prediction, with a 5.5% improvement in mean reciprocal rank on the inductive benchmarks and a 4.4% improvement across all benchmarks, highlighting benefits from complementary geometric representations.

Ciheng Zhang, Decky Aspandi, Steffen Staab

World-wide-web, with the website and webpage as the main interface, facilitates the dissemination of important information. Hence it is crucial to optimize them for better user interaction, which is primarily done by analyzing users' behavior, especially users' eye-gaze locations. However, gathering these data is still considered to be labor and time intensive. In this work, we enable the development of automatic eye-gaze estimations given a website screenshots as the input. This is done by the curation of a unified dataset that consists of website screenshots, eye-gaze heatmap and website's layout information in the form of image and text masks. Our pre-processed dataset allows us to propose an effective deep learning-based model that leverages both image and text spatial location, which is combined through attention mechanism for effective eye-gaze prediction. In our experiment, we show the benefit of careful fine-tuning using our unified dataset to improve the accuracy of eye-gaze predictions. We further observe the capability of our model to focus on the targeted areas (images and text) to achieve high accuracy. Finally, the comparison with other alternatives shows the state-of-the-art result of our model establishing the benchmark for the eye-gaze prediction task.

Nadeem Nazer, Hongkuan Zhou, Lavdim Halilaj et al.

Recent vision language models (VLMs) like CLIP have demonstrated impressive anomaly detection performance under significant distribution shift by utilizing high-level semantic information through text prompts. However, these models often neglect fine-grained details, such as which kind of anomalies, like "hole", "cut", "scratch" that could provide more specific insight into the nature of anomalies. We argue that recognizing fine-grained anomaly types 1) enriches the representation of "abnormal" with structured semantics, narrowing the gap between coarse anomaly signals and fine-grained defect categories; 2) enables manufacturers to understand the root causes of the anomaly and implement more targeted and appropriate corrective measures quickly. While incorporating such detailed semantic information is crucial, designing handcrafted prompts for each defect type is both time-consuming and susceptible to human bias. For this reason, we introduce DAPO, a novel approach for Defect-aware Prompt Optimization based on progressive tuning for the zero-shot multi-type and binary anomaly detection and segmentation under distribution shifts. Our approach aligns anomaly-relevant image features with their corresponding text semantics by learning hybrid defect-aware prompts with both fixed textual anchors and learnable token embeddings. We conducted experiments on public benchmarks (MPDD, VisA, MVTec-AD, MAD, and Real-IAD) and an internal dataset. The results suggest that compared to the baseline models, DAPO achieves a 3.7% average improvement in AUROC and average precision metrics at the image level under distribution shift, and a 6.5% average improvement in localizing novel anomaly types under zero-shot settings.

Daniel Frank, Fahim Shakib, Steffen Staab

This paper presents a method that learns a regionally stable recurrent neural network model from a set of input-output data generated by an unknown dynamical system. Relying on generalized sector conditions on the deadzone activation function, we first derive sufficient conditions that guarantee forward invariance on a compact set of the state space for any inputs from a given set. Such regional properties lead to less conservative conditions compared to variants that offer a global form of stability, and are in line with the system data that is only observed regionally. Our learning method derives conditions for regional stability using a barrier function approach, leading to models equipped with a certificate of regional stability in a subset of the state space and for a given input set. We illustrate our theoretical result with a numerical example and compare it to methods that impose a global form of stability, which fail to identify the system, and with a method that imposes no stability constraints at all, which does not guarantee a stable behavior within any state or input set.

Luu Huu Phuc, Ratan Bahadur Thapa, Mojtaba Nayyeri et al.

We introduce Graph-Augmented Sequence-to-Sequence (GA-S2S), a novel framework that integrates a T5-small encoder-decoder with a Relational Graph Attention Network (RGAT) to improve link prediction in knowledge graphs. While existing Seq2Seq models rely solely on surface-level textual descriptions of entities and relations and at best, flatten the neighborhoods of a query entity into a single linear sequence, thereby discarding the inherent graph structure, GA-S2S jointly encodes both textual features and the full $k$-hop subgraph topology surrounding the query entity. By integrating raw encoder outputs with RGAT's relation-aware embeddings, our model captures and leverages richer multi-hop relational patterns and textual information. Our preliminary experiments on the CoDEx dataset demonstrate that GA-S2S outperforms competitive Seq2Seq-based baseline models, achieving up to a 19\% relative gain in link prediction accuracy.

Bo Xiong, Mojtaba Nayyeri, Linhao Luo et al.

Reasoning with knowledge graphs (KGs) has primarily focused on triple-shaped facts. Recent advancements have been explored to enhance the semantics of these facts by incorporating more potent representations, such as hyper-relational facts. However, these approaches are limited to \emph{atomic facts}, which describe a single piece of information. This paper extends beyond \emph{atomic facts} and delves into \emph{nested facts}, represented by quoted triples where subjects and objects are triples themselves (e.g., ((\emph{BarackObama}, \emph{holds\_position}, \emph{President}), \emph{succeed\_by}, (\emph{DonaldTrump}, \emph{holds\_position}, \emph{President}))). These nested facts enable the expression of complex semantics like \emph{situations} over time and \emph{logical patterns} over entities and relations. In response, we introduce NestE, a novel KG embedding approach that captures the semantics of both atomic and nested factual knowledge. NestE represents each atomic fact as a $1\times3$ matrix, and each nested relation is modeled as a $3\times3$ matrix that rotates the $1\times3$ atomic fact matrix through matrix multiplication. Each element of the matrix is represented as a complex number in the generalized 4D hypercomplex space, including (spherical) quaternions, hyperbolic quaternions, and split-quaternions. Through thorough analysis, we demonstrate the embedding's efficacy in capturing diverse logical patterns over nested facts, surpassing the confines of first-order logic-like expressions. Our experimental results showcase NestE's significant performance gains over current baselines in triple prediction and conditional link prediction. The code and pre-trained models are open available at https://github.com/xiongbo010/NestE.

Jingcheng Wu, Ratan Bahadur Thapa, Mojtaba Nayyeri et al.

Relational databases store much of the world's structured information, and they are essential for driving complex predictive applications. However, deep learning progress on relational data remains limited, as conventional approaches flatten databases into single tables via manual feature engineering, discarding relational context. Relational deep learning (RDL) addresses this by modeling databases as relational entity graphs (REGs) for graph neural networks (GNNs), but remains task- and database-specific. To combine the strengths of both paradigms, we propose a hybrid architecture combining a fine-tuned BART encoder to capture intra-row semantics with a GraphSAGE-based GNN over REGs to inject relational context. Experiments on RelBench show that the GNN substantially enriches BART's row embeddings, achieving a ROC-AUC of 67.40 on the driver-dnf task from the rel-f1 dataset. This performance is competitive with supervised baselines such as LightGBM (68.86) and narrows the gap to RDL (72.62) to within 5.22 points, though a substantial gap remains to state-of-the-art foundation models such as KumoRFM (82.63). These results suggest that lightweight hybrid LM-GNN architectures offer a promising and resource-efficient path towards foundation models for relational databases.

Xinyi Pan, Daniel Hernández, Philipp Seifer et al.

Over the past few years, we have seen the emergence of large knowledge graphs combining information from multiple sources. Sometimes, this information is provided in the form of assertions about other assertions, defining contexts where assertions are valid. A recent extension to RDF which admits statements over statements, called RDF-star, is in revision to become a W3C standard. However, there is no proposal for a semantics of these RDF-star statements nor a built-in facility to operate over them. In this paper, we propose a query language for epistemic RDF-star metadata based on a four-valued logic, called eSPARQL. Our proposed query language extends SPARQL-star, the query language for RDF-star, with a new type of FROM clause to facilitate operating with multiple and sometimes conflicting beliefs. We show that the proposed query language can express four use case queries, including the following features: (i) querying the belief of an individual, (ii) the aggregating of beliefs, (iii) querying who is conflicting with somebody, and (iv) beliefs about beliefs (i.e., nesting of beliefs).

Shashwat Goel, Nikhil Chandak, Arvindh Arun et al.

AI agents are being increasingly deployed in dynamic, open-ended environments that require adapting to new information as it arrives. To efficiently measure this capability for realistic use-cases, we propose building grounded simulations that replay real-world events in the order they occurred. We build FutureSim, where agents forecast world events beyond their knowledge cutoff while interacting with a chronological replay of the world: real news articles arriving and questions resolving over the simulated period. We evaluate frontier agents in their native harness, testing their ability to predict world events over a three-month period from January to March 2026. FutureSim reveals a clear separation in their capabilities, with the best agent's accuracy being 25%, and many having worse Brier skill score than making no prediction at all. Through careful ablations, we show how FutureSim offers a realistic setting to study emerging research directions like long-horizon test-time adaptation, search, memory, and reasoning about uncertainty. Overall, we hope our benchmark design paves the way to measure AI progress on open-ended adaptation spanning long time-horizons in the real world.

Ansgar Scherp, Thomas Franz, Carsten Saathoff et al.

The lack of a formal model of events hinders interoperability in distributed event-based systems. In this paper, we present a formal model of events, called Event-Model-F. The model is based on the foundational ontology DOLCE+DnS Ultralite (DUL) and provides comprehensive support to represent time and space, objects and persons, as well as mereological, causal, and correlative relationships between events. In addition, the Event-Model-F provides a flexible means for event composition, modeling event causality and event correlation, and representing different interpretations of the same event. The Event-Model-F is developed following the pattern-oriented approach of DUL, is modularized in different ontologies, and can be easily extended by domain specific ontologies.

Michael Mink, Thomas Monninger, Steffen Staab

In autonomous driving, High Definition (HD) maps provide a complete lane model that is not limited by sensor range and occlusions. However, the generation and upkeep of HD maps involves periodic data collection and human annotations, limiting scalability. To address this, we investigate automating the lane model generation and the use of sparse vehicle observations instead of dense sensor measurements. For our approach, a pre-processing step generates polylines by aligning and aggregating observed lane boundaries. Aligned driven traces are used as starting points for predicting lane pairs defined by the left and right boundary points. We propose Lane Model Transformer Network (LMT-Net), an encoder-decoder neural network architecture that performs polyline encoding and predicts lane pairs and their connectivity. A lane graph is formed by using predicted lane pairs as nodes and predicted lane connectivity as edges. We evaluate the performance of LMT-Net on an internal dataset that consists of multiple vehicle observations as well as human annotations as Ground Truth (GT). The evaluation shows promising results and demonstrates superior performance compared to the implemented baseline on both highway and non-highway Operational Design Domain (ODD).

Yi Wang, Corina Dima, Liangyu Zhong et al.

Cross-lingual biomedical entity linking (BEL) maps mentions in any language to unique identifiers in a biomedical knowledge base (KB), supporting clinical and biomedical NLP applications. However, expert-annotated training data for BEL are costly, especially for low-resource languages. Moreover, many cross-lingual BEL systems rely on SapBERT-based retrievers trained on predominantly English aliases in the KB, leading to poor generalization to unseen non-English mentions and limited context-aware disambiguation. We propose BioELX, a two-stage cross-lingual BEL framework that requires no task-specific annotated training corpora. In Stage~1, we enrich SapBERT training with Wikidata-derived multilingual aliases and use the resulting retriever to improve cross-lingual candidate retrieval. In Stage~2, we perform context-aware disambiguation with a pre-trained LLM ranker that jointly considers the mention context and candidate, eliminating the need for supervised training. Experiments on five benchmarks (XL-BEL, EMEA, Patent, WikiMed-DE, and MedMentions) show that BioELX achieves new state-of-the-art performance. It improves average Recall@1 on XL-BEL by +19.2, with especially large gains for low-resource languages, e.g., +21.6 on Turkish, +22.1 on Korean, +30.8 on Thai, and delivers consistent improvements on EMEA (+6.2), Patent (+5.4), and WikiMed-DE (+12.8). Code and resources will be released upon publication.

Jiaxin Pan, Mojtaba Nayyeri, Yinan Li et al.

Temporal knowledge graphs represent temporal facts $(s,p,o,τ)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $τ$, where $τ$ could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

Mehdi Azarafza, Mojtaba Nayyeri, Charles Steinmetz et al.

Large Language Models (LLMs) have garnered significant attention for their ability to understand text and images, generate human-like text, and perform complex reasoning tasks. However, their ability to generalize this advanced reasoning with a combination of natural language text for decision-making in dynamic situations requires further exploration. In this study, we investigate how well LLMs can adapt and apply a combination of arithmetic and common-sense reasoning, particularly in autonomous driving scenarios. We hypothesize that LLMs hybrid reasoning abilities can improve autonomous driving by enabling them to analyze detected object and sensor data, understand driving regulations and physical laws, and offer additional context. This addresses complex scenarios, like decisions in low visibility (due to weather conditions), where traditional methods might fall short. We evaluated Large Language Models (LLMs) based on accuracy by comparing their answers with human-generated ground truth inside CARLA. The results showed that when a combination of images (detected objects) and sensor data is fed into the LLM, it can offer precise information for brake and throttle control in autonomous vehicles across various weather conditions. This formulation and answers can assist in decision-making for auto-pilot systems.

Nadeen Fathallah, Steffen Staab, Alsayed Algergawy

Ontology learning in complex domains, such as life sciences, poses significant challenges for current Large Language Models (LLMs). Existing LLMs struggle to generate ontologies with multiple hierarchical levels, rich interconnections, and comprehensive class coverage due to constraints on the number of tokens they can generate and inadequate domain adaptation. To address these issues, we extend the NeOn-GPT pipeline for ontology learning using LLMs with advanced prompt engineering techniques and ontology reuse to enhance the generated ontologies' domain-specific reasoning and structural depth. Our work evaluates the capabilities of LLMs in ontology learning in the context of highly specialized and complex domains such as life science domains. To assess the logical consistency, completeness, and scalability of the generated ontologies, we use the AquaDiva ontology developed and used in the collaborative research center AquaDiva as a case study. Our evaluation shows the viability of LLMs for ontology learning in specialized domains, providing solutions to longstanding limitations in model performance and scalability.

Cosimo Gregucci, Bo Xiong, Daniel Hernandez et al.

Complex query answering (CQA) on knowledge graphs (KGs) is gaining momentum as a challenging reasoning task. In this paper, we show that the current benchmarks for CQA might not be as complex as we think, as the way they are built distorts our perception of progress in this field. For example, we find that in these benchmarks, most queries (up to 98% for some query types) can be reduced to simpler problems, e.g., link prediction, where only one link needs to be predicted. The performance of state-of-the-art CQA models decreases significantly when such models are evaluated on queries that cannot be reduced to easier types. Thus, we propose a set of more challenging benchmarks composed of queries that require models to reason over multiple hops and better reflect the construction of real-world KGs. In a systematic empirical investigation, the new benchmarks show that current methods leave much to be desired from current CQA methods.

Thomas Monninger, Vandana Dokkadi, Md Zafar Anwar et al.

Autonomous driving requires an accurate representation of the environment. A strategy toward high accuracy is to fuse data from several sensors. Learned Bird's-Eye View (BEV) encoders can achieve this by mapping data from individual sensors into one joint latent space. For cost-efficient camera-only systems, this provides an effective mechanism to fuse data from multiple cameras with different views. Accuracy can further be improved by aggregating sensor information over time. This is especially important in monocular camera systems to account for the lack of explicit depth and velocity measurements. Thereby, the effectiveness of developed BEV encoders crucially depends on the operators used to aggregate temporal information and on the used latent representation spaces. We analyze BEV encoders proposed in the literature and compare their effectiveness, quantifying the effects of aggregation operators and latent representations. While most existing approaches aggregate temporal information either in image or in BEV latent space, our analyses and performance comparisons suggest that these latent representations exhibit complementary strengths. Therefore, we develop a novel temporal BEV encoder, TempBEV, which integrates aggregated temporal information from both latent spaces. We consider subsequent image frames as stereo through time and leverage methods from optical flow estimation for temporal stereo encoding. Empirical evaluation on the NuScenes dataset shows a significant improvement by TempBEV over the baseline for 3D object detection and BEV segmentation. The ablation uncovers a strong synergy of joint temporal aggregation in the image and BEV latent space. These results indicate the overall effectiveness of our approach and make a strong case for aggregating temporal information in both image and BEV latent spaces.

Akshit Sinha, Arvindh Arun, Shashwat Goel et al.

Does continued scaling of large language models (LLMs) yield diminishing returns? In this work, we show that short-task benchmarks may give an illusion of slowing progress, as even marginal gains in single-step accuracy can compound into exponential improvements in the length of tasks a model can successfully complete. Then, we argue that failures of LLMs when simple tasks are made longer arise from mistakes in execution, rather than an inability to reason. So, we propose isolating execution capability, by explicitly providing the knowledge and plan needed to solve a long-horizon task. First, we find that larger models can correctly execute significantly more turns even when small models have near-perfect single-turn accuracy. We then observe that the per-step accuracy of models degrades as the number of steps increases. This is not just due to long-context limitations -- curiously, we observe a self-conditioning effect -- models become more likely to make mistakes when the context contains their errors from prior turns. Self-conditioning does not reduce by just scaling the model size. But, we find that thinking mitigates self-conditioning, and also enables execution of much longer tasks in a single turn. We conclude by benchmarking frontier thinking models on the length of tasks they can execute in a single turn. Overall, by focusing on the ability to execute, we hope to reconcile debates on how LLMs can solve complex reasoning problems yet fail at simple tasks when made longer, and highlight the massive benefits of scaling model size and sequential test-time compute for long-horizon tasks.

Nico Potyka, Yuqicheng Zhu, Yunjie He et al.

Large-language models (LLMs) can support a wide range of applications like conversational agents, creative writing or general query answering. However, they are ill-suited for query answering in high-stake domains like medicine because they are typically not robust - even the same query can result in different answers when prompted multiple times. In order to improve the robustness of LLM queries, we propose using ranking queries repeatedly and to aggregate the queries using methods from social choice theory. We study ranking queries in diagnostic settings like medical and fault diagnosis and discuss how the Partial Borda Choice function from the literature can be applied to merge multiple query results. We discuss some additional interesting properties in our setting and evaluate the robustness of our approach empirically.

Ylli Sadikaj, Hongkuan Zhou, Lavdim Halilaj et al.

Precise optical inspection in industrial applications is crucial for minimizing scrap rates and reducing the associated costs. Besides merely detecting if a product is anomalous or not, it is crucial to know the distinct type of defect, such as a bent, cut, or scratch. The ability to recognize the "exact" defect type enables automated treatments of the anomalies in modern production lines. Current methods are limited to solely detecting whether a product is defective or not without providing any insights on the defect type, nevertheless detecting and identifying multiple defects. We propose MultiADS, a zero-shot learning approach, able to perform Multi-type Anomaly Detection and Segmentation. The architecture of MultiADS comprises CLIP and extra linear layers to align the visual- and textual representation in a joint feature space. To the best of our knowledge, our proposal, is the first approach to perform a multi-type anomaly segmentation task in zero-shot learning. Contrary to the other baselines, our approach i) generates specific anomaly masks for each distinct defect type, ii) learns to distinguish defect types, and iii) simultaneously identifies multiple defect types present in an anomalous product. Additionally, our approach outperforms zero/few-shot learning SoTA methods on image-level and pixel-level anomaly detection and segmentation tasks on five commonly used datasets: MVTec-AD, Visa, MPDD, MAD and Real-IAD.

Yunjie He, Bo Xiong, Daniel Hernández et al.

Predicting answers to queries over knowledge graphs is called a complex reasoning task because answering a query requires subdividing it into subqueries. Existing query embedding methods use this decomposition to compute the embedding of a query as the combination of the embedding of the subqueries. This requirement limits the answerable queries to queries having a single free variable and being decomposable, which are called tree-form queries and correspond to the $\mathcal{SROI}^-$ description logic. In this paper, we define a more general set of queries, called DAG queries and formulated in the $\mathcal{ALCOIR}$ description logic, propose a query embedding method for them, called DAGE, and a new benchmark to evaluate query embeddings on them. Given the computational graph of a DAG query, DAGE combines the possibly multiple paths between two nodes into a single path with a trainable operator that represents the intersection of relations and learns DAG-DL from tautologies. We show that it is possible to implement DAGE on top of existing query embedding methods, and we empirically measure the improvement of our method over the results of vanilla methods evaluated in tree-form queries that approximate the DAG queries of our proposed benchmark.

Dongzhuoran Zhou, Yuqicheng Zhu, Xiaxia Wang et al. · oxford

Knowledge Graph based Retrieval-Augmented Generation (KG-RAG) is a technique that enhances Large Language Model (LLM) inference in tasks like Question Answering (QA) by retrieving relevant information from knowledge graphs (KGs). However, real-world KGs are often incomplete, meaning that essential information for answering questions may be missing. Existing benchmarks do not adequately capture the impact of KG incompleteness on KG-RAG performance. In this paper, we systematically evaluate KG-RAG methods under incomplete KGs by removing triples using different methods and analyzing the resulting effects. We demonstrate that KG-RAG methods are sensitive to KG incompleteness, highlighting the need for more robust approaches in realistic settings.

Mojtaba Nayyeri, Athish A Yogi, Nadeen Fathallah et al.

Transforming relational databases into knowledge graphs with enriched ontologies enhances semantic interoperability and unlocks advanced graph-based learning and reasoning over data. However, previous approaches either demand significant manual effort to derive an ontology from a database schema or produce only a basic ontology. We present RIGOR, Retrieval-augmented Iterative Generation of RDB Ontologies, an LLM-driven approach that turns relational schemas into rich OWL ontologies with minimal human effort. RIGOR combines three sources via RAG, the database schema and its documentation, a repository of domain ontologies, and a growing core ontology, to prompt a generative LLM for producing successive, provenance-tagged delta ontology fragments. Each fragment is refined by a judge-LLM before being merged into the core ontology, and the process iterates table-by-table following foreign key constraints until coverage is complete. Applied to real-world databases, our approach outputs ontologies that score highly on standard quality dimensions such as accuracy, completeness, conciseness, adaptability, clarity, and consistency, while substantially reducing manual effort.

Amin Totounferoush, Serge Kotchourko, Michael W. Mahoney et al.

Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning transferable representations across diverse domains. However, SciFMs require large amounts of solution data, which may be scarce or computationally expensive to generate. To maximize generalization while reducing data dependence, we propose incorporating PDE residuals into pre-training either as the sole learning signal or in combination with data loss to compensate for limited or infeasible training data. We evaluate this constraint-aware pre-training across three key benchmarks: (i) generalization to new physics, where material properties, e.g., the diffusion coefficient, is shifted with respect to the training distribution; (ii) generalization to entirely new PDEs, requiring adaptation to different operators; and (iii) robustness against noisy fine-tuning data, ensuring stability in real-world applications. Our results show that pre-training with PDE constraints significantly enhances generalization, outperforming models trained solely on solution data across all benchmarks. These findings prove the effectiveness of our proposed constraint-aware pre-training as a crucial component for SciFMs, providing a scalable approach to data-efficient, generalizable PDE solvers.

Philipp Seifer, Daniel Hernández, Ralf Lämmel et al.

SPARQL CONSTRUCT queries allow for the specification of data processing pipelines that transform given input graphs into new output graphs. It is now common to constrain graphs through SHACL shapes allowing users to understand which data they can expect and which not. However, it becomes challenging to understand what graph data can be expected at the end of a data processing pipeline without knowing the particular input data: Shape constraints on the input graph may affect the output graph, but may no longer apply literally, and new shapes may be imposed by the query template. In this paper, we study the derivation of shape constraints that hold on all possible output graphs of a given SPARQL CONSTRUCT query. We assume that the SPARQL CONSTRUCT query is fixed, e.g., being part of a program, whereas the input graphs adhere to input shape constraints but may otherwise vary over time and, thus, are mostly unknown. We study a fragment of SPARQL CONSTRUCT queries (SCCQ) and a fragment of SHACL (Simple SHACL). We formally define the problem of deriving the most restrictive set of Simple SHACL shapes that constrain the results from evaluating a SCCQ over any input graph restricted by a given set of Simple SHACL shapes. We propose and implement an algorithm that statically analyses input SHACL shapes and CONSTRUCT queries and prove its soundness and complexity.