Humans can leverage both symbolic reasoning and intuitive responses. In contrast, reinforcement learning policies are typically encoded in either opaque systems like neural networks or symbolic systems that rely on predefined symbols and rules. This disjointed approach severely limits the agents’ capabilities, as they often lack either the flexible low-level reaction characteristic of neural agents or the interpretable reasoning of symbolic agents. To overcome this challenge, we introduce *BlendRL*, a neuro-symbolic RL framework that harmoniously integrates both paradigms. We empirically demonstrate that BlendRL agents outperform both neural and symbolic baselines in standard Atari environments, and showcase their robustness to environmental changes. Additionally, we analyze the interaction between neural and symbolic policies, illustrating how their hybrid use helps agents overcome each other's limitations.

Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative dynamics of the system. As a result, new causal relationships may emerge, while existing ones change or disappear, resulting in an altered causal graph. To analyze these qualitative changes on the causal graph, we propose the concept of meta-causal states, which groups classical causal models into clusters based on equivalent qualitative behavior and consolidates specific mechanism parameterizations. We demonstrate how meta-causal states can be inferred from observed agent behavior, and discuss potential methods for disentangling these states from unlabeled data. Finally, we direct our analysis towards the application of a dynamical system, showing that meta-causal states can also emerge from inherent system dynamics, and thus constitute more than a context-dependent framework in which mechanisms emerge only as a result of external factors.

Recently, newly developed Vision-Language Models (VLMs), such as OpenAI’s o1, have emerged, seemingly demonstrating advanced reasoning capabilities across text and image modalities. However, the depth of these advances in language-guided perception and abstract reasoning remains underexplored, and it is unclear whether these models can truly live up to their ambitious promises. To assess the progress and identify shortcomings, we enter the wonderland of Bongard problems, a set of classic visual reasoning puzzles that require human-like abilities of pattern recognition and abstract reasoning. With our extensive evaluation setup, we show that while VLMs occasionally succeed in identifying discriminative concepts and solving some of the problems, they frequently falter. Surprisingly, even elementary concepts that may seem trivial to humans, such as simple spirals, pose significant challenges. Moreover, when explicitly asked to recognize ground truth concepts, they continue to falter, suggesting not only a lack of understanding of these elementary visual concepts but also an inability to generalize to unseen concepts. We compare the results of VLMs to human performance and observe that a significant gap remains between human visual reasoning capabilities and machine cognition.

Predicting agents impacted by legal policies, physical limitations, and operational preferences is inherently difficult. In recent years, neuro-symbolic methods have emerged, integrating machine learning and symbolic reasoning models into end-to-end learnable systems. Hereby, a promising avenue for expressing high-level constraints over multi-modal input data in robotics has opened up. This work introduces an approach for Bayesian estimation of agents expected to comply with a human-interpretable neuro-symbolic model we call its Constitution. Hence, we present the Constitutional Filter (CoFi), leading to improved tracking of agents by leveraging expert knowledge, incorporating deep learning architectures, and accounting for environmental uncertainties. CoFi extends the general, recursive Bayesian estimation setting, ensuring compatibility with a vast landscape of established techniques such as Particle Filters. To underpin the advantages of CoFi, we evaluate its performance on real-world marine traffic data. Beyond improved performance, we show how CoFi can learn to trust and adapt to the level of compliance of an agent, recovering baseline performance even if the assumed Constitution clashes with reality.

Gestalt principles, established in the 1920s, describe how humans perceive individual elements as cohesive wholes. These principles, including proximity, similarity, closure, continuity, and symmetry, play a fundamental role in human perception, enabling structured visual interpretation. Despite their significance, existing AI benchmarks fail to assess models’ ability to infer patterns at the group level, where multiple objects following the same Gestalt principle are considered as a group using these principles. To address this gap, we introduce Gestalt Vision, a diagnostic framework designed to evaluate AI models’ ability to not only identify groups within patterns but also reason about the underlying logical rules governing these patterns. Gestalt Vision provides structured visual tasks and baseline evaluations spanning neural, symbolic, and neural-symbolic approaches, uncovering key limitations in current models’ ability to perform human-like visual cognition. Our findings emphasize the necessity of incorporating richer perceptual mechanisms into AI reasoning frameworks. By bridging the gap between human perception and computational models, Gestalt Vision offers a crucial step toward developing AI systems with improved perceptual organization and visual reasoning capabilities.

Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable predictions. We introduce xLSTM-Mixer, a model designed to effectively integrate temporal sequences, joint time-variate information, and multiple perspectives for robust forecasting. Our approach begins with a linear forecast shared across variates, which is then refined by xLSTM blocks. They serve as key elements for modeling the complex dynamics of challenging time series data. xLSTM-Mixer ultimately reconciles two distinct views to produce the final forecast. Our extensive evaluations demonstrate its superior long-term forecasting performance compared to recent state-of-the-art methods while requiring very little memory. A thorough model analysis provides further insights into its key components and confirms its robustness and effectiveness. This work contributes to the resurgence of recurrent models in forecasting by combining them, for the first time, with mixing architectures.

Causality in time series can be challenging to determine, especially in the presence of non-linear dependencies. Granger causality helps analyze potential relationships between variables, thereby offering a method to determine whether one time series can predict—Granger cause—future values of another. Although successful, Granger causal methods still struggle with capturing long-range relations between variables. To this end, we leverage the recently successful Extended Long Short-Term Memory (xLSTM) architecture and propose Granger causal xLSTMs (GC-xLSTM). It first enforces sparsity between the time series components by using a novel dynamic loss penalty on the initial projection. Specifically, we adaptively improve the model and identify sparsity candidates. Our joint optimization procedure then ensures that the Granger causal relations are recovered robustly. Our experimental evaluation on six diverse datasets demonstrates the overall efficacy of GC-xLSTM.

Many causal inference frameworks rely on a staticity assumption, where repeated interventions are expected to yield consistent outcomes, often summarized by metrics like the Average Treatment Effect (ATE). This assumption, however, frequently fails in dynamic environments where interventions can alter the system's underlying causal structure, rendering traditional `static' ATE insufficient or misleading. Recent works on meta-causal models (MCM) offer a promising avenue by enabling qualitative reasoning over evolving relationships. In this work, we propose a specific class of MCM with desirable properties for explicitly modeling and predicting intervention outcomes under meta-causal dynamics, together with a first method for meta-causal analysis. Through expository examples in high-impact domains of medical treatment and judicial decision-making, we highlight the severe consequences that arise when system dynamics are neglected and demonstrate the successful application of meta-causal strategies to navigate these challenges.

Probabilistic circuits (PCs) enable us to learn joint distributions over a set of random variables and to perform various probabilistic queries in a tractable fashion. Though the tractability property allows PCs to scale beyond non-tractable models such as Bayesian Networks, scaling training and inference of PCs to larger, real-world datasets remains challenging. To remedy the situation, we show how PCs can be learned across multiple machines by recursively partitioning a distributed dataset, thereby unveiling a deep connection between PCs and federated learning (FL). This leads to federated circuits (FCs)—a novel and flexible federated learning (FL) framework that (1) allows one to scale PCs on distributed learning environments (2) train PCs faster and (3) unifies for the first time horizontal, vertical, and hybrid FL in one framework by re-framing FL as a density estimation problem over distributed datasets. We demonstrate FC’s capability to scale PCs on various large-scale datasets. Also, we show FC’s versatility in handling horizontal, vertical, and hybrid FL within a unified framework on multiple classification tasks.

Alarms are an essential part of distributed control systems designed to help plant operators keep the processes stable and safe. In reality, however, alarms are often noisy and thus can be easily overlooked. Early alarm prediction can give the operator more time to assess the situation and introduce corrective actions to avoid downtime and negative impact on human safety and environment. Existing studies on alarm prediction typically rely on signals directly coupled with these alarms. However, using more sources of information could benefit early prediction by letting the model learn characteristic patterns in the interactions of signals and events. Meanwhile, multimodal deep learning has recently seen impressive developments. Combination (or fusion) of modalities has been shown to be a key success factor, yet choosing the best fusion method for a given task introduces a new degree of complexity, in addition to existing architectural choices and hyperparameter tuning. This is one of the reasons why real-world problems are still typically tackled with unimodal approaches. To bridge this gap, we introduce a multimodal Transformer model for early alarm prediction based on a combination of recent events and signal data. The model learns the optimal representation of data from multiple fusion strategies automatically. The model is validated on real-world industrial data. We show that our model is capable of predicting alarms with the given horizon and that the proposed multimodal fusion method yields state-of-the-art predictive performance while eliminating the need to choose among conventional fusion techniques, thus reducing tuning costs and training time.

Distributed control systems (DCS) are essential to operate complex industrial processes. A major part of a DCS is the alarm system, which helps plant operators to keep the processes stable and safe. Alarms are defined as threshold values on individual signals taking into account minimum reaction time of the human operator. In reality, however, alarms are often noisy and overwhelming, and thus can be easily overlooked by the operators. Early alarm prediction can give the operator more time to react and introduce corrective actions to avoid downtime and negative impact on human safety and the environment. In this context, we introduce Alarm Prediction Transformer (APT), a multimodal Transformer-based machine learning model for early alarm prediction based on the combination of recent events and signal data. Specifically, we propose two novel fusion strategies and three methods of label encoding with various levels of granularity. Given a window of several minutes of event logs and signal data, our model predicts whether an alarm is going to be triggered after a few minutes and, if yes, it also predicts its location. Our experiments on two novel real industrial plant data sets and a simulated data set show that the model is capable of predicting alarms with the given horizon and that our proposed fusion technique combining inputs from different modalities, i. e. events and signals, yields more accurate results than any of the modalities alone or conventional fusion techniques. • Multimodal Transformers can successfully predict alarms in industrial settings. • Transformers can predict future alarms based on recent events and signal data. • The proposed hybrid fusion performs on par with or better than early or late fusion. • Granular alarm encoding yields more accurate prediction than the whole tag.

Tractable Probabilistic Models such as Sum-Product Networks are a powerful category of models that offer a rich choice of fast probabilistic queries. However, they are limited in the distributions they can represent, e.g., they cannot define distributions using loops or recursion. To move towards more complex distributions, we introduce a novel neurosymbolic programming language, Sum Product Loop Language (SPLL), along with the Neuro-Symbolic Transpiler (NeST). SPLL aims to build inference code most closely resembling Tractable Probabilistic Models. NeST is the first neuro-symbolic transpiler—a compiler from one high-level language to another. It generates inference code from SPLL but natively supports other computing platforms, too. This way, SPLL can seamlessly interface with e.g. pretrained (neural) models in PyTorch or Julia. The result is a language that can run probabilistic inference on more generalized distributions, reason on neural network outputs, and provide gradients for training.

Advanced Air Mobility (AAM) is a growing field that demands accurate and trustworthy models of legal concepts and restrictions for navigating Unmanned Aircraft Systems (UAS). In addition, any implementation of AAM needs to face the challenges posed by inherently dynamic and uncertain human-inhabited spaces robustly. Nevertheless, the employment of UAS beyond visual line of sight (BVLOS) is an endearing task that promises to significantly enhance today’s logistics and emergency response capabilities. Hence, we propose Probabilistic Mission Design (ProMis), a novel neuro-symbolic approach to navigating UAS within legal frameworks. ProMis is an interpretable and adaptable system architecture that links uncertain geospatial data and noisy perception with declarative, Hybrid Probabilistic Logic Programs (HPLP) to reason over the agent’s state space and its legality. To inform planning with legal restrictions and uncertainty in mind, ProMis yields Probabilistic Mission Landscapes (PML). These scalar fields quantify the belief that the HPLP is satisfied across the agent’s state space. Extending prior work on ProMis’ reasoning capabilities and computational characteristics, we show its integration with potent machine learning models such as Large Language Models (LLM) and Transformer-based vision models. Hence, our experiments underpin the application of ProMis with multi-modal input data and how our method applies to many AAM scenarios.

Structure learning is a crucial task in science, especially in fields such as medicine and biology, where the wrong identification of (in)dependencies among random variables can have significant implications. The primary objective of structure learning is to learn a Directed Acyclic Graph (DAG) that represents the underlying probability distribution of the data. Many prominent DAG learners rely on least square losses or log-likelihood losses for optimization. It is well-known from regression models that least square losses are heavily influenced by the scale of the variables. Recently it has been demonstrated that the scale of data also affects performance of structure learning algorithms, though with a strong focus on linear 2-node systems and simulated data. Moving beyond these results, we provide conditions under which square-based losses are minimal for wrong DAGs in $d$-dimensional cases. Furthermore, we also show that scale can impair performance of structure learners if relations among variables are non-linear for both square based and log-likelihood based losses. We confirm our theoretical findings through extensive experiments on synthetic and real-world data.

Large-scale, pre-trained neural networks have demonstrated strong capabilities in various tasks, including zero-shot image segmentation. To identify concrete objects in complex scenes, humans instinctively rely on deictic descriptions in natural language, i.e., referring to something depending on the context such as "The object that is on the desk and behind the cup.". However, deep learning approaches cannot reliably interpret such deictic representations due to their lack of reasoning capabilities in complex scenarios. To remedy this issue, we propose DeiSAM — a combination of large pre-trained neural networks with differentiable logic reasoners — for deictic promptable segmentation. Given a complex, textual segmentation description, DeiSAM leverages Large Language Models (LLMs) to generate first-order logic rules and performs differentiable forward reasoning on generated scene graphs. Subsequently, DeiSAM segments objects by matching them to the logically inferred image regions. As part of our evaluation, we propose the Deictic Visual Genome (DeiVG) dataset, containing paired visual input and complex, deictic textual prompts. Our empirical results demonstrate that DeiSAM is a substantial improvement over purely data-driven baselines for deictic promptable segmentation.

Graph Neural Networks (GNNs) are non-Euclidean deep learning models for graph-structured data. Despite their successful and diverse applications, oversmoothing prohibits deep architectures due to node features converging to a single fixed point. This severely limits their potential to solve complex tasks. To counteract this tendency, we propose a plug-and-play module consisting of three steps: Cluster→Normalize→Activate (CNA). By applying CNA modules, GNNs search and form super nodes in each layer, which are normalized and activated individually. We demonstrate in node classification and property prediction tasks that CNA significantly improves the accuracy over the state-of-the-art. Particularly, CNA reaches 94.18% and 95.75% accuracy on Cora and CiteSeer, respectively. It further benefits GNNs in regression tasks as well, reducing the mean squared error compared to all baselines. At the same time, GNNs with CNA require substantially fewer learnable parameters than competing architectures.

Causal inference in hybrid domains, characterized by a mixture of discrete and continuous variables, presents a formidable challenge. We take a step towards this direction and propose Characteristic Interventional Sum-Product Network ($\chi$SPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. $\chi$SPN uses characteristic functions in the leaves of an interventional SPN (iSPN) thereby providing a unified view for discrete and continuous random variables through the Fourier{–}Stieltjes transform of the probability measures. A neural network is used to estimate the parameters of the learned iSPN using the intervened data. Our experiments on 3 synthetic heterogeneous datasets suggest that $\chi$SPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that $\chi$SPN generalize to multiple interventions while being trained only on a single intervention data.

The challenge in learning abstract concepts from images in an unsupervised fashion lies in the required integration of visual perception and generalizable relational reasoning. Moreover, the unsupervised nature of this task makes it necessary for human users to be able to understand a model’s learned concepts and potentially revise false behaviors. To tackle both the generalizability and interpretability constraints of visual concept learning, we propose Pix2Code, a framework that extends program synthesis to visual relational reasoning by utilizing the abilities of both explicit, compositional symbolic and implicit neural representations. This is achieved by retrieving object representations from images and synthesizing relational concepts as $\lambda$-calculus programs. We evaluate the diverse properties of Pix2Code on the challenging reasoning domains, Kandinsky Patterns, and CURI, testing its ability to identify compositional visual concepts that generalize to novel data and concept configurations. Particularly, in stark contrast to neural approaches, we show that Pix2Code’s representations remain human interpretable and can easily be revised for improved performance.

Abstract Visual reasoning is essential for building intelligent agents that understand the world and perform problem-solving beyond perception. Differentiable forward reasoning has been developed to integrate reasoning with gradient-based machine learning paradigms. However, due to the memory intensity, most existing approaches do not bring the best of the expressivity of first-order logic, excluding a crucial ability to solve abstract visual reasoning, where agents need to perform reasoning by using analogies on abstract concepts in different scenarios. To overcome this problem, we propose NEUro-symbolic Message-pAssiNg reasoNer (NEUMANN), which is a graph-based differentiable forward reasoner, passing messages in a memory-efficient manner and handling structured programs with functors. Moreover, we propose a computationally-efficient structure learning algorithm to perform explanatory program induction on complex visual scenes. To evaluate, in addition to conventional visual reasoning tasks, we propose a new task, visual reasoning behind-the-scenes, where agents need to learn abstract programs and then answer queries by imagining scenes that are not observed. We empirically demonstrate that NEUMANN solves visual reasoning tasks efficiently, outperforming neural, symbolic, and neuro-symbolic baselines.

Abstract The recent years have been marked by extended research on adversarial attacks, especially on deep neural networks. With this work we intend on posing and investigating the question of whether the phenomenon might be more general in nature, that is, adversarial-style attacks outside classical classification tasks. Specifically, we investigate optimization problems as they constitute a fundamental part of modern AI research. To this end, we consider the base class of optimizers namely Linear Programs (LPs). On our initial attempt of a naïve mapping between the formalism of adversarial examples and LPs, we quickly identify the key ingredients missing for making sense of a reasonable notion of adversarial examples for LPs. Intriguingly, the formalism of Pearl’s notion to causality allows for the right description of adversarial like examples for LPs. Characteristically, we show the direct influence of the Structural Causal Model (SCM) onto the subsequent LP optimization, which ultimately exposes a notion of confounding in LPs (inherited by said SCM) that allows for adversarial-style attacks. We provide both the general proof formally alongside existential proofs of such intriguing LP-parameterizations based on SCM for three combinatorial problems, namely Linear Assignment, Shortest Path and a real world problem of energy systems.

Recent years have seen a growing interest in Scene Graph Generation (SGG), a comprehensive visual scene understanding task that aims to predict entity relationships using a relation encoder-decoder pipeline stacked on top of an object encoder-decoder backbone. Unfortunately, current SGG methods suffer from an information loss regarding the entities’ local-level cues during the relation encoding process. To mitigate this, we introduce the Vision rElation TransfOrmer (VETO), consisting of a novel local-level entity relation encoder. We further observe that many existing SGG methods claim to be unbiased, but are still biased towards either head or tail classes. To overcome this bias, we introduce a Mutually Exclusive ExperT (MEET) learning strategy that captures important relation features without bias towards head or tail classes. Experimental results on the VG and GQA datasets demonstrate that VETO + MEET boosts the predictive performance by up to 47% over the state of the art while being ∼ 10× smaller.1

The limited priors required by neural networks make them the dominating choice to encode and learn policies using reinforcement learning (RL). However, they are also black-boxes, making it hard to understand the agent's behavior, especially when working on the image level. Therefore, neuro-symbolic RL aims at creating policies that are interpretable in the first place. Unfortunately, interpretability is not explainability. To achieve both, we introduce Neurally gUided Differentiable loGic policiEs (NUDGE). NUDGE exploits trained neural network-based agents to guide the search of candidate-weighted logic rules, then uses differentiable logic to train the logic agents. Our experimental evaluation demonstrates that NUDGE agents can induce interpretable and explainable policies while outperforming purely neural ones and showing good flexibility to environments of different initial states and problem sizes.

Structural causal models (SCMs) are a powerful tool for understanding the complex causal relationships that underlie many real-world systems. As these systems grow in size, the number of variables and complexity of interactions between them does, too. Thus, becoming convoluted and difficult to analyze. This is particularly true in the context of machine learning and artificial intelligence, where an ever increasing amount of data demands for new methods to simplify and compress large scale SCM. While methods for marginalizing and abstracting SCM already exist today, they may destroy the causality of the marginalized model. To alleviate this, we introduce the concept of consolidating causal mechanisms to transform large-scale SCM while preserving consistent interventional behaviour. We show consolidation is a powerful method for simplifying SCM, discuss reduction of computational complexity and give a perspective on generalizing abilities of consolidated SCM.

The goal of combining the robustness of neural networks and the expressiveness of symbolic methods has rekindled the interest in Neuro-Symbolic AI. Deep Probabilistic Programming Languages (DPPLs) have been developed for probabilistic logic programming to be carried out via the probability estimations of deep neural networks (DNNs). However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end, we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logic program, united via answer set programming (ASP). NPPs are a novel design principle allowing for combining all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel +/− notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. To scale well, we show how to prune the stochastically insignificant parts of the (ground) program, speeding up reasoning without sacrificing the predictive performance. We evaluate SLASH on various tasks, including the benchmark task of MNIST addition and Visual Question Answering (VQA).

Abstract Deep neural learning has shown remarkable performance at learning representations for visual object categorization. However, deep neural networks such as CNNs do not explicitly encode objects and relations among them. This limits their success on tasks that require a deep logical understanding of visual scenes, such as Kandinsky patterns and Bongard problems. To overcome these limitations, we introduce $$\alpha {\textit{ILP}}$$ αILP , a novel differentiable inductive logic programming framework that learns to represent scenes as logic programs—intuitively, logical atoms correspond to objects, attributes, and relations, and clauses encode high-level scene information. $$\alpha$$ α ILP has an end-to-end reasoning architecture from visual inputs. Using it, $$\alpha$$ α ILP performs differentiable inductive logic programming on complex visual scenes, i.e., the logical rules are learned by gradient descent. Our extensive experiments onKandinsky patternsandCLEVR-Hansbenchmarks demonstrate the accuracy and efficiency of $$\alpha {\textit{ILP}}$$ αILP in learning complex visual-logical concepts.

Recent developments have shown that modeling in the spectral domain improves the accuracy in time series forecasting. However, state-of-the-art neural spectral forecasters do not generally yield trustworthy predictions. In particular, they lack the means to gauge predictive likelihoods and provide uncertainty estimates. We propose predictive Whittle networks to bridge this gap, which exploit both the advances of neural forecasting in the spectral domain and leverage tractable likelihoods of probabilistic circuits. For this purpose, we propose a novel Whittle forecasting loss that makes use of these predictive likelihoods to guide the training of the neural forecasting component. We demonstrate how predictive Whittle networks improve real-world forecasting accuracy, while also allowing a transformation back into the time domain, in order to provide the necessary feedback of when the model’s prediction may become erratic.

While Generative Adversarial Networks (GANs) have accelerated the use of generative modelling within the machine learning community, most of the adaptations of GANs are restricted to images. The use of GANs to generate clinical data has been rare due to the inability of GANs to faithfully capture the intrinsic relationships between features given a small amount of observational data. We hypothesize and verify that this challenge can be mitigated by incorporating rich domain knowledge in the form of expert advice in the generative process. Specifically, we propose human-allied GANs that uses correlation advice from humans to create synthetic clinical data. We construct a system that takes a symbolic representation of the expert advice and converts it into constraints on correlation of the features during the generative process. Our empirical evaluation demonstrates (a) the superiority of our approach over other GAN models, (b) the importance of incorporating advice over instance noise and (c) an initial framework for incorporation of privacy in our model while capturing the relationships between features.

While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed around personal health. Our empirical evaluation against competing methods from both generative and causal modelling demonstrates that interventional SPNs indeed are both expressive and causally adequate.

Counting the number of true instances of a clause is arguably a major bottleneck in relational probabilistic inference and learning. We approximate counts in two steps: (1) transform the fully grounded relational model to a large hypergraph, and partially-instantiated clauses to hypergraph motifs; (2) since the expected counts of the motifs are provably the clause counts, approximate them using summary statistics (in/outdegrees, edge counts, etc). Our experimental results demonstrate the efficiency of these approximations, which can be applied to many complex statistical relational models, and can be significantly faster than state-of-the-art, both for inference and learning, without sacrificing effectiveness.