Publications

Language models solve complex problems by articulating intermediate reasoning steps in natural language. While effective, this process is computationally bottlenecked: each reasoning step conveys only a single subword, and many are spent expressing a thought instead of carrying out computation. We propose MUX, a simple method for high-bandwidth and compact reasoning based on distillation of discrete reasoning into continuous multiplexed tokens in a latent space. Here, each latent token is trained to represent a weighted linear superposition (multiplexing) of a span of discrete reasoning subwords, where this superposition is lossless by construction and the span can be fully recovered (demultiplexing). We prove that simple position-dependent weightings, such as suitable geometric decay, support lossless multiplexing, which in turn prevents shortcut behaviors caused by latent collapse. We further show that multiplexed reasoning can perform parallel exploration in problems that require search. Across 32 evaluation settings spanning four language models, MUX outperforms strong latent reasoning baselines. Ablation and probing analyses further show that the learned latent tokens encode faithful and interpretable reasoning. Our results suggest that lossless superposition as local learning targets constitutes a sufficient condition for achieving strong and efficient latent continuous reasoning.

Relational learning is a challenging problem that has motivated a wide range of approaches, including graph-based models (e.g., graph neural networks, graph transformers), tabular methods (e.g., tabular foundation models), and sequence-based approaches (e.g., large language models), each with its own advantages and limitations. We propose RelAgent, an LLM-based autonomous data scientist for relational learning, which operates in two phases. In the search phase, an LLM agent uses database, validation, and evaluation workspace tools to construct SQL feature programs and select a predictive model. In the inference phase, the resulting program is executed without further LLM calls. The final predictor consists of SQL queries and a classical model, enabling fast, deterministic, and intrinsically interpretable predictions: features are human-readable queries, and predictions depend only on the resulting query-defined feature map, enabling scalable deployment using standard database systems.

Optimal-transport couplings have been shown to reduce training variance in unconditional flow models, but their role in conditional generation remains unclear. A natural approach constructs separate couplings for each condition, but this is impractical for large or continuous conditioning spaces found in modern image foundation models. We introduce Global Transport (GT), a global class-agnostic optimal-transport coupling, computed without class labels. GT can associate different conditions with different regions of the source noise, and consequently worsens performance without guidance. However, when combined with classifier-free guidance (CFG), GT consistently improves generation across domains, model scales, and sampling budgets. This reversal suggests that couplings for conditional flows should be evaluated both empirically and theoretically under the guided flow used at inference, rather than on unguided generation. We evaluate GT over both discrete class and continuous text conditioned image generation across model scales, and investigate how coupling choice alters guided trajectories. These results identify coupling design in the guided flow setting as a simple training time axis to improve performance without modifying existing architectures, samplers, or guidance mechanisms.

Graph foundation models aim to transfer across graphs, feature spaces, relational schemas, and prediction tasks, yet existing approaches typically generalize only within particular graph modalities or tasks. We propose Wander, a graph foundation model designed to operate across these settings within a single pretrained checkpoint. Following the prior-predictive perspective, we formulate graph learning as completion of a partially observed graph. We realize this task-general view through a common interface based on random walks, allowing the same model to operate across homogeneous and multi-relational graphs with varying features, labels, and relational schemas. Wander can increase its structural context at inference time without changing its learned parameters and, under suitable assumptions, universally approximates the corresponding Bayes-optimal predictor on bounded connected graphs. Empirically, a single pretrained checkpoint achieves state-of-the-art or highly competitive results across node classification, homogeneous link prediction, and knowledge-graph link prediction. Moreover, joint pretraining across graph modalities and tasks preserves performance in specialized settings while enabling positive transfer and the composition of separately learned capabilities at inference time.

Humans and machines often solve harder problems by spending more time on computation. In deep learning, looped models implement this idea during inference by recurrently updating a hidden state. In practice, however, their training backpropagates through only one or a few updates, making it hard to train early updates to support future ones. We propose looped flows, an approach that sidesteps this issue by training the recurrence with local denoising objectives. By imposing temporal association across denoising objectives through progressively decreasing noise levels and shared noise, the model is incentivized to learn recurrent states that transfer useful computation over time, even when gradients cover only a few updates. We then formulate inference as integrating the velocity of a probability flow parameterized by the learned denoiser, coupled with recurrent states. This allows solving harder problems by spending more computation through a finer temporal grid and enables multiple valid predictions from different initial noise samples. Across six reasoning benchmarks including two multi-solution benchmarks, looped flows outperform prior state-of-the-art looped models overall, achieving 58.8% test accuracy on ARC-AGI-1 and 12.2% on ARC-AGI-2.

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

Macrocycles are ring-shaped molecules that offer a promising alternative to small-molecule drugs due to their enhanced selectivity and binding affinity against difficult targets. Despite their chemical value, they remain underexplored in generative modeling, likely owing to their scarcity in public datasets and the challenges of enforcing topological constraints in standard deep generative models. We introduce MacroGuide: Topological Guidance for Macrocycle Generation, a diffusion guidance mechanism that uses Persistent Homology to steer the sampling of pretrained molecular generative models toward the generation of macrocycles, in both unconditional and conditional (protein pocket) settings. At each denoising step, MacroGuide constructs a Vietoris-Rips complex from atomic positions and promotes ring formation by optimizing persistent homology features. Empirically, applying MacroGuide to pretrained diffusion models increases macrocycle generation rates from 1% to 99%, while matching or exceeding state-of-the-art performance on key quality metrics such as chemical validity, diversity, and PoseBusters checks.

Formal theorem provers based on large language models (LLMs) are highly sensitive to superficial variations in problem representation: semantically equivalent statements can exhibit drastically different proof success rates, revealing a failure to respect structural symmetries inherent in formal mathematics. This raises a central question: what are the right symmetries for formal theorem proving? We introduce rewriting categories, a category-theoretic framework capturing the compositional, generally non-invertible transformations induced by proof tactics, and use it to formalize two symmetry notions: proof equivariance, governing how proof distributions transform under rewrites, and success invariance (i.e., invariance of success probability), requiring equivalent statements to be solved with the same probability. We observe that state-based next-tactic provers naturally satisfy proof equivariance by operating on proof states. In contrast, state-of-the-art LLM-based provers satisfy neither property, exhibiting large performance variation across equivalent formulations. To mitigate this, we propose test-time methods that aggregate over equivalent rewritings of the input, showing theoretically that they recover success invariance in the sampling limit, and empirically, that they improve robustness and performance under fixed inference budgets. Our results highlight symmetry as a key missing inductive bias in LLM-based theorem proving and suggest test-time computation as a practical route to approximate it.

We study the problem of zero-shot link prediction on knowledge graphs (KGs), which requires models to generalize to novel entities and novel relations. Knowledge graph foundation models (KGFMs) address this task by enforcing equivariance over both nodes and relations, which enables them to learn structural properties of nodes and relations that transfer to novel KGs with similar structure. However, the conventional notion of deterministic equivariance inherently limits the expressive power of KGFMs, as it prevents them from distinguishing relations that are structurally similar but semantically distinct. To overcome this limitation, we propose to leverage probabilistic node-relation equivariance, which preserves equivariance in distribution while using structured randomness to break symmetries at inference time. Building on this principle, we present Flock, a KGFM that iteratively samples random walks, encodes them into sequences, embeds them with a sequence model, and aggregates node and relation representations through learned pooling. Flock respects probabilistic node-relation equivariance and, crucially, is a universal approximator for isomorphism-invariant link-level functions over KGs. Empirically, Flock perfectly solves our new diagnostic dataset Petals on which current KGFMs fail, and achieves state-of-the-art performance on entity and relation prediction tasks across 54 KGs from diverse domains. Code is available at https://github.com/jw9730/flock.

Inductive link prediction with knowledge hypergraphs is the task of predicting missing hyperedges involving completely novel entities (i.e., nodes unseen during training). Existing methods for inductive link prediction with knowledge hypergraphs assume a fixed relational vocabulary and, as a result, cannot generalize to knowledge hypergraphs with novel relation types (i.e., relations unseen during training). Inspired by knowledge graph foundation models, we propose HYPER as a foundation model for link prediction, which can generalize to any knowledge hypergraph, including novel entities and novel relations. Importantly, HYPER can learn and transfer across different relation types of varying arities, by encoding the entities of each hyperedge along with their respective positions in the hyperedge. To evaluate HYPER, we construct 16 new inductive datasets from existing knowledge hypergraphs, covering a diverse range of relation types of varying arities. Empirically, HYPER consistently outperforms all existing methods in both node-only and node-and-relation inductive settings, showing strong generalization to unseen, higher-arity relational structures.

Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance. However, its standard formulation treats signals on structured spaces, such as fMRI data on brain graphs, as points in Euclidean space, overlooking the rich topological features of their domains. To address this, we introduce topological flow matching, a topology-aware generalization of flow matching. We interpret flow matching as a framework for solving a degenerate Schr\"odinger bridge problem and inject topological information by augmenting the reference process with a Laplacian-derived drift. This principled modification captures the structure of the underlying domain while preserving the desirable properties of flow matching: a stable, simulation-free objective and deterministic sample paths. As a result, our framework serves as a drop-in replacement for standard flow matching. We demonstrate its effectiveness on diverse structured datasets, including brain fMRIs, ocean currents, seismic events, and traffic flows.

Motivated by the incompleteness of modern knowledge graphs, a new setup for query answering has emerged, where the goal is to predict answers that do not necessarily appear in the knowledge graph, but are present in its completion. In this paper, we formally introduce and study two query answering problems, namely, query answer classification and query answer retrieval. To solve these problems, we propose AnyCQ, a model that can classify answers to any conjunctive query on any knowledge graph. At the core of our framework lies a graph neural network trained using a reinforcement learning objective to answer Boolean queries. Trained only on simple, small instances, AnyCQ generalizes to large queries of arbitrary structure, reliably classifying and retrieving answers to queries that existing approaches fail to handle. This is empirically validated through our newly proposed, challenging benchmarks. Finally, we empirically show that AnyCQ can effectively transfer to completely novel knowledge graphs when equipped with an appropriate link prediction model, highlighting its potential for querying incomplete data.

Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models capable of generalizing across arbitrary graphs and features? In this work, we present a recipe for designing graph foundation models for node-level tasks from first principles. The key ingredient underpinning our study is a systematic investigation of the symmetries that a graph foundation model must respect. In a nutshell, we argue that label permutation-equivariance alongside feature permutation-invariance are necessary in addition to the common node permutation-equivariance on each local neighborhood of the graph. To this end, we first characterize the space of linear transformations that are equivariant to permutations of nodes and labels, and invariant to permutations of features. We then prove that the resulting network is a universal approximator on multisets that respect the aforementioned symmetries. Our recipe uses such layers on the multiset of features induced by the local neighborhood of the graph to obtain a class of graph foundation models for node property prediction. We validate our approach through extensive experiments on 29 real-world node classification datasets, demonstrating both strong zero-shot empirical performance and consistent improvement as the number of training graphs increases.

Modeling the transport dynamics of natural processes from population-level observations is a ubiquitous problem in the natural sciences. Such models rely on key assumptions about the underlying process in order to enable faithful learning of governing dynamics that mimic the actual system behavior. The de facto assumption in current approaches relies on the principle of least action that results in gradient field dynamics and leads to trajectories minimizing an energy functional between two probability measures. However, many real-world systems, such as cell cycles in single-cell RNA, are known to exhibit non-gradient, periodic behavior, which fundamentally cannot be captured by current state-of-the-art methods such as flow and bridge matching. In this paper, we introduce Curly Flow Matching (Curly-FM), a novel approach that is capable of learning non-gradient field dynamics by designing and solving a Schr\"odinger bridge problem with a non-zero drift reference process -- in stark contrast to typical zero-drift reference processes -- which is constructed using inferred velocities in addition to population snapshot data. We showcase Curly-FM by solving the trajectory inference problems for single cells, computational fluid dynamics, and ocean currents with approximate velocities. We demonstrate that Curly-FM can learn trajectories that better match both the reference process and population marginals. Curly-FM expands flow matching models beyond the modeling of populations and towards the modeling of known periodic behavior in physical systems. Our code repository is accessible at: https://github.com/kpetrovicc/curly-flow-matching.git

Graph foundation models (GFMs) have recently emerged as a promising paradigm for achieving broad generalization across various graph data. However, existing GFMs are often trained on datasets that may not fully reflect real-world graphs, limiting their generalization performance. In contrast, tabular foundation models (TFMs) not only excel at classical tabular prediction tasks but have also shown strong applicability in other domains such as time series forecasting, natural language processing, and computer vision. Motivated by this, we take an alternative view to the standard perspective of GFMs and reformulate node classification as a tabular problem. In this reformulation, each node is represented as a row with feature, structure, and label information as columns, enabling TFMs to directly perform zero-shot node classification via in-context learning. In this work, we introduce TAG, a tabular approach for graph learning that first converts a graph into a table via feature and structural encoders, applies multiple TFMs to diversely subsampled tables, and then aggregates their outputs through ensemble selection. Experiments on 28 real-world datasets demonstrate that TAG consistently improves upon task-specific GNNs and state-of-the-art GFMs, highlighting the potential of the tabular reformulation for scalable and generalizable graph learning.

Knowledge Graph Foundation Models (KGFMs) are at the frontier for deep learning on knowledge graphs (KGs), as they can generalize to completely novel knowledge graphs with different relational vocabularies. Despite their empirical success, our theoretical understanding of KGFMs remains very limited. In this paper, we conduct a rigorous study of the expressive power of KGFMs. Specifically, we show that the expressive power of KGFMs directly depends on the motifs that are used to learn the relation representations. We then observe that the most typical motifs used in the existing literature are binary, as the representations are learned based on how pairs of relations interact, which limits the model's expressiveness. As part of our study, we design more expressive KGFMs using richer motifs, which necessitate learning relation representations based on, e.g., how triples of relations interact with each other. Finally, we empirically validate our theoretical findings, showing that the use of richer motifs results in better performance on a wide range of datasets drawn from different domains.

Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use of positional encodings (e.g., Laplacian positional encoding) or structural encodings (e.g., random-walk structural encoding). The quality of such encodings is critical, since they provide the necessary $\textit{graph inductive biases}$ to condition the model on graph structure. In this work, we propose $\textit{motif structural encoding}$ (MoSE) as a flexible and powerful structural encoding framework based on counting graph homomorphisms. Theoretically, we compare the expressive power of MoSE to random-walk structural encoding and relate both encodings to the expressive power of standard message passing neural networks. Empirically, we observe that MoSE outperforms other well-known positional and structural encodings across a range of architectures, and it achieves state-of-the-art performance on a widely studied molecular property prediction dataset.

Ontology-based data access is an extensively studied paradigm aiming at improving query answers with the use of an "ontology". An ontology is a specification of a domain of interest, which, in this context, is described via a logical theory. As a form of logical entailment, ontology-mediated query answering is fully interpretable, which makes it possible to derive explanations for ontological query answers. This is a quite important aspect, as the fact that many recent AI systems mostly operating as black boxes has led to some serious concerns. In the literature, various works on explanations in the context of description logics (DLs) have appeared, mostly focusing on explaining concept subsumption and concept unsatisfiability in the ontologies. Some works on explaining query entailment in DLs have appeared as well, however, mainly dealing with inconsistency-tolerant semantics and, actually, non-entailment of the queries. Surprisingly, explaining ontological query entailment has received little attention for ontology languages based on existential rules. In fact, although DLs are popular formalisms to model ontologies, it is generally agreed that rule-based ontologies are well-suited for data-intensive applications, as they allow us to conveniently deal with higher-arity relations, which naturally occur in standard relational databases. The goal of this work is to close this gap, and study the problem of explaining query entailment in the context of existential rules ontologies in terms of minimal subsets of database facts. We provide a thorough complexity analysis for several decision problems associated with minimal explanations for various classes of existential rules, and for different complexity measures.

Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the success of these architectures to relational hypergraphs, where the task of link prediction is over $k$-ary relations, which is substantially harder than link prediction with knowledge graphs. In this paper, we propose a framework for link prediction with relational hypergraphs, unlocking applications of graph neural networks to fully relational structures. Theoretically, we conduct a thorough analysis of the expressive power of the resulting model architectures via corresponding relational Weisfeiler-Leman algorithms and also via logical expressiveness. Empirically, we validate the power of the proposed model architectures on various relational hypergraph benchmarks. The resulting model architectures substantially outperform every baseline for inductive link prediction, and lead to state-of-the-art results for transductive link prediction.

We present a new angle on the expressive power of graph neural networks (GNNs) by studying how the predictions of real-valued GNN classifiers, such as those classifying graphs probabilistically, evolve as we apply them on larger graphs drawn from some random graph model. We show that the output converges to a constant function, which upper-bounds what these classifiers can uniformly express. This strong convergence phenomenon applies to a very wide class of GNNs, including state of the art models, with aggregates including mean and the attention-based mechanism of graph transformers. Our results apply to a broad class of random graph models, including sparse and dense variants of the Erd\H{o}s-R\'enyi model, the stochastic block model, and the Barab\'asi-Albert model. We empirically validate these findings, observing that the convergence phenomenon appears not only on random graphs but also on some real-world graphs.

Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm for discrete data is still autoregressive, with more recent alternatives based on diffusion or flow-matching falling short of their impressive performance in continuous data settings, such as image or video generation. In this work, we introduce Fisher-Flow, a novel flow-matching model for discrete data. Fisher-Flow takes a manifestly geometric perspective by considering categorical distributions over discrete data as points residing on a statistical manifold equipped with its natural Riemannian metric: the $\textit{Fisher-Rao metric}$. As a result, we demonstrate discrete data itself can be continuously reparameterised to points on the positive orthant of the $d$-hypersphere $\mathbb{S}^d_+$, which allows us to define flows that map any source distribution to target in a principled manner by transporting mass along (closed-form) geodesics of $\mathbb{S}^d_+$. Furthermore, the learned flows in Fisher-Flow can be further bootstrapped by leveraging Riemannian optimal transport leading to improved training dynamics. We prove that the gradient flow induced by Fisher-Flow is optimal in reducing the forward KL divergence. We evaluate Fisher-Flow on an array of synthetic and diverse real-world benchmarks, including designing DNA Promoter, and DNA Enhancer sequences. Empirically, we find that Fisher-Flow improves over prior diffusion and flow-matching models on these benchmarks.

Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node's representation in an input graph by aggregating messages from the node's neighbors, which necessitates a memory complexity of the order of the number of graph edges. This complexity might quickly become prohibitive for large graphs provided they are not very sparse. In this paper, we propose a novel approach to alleviate this problem by approximating the input graph as an intersecting community graph (ICG) -- a combination of intersecting cliques. The key insight is that the number of communities required to approximate a graph does not depend on the graph size. We develop a new constructive version of the Weak Graph Regularity Lemma to efficiently construct an approximating ICG for any input graph. We then devise an efficient graph learning algorithm operating directly on ICG in linear memory and time with respect to the number of nodes (rather than edges). This offers a new and fundamentally different pipeline for learning on very large non-sparse graphs, whose applicability is demonstrated empirically on node classification tasks and spatio-temporal data processing.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain patterns (e.g., cycles) in a graph lies at the heart of such limitations, since many functions to be learned rely on the ability of counting such patterns. Two prominent paradigms aim to address this limitation by enriching the graph features with subgraph or homomorphism pattern counts. In this work, we show that both of these approaches are sub-optimal in a certain sense and argue for a more fine-grained approach, which incorporates the homomorphism counts of all structures in the ``basis'' of the target pattern. This yields strictly more expressive architectures without incurring any additional overhead in terms of computational complexity compared to existing approaches. We prove a series of theoretical results on node-level and graph-level motif parameters and empirically validate them on standard benchmark datasets.

Graph neural networks are prominent models for representation learning over graphs, where the idea is to iteratively compute representations of nodes of an input graph through a series of transformations in such a way that the learned graph function is isomorphism invariant on graphs, which makes the learned representations graph invariants. On the other hand, it is well-known that graph invariants learned by these class of models are incomplete: there are pairs of non-isomorphic graphs which cannot be distinguished by standard graph neural networks. This is unsurprising given the computational difficulty of graph isomorphism testing on general graphs, but the situation begs to differ for special graph classes, for which efficient graph isomorphism testing algorithms are known, such as planar graphs. The goal of this work is to design architectures for efficiently learning complete invariants of planar graphs. Inspired by the classical planar graph isomorphism algorithm of Hopcroft and Tarjan, we propose PlanE as a framework for planar representation learning. PlanE includes architectures which can learn complete invariants over planar graphs while remaining practically scalable. We empirically validate the strong performance of the resulting model architectures on well-known planar graph benchmarks, achieving multiple state-of-the-art results.

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the context of knowledge graphs. Our goal is to provide a systematic understanding of the landscape of graph neural networks for knowledge graphs pertaining to the prominent task of link prediction. Our analysis entails a unifying perspective on seemingly unrelated models and unlocks a series of other models. The expressive power of various models is characterized via a corresponding relational Weisfeiler-Leman algorithm. This analysis is extended to provide a precise logical characterization of the class of functions captured by a class of graph neural networks. The theoretical findings presented in this paper explain the benefits of some widely employed practical design choices, which are validated empirically.

Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to information propagation bottlenecks, as information is repeatedly compressed at intermediary node representations, which causes loss of information, making it practically impossible to gather meaningful signals from distant nodes. To address this, we propose shortest path message passing neural networks, where the node representations of a graph are propagated to each node in the shortest path neighborhoods. In this setting, nodes can directly communicate between each other even if they are not neighbors, breaking the information bottleneck and hence leading to more adequately learned representations. Our framework generalizes message passing neural networks, resulting in a class of more expressive models, including some recent state-of-the-art models. We verify the capacity of a basic model of this framework on dedicated synthetic experiments, and on real-world graph classification and regression benchmarks, and obtain state-of-the art results.

Weighted model counting consists of computing the weighted sum of all satisfying assignments of a propositional formula. Weighted model counting is well-known to be #P-hard for exact solving, but admits a fully polynomial randomized approximation scheme when restricted to DNF structures. In this work, we study weighted model integration, a generalization of weighted model counting which involves real variables in addition to propositional variables, and pose the following question: Does weighted model integration on DNF structures admit a fully polynomial randomized approximation scheme? Building on classical results from approximate weighted model counting and approximate volume computation, we show that weighted model integration on DNF structures can indeed be approximated for a class of weight functions. Our approximation algorithm is based on three subroutines, each of which can be a weak (i.e., approximate), or a strong (i.e., exact) oracle, and in all cases, comes along with accuracy guarantees. We experimentally verify our approach over randomly generated DNF instances of varying sizes, and show that our algorithm scales to large problem instances, involving up to 1K variables, which are currently out of reach for existing, general-purpose weighted model integration solvers.

Knowledge graph completion is the task of inferring missing facts based on existing data in a knowledge graph. Temporal knowledge graph completion (TKGC) is an extension of this task to temporal knowledge graphs, where each fact is additionally associated with a time stamp. Current approaches for TKGC primarily build on existing embedding models which are developed for static knowledge graph completion, and extend these models to incorporate time, where the idea is to learn latent representations for entities, relations, and timestamps and then use the learned representations to predict missing facts at various time steps. In this paper, we propose BoxTE, a box embedding model for TKGC, building on the static knowledge graph embedding model BoxE. We show that BoxTE is fully expressive, and possesses strong inductive capacity in the temporal setting. We then empirically evaluate our model and show that it achieves state-of-the-art results on several TKGC benchmarks

Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman graph isomorphism heuristic. In order to break this expressiveness barrier, GNNs have been enhanced with random node initialization (RNI), where the idea is to train and run the models with randomized initial node features. In this work, we analyze the expressive power of GNNs with RNI, and prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties. This universality result holds even with partially randomized initial node features, and preserves the invariance properties of GNNs in expectation. We then empirically analyze the effect of RNI on GNNs, based on carefully constructed datasets. Our empirical findings support the superior performance of GNNs with RNI over standard GNNs.

Node classification and link prediction are widely studied in graph representation learning. While both transductive node classification and link prediction operate over a single input graph, they have so far been studied separately. Node classification models take an input graph with node features and incomplete node labels, and implicitly assume that the graph is relationally complete, i.e., no edges are missing. By contrast, link prediction models are solely motivated by relational incompleteness of the input graphs, and do not typically leverage node features or classes. We propose a unifying perspective and study the problems of (i) transductive node classification over incomplete graphs and (ii) link prediction over graphs with node features, introduce a new dataset for this setting, WikiAlumni, and conduct an extensive benchmarking study.

Recently, explanations for query answers under existential rules have been investigated, where an explanation is an inclusion-minimal subset of a given database that, together with the ontology, entails the query. In this paper, we take a step further and study explanations under different minimality criteria. In particular, we first study cardinality-minimal explanations and hence focus on deriving explanations of minimum size. We then study a more general preference order induced by a weight distribution. We assume that every database fact is annotated with a (penalization) weight, and we are interested in explanations with minimum overall weight. For both preference orders, we study a variety of explanation problems, such as recognizing a preferred explanation, all preferred explanations, a relevant or necessary fact, and the existence of a preferred explanation not containing forbidden sets of facts. We provide a detailed complexity analysis for all the aforementioned problems, thereby providing a more complete picture for explaining query answers under existential rules.

Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.

Ontology-mediated query answering is an extensively studied paradigm, where the conceptual knowledge provided by an ontology is leveraged towards more enhanced querying of data sources. A major advantage of ontological reasoning is its interpretability, which allows one to derive explanations for query answers. Indeed, explanations have a long history in knowledge representation, and have also been investigated for ontology languages based on description logics and existential rules. Existing works on existential rules, however, merely focus on understanding why a query is entailed, i.e., explaining positive query answers. In this paper, we continue this line of research and address another important problem, namely, explaining why a query is not entailed under existential rules, i.e., explaining negative query answers. We consider various problems related to explaining non-entailments from the abduction literature, and also introduce new problems. For all considered problems, we give a detailed complexity analysis for a wide range of existential rule languages and complexity measures.

Weighted model counting (WMC) consists of computing the weighted sum of all satisfying assignments of a propositional formula. WMC is well-known to be #P-hard for exact solving, but admits a fully polynomial randomised approximation scheme (FPRAS) when restricted to DNF structures. In this work, we study weighted model integration, a generalization of weighted model counting which involves real variables in addition to propositional variables, and pose the following question: Does weighted model integration on DNF structures admit an FPRAS? Building on classical results from approximate volume computation and approximate weighted model counting, we show that weighted model integration on DNF structures can indeed be approximated for a class of weight functions. Our approximation algorithm is based on three subroutines, each of which can be a weak (i.e., approximate), or a strong (i.e., exact) oracle, and in all cases, comes along with accuracy guarantees. We experimentally verify our approach over randomly generated DNF instances of varying sizes, and show that our algorithm scales to large problem instances, involving up to 1K variables, which are currently out of reach for existing, general-purpose weighted model integration solvers.

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.

Ontology-mediated query answering is an extensively studied paradigm, which aims at improving query answers with the use of a logical theory. As a form of logical entailment, ontology-mediated query answering is fully interpretable, which makes it possible to derive explanations for query answers. Surprisingly, however, explaining answers for ontology-mediated queries has received little attention for ontology languages based on existential rules. In this paper, we close this gap, and study the problem of explaining query answers in terms of minimal subsets of database facts. We provide a thorough complexity analysis for several decision problems associated with minimal explanations under existential rules.