To Örebro University

We consider a novel concept-learning and merging task, motivated by two use-cases. The first is about merging and compressing music playlists, and the second about federated learning with data privacy constraints. Both settings involve multiple learned concepts that must be merged and compressed into a single interpretable and accurate concept description. Our concept descriptions are logical formulae in CNF, for which merging, i.e. disjoining, multiple CNFs may lead to very large concept descriptions. To make the concepts interpretable, we compress them relative to a dataset. We propose a new method named CoWC (Compression Of Weighted Cnf) that approximates a CNF by exploiting techniques of itemset mining and inverse resolution. CoWC compresses the CNF size while also considering the F1-score w.r.t. the dataset. Our empirical evaluation shows that CoWC outperforms alternative compression approaches.

Large Language Models (LLMs) have been touted as AI models possessing advanced reasoning abilities. However, recent works have shown that LLMs often bypass true reasoning using shortcuts, sparking skepticism. To study the reasoning capabilities in a principled fashion, we adopt a computational theory perspective and propose an experimental protocol centered on 3-SAT – the prototypical NP-complete problem lying at the core of logical reasoning and constraint satisfaction tasks. Specifically, we examine the phase transitions in random 3-SAT and characterize the reasoning abilities of LLMs by varying the inherent hardness of the problem instances. Our experimental evidence shows that LLMs are incapable of performing true reasoning, as required for solving 3-SAT problems. Moreover, we observe significant performance variation based on the inherent hardness of the problems – performing poorly on harder instances and vice versa. Importantly ,we show that integrating external reasoners can considerably enhance LLM performance. By following a principled experimental protocol, our study draws concrete conclusions and moves beyond the anecdotal evidence often found in LLM reasoning research.

Probabilistic logic shields integrate deep reinforcement learning (RL) with probabilistic logic reasoning to train agents that operate in uncertain environments while giving strong guarantees with respect to logical constraints, such as safety properties. In this demo paper, we introduce a codebase that streamlines the design of custom MiniHack environments where neurosymbolic RL agents leverage probabilistic logic shields to learn safe and interpretable policies with strong guarantees. Our framework allows expert users to easily define and train agents that integrate deep neural policies with probabilistic logic in arbitrarily complex games: from simple exploration to planning and interacting with enemies. Additionally, we provide a web-based platform that showcases our application, offering an interactive interface for the broader community to experiment with and explore the capabilities of neurosymbolic reinforcement learning. This lowers the barrier for researchers and developers, making it accessible for a wider audience to engage with safety-critical RL scenarios.

Sequential problems are ubiquitous in AI, such as in reinforcement learning or natural language processing. State-of-the-art deep sequential models, like transformers, excel in these settings but fail to guarantee the satisfaction of constraints necessary for trustworthy deployment. In contrast, neurosymbolic AI (NeSy) provides a sound formalism to enforce constraints in deep probabilistic models but scales exponentially on sequential problems. To overcome these limitations, we introduce relational neurosymbolic Markov models (NeSy-MMs), a new class of end-to-end differentiable sequential models that integrate and provably satisfy relational logical constraints. We propose a strategy for inference and learning that scales on sequential settings, and that combines approximate Bayesian inference, automated reasoning, and gradient estimation. Our experiments show that NeSy-MMs can solve problems beyond the current state-of-the-art in neurosymbolic AI and still provide strong guarantees with respect to desired properties. Moreover, we show that our models are more interpretable and that constraints can be adapted at test time to out-of-distribution scenarios.

Code - https://github.com/ML-KULeuven/nesy-mm

Extended version - https://arxiv.org/abs/2412.13023

Algebraic model counting unifies many inference tasks on logic formulas by exploiting semirings. Rather than focusing on inference, we consider learning, especially in statistical-relational and neurosymbolic AI, which combine logical, probabilistic and neural representations. Concretely, we show that the very same semiring perspective of algebraic model counting also applies to learning. This allows us to unify various learning algorithms by generalizing gradients and backpropagation to different semirings. Furthermore, we show how cancellation and ordering properties of a semiring can be exploited for more memory-efficient backpropagation. This allows us to obtain some interesting variations of state-of-the-art gradient-based optimisation methods for probabilistic logical models. We also discuss why algebraic model counting on tractable circuits does not lead to more efficient second-order optimization. Empirically, our algebraic backpropagation exhibits considerable speed-ups as compared to existing approaches.

Code - https://github.com/ML-KULeuven/amc-grad

Recent developments in AI have reinvigorated pursuits to advance the (life) sciences using AI techniques, thereby creating a renewed opportunity to bridge different fields and find synergies. Headlines for AI and the life sciences have been dominated by data-driven techniques, for instance, to solve protein folding with next to no expert knowledge. In contrast to this, we argue for the necessity of a formal representation of expert knowledge -- either to develop explicit scientific theories or to compensate for the lack of data. Specifically, we argue that the fields of knowledge representation (KR) and systems biology (SysBio) exhibit important overlaps that have been largely ignored so far. This, in turn, means that relevant scientific questions are ready to be answered using the right domain knowledge (SysBio), encoded in the right way (SysBio/KR), and by combining it with modern automated reasoning tools (KR). Hence, the formal representation of domain knowledge is a natural meeting place for SysBio and KR. On the one hand, we argue that such an interdisciplinary approach will advance the field SysBio by exposing it to industrial-grade reasoning tools and thereby allowing novel scientific questions to be tackled. On the other hand, we see ample opportunities to move the state-of-the-art in KR by tailoring KR methods to the field of SysBio, which comes with challenging problem characteristics, e.g., scale, partial knowledge, noise, or sub-symbolic data. We stipulate that this proposed interdisciplinary research is necessary to attain a prominent long-term goal in the health sciences: precision medicine.

The integration of learning and reasoning is high on the research agenda in AI. Nevertheless, there is only a little attention to use existing background knowledge for reasoning about partially observed scenes to answer questions about the scene. Yet, we as humans use such knowledge frequently to infer plausible answers to visual questions (by eliminating all inconsistent ones). Such knowledge often comes in the form of constraints about objects and it tends to be highly domain or environment-specific. We contribute a novel benchmark called CLEVR-POC for reasoning-intensive visual question answering (VQA) in partially observable environments under constraints. In CLEVR-POC, knowledge in the form of logical constraints needs to be leveraged to generate plausible answers to questions about a hidden object in a given partial scene. For instance, if one has the knowledge that all cups are colored either red, green or blue and that there is only one green cup, it becomes possible to deduce the color of an occluded cup as either red or blue, provided that all other cups, including the green one, are observed. Through experiments, we observe that the low performance of pre-trained vision language models like CLIP (≈ 22%) and a large language model (LLM) like GPT-4 (≈ 46%) on CLEVR-POC ascertains the necessity for frameworks that can handle reasoning-intensive tasks where environment-specific background knowledge is available and crucial. Furthermore, our demonstration illustrates that a neuro-symbolic model, which integrates an LLM like GPT-4 with a visual perception network and a formal logical reasoner, exhibits exceptional performance on CLEVR-POC.

Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming languages owes much of its success to a declarative semantics, the so-called distribution semantics. However, the distribution semantics is limited to discrete random variables only. While PLP has been extended in various ways for supporting hybrid, that is, mixed discrete and continuous random variables, we are still lacking a declarative semantics for hybrid PLP that not only generalizes the distribution semantics and the modeling language but also the standard inference algorithm that is based on knowledge compilation. We contribute the measure semantics together with the hybrid PLP language DC-ProbLog (where DC stands for distributional clauses) and its inference engine infinitesimal algebraic likelihood weighting (IALW). These have the original distribution semantics, standard PLP languages such as ProbLog, and standard inference engines for PLP based on knowledge compilation as special cases. Thus, we generalize the state of the art of PLP towards hybrid PLP in three different aspects: semantics, language and inference. Furthermore, IALW is the first inference algorithm for hybrid probabilistic programming based on knowledge compilation.

This survey explores the integration of learning and reasoning in two different fields of artificial intelligence: neurosymbolic and statistical relational artificial intelligence. Neurosymbolic artificial intelligence (NeSy) studies the integration of symbolic reasoning and neural networks, while statistical relational artificial intelligence (StarAI) focuses on integrating logic with probabilistic graphical models. This survey identifies seven shared dimensions between these two subfields of AI. These dimensions can be used to characterize different NeSy and StarAI systems. They are concerned with (1) the approach to logical inference, whether model or proofbased; (2) the syntax of the used logical theories; (3) the logical semantics of the systems and their extensions to facilitate learning; (4) the scope of learning, encompassing either parameter or structure learning; (5) the presence of symbolic and subsymbolic representations; (6) the degree to which systems capture the original logic, probabilistic, and neural paradigms; and (7) the classes of learning tasks the systems are applied to. By positioning various NeSy and StarAI systems along these dimensions and pointing out similarities and differences between them, this survey contributes fundamental concepts for understanding the integration of learning and reasoning.

Decision making under uncertainty in dynamic environments is a fundamental AI problem in which agents need to determine which decisions (or actions) to make at each time step to maximise their expected utility. Dynamic decision networks (DDNs) are an extension of dynamic Bayesian networks with decisions and utilities, and can be used to compactly represent Markov decision processes (MDPs). We propose a novel algorithm called mapl-cirup that leverages knowledge compilation techniques developed for (dynamic) Bayesian networks to perform inference and gradient-based learning in DDNs. Specifically, we knowledge-compile the Bellman update present in DDNs into dynamic decision circuits and evaluate them within an (algebraic) model counting framework. In contrast to other exact symbolic MDP approaches, we obtain differentiable circuits that enable gradient-based parameter learning.