We study planning in a fragment of PDDL with qualitative state-trajectory constraints, capturing safety requirements, task ordering conditions, and intermediate sub-goals commonly found in real-world problems. A prominent approach to tackle such problems is to compile their constraints away, leading to a problem that is supported by state-of-the-art planners. Unfortunately, existing compilers do not scale on problems with a large number of objects and high-arity actions, as they necessitate grounding the problem before compilation. To address this issue, we propose two methods for compiling away constraints without grounding, making them suitable for large-scale planning problems. We prove the correctness of our compilers and outline their worst-case time complexity. Moreover, we present a reproducible empirical evaluation on the domains used in the latest International Planning Competition. Our results demonstrate that our methods are efficient and produce planning specifications that are orders of magnitude more succinct than the ones produced by compilers that ground the domain, while remaining competitive when used for planning with a state-of-the-art planner.

A central challenge in building continually improving agents is that training environments are typically static or manually constructed. This restricts continual learning and generalization beyond the training distribution. We address this with COvolve, a co-evolutionary framework that leverages large language models (LLMs) to generate both environments and agent policies, expressed as executable Python code. We model the interaction between environment and policy designers as a two-player zero-sum game, ensuring adversarial co-evolution in which environments expose policy weaknesses and policies adapt in response. This process induces an automated curriculum in which environments and policies co-evolve toward increasing complexity. To guarantee robustness and prevent forgetting as the curriculum progresses, we compute the mixed-strategy Nash equilibrium (MSNE) of the zero-sum game, thereby yielding a meta-policy. This MSNE meta-policy ensures that the agent does not forget to solve previously seen environments while learning to solve previously unseen ones. Experiments in urban driving, symbolic maze-solving, and geometric navigation showcase that COvolve produces progressively more complex environments. Our results demonstrate the potential of LLM-driven co-evolution to achieve open-ended learning without predefined task distributions or manual intervention.

Designing effective reward functions is crucial to training reinforcement learning (RL) algorithms. However, this design is non-trivial, even for domain experts, due to the subjective nature of certain tasks that are hard to quantify explicitly. In recent works, large language models (LLMs) have been used for reward generation from natural language task descriptions, leveraging their extensive instruction tuning and commonsense understanding of human behavior. In this work, we hypothesize that LLMs, guided by human feedback, can be used to formulate reward functions that reflect human implicit knowledge. We study this in three challenging settings -- autonomous driving, humanoid locomotion, and dexterous manipulation -- wherein notions of ``good" behavior are tacit and hard to quantify. To this end, we introduce REvolve, a truly evolutionary framework that uses LLMs for reward design in RL. REvolve generates and refines reward functions by utilizing human feedback to guide the evolution process, effectively translating implicit human knowledge into explicit reward functions for training (deep) RL agents. Experimentally, we demonstrate that agents trained on REvolve-designed rewards outperform other state-of-the-art baselines.

A popular approach to neurosymbolic AI involves mapping logic formulas to arithmetic circuits (computation graphs consisting of sums and products) and passing the outputs of a neural network through these circuits. This approach enforces symbolic constraints onto a neural network in a principled and end-to-end differentiable way. Unfortunately, arithmetic circuits are challenging to run on modern tensor accelerators as they exhibit a high degree of irregular sparsity. To address this limitation, we introduce knowledge layers (KLay), a new data structure to represent arithmetic circuits that can be efficiently parallelized on GPUs. Moreover, we contribute two algorithms used in the translation of traditional circuit representations to KLay and a further algorithm that exploits parallelization opportunities during circuit evaluations. We empirically show that KLay achieves speedups of multiple orders of magnitude over the state of the art, thereby paving the way towards scaling neurosymbolic AI to larger real-world applications.

Owing to their reasoning capabilities, large language models (LLMs) have been evaluated on planning tasks described in natural language. However, LLMs have largely been tested on planning domains without constraints. In order to deploy them in real-world settings where adherence to constraints, in particular safety constraints, is critical, we need to evaluate their performance on constrained planning tasks. We introduce LexiCon—a natural language-based (Lexi) constrained (Con) planning benchmark, consisting of a suite of environments, that can be used to evaluate the planning capabilities of LLMs in a principled fashion. The core idea behind LexiCon is to take existing planning environments and impose temporal constraints on the states. These constrained problems are then translated into natural language and given to an LLM to solve. A key feature of LexiCon is its extensibility. That is, the set of supported environments can be extended with new (unconstrained) environment generators, for which temporal constraints are constructed automatically. This renders LexiCon future-proof: the hardness of the generated planning problems can be increased as the planning capabilities of LLMs improve. Our experiments reveal that the performance of state-of-the-art LLMs, including reasoning models like GPT-5, o3, and R1, deteriorates as the degree of constrainedness of the planning tasks increases.

By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.

Large Language Models (LLMs) have demonstrated impressive planning abilities due to their vast "world knowledge". Yet, obtaining plans that are both feasible (grounded in affordances) and cost-effective (in plan length), remains a challenge, despite recent progress. This contrasts with heuristic planning methods that employ domain knowledge (formalized in action models such as PDDL) and heuristic search to generate feasible, optimal plans. Inspired by this, we propose to combine the power of LLMs and heuristic planning by leveraging the world knowledge of LLMs and the principles of heuristic search. Our approach, SayCanPay, employs LLMs to generate actions (Say) guided by learnable domain knowledge, that evaluates actions' feasibility (Can) and long-term reward/payoff (Pay), and heuristic search to select the best sequence of actions. Our contributions are (1) a novel framing of the LLM planning problem in the context of heuristic planning, (2) integrating grounding and cost-effective elements into the generated plans, and (3) using heuristic search over actions. Our extensive evaluations show that our model surpasses other LLM planning approaches.

Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions. Nevertheless, tractability comes at a cost: PCs are less expressive than neural networks. In this paper we introduce probabilistic neural circuits (PNCs), which strike a balance between PCs and neural nets in terms of tractability and expressive power. Theoretically, we show that PNCs can be interpreted as deep mixtures of Bayesian networks. Experimentally, we demonstrate that PNCs constitute powerful function approximators.

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.

As illustrated by the success of integer linear programming, linear integer arithmetics is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate problems in neurosymbolic AI. However, two key problems persist that prevent the adoption of neurosymbolic techniques beyond toy problems. First, probabilistic inference is inherently hard, #P-hard to be precise. Second, the discrete nature of integers renders the construction of meaningful gradients challenging, which is problematic for learning. In order to mitigate these issues, we formulate linear arithmetics over integer-valued random variables as tensor manipulations that can be implemented in a straightforward fashion using modern deep learning libraries. At the core of our formulation lies the observation that the addition of two integer-valued random variables can be performed by adapting the fast Fourier transform to probabilities in the log-domain. By relying on tensor operations we obtain a differentiable data structure, which unlocks, virtually for free, gradient-based learning. In our experimental validation we show that tensorising probabilistic integer linear arithmetics and leveraging the fast Fourier transform allows us to push the state of the art by several orders of magnitude in terms of inference and learning times.

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.

Categorical random variables can faithfully represent the discrete and uncertain aspects of data as part of a discrete latent variable model. Learning in such models necessitates taking gradients with respect to the parameters of the categorical probability distributions, which is often intractable due to their combinatorial nature. A popular technique to estimate these otherwise intractable gradients is the Log-Derivative trick. This trick forms the basis of the well-known REINFORCE gradient estimator and its many extensions. While the Log-Derivative trick allows us to differentiate through samples drawn from categorical distributions, it does not take into account the discrete nature of the distribution itself. Our first contribution addresses this shortcoming by introducing the CatLog-Derivative trick -- a variation of the Log-Derivative trick tailored towards categorical distributions. Secondly, we use the CatLog-Derivative trick to introduce IndeCateR, a novel and unbiased gradient estimator for the important case of products of independent categorical distributions with provably lower variance than REINFORCE. Thirdly, we empirically show that IndeCateR can be efficiently implemented and that its gradient estimates have significantly lower bias and variance for the same number of samples compared to the state of the art.

Neural-symbolic AI (NeSy) allows neural networks to exploit symbolic background knowledge in the form of logic. It has been shown to aid learning in the limited data regime and to facilitate inference on out-of-distribution data. Probabilistic NeSy focuses on integrating neural networks with both logic and probability theory, which additionally allows learning under uncertainty. A major limitation of current probabilistic NeSy systems, such as DeepProbLog, is their restriction to finite probability distributions, i.e., discrete random variables. In contrast, deep probabilistic programming (DPP) excels in modelling and optimising continuous probability distributions. Hence, we introduce DeepSeaProbLog, a neural probabilistic logic programming language that incorporates DPP techniques into NeSy. Doing so results in the support of inference and learning of both discrete and continuous probability distributions under logical constraints. Our main contributions are 1) the semantics of DeepSeaProbLog and its corresponding inference algorithm, 2) a proven asymptotically unbiased learning algorithm, and 3) a series of experiments that illustrate the versatility of our approach.

An issue that has so far received only limited attention in probabilistic logic programming (PLP) is the modelling of so-called epistemic uncertainty, the uncertainty about the model itself. Accurately quantifying this model uncertainty is paramount to robust inference, learning and ultimately decision making. We introduce BetaProbLog, a PLP language that can model epistemic uncertainty. BetaProbLog has sound semantics, an effective inference algorithm that combines Monte Carlo techniques with knowledge compilation, and a parameter learning algorithm. We empirically outperform state-of-the-art methods on probabilistic inference tasks in second-order Bayesian networks, digit classification and discriminative learning in the presence of epistemic uncertainty.

Real world decision making problems often involve both discrete and continuous variables and require a combination of probabilistic and deterministic knowledge. Stimulated by recent advances in automated reasoning technology, hybrid (discrete+continuous) probabilistic reasoning with constraints has emerged as a lively and fast growing research field. In this paper we provide a survey of existing techniques for hybrid probabilistic inference with logic and algebraic constraints. We leverage weighted model integration as a unifying formalism and discuss the different paradigms that have been used as well as the expressivity-efficiency trade-offs that have been investigated. We conclude the survey with a comparative overview of existing implementations and a critical discussion of open challenges and promising research directions.

Modeling object representations derived from perceptual observations, in a way that is also semantically meaningful for humans as well as autonomous agents, is a prerequisite for joint human-agent understanding of the world. A practical approach that aims to model such representations is perceptual anchoring, which handles the problem of mapping sub-symbolic sensor data to symbols and maintains these mappings over time. In this paper, we present ProbAnch, a modular data-driven anchoring framework, whose implementation requires a variety of well-orchestrated components, including a probabilistic reasoning system.

State-of-the-art probabilistic inference algorithms, such as variable elimination and search-based approaches, rely heavily on the order in which variables are marginalized. Finding the optimal ordering is an NP-complete problem. This computational hardness has led to heuristics to find adequate variable orderings. However, these heuristics have mostly been targeting discrete random variables. We show how variable ordering heuristics from the discrete domain can be ported to the discrete-continuous domain. We equip the state-of-the-art F-XSDD(BR) solver for discrete-continuous problems with such heuristics. Additionally, we propose a novel heuristic called bottom-up min-fill (BU-MiF), yielding a solver capable of determining good variable orderings without having to rely on the user to provide such an ordering. We empirically demonstrate its performance on a set of benchmark problems.

Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

Weighted Model Integration (WMI) is a popular technique for probabilistic inference that extends Weighted Model Counting (WMC) -- the standard inference technique for inference in discrete domains -- to domains with both discrete and continuous variables. However, existing WMI solvers each have different interfaces and use different formats for representing WMI problems. Therefore, we introduce pywmi (http://pywmi.org), an open source framework and toolbox for probabilistic inference using WMI, to address these shortcomings. Crucially, pywmi fixes a common internal format for WMI problems and introduces a common interface for WMI solvers. To assist users in modeling WMI problems, pywmi introduces modeling languages based on SMT-LIB.v2 or MiniZinc and parsers for both. To assist users in comparing WMI solvers, pywmi includes implementations of several state-of-the-art solvers, a fast approximate WMI solver, and a command-line interface to solve WMI problems. Finally, to assist developers in implementing new solvers, pywmi provides Python implementations of commonly used subroutines.