Pedro Zuidberg Dos Martires

Rishi Hazra, Pedro Zuidberg Dos Martires, Luc De Raedt

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.

Lennert De Smet, Pedro Zuidberg Dos Martires, Robin Manhaeve et al.

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.

Rishi Hazra, Gabriele Venturato, Pedro Zuidberg Dos Martires et al.

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.

Pedro Zuidberg Dos Martires, Luc De Raedt, Angelika Kimmig

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

Meraj Mammadov, Pedro Zuidberg Dos Martires, Johannes Andreas Stork

Imitation learning (IL) from a state-based reinforcement learning (RL) policy is a common approach to overcome the curse of dimensionality in complex and high-dimensional observation spaces prevalent in robotics. This paper addresses the irreducible imitation gap that emerges when teacher and student are learned in isolation, and the teacher policy has the liberty to rely on privileged state information that the student cannot infer from its observations. Instead of improving poor student performance with RL finetuning after IL, which often requires a whole new training setup, we propose a novel algorithm which learns a shared embedding space that hides agent-specific observations and thus trains imitable teacher policies by construction. We train the shared embedding space with self-supervised contrastive learning in parallel to the teacher policy and prevent it from extracting private information by limiting its gradients from updating the encoder networks. We perform evaluations on several example domains and compare to state-of-the-art baselines showing that our algorithm enables higher student performance with substantially reduced imitation gap.

Lennert De Smet, Emanuele Sansone, Pedro Zuidberg Dos Martires

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.

Finn Rietz, Pedro Zuidberg dos Martires, Johannes Andreas Stork

Incorporating demonstration data into reinforcement learning (RL) can greatly accelerate learning, but existing approaches often assume demonstrations are optimal and fully aligned with the target task. In practice, demonstrations are frequently sparse, suboptimal, or misaligned, which can degrade performance when these demonstrations are integrated into RL. We propose Adaptive Policy Composition (APC), a hierarchical model that adaptively composes multiple data-driven Normalizing Flow (NF) priors. Instead of enforcing strict adherence to the priors, APC estimates each prior's applicability to the target task while leveraging them for exploration. Moreover, APC either refines useful priors, or sidesteps misaligned ones when necessary to optimize downstream reward. Across diverse benchmarks, APC accelerates learning when demonstrations are aligned, remains robust under severe misalignment, and leverages suboptimal demonstrations to bootstrap exploration while avoiding performance degradation caused by overly strict adherence to suboptimal demonstrations.

Vincent Derkinderen, Pedro Zuidberg Dos Martires, Samuel Kolb et al.

Propositional model counting (#SAT) can be solved efficiently when the input formula is in deterministic decomposable negation normal form (d-DNNF). Translating an arbitrary formula into a representation that allows inference tasks, such as counting, to be performed efficiently, is called knowledge compilation. Top-down knowledge compilation is a state-of-the-art technique for solving #SAT problems that leverages the traces of exhaustive DPLL search to obtain d-DNNF representations. While knowledge compilation is well studied for propositional approaches, knowledge compilation for the (quantifier free) counting modulo theory setting (#SMT) has been studied to a much lesser degree. In this paper, we discuss compilation strategies for #SMT. We specifically advocate for a top-down compiler based on the traces of exhaustive DPLL(T) search.

Alkis Sygkounas, Rishi Hazra, Andreas Persson et al.

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.

Periklis Mantenoglou, Luigi Bonassi, Enrico Scala et al.

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.

Jaron Maene, Vincent Derkinderen, Pedro Zuidberg Dos Martires

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 AI 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.

Vincent Derkinderen, Robin Manhaeve, Pedro Zuidberg Dos Martires et al.

The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference and learning in probabilistic logic programs. While originally PLP focused on discrete probability, more recent approaches have incorporated continuous distributions as well as neural networks, effectively yielding neural-symbolic methods. We provide a unified algebraic perspective on PLP, showing that many if not most of the extensions of PLP can be cast within a common algebraic logic programming framework, in which facts are labeled with elements of a semiring and disjunction and conjunction are replaced by addition and multiplication. This does not only hold for the PLP variations itself but also for the underlying execution mechanism that is based on (algebraic) model counting.

Rishi Hazra, Gabriele Venturato, Pedro Zuidberg Dos Martires et al.

Large Language Models (LLMs) have been touted as AI models possessing advanced reasoning abilities. In theory, autoregressive LLMs with Chain-of-Thought (CoT) can perform more serial computations to solve complex reasoning tasks. However, recent studies suggest that, despite this capacity, LLMs do not truly learn to reason but instead fit on statistical features. 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 state-of-the-art LLMs by varying the inherent hardness of the problem instances. By comparing DeepSeek R1 with other LLMs, our findings reveal two key insights (1) LLM accuracy drops significantly on harder instances, suggesting all current models struggle when statistical shortcuts are unavailable (2) Unlike other LLMs, R1 shows signs of having learned the underlying reasoning. Following a principled experimental protocol, our study moves beyond the benchmark-driven evidence often found in LLM reasoning research. Our findings highlight important gaps and suggest clear directions for future research.

Pedro Zuidberg Dos Martires

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.

Lennert De Smet, Pedro Zuidberg Dos Martires

As illustrated by the success of integer linear programming, linear integer arithmetic 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 arithmetic 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 linear integer arithmetic 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.

Pedro Zuidberg Dos Martires

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.

Håkan Karlsson Faronius, Pedro Zuidberg Dos Martires

A popular approach to neurosymbolic AI is to take the output of the last layer of a neural network, e.g. a softmax activation, and pass it through a sparse computation graph encoding certain logical constraints one wishes to enforce. This induces a probability distribution over a set of random variables, which happen to be conditionally independent of each other in many commonly used neurosymbolic AI models. Such conditionally independent random variables have been deemed harmful as their presence has been observed to co-occur with a phenomenon dubbed deterministic bias, where systems learn to deterministically prefer one of the valid solutions from the solution space over the others. We provide evidence contesting this conclusion and show that the phenomenon of deterministic bias is an artifact of improperly applying neurosymbolic AI.

Periklis Mantenoglou, Rishi Hazra, Pedro Zuidberg Dos Martires et al.

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.

Matthias Möller, Arvid Norlander, Pedro Zuidberg Dos Martires et al.

Neurosymbolic (NeSy) AI studies the integration of neural networks (NNs) and symbolic reasoning based on logic. Usually, NeSy techniques focus on learning the neural, probabilistic and/or fuzzy parameters of NeSy models. Learning the symbolic or logical structure of such models has, so far, received less attention. We introduce neurosymbolic decision trees (NDTs), as an extension of decision trees together with a novel NeSy structure learning algorithm, which we dub NeuID3. NeuID3 adapts the standard top-down induction of decision tree algorithms and combines it with a neural probabilistic logic representation, inherited from the DeepProbLog family of models. The key advantage of learning NDTs with NeuID3 is the support of both symbolic and subsymbolic data (such as images), and that they can exploit background knowledge during the induction of the tree structure, In our experimental evaluation we demonstrate the benefits of NeSys structure learning over more traditonal approaches such as purely data-driven learning with neural networks.

Rishi Hazra, Alkis Sygkounas, Andreas Persson et al.

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.

Ivan Miosic, Pedro Zuidberg Dos Martires

Weighted model counting (WMC) is a popular framework to perform probabilistic inference with discrete random variables. Recently, WMC has been extended to weighted model integration (WMI) in order to additionally handle continuous variables. At their core, WMI problems consist of computing integrals and sums over weighted logical formulas. From a theoretical standpoint, WMI has been formulated by patching the sum over weighted formulas, which is already present in WMC, with Riemann integration. A more principled approach to integration, which is rooted in measure theory, is Lebesgue integration. Lebesgue integration allows one to treat discrete and continuous variables on equal footing in a principled fashion. We propose a theoretically sound measure theoretic formulation of weighted model integration, which naturally reduces to weighted model counting in the absence of continuous variables. Instead of regarding weighted model integration as an extension of weighted model counting, WMC emerges as a special case of WMI in our formulation.

Pedro Zuidberg Dos Martires, Nitesh Kumar, Andreas Persson et al.

Robotic agents should be able to learn from sub-symbolic sensor data, and at the same time, be able to reason about objects and communicate with humans on a symbolic level. This raises the question of how to overcome the gap between symbolic and sub-symbolic artificial intelligence. We propose a semantic world modeling approach based on bottom-up object anchoring using an object-centered representation of the world. Perceptual anchoring processes continuous perceptual sensor data and maintains a correspondence to a symbolic representation. We extend the definitions of anchoring to handle multi-modal probability distributions and we couple the resulting symbol anchoring system to a probabilistic logic reasoner for performing inference. Furthermore, we use statistical relational learning to enable the anchoring framework to learn symbolic knowledge in the form of a set of probabilistic logic rules of the world from noisy and sub-symbolic sensor input. The resulting framework, which combines perceptual anchoring and statistical relational learning, is able to maintain a semantic world model of all the objects that have been perceived over time, while still exploiting the expressiveness of logical rules to reason about the state of objects which are not directly observed through sensory input data. To validate our approach we demonstrate, on the one hand, the ability of our system to perform probabilistic reasoning over multi-modal probability distributions, and on the other hand, the learning of probabilistic logical rules from anchored objects produced by perceptual observations. The learned logical rules are, subsequently, used to assess our proposed probabilistic anchoring procedure. We demonstrate our system in a setting involving object interactions where object occlusions arise and where probabilistic inference is needed to correctly anchor objects.

Pedro Zuidberg Dos Martires, Samuel Kolb

Probabilistic inference in the hybrid domain, i.e. inference over discrete-continuous domains, requires tackling two well known #P-hard problems 1)~weighted model counting (WMC) over discrete variables and 2)~integration over continuous variables. For both of these problems inference techniques have been developed separately in order to manage their #P-hardness, such as knowledge compilation for WMC and Monte Carlo (MC) methods for (approximate) integration in the continuous domain. Weighted model integration (WMI), the extension of WMC to the hybrid domain, has been proposed as a formalism to study probabilistic inference over discrete and continuous variables alike. Recently developed WMI solvers have focused on exploiting structure in WMI problems, for which they rely on symbolic integration to find the primitive of an integrand, i.e. to perform anti-differentiation. To combine these advances with state-of-the-art Monte Carlo integration techniques, we introduce \textit{Monte Carlo anti-differentiation} (MCAD), which computes MC approximations of anti-derivatives. In our empirical evaluation we substitute the exact symbolic integration backend in an existing WMI solver with an MCAD backend. Our experiments show that that equipping existing WMI solvers with MCAD yields a fast yet reliable approximate inference scheme.

Ozan Arkan Can, Pedro Zuidberg Dos Martires, Andreas Persson et al.

Human-robot interaction often occurs in the form of instructions given from a human to a robot. For a robot to successfully follow instructions, a common representation of the world and objects in it should be shared between humans and the robot so that the instructions can be grounded. Achieving this representation can be done via learning, where both the world representation and the language grounding are learned simultaneously. However, in robotics this can be a difficult task due to the cost and scarcity of data. In this paper, we tackle the problem by separately learning the world representation of the robot and the language grounding. While this approach can address the challenges in getting sufficient data, it may give rise to inconsistencies between both learned components. Therefore, we further propose Bayesian learning to resolve such inconsistencies between the natural language grounding and a robot's world representation by exploiting spatio-relational information that is implicitly present in instructions given by a human. Moreover, we demonstrate the feasibility of our approach on a scenario involving a robotic arm in the physical world.

Andreas Persson, Pedro Zuidberg Dos Martires, Amy Loutfi et al.

This paper addresses the topic of semantic world modeling by conjoining probabilistic reasoning and object anchoring. The proposed approach uses a so-called bottom-up object anchoring method that relies on the rich continuous data from perceptual sensor data. A novel anchoring matching function method learns to maintain object entities in space and time and is validated using a large set of trained humanly annotated ground truth data of real-world objects. For more complex scenarios, a high-level probabilistic object tracker has been integrated with the anchoring framework and handles the tracking of occluded objects via reasoning about the state of unobserved objects. We demonstrate the performance of our integrated approach through scenarios such as the shell game scenario, where we illustrate how anchored objects are retained by preserving relations through probabilistic reasoning.

Pedro Zuidberg Dos Martires, Anton Dries, Luc De Raedt

In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs on either the inference on discrete or continuous random variables. We introduce a novel approach based on weighted model integration and algebraic model counting that circumvents these trade-offs. We then show how it supports knowledge compilation and exact probabilistic inference. Moreover, we introduce the hybrid probabilistic logic programming language HAL-ProbLog, an extension of ProbLog, to which we apply our inference approach.