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Vincent Derkinderen

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10 papers

2 author rows

IJCAI Conference 2025 Conference Paper

Circuit-Aware d-DNNF Compilation

Vincent Derkinderen
Jean-Marie Lagniez

Boolean circuits in d-DNNF (determinstic Decomposable Negation Normal Form) enable tractable probabilistic inference, motivating research into compilers that transform arbitrary Boolean circuit into this form. However, d-DNNF compilers commonly require the input to be in conjunctive normal form (CNF), which means that a user must first convert their Boolean circuit into CNF. In this work, we argue that d-DNNF compilation would substantially benefit from reasoning over the original input circuit's structure, rather than solely relying on its CNF representation. To this end, we adapt an existing compiler and implement an optimisation that becomes more readily available once we reason over the input circuit: the identification and elimination of don't care variables. We empirically demonstrate the effectiveness of this approach, achieving a significant improvement in both the number of solved instances and the size of the resulting circuits.

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ICLR Conference 2025 Conference Paper

KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI

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 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.

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NeurIPS Conference 2025 Conference Paper

Model Reconciliation via Cost-Optimal Explanations in Probabilistic Logic Programming

Yinxu Tang
Stylianos Loukas Vasileiou
Vincent Derkinderen
William Yeoh

In human-AI interaction, effective communication relies on aligning the AI agent’s model with the human user’s mental model, a process known as model reconciliation. However, existing model reconciliation approaches predominantly assume deterministic models, overlooking the fact that human knowledge is often uncertain or probabilistic. To bridge this gap, we present a probabilistic model reconciliation framework that resolves inconsistencies in MPE outcome probabilities between an agent’s and a user’s models. Our approach is built on probabilistic logic programming (PLP) using ProbLog, where explanations are generated as cost-optimal model updates that reconcile these probabilistic differences. We develop two search algorithms -- a generic baseline and an optimized version. The latter is guided by theoretical insights and further extended with greedy and weighted variants to enhance scalability and efficiency. Our approach is validated through a user study on explanation types and computational experiments showing that the optimized version consistently outperforms the generic baseline.

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KR Conference 2024 Conference Paper

Automated Reasoning in Systems Biology: A Necessity for Precision Medicine

Pedro Zuidberg Dos Martires
Vincent Derkinderen
Luc De Raedt
Marcus Krantz

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.

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AAAI Conference 2024 Conference Paper

Inference and Learning in Dynamic Decision Networks Using Knowledge Compilation

Gabriele Venturato
Vincent Derkinderen
Pedro Zuidberg Dos Martires
Luc De Raedt

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. DDNs 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.

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ICML Conference 2024 Conference Paper

On the Hardness of Probabilistic Neurosymbolic Learning

Jaron Maene
Vincent Derkinderen
Luc De Raedt

The limitations of purely neural learning have sparked an interest in probabilistic neurosymbolic models, which combine neural networks with probabilistic logical reasoning. As these neurosymbolic models are trained with gradient descent, we study the complexity of differentiating probabilistic reasoning. We prove that although approximating these gradients is intractable in general, it becomes tractable during training. Furthermore, we introduce WeightME, an unbiased gradient estimator based on model sampling. Under mild assumptions, WeightME approximates the gradient with probabilistic guarantees using a logarithmic number of calls to a SAT solver. Lastly, we evaluate the necessity of these guarantees on the gradient. Our experiments indicate that the existing biased approximations indeed struggle to optimize even when exact solving is still feasible.

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AAAI Conference 2022 Conference Paper

Inference and Learning with Model Uncertainty in Probabilistic Logic Programs

Victor Verreet
Vincent Derkinderen
Pedro Zuidberg Dos Martires
Luc De Raedt

An issue that has so far received only limited attention in probabilistic logic programming (PLP) is the modeling 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.

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AAAI Conference 2021 Conference Paper

Symmetric Component Caching for Model Counting on Combinatorial Instances

Timothy van Bremen
Vincent Derkinderen
Shubham Sharma
Subhajit Roy
Kuldeep S. Meel

Given a propositional formula ψ, the model counting problem, also referred to as #SAT, seeks to compute the number of satisfying assignments (or models) of ψ. Modern search-based model counting algorithms are built on conflict-driven clause learning, combined with the caching of certain subformulas (called components) encountered during the search process. Despite significant progress in these algorithms over the years, state-of-the-art model counters often struggle to handle large but structured instances that typically arise in combinatorial settings. Motivated by the observation that these counters do not exploit the inherent symmetries exhibited in such instances, we revisit the component caching architecture employed in current counters and introduce a novel caching scheme that focuses on identifying symmetric components. We first prove the soundness of our approach, and then integrate it into the stateof-the-art model counter GANAK. Our extensive experiments on hard combinatorial instances demonstrate that the resulting counter, SYMGANAK, leads to improvements over GANAK both in terms of PAR-2 score and the number of instances solved.

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ECAI Conference 2020 Conference Paper

Algebraic Circuits for Decision Theoretic Inference and Learning

Vincent Derkinderen
Luc De Raedt

While it is well known that arithmetic circuits can be used for efficient probabilistic inference, arithmetic circuits can also be used for other tasks. In this paper, we show how arithmetic circuits in a semiring setting (i. e. , algebraic circuits) can solve decision theoretic inference tasks and a utility learning task under partial observability. The former involves finding the set of decisions that maximises the expected utility. We introduce two approaches for this, both applying algebraic circuits. The learning task involves learning unknown utility values from partially observed interpretations of which the total utility is given. We provide the necessary theory and also perform an experimental evaluation of the approaches.

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UAI Conference 2020 Conference Paper

Ordering Variables for Weighted Model Integration

Vincent Derkinderen
Evert Heylen
Pedro Zuidberg Dos Martires
Samuel Kolb
Luc De Raedt

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.

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