Sebastijan Dumančić

Jonas Witt, Sebastijan Dumančić, Tias Guns et al.

A major bottleneck in search-based program synthesis is the exponentially growing search space which makes learning large programs intractable. Humans mitigate this problem by leveraging the compositional nature of the real world: In structured domains, a logical specification can often be decomposed into smaller, complementary solution programs. We show that compositional segmentation can be applied in the programming by examples setting to divide the search for large programs across multiple smaller program synthesis problems. For each example, we search for a decomposition into smaller units which maximizes the reconstruction accuracy in the output under a latent task program. A structural alignment of the constituent parts in the input and output leads to pairwise correspondences used to guide the program synthesis search. In order to align the input/output structures, we make use of the Structure-Mapping Theory (SMT), a formal model of human analogical reasoning which originated in the cognitive sciences. We show that decomposition-driven program synthesis with structural alignment outperforms Inductive Logic Programming (ILP) baselines on string transformation tasks even with minimal knowledge priors. Unlike existing methods, the predictive accuracy of our agent monotonically increases for additional examples and achieves an average time complexity of $\mathcal{O}(m)$ in the number $m$ of partial programs for highly structured domains such as strings. We extend this method to the complex setting of visual reasoning in the Abstraction and Reasoning Corpus (ARC) for which ILP methods were previously infeasible.

Céline Hocquette, Sebastijan Dumančić, Andrew Cropper

We introduce the higher-order refactoring problem, where the goal is to compress a logic program by discovering higher-order abstractions, such as map, filter, and fold. We implement our approach in Stevie, which formulates the refactoring problem as a constraint optimisation problem. Our experiments on multiple domains, including program synthesis and visual reasoning, show that refactoring can improve the learning performance of an inductive logic programming system, specifically improving predictive accuracies by 27% and reducing learning times by 47%. We also show that Stevie can discover abstractions that transfer to multiple domains.

Ruben Sharma, Sebastijan Dumančić, Ross D. King et al.

Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length programs from noisy data. Our approach balances hypothesis complexity and data fit through priors, which explicitly favour more general programs, and a likelihood that favours accurate programs. Our experiments on several domains, including game playing and drug design, show that our method significantly outperforms previous methods, notably those that learn minimum description length programs. Our results also show that our approach is data-efficient and insensitive to example balance, including the ability to learn from exclusively positive examples.

Issa Hanou, Sebastijan Dumančić, Mathijs de Weerdt

We propose a new framework for discovering landmarks that automatically generalize across a domain. These generalized landmarks are learned from a set of solved instances and describe intermediate goals for planning problems where traditional landmark extraction algorithms fall short. Our generalized landmarks extend beyond the predicates of a domain by using state functions that are independent of the objects of a specific problem and apply to all similar objects, thus capturing repetition. Based on these functions, we construct a directed generalized landmark graph that defines the landmark progression, including loop possibilities for repetitive subplans. We show how to use this graph in a heuristic to solve new problem instances of the same domain. Our results show that the generalized landmark graphs learned from a few small instances are also effective for larger instances in the same domain. If a loop that indicates repetition is identified, we see a significant improvement in heuristic performance over the baseline. Generalized landmarks capture domain information that is interpretable and useful to an automated planner. This information can be discovered from a small set of plans for the same domain.

Giuseppe Marra, Sebastijan Dumančić, Robin Manhaeve et al.

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 proof-based; (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.

Andrew Cropper, Sebastijan Dumančić, Richard Evans et al.

Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs, (iii) new approaches for predicate invention, and (iv) the use of different technologies. We conclude by discussing current limitations of ILP and directions for future research.

Andrew Cropper, Sebastijan Dumančić

Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.

Andrew Cropper, Sebastijan Dumančić

A major challenge in inductive logic programming (ILP) is learning large programs. We argue that a key limitation of existing systems is that they use entailment to guide the hypothesis search. This approach is limited because entailment is a binary decision: a hypothesis either entails an example or does not, and there is no intermediate position. To address this limitation, we go beyond entailment and use \emph{example-dependent} loss functions to guide the search, where a hypothesis can partially cover an example. We implement our idea in Brute, a new ILP system which uses best-first search, guided by an example-dependent loss function, to incrementally build programs. Our experiments on three diverse program synthesis domains (robot planning, string transformations, and ASCII art), show that Brute can substantially outperform existing ILP systems, both in terms of predictive accuracies and learning times, and can learn programs 20 times larger than state-of-the-art systems.

Luc De Raedt, Sebastijan Dumančić, Robin Manhaeve et al.

Neuro-symbolic and statistical relational artificial intelligence both integrate frameworks for learning with logical reasoning. This survey identifies several parallels across seven different dimensions between these two fields. These cannot only be used to characterize and position neuro-symbolic artificial intelligence approaches but also to identify a number of directions for further research.

Andrew Cropper, Sebastijan Dumančić, Stephen H. Muggleton

Common criticisms of state-of-the-art machine learning include poor generalisation, a lack of interpretability, and a need for large amounts of training data. We survey recent work in inductive logic programming (ILP), a form of machine learning that induces logic programs from data, which has shown promise at addressing these limitations. We focus on new methods for learning recursive programs that generalise from few examples, a shift from using hand-crafted background knowledge to \emph{learning} background knowledge, and the use of different technologies, notably answer set programming and neural networks. As ILP approaches 30, we also discuss directions for future research.

Robin Manhaeve, Sebastijan Dumančić, Angelika Kimmig et al.

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic programming language ProbLog can be adapted for the new language. We theoretically and experimentally demonstrate that DeepProbLog supports (i) both symbolic and subsymbolic representations and inference, (ii) program induction, (iii) probabilistic (logic) programming, and (iv) (deep) learning from examples. To the best of our knowledge, this work is the first to propose a framework where general-purpose neural networks and expressive probabilistic-logical modeling and reasoning are integrated in a way that exploits the full expressiveness and strengths of both worlds and can be trained end-to-end based on examples.

Alberto García-Durán, Sebastijan Dumančić, Mathias Niepert

Research on link prediction in knowledge graphs has mainly focused on static multi-relational data. In this work we consider temporal knowledge graphs where relations between entities may only hold for a time interval or a specific point in time. In line with previous work on static knowledge graphs, we propose to address this problem by learning latent entity and relation type representations. To incorporate temporal information, we utilize recurrent neural networks to learn time-aware representations of relation types which can be used in conjunction with existing latent factorization methods. The proposed approach is shown to be robust to common challenges in real-world KGs: the sparsity and heterogeneity of temporal expressions. Experiments show the benefits of our approach on four temporal KGs. The data sets are available under a permissive BSD-3 license 1.

Robin Manhaeve, Sebastijan Dumančić, Angelika Kimmig et al.

We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments demonstrate that DeepProbLog supports both symbolic and subsymbolic representations and inference, 1) program induction, 2) probabilistic (logic) programming, and 3) (deep) learning from examples. To the best of our knowledge, this work is the first to propose a framework where general-purpose neural networks and expressive probabilistic-logical modeling and reasoning are integrated in a way that exploits the full expressiveness and strengths of both worlds and can be trained end-to-end based on examples.

Toon Van Craenendonck, Sebastijan Dumančić, Elia Van Wolputte et al.

Constraint-based clustering algorithms exploit background knowledge to construct clusterings that are aligned with the interests of a particular user. This background knowledge is often obtained by allowing the clustering system to pose pairwise queries to the user: should these two elements be in the same cluster or not? Active clustering methods aim to minimize the number of queries needed to obtain a good clustering by querying the most informative pairs first. Ideally, a user should be able to answer a couple of these queries, inspect the resulting clustering, and repeat these two steps until a satisfactory result is obtained. We present COBRAS, an approach to active clustering with pairwise constraints that is suited for such an interactive clustering process. A core concept in COBRAS is that of a super-instance: a local region in the data in which all instances are assumed to belong to the same cluster. COBRAS constructs such super-instances in a top-down manner to produce high-quality results early on in the clustering process, and keeps refining these super-instances as more pairwise queries are given to get more detailed clusterings later on. We experimentally demonstrate that COBRAS produces good clusterings at fast run times, making it an excellent candidate for the iterative clustering scenario outlined above.

Sebastijan Dumančić, Hendrik Blockeel

Latent features learned by deep learning approaches have proven to be a powerful tool for machine learning. They serve as a data abstraction that makes learning easier by capturing regularities in data explicitly. Their benefits motivated their adaptation to relational learning context. In our previous work, we introduce an approach that learns relational latent features by means of clustering instances and their relations. The major drawback of latent representations is that they are often black-box and difficult to interpret. This work addresses these issues and shows that (1) latent features created by clustering are interpretable and capture interesting properties of data; (2) they identify local regions of instances that match well with the label, which partially explains their benefit; and (3) although the number of latent features generated by this approach is large, often many of them are highly redundant and can be removed without hurting performance much.