Our most powerful artificial agents cannot be told exactly what to do, especially in complex planning environments. They almost exclusively rely on neural networks to perform their tasks, but neural networks cannot easily be told to obey certain rules or adhere to existing background knowledge. While such uncontrolled behaviour might be nothing more than a simple annoyance next time you ask an LLM to generate a schedule for reaching a deadline in two days and it starts to hallucinate that days have 48 hours instead of 24, it can be much more impactful when that same LLM is controlling an agent responsible for navigating a warehouse filled with TNT and it decides to go just a little too close to the storage compartments. Luckily, controlling neural networks has gained a lot of attention over the last years through the development of . Neurosymbolic AI, or NeSy for short, aims to combine the learning abilities of neural networks with the guarantees that symbolic methods based on automated mathematical reasoning offer.

Welcome to our monthly digest, where you can catch up with any AIhub stories you may have missed, peruse the latest news, recap recent events, and more. This month, we hear about the latest research on soccer ball detection, learn about energy-based transformers, find out about memory traces in reinforcement learning, and explore some potential solutions to the problems with conference reviewing. Issues with the peer-review process, and pertaining to conferences in particular, are often discussed among authors, reviewers and conference chairs alike. However, coming up with potential solutions to the problem has proved challenging. Jaeho told us more in this interview .

Should AI continue to be driven by a single paradigm, or does real progress lie in combining the strengths and weaknesses of many? Professor Luc De Raedt of KU Leuven has spent much of his career persistently addressing this question. Through pioneering work that bridges logic, probability, and machine learning, he has helped shape the field of neurosymbolic AI. In our conversation at IJCAI 2025 in Montreal, he spoke about what continues to fascinate him in this line of research, how he responds to criticisms of neurosymbolic AI, and why reconciling multiple paradigms is such an exciting challenge. Hello Professor De Raedt, thank you very much for joining me.

We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational mechanisms used in neurosymbolic AI. DeepLog can represent and emulate a wide range of neurosymbolic systems. It consists of two key components. The first is the DeepLog language for specifying neurosymbolic models and inference tasks. This language consists of an annotated neural extension of grounded first-order logic, and makes abstraction of the type of logic, e.g. boolean, fuzzy or probabilistic, and whether logic is used in the architecture or in the loss function. The second DeepLog component is situated at the computational level and uses extended algebraic circuits as computational graphs. Together these two components are to be considered as a neurosymbolic abstract machine, with the DeepLog language as the intermediate level of abstraction and the circuits level as the computational one. DeepLog is implemented in software, relies on the latest insights in implementing algebraic circuits on GPUs, and is declarative in that it is easy to obtain different neurosymbolic models by making different choices for the underlying algebraic structures and logics. The generality and efficiency of the DeepLog neurosymbolic machine is demonstrated through an experimental comparison between 1) different fuzzy and probabilistic logics, 2) between using logic in the architecture or in the loss function, and 3) between a standalone CPU-based implementation of a neurosymbolic AI system and a DeepLog GPU-based one.

Neurosymbolic AI combines neural network adaptability with symbolic reasoning, promising an approach to address the complex regulatory, operational, and safety challenges in Advanced Air Mobility (AAM). This survey reviews its applications across key AAM domains such as demand forecasting, aircraft design, and real-time air traffic management. Our analysis reveals a fragmented research landscape where methodologies, including Neurosymbolic Reinforcement Learning, have shown potential for dynamic optimization but still face hurdles in scalability, robustness, and compliance with aviation standards. We classify current advancements, present relevant case studies, and outline future research directions aimed at integrating these approaches into reliable, transparent AAM systems. By linking advanced AI techniques with AAM's operational demands, this work provides a concise roadmap for researchers and practitioners developing next-generation air mobility solutions.

Neurosymbolic AI focuses on integrating learning and reasoning, in particular, on unifying logical and neural representations. Despite the existence of an alphabet soup of neurosymbolic AI systems, the field is lacking a generally accepted formal definition of what neurosymbolic models and inference really are. We introduce a formal definition for neurosymbolic AI that makes abstraction of its key ingredients. More specifically, we define neurosymbolic inference as the computation of an integral over a product of a logical and a belief function. We show that our neurosymbolic AI definition makes abstraction of key representative neurosymbolic AI systems.

Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the area of neurosymbolic Artificial Intelligence (AI). In this chapter, a simple energy-based neurosymbolic AI system is described that can represent and reason formally about any propositional logic formula. This creates a powerful combination of learning from data and knowledge and logical reasoning. We start by positioning neurosymbolic AI in the context of the current AI landscape that is unsurprisingly dominated by Large Language Models (LLMs). We identify important challenges of data efficiency, fairness and safety of LLMs that might be addressed by neurosymbolic reasoning systems with formal reasoning capabilities. We then discuss the representation of logic by the specific energy-based system, including illustrative examples and empirical evaluation of the correspondence between logical reasoning and energy minimization using Restricted Boltzmann Machines (RBM). Learning from data and knowledge is also evaluated empirically and compared with a symbolic, neural and a neurosymbolic system. Results reported in this chapter in an accessible way are expected to reignite the research on the use of neural networks as massively-parallel models for logical reasoning and promote the principled integration of reasoning and learning in deep networks. We conclude the chapter with a discussion of the importance of positioning neurosymbolic AI within a broader framework of formal reasoning and accountability in AI, discussing the challenges for neurosynbolic AI to tackle the various known problems of reliability of deep learning.

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 determinis-tically 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. Keywords: neurosymbolic AI partial label learning 1 Introduction Neurosymbolic (NeSy) AI is an approach to AI which seeks to combine logic and neural networks [13].

This chapter investigates the concept of mutual understanding between humans and systems, positing that Neuro-symbolic Artificial Intelligence (NeSy AI) methods can significantly enhance this mutual understanding by leveraging explicit symbolic knowledge representations with data-driven learning models. We start by introducing three critical dimensions to characterize mutual understanding: sharing knowledge, exchanging knowledge, and governing knowledge. Sharing knowledge involves aligning the conceptual models of different agents to enable a shared understanding of the domain of interest. Exchanging knowledge relates to ensuring the effective and accurate communication between agents. Governing knowledge concerns establishing rules and processes to regulate the interaction between agents. Then, we present several different use case scenarios that demonstrate the application of NeSy AI and Knowledge Graphs to aid meaningful exchanges between human, artificial, and robotic agents. These scenarios highlight both the potential and the challenges of combining top-down symbolic reasoning with bottom-up neural learning, guiding the discussion of the coverage provided by current solutions along the dimensions of sharing, exchanging, and governing knowledge. Concurrently, this analysis facilitates the identification of gaps and less developed aspects in mutual understanding to address in future research.

Travel demand prediction is crucial for optimizing transportation planning, resource allocation, and infrastructure development, ensuring efficient mobility and economic sustainability. This study introduces a Neurosymbolic Artificial Intelligence (Neurosymbolic AI) framework that integrates decision tree (DT)-based symbolic rules with neural networks (NNs) to predict travel demand, leveraging the interpretability of symbolic reasoning and the predictive power of neural learning. The framework utilizes data from diverse sources, including geospatial, economic, and mobility datasets, to build a comprehensive feature set. DTs are employed to extract interpretable if-then rules that capture key patterns, which are then incorporated as additional features into a NN to enhance its predictive capabilities. Experimental results show that the combined dataset, enriched with symbolic rules, consistently outperforms standalone datasets across multiple evaluation metrics, including Mean Absolute Error (MAE), \(R^2\), and Common Part of Commuters (CPC). Rules selected at finer variance thresholds (e.g., 0.0001) demonstrate superior effectiveness in capturing nuanced relationships, reducing prediction errors, and aligning with observed commuter patterns. By merging symbolic and neural learning paradigms, this Neurosymbolic approach achieves both interpretability and accuracy.