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In this paper, we review recent approaches for explaining concepts in neural networks. Concepts can act as a natural link between learning and reasoning: once the concepts are identified that a neural learning system uses, one can integrate…

Knowledge graph reasoning is pivotal in various domains such as data mining, artificial intelligence, the Web, and social sciences. These knowledge graphs function as comprehensive repositories of human knowledge, facilitating the inference…

Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…

Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real-world applications.…

Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…

Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…

The currently dominating artificial intelligence and machine learning technology, neural networks, builds on inductive statistical learning. Neural networks of today are information processing systems void of understanding and reasoning…

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking…

This work presents a novel computer architecture that extends the Von Neumann model with a dedicated Reasoning Unit (RU) to enable native artificial general intelligence capabilities. The RU functions as a specialized co-processor that…

Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with…

Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…

Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations…

Many recent studies have found evidence for emergent reasoning capabilities in large language models (LLMs), but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning…

Deep learning based data-driven approaches have been successfully applied in various image understanding applications ranging from object recognition, semantic segmentation to visual question answering. However, the lack of knowledge…

Consider a binary classification problem solved using a feed-forward artificial neural network (ANN). Let the ANN be composed of a ReLU layer and several linear layers (convolution, sum-pooling, or fully connected). We assume the network…

In this paper, we focus on exploiting neural networks for the analysis and planning stage in self-adaptive architectures. The studied motivating cases in the paper involve existing (legacy) self-adaptive architectures and their adaptation…

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…

A hallmark of intelligence is the ability to use a familiar domain to make inferences about a less familiar domain, known as analogical reasoning. In this article, we delve into the performance of Large Language Models (LLMs) in dealing…