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It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present…

Compositionality is a cognitive mechanism that allows humans to systematically combine known concepts in novel ways. This study demonstrates how artificial neural agents acquire and utilize compositional generalization to describe…

In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition…

We consider biological individuality in terms of information theoretic and graphical principles. Our purpose is to extract through an algorithmic decomposition system-environment boundaries supporting individuality. We infer or detect…

Language models retain a significant amount of world knowledge from their pre-training stage. This allows knowledgeable models to be applied to knowledge-intensive tasks prevalent in information retrieval, such as ranking or question…

Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…

Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate…

Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…

Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…

Reinforcement Learning formalises an embodied agent's interaction with the environment through observations, rewards and actions. But where do the actions come from? Actions are often considered to represent something external, such as the…

Deep learning models achieve high predictive performance but lack intrinsic interpretability, hindering our understanding of the learned prediction behavior. Existing local explainability methods focus on associations, neglecting the causal…

A fundamental requirement for intelligent systems is the ability to learn continuously under changing environments. However, models trained in this regime often suffer from catastrophic forgetting. Leveraging pre-trained models has recently…

We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model…

Video prediction is a crucial task for intelligent agents such as robots and autonomous vehicles, since it enables them to anticipate and act early on time-critical incidents. State-of-the-art video prediction methods typically model the…

Concept-based explanation approach is a popular model interpertability tool because it expresses the reasons for a model's predictions in terms of concepts that are meaningful for the domain experts. In this work, we study the problem of…

We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known…

Continual learning requires models to adapt to new data while preserving previously acquired knowledge. At its core, this challenge can be viewed as principled one-step adaptation: incorporating new information with minimal interference to…

Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…