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Theoretical foundations

(Basic theoretical research)

This area focuses on the study of the mathematical and conceptual foundations of artificial intelligence. It draws on methods from optimization, statistics, logic, linear and abstract algebra, as well as information theory and the theory of computation. Research in this area is predominantly theoretical and addresses the formal analysis of algorithms and models, with the objective of characterizing their properties, limitations, and conditions of validity. These results underpin the development of AI systems whose behavior can be analyzed and reasoned about using well-defined theoretical frameworks.

 

The main research sublines include:

Information fusion

Investigation of methods for integrating information from multiple sources or modalities, with emphasis on joint representations, consistency across sources, uncertainty management, and principled evidence combination in inference.

Explainability

Analysis of explainability as a formal property of AI models, including the study of explanatory mechanisms, their expressiveness and limitations, and their relationship to model complexity and predictive performance.

Computational neuroscience

Development and analysis of computational models inspired by neural systems, aimed at understanding information-processing mechanisms and informing the design of learning algorithms and architectures grounded in neurocomputational principles.

Quantum communication and AI

Study of the interaction between artificial intelligence and quantum communication and computation, addressing both the use of quantum principles in learning and optimization and the application of AI techniques to the control and operation of quantum systems.

Multimodal learning

Research on learning models that integrate information from multiple modalities, focusing on the theoretical foundations of alignment, shared representation, and information transfer across heterogeneous data types.

Learning theory

Formal study of machine learning processes, including generalization properties, model complexity, theoretical limits of learnability, and conditions for stability and convergence.