Major achievements in the AI sector at large come from the application of statistical learning and machine learning techniques. In this field, the boost towards quick adoption of successful solutions must be paired with efforts in the construction of a global theory of the learning process which may stand as the theoretical basis for future advancements in this field.
This area of work includes geometrical and topological methods, study of disordered and complex systems, Boltzmann machines and statistical mechanics, algebraic and combinatorial methods, partial differential equations and optimal transport, foundation of statistical learning, functional and harmonic analysis, probability and inference, optimization and stochastic optimization, decision theory, complex network theory, data visualization and representation, multi-channel data integration.
Results from the hard sciences have direct contamination, through the development of modern algorithms and their application, in a variety of areas like in computer aided diagnostics, precision medicine, systems biology.
Looking forward, quantum information science and quantum machine learning also stand as areas deserving focussed efforts and needing major attention and investments in the next decades. The ubiquitous use of advanced architectures for discriminative and generative neural networks also points to the current lack of optimized models for ML-empowered high-throughput big data analytics, as well as for AI systems running on heterogeneous computing resources (e.g. CPU, GPU, TPU, FPGA, ..), both on-premise and on the cloud. The need for modern science communication on AI topics, and learning analytics in AI-enabled education programs on hard sciences will also be fundamental in bringing students toward the topic and in strengthening the impact of AI research on society.