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Enseignement ATHENS - TPT37 : From complexity to intelligence (Télécom Paris)

Domaine > Informatique.



The notion of complexity has been invented 50 years ago to solve mathematical issues related to machine learning, randomness and proof theory. It led to the development of Algorithmic Information Theory (AIT). Complexity and AIT have more recently been shown essential to address aspects of human intelligence, such as perception, relevance, decision making and emotional intensity. These aspects of cognition were sometimes considered mysterious and unpredictable. They can now be regarded as resulting in part from computations based on complexity and its converse, simplicity. For instance, abnormally simple situations such as a coincidence (two colleagues having dressed in purple independently) or a remarkable lottery draw (e.g. 1-2-3-4-5-6) are systematically perceived as unexpected and interesting. When crediting or blaming a person for an action (e.g. giving the wrong medicine to an allergic child), one considers the simplicity of the causal link leading to the consequences. One also considers the person’s ability to measure that simplicity. A dramatic event is perceived as more emotional if the victims can be defined simply (celebrities, friends’ friends), if the place is simple (famous location or close to one’s home) or if the circumstances are causally complex (e.g. the victim was unlikely to be there). The design of intelligent systems must take advantage of this sensitivity of the human mind to complexity and simplicity.


  • This course does not address the notion of "computational complexity" which measures the speed of algorithms.
  • This course is not about Complex Systems either (for this, see TPT-09: Emergence in complex systems).


Objectifs pédagogiques

Course exam

Students will also be asked to make a small original contribution and to present it orally. They will also have to answer a short quiz on the last day.

30 heures en présentiel

effectifs minimal / maximal:


Diplôme(s) concerné(s)

Pour les étudiants du diplôme Diplôme d'ingénieur

Prerequisites    - Ability to follow mathematical reasoning. - Mastery of object-oriented programming. Elementary knowledge of the Python programming language is recommended.

Format des notes

Numérique sur 20

Littérale/grade réduit

Pour les étudiants du diplôme Echange international non diplomant

La note obtenue rentre dans le calcul de votre GPA.

Pour les étudiants du diplôme Diplôme d'ingénieur

L'UE est acquise si Note finale >= 10
  • Crédits ECTS acquis : 3 ECTS
  • Crédit d'UE électives acquis : 3

La note obtenue rentre dans le calcul de votre GPA.

Programme détaillé


This course begins with an introduction to the mathematical notion of complexity (also known as Kolmogorov complexity). The notion will be shown to be useful for the study of reasoning, for the definition of relevance (interestingness, unexpectedness), and for machine learning. We will also explore applications to the study of perception (hidden shapes, pattern recognition), of decision making (subjective probability), of responsibility and of emotional intensity.

All these aspects will be studied using concrete examples. Half of the time will be devoted to personal work in lab sessions.

Mots clés

Complexity, simplicity, artificial intelligence, cognition

Méthodes pédagogiques

Lectures + lab sessions
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