(TODAY!): [ICTP COLLOQUIUM ON AI FOR SCIENTIFIC DISCOVERY]: Wednesday, 28 October, Colloquium by Prof. Pierluigi Contucci

[Infopoint]

*ICTP COLLOQUIUM ON AI FOR SCIENTIFIC DISCOVERY*

/The Language of Natural Numbers: Statistical Properties and Neural 
Learning of Arithmetic Structures/

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*Date and Venue*: Wednesday, 28 October, at 14:00 - ICTP Leonardo 
Building - /**Euler *Lecture Hall*/

*Speaker: *Pierluigi Contucci (Universita' di Bologna, Italy)
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*Title:* *The Language of Natural Numbers: Statistical Properties and 
Neural Learning of Arithmetic Structures*

*Abstract:*
The relationship between artificial intelligence and science is 
increasingly bidirectional: AI offers new tools for discovering and 
exploring scientific structures, while science provides controlled 
domains in which to investigate the capabilities and limitations of AI. 
We examine this interplay in the fundamental setting of arithmetic. 
Iterated prime factorization turns the integers into a deterministic 
sequence of words whose vocabulary and admissible combinations are 
governed by arithmetic. We establish asymptotic laws for vocabulary 
growth and word frequencies, examine statistical dependencies, and show 
that a transformer trained solely on such text captures structural 
regularities, including sensitivity to arithmetically forbidden 
sequences. This resulting language supports both directions of inquiry: 
neural models make arithmetic structure accessible through learning, 
while arithmetic supplies precise constraints against which to examine 
what these models learn and how they represent it.

*About the Speaker:*
PhD in Mathematics and MS in Mathematical Physics (ISAS, Trieste), 
Laurea in Physics (University La Sapienza, Rome). Postdoc at Princeton 
University and University of California. Visiting Professor at the Tokyo 
Institute of Technology, at the Institut Henri Poincaré and at New York 
University. Research interests in Mathematical Physics, Statistical 
Mechanics and applications (machine learning, data science). Author of 
Perspectives on Spin Glasses (Cambridge University Press, 2012) and 
Probabilità Elementare, Teoria ed Esperimenti (Zanichelli, 2008). 
Publications in Communications in Mathematical Physics, Nature 
Scientific Reports, Journal of Statistical Physics, Annales Henri 
Poincare, Physical Review Letters. Writes on scientific debates of 
public interest in newspapers like Il Corriere della Sera, Il Sole 24 
Ore and magazines like Il Mulino 
<https://www.rivistailmulino.it/isni/829> and Vanity Fair. Schloessman 
Award (2000) from the Max Planck Society. Member of the Science Academy 
of Bologna.

Refreshments will be served in the LB Cafeteria after the talk.

The event will be livetreamed at: http://ictp.it/livestream

All are welcome to join.

Indico: https://indico.ictp.it/event/11555/

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