Αγαπητοί Συνάδελφοι, Φοιτητές και Φίλοι,
Θα θέλαμε να σας ενημερώσουμε ότι τη Δευτέρα 6 Μαρτίου στις 16:00, στο πλαίσιο του Διαδικτυακού Σεμιναρίου Άλγεβρας και Θεωρίας Αριθμών, θα δώσει ομιλία ο Ιωάννης Βλασσόπουλος (Athena RC).
Περίληψη: Neural networks (like ChatGPT) trained to probabilistically predict the next word to a text, have recently achieved human like capabilities in language understanding and use.
What is though the underlying mathematical structure that these models learn and how is semantic information encoded in the statistics of word co-occurances?
We will introduce a category L whose objects are texts in the language and a morphism from text x to text y is the probability of extension from x to y, in order to propose a partial answer to these questions. The category is enriched over the monoidal closed category whose set of objects is [0, 1] and monoidal structure is multiplication. The Yoneda embedding of L into its category of presheaves naturally encodes co-occurance information. Applying −log to morphisms we obtain an equivalent category which is also a Lawvere metric space and a tropical linear space. We will then explain the Isbell completion which relates completion by op co-presheaves (probabilites of extending a text) to completion by presheaves (probabilities of extending to a text). This is based on joint work with T.D. Bradley, J. Terilla and S. Gaubert.
Zoom link: https://authgr.zoom.us/j/97698390911?pwd=SVk0SlFMU25NVVlnZHFIQU1KZ3liUT09
Meeting ID: 976 9839 0911
Passcode: 956866
Για πληροφορίες σχετικά με τις επόμενες ομιλίες επισκεφθείτε την
ιστοσελίδα του σεμιναρίου (https://sites.google.com/view/gantseminar/home).
Θα χαρούμε να σας δούμε όλους!
Με εκτίμηση,
Κώστας Καραγιάννης
Άγγελος Κουτσιανάς
Ιωάννης Ντόκας
Δημήτρης Χατζάκος
Χρυσόστομος Ψαρουδάκης