Видео

transformers and mechanistic interpretability, attention layers and encoding of syntactic relations, prediction versus explanation, control theory and transformers, comparison of mathematical models, physics as metaphor

generative power of adjunctions (continued) Tamari order and Loday sums; LLMs and Zellig Harris' distributional theory, transformers attention modules as Hopf algebra characters, inverse problem of syntax, dimensionality of human and AI text, LI-Adger database and detection of syntactic phenomena by humans and LLMs

semiring parsing, algebra of Merge derivations, Laurent series and Minimal Yield constraints, Birkhoff factorization, Hopf algebroids and groupoid schemes, bialgebroids and semigroupoid schemes, algebroids and directed graph schemes, Birkhoff algebroids and semiringoids, Birkhoff factorization in semiringoids; adjunctions, Pair-Merge problem, generative power of adjunctions, Tamari order

Heim-Kratzer semantics, interpretability, inductive types and Boolean characters, topological Heim-Kratzer types, fuzzy Heim-Kratzer types, Boolean and Heyting algebras, logic from topology in semantic spaces; semiring parsing, algebra of Merge derivations

semiring Birkhoff factorization and syntax-semantics interface, geometric interaction of externalization and syntax-semantics interface: associahedra, BHV moduli spaces of trees, moduli spaces of real genus-zero curves; Pietroski's compositional semantics and Merge.

comparison with Manin's Renormalization & Computation; models of the Syntax-Semantics interface, minimal conceptual assumptions on semantics, Birkhoff factorization as an interface model, image of syntax in semantic spaces, Birkhoff factorization in semirings

comparison with physics: Hopf algebras and renormalization in quantum field theory, generative process of Feynman graphs, Birkhoff factorization and extraction of meaningful physical values, insertion Lie algebra, combinatorial Dyson-Schwinger equations, comparison with formal languages and graph grammars description of Feynman graphs

syntactic parameters (continued); comparison with Old Minimalism: Loday-Ronco Hopf algebra of planar trees, feature checking and domains, Old Internal Merge and projective systems of right-module coalgebras, Old External Merge and operated algebras; comparison with theoretical physics

syntactic parameters, evidence of relations, parametric comparison as codes, dimensionality estimates, independent variables and low dimensional embeddings, Belkin-Niyogi heat kernel method, networks of parameter relations and variance

Theta theory, operads, colored operads, obligatory control and diagonals; Externalization as two-step procedure (planarization & quotient), externalization and correspondences, 2-category of spans

Merge as Hopf algebra Markov chain (continued), insertion Lie algebra and countercyclic movement, head functions, phases, labeling algorithm, FormSet, prelude to Externalization

formulation of the action of Merge on workspaces in terms of Hopf algebras, constraints of Minimal Search and Minimal Yield, Merge as a Hopf algebra Markov chain

mathematical formulation of free symmetric Merge: magma of syntactic objects and Hopf algebra of workspaces

continuation of discussion of probabilities in formal languages; Chomsky's new model of Merge and the Strong Minimalist Thesis; from Strong Minimalist Thesis to Strong Minimalist Theorem

Lecture N.4: Mathematical Models of Generative Linguistics - Merge Grammars; Probabilities

Lecture N.3: Mathematical Models of Generative Linguistics - Generative Linguistics (Part 2)

Lecture N.2: Mathematical Models of Generative Linguistics - Introduction to Generative Linguistics

Lecture N.1: Mathematical Models of Generative Linguistics - What is Linguistics?

Lecture 5: Mathematical Structure of Syntactic Merge - An Algebraic Model for Generative Linguistics

Lecture 4: Mathematical Structure of Syntactic Merge - An Algebraic Model for Generative Linguistics

Lecture 3: Mathematical Structure of Syntactic Merge - An Algebraic Model for Generative Liguistics

Lecture 2: Mathematical Structure of Syntactic Merge - An Algebraic Model for Generative Linguistics

Lecture 1: Mathematical Structure of Syntactic Merge - An Algebraic Model for Generative Linguistics

Public Address on Generative Linguistics