11 papers
Hierarchical Grading in Large Language Models
T. Shaska
We introduce Graded Large Language Models (GLLMs), an algebraic framework that equips the representation space of a transformer with a grading and propagates the induced weighted s…
Rational Functions on the Projective Line from a Computational Viewpoint
Eslam Badr, Elira Shaska, Tony Shaska
An explicit invariant-theoretic description of the moduli space of degree-three rational maps on is developed. A cubic map is represented, up…
Weighted Heights and GIT Heights
Elira Shaska, Tony Shaska
We investigate the relationship between Geometric Invariant Theory (GIT) heights and weighted heights, with a focus on their interaction in weighted projective spaces and their app…
Internalizing Tools as Morphisms in Graded Transformers
Tony Shaska
We introduce a graded formulation of internal symbolic computation for transformers. The hidden space is endowed with a grading , and symbolic operations a…
Graded Transformers
Tony Shaska
We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Gra…
Graded Neural Networks
Tony Shaska
This paper presents a novel framework for graded neural networks (GNNs) built over graded vector spaces $\V_\w^n$, extending classical neural architectures by incorporating algebra…