22 citations · 28 across the 10 of their papers we have counts for
13 papers
Stacky Heights, Entropy, and Zeta Functions of Weighted Hypersurfaces over Finite Fields
S. Salami, T. Shaska
Let \(X\subset \mathbb P^n_{\mathbf w}\) be a weighted hypersurface over \(\mathbb F_q\), with associated stack \(\mathfrak X\). For \(\mathbf x\in X(\mathbb F_{q^r})\), let \(g_{\…
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…
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…
Rational Points and Zeta Functions of Humbert Surfaces with Square Discriminant
Elira Shaska, Jorge Mello, Sajad Salami +1
This paper examines the arithmetic of the loci \(\cL_n\), parameterizing genus 2 curves with \((n, n)\)-split Jacobians over finite fields \(\F_q\). We compute rational points \(|\…
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…
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 t…
Neuro-Symbolic Learning for Galois Groups: Unveiling Probabilistic Trends in Polynomials
Elira Shaska, Tony Shaska
This paper presents a neurosymbolic approach to classifying Galois groups of polynomials, integrating classical Galois theory with machine learning to address challenges in algebra…
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…
Galois groups of polynomials and neurosymbolic networks
Elira Shaska, Tony Shaska
This paper introduces a novel approach to understanding Galois theory, one of the foundational areas of algebra, through the lens of machine learning. By analyzing polynomial equat…
A Neurosymbolic Framework for Geometric Reduction of Binary Forms
Ilias Kotsireas, Tony Shaska
This paper compares Julia reduction and hyperbolic reduction with the aim of finding equivalent binary forms with minimal coefficients. We demonstrate that hyperbolic reduction gen…
Artificial Neural Networks on Graded Vector Spaces
Tony Shaska
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic…
Quantum codes from superelliptic curves
A. Elezi, T. Shaska
Let $\X$ be an algebraic curve of genus defined over a field $\F_q$ of characteristic . From $\X$, under certain conditions, we can construct an algebraic geometr…
Thetanulls of cyclic curves of small genus
E. Previato, T. Shaska, G. S. Wijesiri
We study relations among the classical thetanulls of cyclic curves, namely curves (of genus ) with an automorphism such that generates a norma…