Algebraic Geometric Learning

A library that fuses Algebraic Geometry with Neural Networks i.e [commutative algebra] with polynomial neural networks: Groebner bases, ideals and algebraic varieties act as hard structural constraints on learning, while orthogonal polynomial layers (Chebyshev, Legendre, Hermite, Laguerre) provide stable, exactly symbolic function approximation.

What is inside

Package	Contents
src.alggeom	Polynomials, monomial orders, Groebner bases, ideals, algebraic varieties, system solving
src.layers	PolynomialLayer, OrthoPolyLayer (additive/multiplicative), RationalPolyLayer, GroebnerLayer, VarietyLayer
src.nn	PolynomialNeuralNetwork with exact symbolic distillation, OrthoPolyNetwork
src.training	Loss functions (ideal membership, variety constraint), polynomial-aware optimizers
src.utils	Symbolic utilities and visualization

Documentation series

The Algebraic Geometry, Neural Networks and Utilities parts develop the mathematics from definitions to working code. The six Tutorials apply the library to real datasets (NASA exoplanets, Mauna Loa CO2, SILSO sunspots, UCI concrete / power plant / airfoil) with every result reproduced by a runnable script under experiments/.

Getting started

pip install torch --index-url https://download.pytorch.org/whl/cpu
pip install -r requirements.txt
pytest          # run the test suite

All code blocks in the docs were executed against the real library; the test suite keeps them honest.