GAIA Framework Documentation
Welcome to the GAIA () Framework documentation!
GAIA is a deep learning framework that leverages categorical deep learning and geometric algebra principles to create more interpretable and mathematically grounded neural networks.
API Reference
- gaia package
SimplicialFunctorSimplicialFunctor.__getitem__()SimplicialFunctor.__init__()SimplicialFunctor.add()SimplicialFunctor.create_coalgebra_structure_map()SimplicialFunctor.create_morphism()SimplicialFunctor.create_object()SimplicialFunctor.create_triangle()SimplicialFunctor.define_degeneracy()SimplicialFunctor.define_face()SimplicialFunctor.degeneracy()SimplicialFunctor.diagnose_partial_structure()SimplicialFunctor.face()SimplicialFunctor.find_horns()SimplicialFunctor.get_endofunctor_trajectory()SimplicialFunctor.has_lift()SimplicialFunctor.load_state_dict()SimplicialFunctor.register_endofunctor_update()SimplicialFunctor.state_dict()SimplicialFunctor.verify_simplicial_identities()
Simplex0Simplex1SimplexNFuzzySetFuzzySimplicialSetKanComplexVerifiercreate_model()get_training_components()get_advanced_components()version()info()status()list_components()- Subpackages
- Submodules
- gaia
Core Components
- gaia.core package
SimplicialObjectSimplex0Simplex1Simplex2SimplexNSimplicialFunctorMapTypeHornErrorIntegratedFuzzySetIntegratedSimplexIntegratedFuzzySimplicialSetIntegratedCoalgebraTConormFuzzyElementcreate_fuzzy_simplex()create_fuzzy_simplicial_set_from_data()merge_fuzzy_simplicial_sets()KanComplexVerifierKanConditionTypeKanConditionResultget_training_components()get_advanced_components()- Submodules
- gaia.models package
- gaia.nn module
- gaia.data package
- gaia.integration package
FCoalgebraCoalgebraHomomorphismBisimulationGenerativeCoalgebraCoalgebraCategoryEndofunctorPowersetFunctorStreamFunctorNeuralFunctorcreate_llm_coalgebra()create_diffusion_coalgebra()create_transformer_coalgebra()GeneralizedMetricSpaceEnrichedCategoryYonedaEmbeddingMetricYonedaApplicationsUniversalRepresentercreate_llm_metric_space()create_causal_metric_space()IntegratedFuzzySetIntegratedSimplexIntegratedFuzzySimplicialSetIntegratedCoalgebraTConormFuzzyElementcreate_fuzzy_simplex()create_fuzzy_simplicial_set_from_data()merge_fuzzy_simplicial_sets()get_training_components()get_verification_components()
Training & Optimization
Key Features
Categorical Deep Learning: Built on solid category theory foundations
Geometric Algebra: Leverages geometric algebra for enhanced mathematical representation
Interpretable Models: Focus on mathematical interpretability and explainability
Modular Architecture: Flexible and extensible design
PyTorch Integration: Seamless integration with PyTorch ecosystem
Quick Links
gaia.models package - Core model implementations including CategoricalMLP and GAIATransformer
gaia.core package - Fundamental framework components and mathematical foundations
gaia.training package - Training utilities and optimization algorithms
gaia.nn module - Neural network building blocks and layers