Expand description
§RuVector Math
Advanced mathematics for next-generation vector search and AI governance, featuring:
§Core Modules
- Optimal Transport: Wasserstein distances, Sinkhorn algorithm, Sliced Wasserstein
- Information Geometry: Fisher Information, Natural Gradient, K-FAC
- Product Manifolds: Mixed-curvature spaces (Euclidean × Hyperbolic × Spherical)
- Spherical Geometry: Geodesics on the n-sphere for cyclical patterns
§Theoretical CS Modules (New)
- Tropical Algebra: Max-plus semiring for piecewise linear analysis and routing
- Tensor Networks: TT/Tucker/CP decomposition for memory compression
- Spectral Methods: Chebyshev polynomials for graph diffusion without eigendecomposition
- Persistent Homology: TDA for topological drift detection and coherence monitoring
- Polynomial Optimization: SOS certificates for provable bounds on attention policies
§Design Principles
- Pure Rust: No BLAS/LAPACK dependencies for full WASM compatibility
- SIMD-Ready: Hot paths optimized for auto-vectorization
- Numerically Stable: Log-domain arithmetic, clamping, and stable softmax
- Modular: Each component usable independently
- Mincut as Spine: All modules designed to integrate with mincut governance
§Architecture: Mincut as Unifying Signal
┌─────────────────────────────────────────────────────────────┐
│ Mincut Governance │
│ (Structural tension meter for attention graphs) │
└───────────────────────┬─────────────────────────────────────┘
│
┌───────────────────┼───────────────────┐
▼ ▼ ▼
┌─────────┐ ┌───────────┐ ┌───────────┐
│ Tensor │ │ Spectral │ │ TDA │
│ Networks│ │ Methods │ │ Homology │
│ (TT) │ │(Chebyshev)│ │ │
└─────────┘ └───────────┘ └───────────┘
Compress Smooth within Monitor drift
representations partitions over time
┌───────────────────┼───────────────────┐
▼ ▼ ▼
┌─────────┐ ┌───────────┐ ┌───────────┐
│Tropical │ │ SOS │ │ Optimal │
│ Algebra │ │ Certs │ │ Transport │
└─────────┘ └───────────┘ └───────────┘
Plan safe Certify policy Measure
routing paths constraints distributional
distances§Quick Start
use ruvector_math::optimal_transport::{SlicedWasserstein, SinkhornSolver, OptimalTransport};
use ruvector_math::information_geometry::FisherInformation;
use ruvector_math::product_manifold::ProductManifold;
// Sliced Wasserstein distance between point clouds
let sw = SlicedWasserstein::new(100).with_seed(42);
let points_a = vec![vec![0.0, 0.0], vec![1.0, 0.0]];
let points_b = vec![vec![0.5, 0.5], vec![1.5, 0.5]];
let dist = sw.distance(&points_a, &points_b);
assert!(dist > 0.0);
// Sinkhorn optimal transport
let solver = SinkhornSolver::new(0.1, 100);
let cost_matrix = vec![vec![0.0, 1.0], vec![1.0, 0.0]];
let weights_a = vec![0.5, 0.5];
let weights_b = vec![0.5, 0.5];
let result = solver.solve(&cost_matrix, &weights_a, &weights_b).unwrap();
assert!(result.converged);
// Product manifold operations (Euclidean only for simplicity)
let manifold = ProductManifold::new(2, 0, 0);
let point_a = vec![0.0, 0.0];
let point_b = vec![3.0, 4.0];
let dist = manifold.distance(&point_a, &point_b).unwrap();
assert!((dist - 5.0).abs() < 1e-10);Re-exports§
pub use error::MathError;pub use error::Result;pub use optimal_transport::SlicedWasserstein;pub use optimal_transport::SinkhornSolver;pub use optimal_transport::GromovWasserstein;pub use optimal_transport::TransportPlan;pub use optimal_transport::WassersteinConfig;pub use information_geometry::FisherInformation;pub use information_geometry::NaturalGradient;pub use information_geometry::KFACApproximation;pub use spherical::SphericalSpace;pub use spherical::SphericalConfig;pub use product_manifold::ProductManifold;pub use product_manifold::ProductManifoldConfig;pub use product_manifold::CurvatureType;pub use tropical::Tropical;pub use tropical::TropicalSemiring;pub use tropical::TropicalPolynomial;pub use tropical::TropicalMatrix;pub use tropical::LinearRegionCounter;pub use tropical::TropicalNeuralAnalysis;pub use tensor_networks::DenseTensor;pub use tensor_networks::TensorTrain;pub use tensor_networks::TensorTrainConfig;pub use tensor_networks::TuckerDecomposition;pub use tensor_networks::TuckerConfig;pub use tensor_networks::CPDecomposition;pub use tensor_networks::CPConfig;pub use tensor_networks::TensorNetwork;pub use tensor_networks::TensorNode;pub use spectral::ChebyshevPolynomial;pub use spectral::ChebyshevExpansion;pub use spectral::SpectralFilter;pub use spectral::GraphFilter;pub use spectral::FilterType;pub use spectral::SpectralWaveletTransform;pub use spectral::GraphWavelet;pub use spectral::SpectralClustering;pub use spectral::ScaledLaplacian;pub use homology::PersistenceDiagram;pub use homology::PersistentHomology;pub use homology::BirthDeathPair;pub use homology::Simplex;pub use homology::SimplicialComplex;pub use homology::Filtration;pub use homology::VietorisRips;pub use homology::BottleneckDistance;pub use homology::WassersteinDistance as HomologyWasserstein;pub use optimization::Polynomial;pub use optimization::Monomial;pub use optimization::Term;pub use optimization::SOSDecomposition;pub use optimization::SOSResult;pub use optimization::NonnegativityCertificate;pub use optimization::BoundsCertificate;
Modules§
- error
- Error types for ruvector-math
- homology
- Persistent Homology and Topological Data Analysis
- information_
geometry - Information Geometry
- optimal_
transport - Optimal Transport Algorithms
- optimization
- Polynomial Optimization and Sum-of-Squares
- prelude
- Prelude module for convenient imports
- product_
manifold - Product Manifolds: Mixed-Curvature Geometry
- spectral
- Spectral Methods for Graph Analysis
- spherical
- Spherical Geometry
- tensor_
networks - Tensor Networks
- tropical
- Tropical Algebra (Max-Plus Semiring)
- utils
- Utility functions for numerical operations