Crate tenferro_tropical 

Tropical semiring tensor operations for the tenferro workspace.

This crate extends the tenferro algebra-parameterized architecture with three tropical semirings:

Semiring	⊕ (add)	⊗ (mul)	Zero	One	Use case
MaxPlus	max	+	−∞	0	Shortest path, optimal alignment
MinPlus	min	+	+∞	0	Shortest path (Dijkstra)
MaxMul	max	×	0	1	Viterbi, max-probability paths

Architecture

The crate provides:

• Scalar wrappers (MaxPlus<T>, MinPlus<T>, MaxMul<T>): #[repr(transparent)] newtypes that redefine Add/Mul with tropical semantics. Satisfy the Scalar blanket impl.

• Algebra markers (MaxPlusAlgebra, MinPlusAlgebra, MaxMulAlgebra): Zero-sized types used as the algebra parameter A in TensorPrims<A>.

• TensorPrims implementations: impl TensorPrims<MaxPlusAlgebra> for CpuBackend etc. Orphan rule compatible because algebra markers are defined locally.

• ArgmaxTracker: Records winner indices during tropical forward pass for use in automatic differentiation.

Examples

Scalar arithmetic

use tenferro_tropical::MaxPlus;

let a = MaxPlus(3.0_f64);
let b = MaxPlus(5.0_f64);
let c = a + b;   // MaxPlus(5.0) — tropical add = max
let d = a * b;   // MaxPlus(8.0) — tropical mul = ordinary +

Algebra dispatch

use tenferro_algebra::HasAlgebra;
use tenferro_tropical::{MaxPlus, MaxPlusAlgebra};

// MaxPlus<f64> automatically maps to MaxPlusAlgebra
fn check<T: HasAlgebra<Algebra = MaxPlusAlgebra>>() {}
check::<MaxPlus<f64>>();

Plan-based tropical contraction

use tenferro_prims::{CpuBackend, TensorPrims, PrimDescriptor};
use tenferro_tropical::MaxPlusAlgebra;

let desc = PrimDescriptor::BatchedGemm {
    batch_dims: vec![], m: 3, n: 5, k: 4,
};
// Under MaxPlusAlgebra, GEMM computes:
//   C[i,j] = max_k (A[i,k] + B[k,j])
let plan = <CpuBackend as TensorPrims<MaxPlusAlgebra>>::plan::<f64>(
    &desc, &[&[3, 4], &[4, 5], &[3, 5]],
).unwrap();

Re-exports

pub use algebra::MaxMulAlgebra;

pub use algebra::MaxPlusAlgebra;

pub use algebra::MinPlusAlgebra;

pub use argmax::ArgmaxTracker;

pub use prims::TropicalPlan;

pub use scalar::MaxMul;

pub use scalar::MaxPlus;

pub use scalar::MinPlus;

Modules

algebra

Tropical algebra markers, HasAlgebra, and Semiring implementations.

argmax

Argmax tracking for tropical backward pass (automatic differentiation).

prims

[TensorPrims] implementations for tropical algebras on [CpuBackend].

scalar

Tropical scalar wrapper types.