Crate tenferro_ext_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<T>, MinPlusAlgebra<T>, MaxMulAlgebra<T>): Zero-sized types used as the algebra parameter Alg in semiring-family execution traits such as TensorSemiringCore<Alg>.

• Semiring-family implementations: impl TensorSemiringCore<MaxPlusAlgebra<f64>> 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_ext_tropical::MaxPlus;

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

Algebra dispatch

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

// MaxPlus<f64> maps to MaxPlusAlgebra<f64>
fn check_f64<T: HasAlgebra<Algebra = MaxPlusAlgebra<f64>>>() {}
check_f64::<MaxPlus<f64>>();

// MaxPlus<f32> maps to MaxPlusAlgebra<f32>
fn check_f32<T: HasAlgebra<Algebra = MaxPlusAlgebra<f32>>>() {}
check_f32::<MaxPlus<f32>>();

Plan-based tropical contraction

use tenferro_device::LogicalMemorySpace;
use tenferro_prims::{
    CpuBackend, CpuContext, SemiringCoreDescriptor, TensorSemiringCore,
};
use tenferro_tensor::{MemoryOrder, Tensor};
use tenferro_ext_tropical::{MaxPlus, MaxPlusAlgebra};

let mut ctx = CpuContext::new(1);
let col = MemoryOrder::ColumnMajor;
let mem = LogicalMemorySpace::MainMemory;
let a = Tensor::<MaxPlus<f64>>::zeros(&[3, 4], mem, col);
let b = Tensor::<MaxPlus<f64>>::zeros(&[4, 5], mem, col);
let mut c = Tensor::<MaxPlus<f64>>::zeros(&[3, 5], mem, col);
let desc = SemiringCoreDescriptor::BatchedGemm {
    batch_dims: vec![], m: 3, n: 5, k: 4,
};
// Under MaxPlusAlgebra<f64>, GEMM computes:
//   C[i,j] = max_k (A[i,k] + B[k,j])
let plan = <CpuBackend as TensorSemiringCore<MaxPlusAlgebra<f64>>>::plan(
    &mut ctx,
    &desc,
    &[&[3, 4], &[4, 5], &[3, 5]],
)
.unwrap();
<CpuBackend as TensorSemiringCore<MaxPlusAlgebra<f64>>>::execute(
    &mut ctx,
    &plan,
    MaxPlus::one(),
    &[&a, &b],
    MaxPlus::zero(),
    &mut c,
)
.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

ad

Tropical automatic differentiation via argmax routing.

algebra

Tropical algebra markers, HasAlgebra, and Semiring implementations.

argmax

Argmax tracking for tropical backward pass (automatic differentiation).

prims

Semiring-family implementations for tropical algebras on tenferro_prims::CpuBackend.

scalar

Tropical scalar wrapper types.