Algebra

omeinsum::algebra

Trait Algebra 

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pub trait Algebra: Semiring {
    type Index: Copy + Clone + Send + Sync + Default + Debug + 'static;

    // Required methods
    fn add_with_argmax(
        self,
        self_idx: Self::Index,
        rhs: Self,
        rhs_idx: Self::Index,
    ) -> (Self, Self::Index);
    fn add_backward(
        self,
        rhs: Self,
        grad_out: Self::Scalar,
        winner_idx: Option<Self::Index>,
    ) -> (Self::Scalar, Self::Scalar);
    fn mul_backward(
        self,
        rhs: Self,
        grad_out: Self::Scalar,
    ) -> (Self::Scalar, Self::Scalar);
    fn is_better(&self, other: &Self) -> bool;

    // Provided method
    fn needs_argmax() -> bool { ... }
}
Expand description

Extended semiring operations for automatic differentiation.

This trait adds argmax tracking needed for tropical backpropagation.

Required Associated Types§

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type Index: Copy + Clone + Send + Sync + Default + Debug + 'static

Index type for argmax tracking

Required Methods§

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fn add_with_argmax( self, self_idx: Self::Index, rhs: Self, rhs_idx: Self::Index, ) -> (Self, Self::Index)

Addition with argmax tracking.

Returns (result, winner_index) where winner_index indicates which operand “won” the addition (relevant for tropical max/min).

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fn add_backward( self, rhs: Self, grad_out: Self::Scalar, winner_idx: Option<Self::Index>, ) -> (Self::Scalar, Self::Scalar)

Backward pass for addition.

Given output gradient grad_out, compute gradients for inputs. For standard arithmetic: both inputs get grad_out. For tropical: only the winner gets grad_out.

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fn mul_backward( self, rhs: Self, grad_out: Self::Scalar, ) -> (Self::Scalar, Self::Scalar)

Backward pass for multiplication.

Given output gradient grad_out, compute gradients for inputs. Standard: grad_a = grad_out × b, grad_b = grad_out × a Tropical (add): grad_a = grad_out, grad_b = grad_out

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fn is_better(&self, other: &Self) -> bool

Check if self is “better” than other for tropical selection.

For MaxPlus: returns true if self > other For MinPlus: returns true if self < other For Standard: not meaningful (always false)

Provided Methods§

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fn needs_argmax() -> bool

Whether this algebra requires argmax tracking for backprop.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors§

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impl<T: Scalar + Zero + One + PartialEq + Add<Output = T> + Mul<Output = T>> Algebra for Standard<T>

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type Index = u32