# Semirings#

## Semiring#

class supar.structs.semiring.Semiring[source]#

Base semiring class Goodman (1999).

A semiring is defined by a tuple $$<K, \oplus, \otimes, \mathbf{0}, \mathbf{1}>$$. $$K$$ is a set of values; $$\oplus$$ is commutative, associative and has an identity element 0; $$\otimes$$ is associative, has an identity element 1 and distributes over +.

## LogSemiring#

class supar.structs.semiring.LogSemiring[source]#

Log-space semiring $$<\mathrm{logsumexp}, +, -\infty, 0>$$.

## MaxSemiring#

class supar.structs.semiring.MaxSemiring[source]#

Max semiring $$<\mathrm{max}, +, -\infty, 0>$$.

## KMaxSemiring#

class supar.structs.semiring.KMaxSemiring(k)[source]#

k-max semiring $$<\mathrm{kmax}, +, [-\infty, -\infty, \dots], [0, -\infty, \dots]>$$.

## EntropySemiring#

class supar.structs.semiring.EntropySemiring[source]#

Entropy expectation semiring $$<\oplus, +, [-\infty, 0], [0, 0]>$$, where $$\oplus$$ computes the log-values and the running distributional entropy $$H[p]$$ Li & Eisner 2009,Hwa 2000,Kim et al. (2019).

## CrossEntropySemiring#

class supar.structs.semiring.CrossEntropySemiring[source]#

Cross Entropy expectation semiring $$<\oplus, +, [-\infty, -\infty, 0], [0, 0, 0]>$$, where $$\oplus$$ computes the log-values and the running distributional cross entropy $$H[p,q]$$ of the two distributions Li & Eisner (2009).

## KLDivergenceSemiring#

class supar.structs.semiring.KLDivergenceSemiring[source]#

KL divergence expectation semiring $$<\oplus, +, [-\infty, -\infty, 0], [0, 0, 0]>$$, where $$\oplus$$ computes the log-values and the running distributional KL divergence $$KL[p \parallel q]$$ of the two distributions Li & Eisner (2009).

## SampledSemiring#

class supar.structs.semiring.SampledSemiring[source]#

Sampling semiring $$<\mathrm{logsumexp}, +, -\infty, 0>$$, which is an exact forward-filtering, backward-sampling approach.

## SparsemaxSemiring#

class supar.structs.semiring.SparsemaxSemiring[source]#

Sparsemax semiring $$<\mathrm{sparsemax}, +, -\infty, 0>$$ Martins & Astudillo 2016,Mensch & Blondel 2018,Correia et al. (2020).