Advanced Usage: Semirings

All of the distributional code is implemented through a series of semiring objects. These are passed through dynamic programming backends to compute the distributions.

Standard Semirings

class torch_struct.LogSemiring

Implements the log-space semiring (logsumexp, +, -inf, 0).

Gradients give marginals.

class torch_struct.StdSemiring

Implements the counting semiring (+, *, 0, 1).

class torch_struct.MaxSemiring

Implements the max semiring (max, +, -inf, 0).

Gradients give argmax.

Higher-Order Semirings

class torch_struct.EntropySemiring

Implements an entropy expectation semiring.

Computes both the log-values and the running distributional entropy.

Based on descriptions in:

• Parameter estimation for probabilistic finite-state transducers [Eis02]

• First-and second-order expectation semirings with applications to minimum-risk training on translation forests [LE09]

• Sample Selection for Statistical Grammar Induction []

Sampling Semirings

class torch_struct.SampledSemiring

Implements a sampling semiring (logsumexp, +, -inf, 0).

“Gradients” give sample.

This is an exact forward-filtering, backward-sampling approach.

class torch_struct.MultiSampledSemiring

Implements a multi-sampling semiring (logsumexp, +, -inf, 0).

“Gradients” give up to 16 samples with replacement.

Dynamic Programming

class torch_struct.LinearChain(semiring=<class 'torch_struct.semirings.semirings.LogSemiring'>)

Represents structured linear-chain CRFs, generalizing HMMs smoothing, tagging models, and anything with chain-like dynamics.

class torch_struct.SemiMarkov(semiring=<class 'torch_struct.semirings.semirings.LogSemiring'>)

edge : b x N x K x C x C semimarkov potentials

class torch_struct.DepTree(semiring=<class 'torch_struct.semirings.semirings.LogSemiring'>)

A projective dependency CRF.

Parameters

• arc_scores_in – Arc scores of shape (B, N, N) or (B, N, N, L) with root scores on

• diagonal. –

Note: For single-root case, do not set cache=True for now.

class torch_struct.CKY(semiring=<class 'torch_struct.semirings.semirings.LogSemiring'>)