Struct SparseMap 

pub struct SparseMap { /* private fields */ }

A SparseMap layer: structured prediction with sparse marginals.

Solves the QP:

max θᵀμ - ½ μᵀ μ s.t. μ ∈ M

where M is the marginal polytope (e.g., the simplex for unstructured classification). The solution is a sparse probability distribution.

The backward pass uses the KKT conditions of the QP.

Implementations

impl SparseMap

pub fn new(a_marginal: Vec<Vec<f64>>, b_marginal: Vec<f64>) -> Self

Create a new SparseMap layer for a given marginal polytope.

Arguments

• a_marginal – equality constraints defining the polytope (Ax = b, x ≥ 0).
• b_marginal – equality rhs.

pub fn simplex(n: usize) -> Self

Create a SparseMap for the simplex: Σ μ_i = 1, μ_i ≥ 0.

pub fn with_config( a_marginal: Vec<Vec<f64>>, b_marginal: Vec<f64>, config: SparseMapConfig, ) -> Self

Create a SparseMap with custom configuration.

pub fn forward(&mut self, theta: &[f64]) -> OptimizeResult<Vec<f64>>

Forward pass: solve the QP on the marginal polytope.

μ* = argmax_{μ ∈ M} θᵀμ - ½ ||μ||² = argmin_{μ ∈ M} ½ ||μ - θ||² = Π_M(θ) (Euclidean projection onto M)

Uses iterative projected gradient on the Lagrangian.

Arguments

• theta – score vector (length n).

pub fn backward(&self, dl_dmu: &[f64]) -> OptimizeResult<Vec<f64>>

Backward pass: compute dL/dθ via KKT sensitivity.

At the optimal μ*, the KKT conditions of the QP are:

μ* - θ + Aᵀν* + s = 0 (stationarity, s = -min(μ*, 0)) Aμ* = b (equality) μ* ≥ 0, s ≥ 0, s⊙μ* = 0 (complementarity)

For the active variables (μ*_i > 0), we have s_i = 0, and the KKT system reduces to an equality system on the support.

Arguments

• dl_dmu – upstream gradient dL/dμ (length n).

pub fn project_simplex(v: &[f64]) -> Vec<f64>

Project a vector onto the probability simplex.

Solves: argmin_{μ ≥ 0, Σμ = 1} ||μ - v||²

Uses the O(n log n) sorting algorithm.

Trait Implementations

impl Clone for SparseMap

fn clone(&self) -> SparseMap

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SparseMap

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.