fynch

Differentiable sorting and ranking.

Dual-licensed under MIT or Apache-2.0.

What it does

fynch provides smooth numerical approximations to sorting, ranking, and simplex prediction. It includes soft ranks and sorts, the entmax/sparsemax/softmax family, and selected loss and curvature helpers. The crate provides forward computations; it does not integrate with an autodiff runtime.

The simplex predictors use the Fenchel-Young framework (Blondel, Martins, and Niculae 2020), which derives a prediction function and matching convex loss from one regularizer.

Quickstart

[dependencies]
fynch = "0.3.2"

use fynch::fenchel::{entmax, softmax, sparsemax};
use fynch::{pava, soft_rank};

let theta = [2.0, 1.0, 0.1];

// Fenchel-Young predictions: dense, sparse, or tunable sparsity.
let dense = softmax(&theta); // sums to 1, all positive
let sparse = sparsemax(&theta); // exact zeros for low scores
let tunable = entmax(&theta, 1.5); // between the two

// Isotonic regression (PAVA): nearest non-decreasing fit.
let monotonic = pava(&[3.0, 1.0, 2.0, 5.0, 4.0]);

// Smooth ranks: a continuous numerical stand-in for argsort.
let ranks = soft_rank(&[0.5, 0.2, 0.8, 0.1], 0.1).unwrap();

Lower temperature makes soft_rank and soft_sort approach the hard (discrete) result; higher temperature smooths them out.

Modules

• fenchel: the generic framework (regularizers, prediction functions, losses).
• sinkhorn: entropic optimal transport for soft permutations.
• lapsum: LapSum soft sort, rank, and top-k; the earlier kernel smoother is retained under laplacian_kernel_* names.
• loss: learning-to-rank losses (Spearman, ListNet).
• metrics: IR evaluation (MRR, NDCG, Hits@k).

Examples

Runnable examples live in examples/:

• soft_rank_shootout compares fynch and rankit ranking methods on data with a known ground-truth order, measuring how closely each recovers the true ranks.
• soft_estimator_validation checks the soft estimators against exact references: soft_rank and soft_sort collapsing to their hard counterparts as temperature goes to zero, and PAVA against hand-computed isotonic fits.