📐algorithm-coordinate-descent-lasso-tests

The groupant beside algorithms/src/coordinate_descent_lasso/tests.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

Facts

Components

Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

Model text

descriptant

coordinate_descent_lasso finite checks

The test harness observes finite assertions on coordinate_descent_lasso. Analytic formulas and finite grid competitors are distinct forms of evidence; the grid alone proves no optimizer bound.

Prospective epoch

The prospective model was saved before source creation in the external wave20 optimization run and retained in prospective.md. Original standard-library Rust, no downloaded solution code.

Observations retained

17 orthogonal designs against scalar analytic shrinkage; correlated design against 1681 grid objectives and KKT tolerance; true zero column; zero budget with/without optimal zero; negative penalty and NaN; deterministic repeat; nonzero underflowing column rejection.

Limits

Maximum recomputed KKT violation<=tolerance precedes budget exhaustion. Budget counts full sweeps. A full sweep without any representable coefficient change returns Stagnated, retaining the already recomputed objective and residual at the unchanged vector. No timing or universal machine-accuracy claim.

Reference: Friedman, Hastie and Tibshirani, Regularization Paths for Generalized Linear Models via Coordinate Descent, Journal of Statistical Software 33(1), 2010; Parikh and Boyd (2014), section 6.5.2.

model

Mathematical combiner

Inputs are the authoritative tests.rs, source-bound partial syntax, forward relation, typed complement first and reverse reconstruction second, specialized relations and named finite evidence. Intersect the accepted-domain relation with each update relation, then partition termination by convergence, budget, stagnation or error. Minimize .5||Ax-y||²+lambda||x||1 from x=0. For each cyclic coordinate j, q_j=sum_i A_ij², correlation=A_j'r+q_jx_j, x_new=soft_threshold(correlation,lambda)/q_j, and r<-r-A_j(x_new-x_j). Zero columns remain zero. Recompute r=y-Ax each sweep before objective and KKT stopping, limiting cumulative cached-residual drift.

Tests are sibling source nodes; manifest children are absent because these compact files have no independent nested fragment contracts. Syntax does not expand macros or prove semantics.

Retained observation: 17 orthogonal designs against scalar analytic shrinkage; correlated design against 1681 grid objectives and KKT tolerance; true zero column; zero budget with/without optimal zero; negative penalty and NaN; deterministic repeat; nonzero underflowing column rejection.

Composition limits: Validate all inputs before checked x/residual/norm allocations. Each threshold call can separately fail allocation; map that case to AllocationFailed and other threshold errors to NonFiniteArithmetic. Fixed ascending cyclic order, no callbacks. Shared bounded/buffer/report types compose with the standalone threshold kernel. Maximum recomputed KKT violation<=tolerance precedes budget exhaustion. Budget counts full sweeps. A full sweep without any representable coefficient change returns Stagnated, retaining the already recomputed objective and residual at the unchanged vector.

approximant

Forward approximant and invariant

The test harness observes finite assertions on coordinate_descent_lasso. Analytic formulas and finite grid competitors are distinct forms of evidence; the grid alone proves no optimizer bound.

Domain and invariant

Rectangular 1..256 by 1..64 design; finite data and lambda abs<=1e50, lambda>=0; positive finite tolerance and budget<=100000. Nonfinite correlation, coefficient, residual, objective or violation returns NonFiniteArithmetic. Underflowed nonzero column norm is explicitly rejected. Remaining rounding/cancellation is not certified by real KKT identities.

Orthogonal columns decouple, giving x_j=sign(A_j'y)*max(|A_j'y|-lambda,0)/q_j. The independent scalar formula verifies coefficient values. The dense grid is only a finite objective comparison, while reported KKT checks validate its chosen stopping metric.

Cost

O(kmn) arithmetic, O(m+n) scratch; m<=256,n<=64. Existing soft_threshold allocates one scalar vector per nonzero-coordinate update; up to k*n tiny allocations, explicitly not an allocation-free optimization. Harness repeats only the named bounded fixture set; no production throughput claim.

Executable approximation gap

No useful percentage-bounded cheaper surrogate is attached. A sampled decrease, projected step, bracket width or KKT/dual residual is not a universal relative objective/solution certificate. No 1/2/5/10% claim is inferred from finite success; zero-reference relative error is undefined without a separately specified metric. This gap is explicit rather than wrapping the exact implementation.

Reference: Friedman, Hastie and Tibshirani, Regularization Paths for Generalized Linear Models via Coordinate Descent, Journal of Statistical Software 33(1), 2010; Parikh and Boyd (2014), section 6.5.2.

models

Typed obernant family

These are scoped partial relations, not executable inverses or semantic proofs.

behavior_complement

The observation suite excludes the named wrong coefficients, vertices, brackets and statuses on these fixtures: 17 orthogonal designs against scalar analytic shrinkage; correlated design against 1681 grid objectives and KKT tolerance; true zero column; zero budget with/without optimal zero; negative penalty and NaN; deterministic repeat; nonzero underflowing column rejection.. It says nothing about callbacks or matrices outside these finite cases; arbitrary unseen bugs remain compatible with all passes.

reverse_reconstruction

A passing transcript reconstructs only a family of implementations agreeing on these assertions. The analytic oracle is Orthogonal columns decouple, giving x_j=sign(A_j'y)*max(|A_j'y|-lambda,0)/q_j. The independent scalar formula verifies coefficient values. The dense grid is only a finite objective comparison, while reported KKT checks validate its chosen stopping metric.. Many different update orders or untested behaviors have the same pass transcript, so source recovery is not unique.

independent_oracle

Orthogonal columns decouple, giving x_j=sign(A_j'y)*max(|A_j'y|-lambda,0)/q_j. The independent scalar formula verifies coefficient values. The dense grid is only a finite objective comparison, while reported KKT checks validate its chosen stopping metric.

mutation_sensitivity

Pass zero lambda to production soft_threshold; orthogonal_oracle must reject the compiled wrong shrinkage coefficients.

boundary_partition

A true zero column stays zero, an underflowing nonzero column fails arithmetic, a high lambda can converge at zero even with zero budget, but low lambda with zero budget exhausts it.

tests

Executable checks

Run cargo test -p mova-algorithms coordinate_descent_lasso::tests.

17 orthogonal designs against scalar analytic shrinkage; correlated design against 1681 grid objectives and KKT tolerance; true zero column; zero budget with/without optimal zero; negative penalty and NaN; deterministic repeat; nonzero underflowing column rejection.

Independent oracle: Orthogonal columns decouple, giving x_j=sign(A_j'y)*max(|A_j'y|-lambda,0)/q_j. The independent scalar formula verifies coefficient values. The dense grid is only a finite objective comparison, while reported KKT checks validate its chosen stopping metric.

Compiled negative control: Pass zero lambda to production soft_threshold; orthogonal_oracle must reject the compiled wrong shrinkage coefficients.

No allocator failure injection, all-input proof or benchmark is claimed.

prospective

Prospective optimization model

Before source creation. Brent maintains unimodal bracket and three sampled points; accepts safeguarded parabolic proposals, otherwise golden contraction. O(k) callbacks, O(1) storage. Deterministic callback is assumed; strict unimodality cannot be checked. Armijo shrinks positive alpha by rho until f(alpha)<=f0+calphaslope, slope<0. O(k) callbacks, O(1) space; supplied f0 and slope are caller premises. Dense quadratics f=.5*x'Qx-b'x use symmetric diagonally dominant nonnegative Q, dimension<=64, finite magnitudes<=1e50. This is a sufficient restricted PSD domain, not arbitrary convex quadratics. PG clips x-g/L into finite bounds with L=max absolute row sum; mapping residual is max |x-clip(x-g/L)|. FW on unit simplex selects earliest minimum gradient vertex, gap=g'(x-s), step=min(1,gap/(d'Qd)); linear curvature uses step 1. O(kn²) time O(n) scratch. These real identities are not floating error guarantees. Lasso minimizes .5||Ax-y||²+lambda||x||1 by cyclic exact coordinate minimization and residual maintenance, using existing soft threshold kernel. Up to 256 rows and 64 columns. O(kmn) time O(m+n) space. Stop on recomputed KKT max violation. Zero columns set zero. Deterministic ties and iteration orders. All validation precedes work; checked allocation and nonfinite arithmetic explicit; budget<=100000, tolerance positive finite. Each routine distinguishes convergence, budget exhaustion and representational stagnation. No percent objective/solution bound. Expected algorithmic advantage: interpolation avoids golden-only work on smooth functions; cached residual updates avoid recomputing predictions per coordinate. No measured speed claim. Executable approximate surrogate deferred: residual and finite samples lack a justified universal supported percentage metric. References: Brent, Algorithms for Minimization without Derivatives (1973); Armijo (1966); Nocedal and Wright (2006); Friedman et al., Regularization Paths for Generalized Linear Models via Coordinate Descent (2010); Frank and Wolfe (1956).

validation

Validation epoch 2026-10-30

External receipts: $MOVA_DATA/runs/octopus-wave20-optimization-2026-10-30. Two debug and two release library runs each pass 568 tests, including 21 new native tests, with identical sorted test-name/outcome transcripts. Strict all-target algorithms Clippy and focused rustfmt pass.

Five independently compiled production mutants are rejected by named runtime assertions; source bytes restored before the positive rerun. This source's control: Pass zero lambda to production soft_threshold; orthogonal_oracle must reject the compiled wrong shrinkage coefficients.

Fresh syntax projections are generated twice and compared before installing syntax.json. These are partial structural observations, not macro-expanded AST or semantic proofs. No performance or universal <=10% result follows.

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