Parity tolerances

This table records the documented per-pair tolerances between every two reference PLS implementations pls4all cross-checks against. Numbers in bold are the relaxations applied after Codex review of the Phase 0 roadmap.

For cross-algorithm rows the comparator gates on predictions, coefficients, intercept, x_mean, x_scale, y_mean, y_scale only — raw latent matrices (weights_W, loadings_P, y_loadings_Q, rotations_R, scores_T, y_scores_U) are diagnostic when algorithms differ.

Truth-source legend

• 📐 marks the column (A or B) whose implementation produced the expected values in the corresponding fixture under parity/fixtures/. The pls4all C++ kernel and other binding-side ports are tested for bit-equivalence against that side; the marked column is the library-of-record for the row.

  • For pairs where the producer is pls4all itself (e.g. pls4all-refcpu-vs-pls4all-blas, pls4all-linux-vs-pls4all-macos-arm64), the 📐 sits on column A (the REFERENCE_CPU build) — that build is the deterministic baseline every other build is compared against.

  • For solver-parity rows generated by a NumPy / sklearn / R mirror (e.g. pls4all-numpy-simpls, sklearn/PLSRegression/self_roundtrip, pls-r-oscorespls), the 📐 sits on column A (the generator side).

  • For the bench-AOM_v0-* rows, the 📐 sits on column A — the bench oracle is the canonical AOM reference per user policy.

• 📜 flags rows whose A/B pair is documented but has no active fixture producer yet (e.g. R-generator stubs still on the roadmap). These rows describe the intended tolerance once the matching fixture is wired up; they are not gating any test today.

• Unmarked rows are pair-tolerance specifications that don’t yet correspond to a single canonical producer (typically cross-implementation comparisons where neither side is strictly the truth).

This convention mirrors the 📐 icon used in the per-method benchmark dashboards under docs/methods/, sourced from benchmarks/parity_timing/registry.py. The two layers gate different surfaces — JSON fixtures + C++ ctest here, live cross-binding runs there — but both honour the same “registry-declared canonical reference” notion.

Row key	A	B	Variant	Algorithm	abs_tol	rel_tol	Comparison set	Notes
sklearn/PLSRegression/self_roundtrip	📐 sklearn 1.4 PLSRegression	sklearn (round-trip)	regression	NIPALS	1e-15	1e-15	all	sanity
sklearn-vs-pls-kernelpls	sklearn 1.4 PLSRegression	R pls 2.8 plsr(method='kernel')	regression	NIPALS vs kernel	5e-7	1e-6	predictions, coefficients, intercept, x/y mean+scale	cross-algorithm — 📜 documented pair (no active fixture producer)
sklearn-vs-pls-simpls	sklearn 1.4 PLSRegression	R pls 2.8 plsr(method='simpls')	regression	NIPALS vs SIMPLS	1e-5	1e-4	predictions, coefficients, intercept, x/y mean+scale	cross-algorithm — 📜 documented pair (no active fixture producer)
sklearn-vs-mixomics-pls	sklearn 1.4 PLSRegression	mixOmics 6.28 pls	regression	NIPALS	1e-7	1e-7	predictions, coefficients, intercept, x/y mean+scale	mixOmics scales differently — predictions agree; 📜 documented pair (no active fixture producer)
sklearn-vs-nirs4all-simpls	sklearn 1.4 PLSRegression	nirs4all 0.8 SIMPLS	regression	SIMPLS	1e-6	1e-5	predictions, coefficients, intercept, x/y mean+scale	cross-algorithm — 📜 documented pair (no active fixture producer)
pls4all-numpy-preprocessing	📐 NumPy/SciPy preprocessing fixture	pls4all C++ n4m_pipeline_*	preprocessing	identity / center / autoscale / Pareto / SNV / MSC / EMSC / detrend / Savitzky-Golay / Norris-Williams / ASLS / Haar wavelet / OSC / EPO	1e-12	1e-12	transform outputs	operator parity
pls4all-numpy-aom-preprocessing	📐 NumPy soft/hard AOM preprocessing-bank fixture	pls4all C++ internal AOM preprocessing kernel	preprocessing	operator-bank output mixing	1e-10	1e-10	operator outputs, gating weights, mixed transform, operator kind trace	Phase 6a AOM preprocessing parity
bench-AOM_v0-aom-operators	📐 nirs4all/bench/AOM_v0/aompls strict-linear operators	pls4all C++ internal AOM strict operator kernels	AOM	identity / detrend / zero-padded SG / finite difference / Norris-Williams / Whittaker / FCK	1e-10	1e-10	operator transform outputs	Phase 6c/6d bench AOM_v0 operator parity
bench-AOM_v0-aom-selection	📐 nirs4all/bench/AOM_v0/aompls global AOM CV fixture	pls4all C++ internal AOM global-selection kernel	AOM	SIMPLS materialized global selection	1e-8	1e-8	per-operator RMSE curves, best scores, selected operator/component count, predictions	Phase 6b/6c/6d bench AOM_v0 parity; current tranche covers identity, detrend, zero-padded SG, finite difference, Norris-Williams, Whittaker and FCK strict-linear operators
bench-AOM_v0-pop-selection	📐 nirs4all/bench/AOM_v0/aompls POP per-component CV fixture	pls4all C++ internal POP selection kernel	POP	SIMPLS covariance per-component selection	1e-8	1e-8	component candidate scores, prefix scores, selected operator sequence, predictions	Phase 6e bench AOM_v0 parity; intentionally matches bench POP’s historical PLS1 CV residual broadcasting
pls4all-numpy-regression-metrics	📐 NumPy regression metrics fixture	pls4all C++ internal metric kernels	validation	RMSE / MAE / bias / R2 / Q2 / slope / intercept / RPD / RPIQ	1e-12	1e-12	scalar metrics	metric parity
pls4all-numpy-binary-classification-metrics	📐 NumPy binary classification metrics fixture	pls4all C++ internal metric kernels	validation	sensitivity / specificity / balanced accuracy / precision / F1 / MCC / AUC	1e-12	1e-12	scalar metrics	metric parity
pls4all-numpy-classification-extensions	📐 NumPy classification extension fixtures	pls4all C++ internal metric kernels	validation	multiclass macro/micro metrics / one-vs-rest AUC / fixed-bin calibration	1e-12	1e-12	scalar metrics, confusion matrix, calibration bins	extension parity
sklearn/PLSRegression/variable-importance	📐 sklearn 1.4 PLSRegression score/loading formulas	pls4all C++ internal variable-importance kernels	validation	VIP / selectivity ratio	1e-8	1e-8	per-feature vectors	variable importance parity
sklearn/PLSRegression-variable-selection-rankers	📐 sklearn 1.4 PLSRegression score/loading/coefficient formulas	pls4all C++ internal variable-selection rankers	selection	VIP / coefficient magnitude / selectivity ratio	1e-8	1e-8	per-feature scores plus exact top-k indices	deterministic score-desc/index-asc ranker parity
sklearn/PLSRegression-interval-selection-cv	📐 sklearn 1.4 PLSRegression with deterministic k-fold intervals	pls4all C++ internal interval-selection kernel	selection	moving-window / interval CV	1e-8	1e-8	metrics by interval, RMSE vector, exact best interval	contiguous interval scan parity
sklearn/PLSRegression-biPLS-selection	📐 sklearn 1.4 PLSRegression deterministic backward interval elimination	pls4all C++ internal biPLS-selection kernel	selection	backward interval PLS	1e-8	1e-8	interval partition, removal path, RMSE path, best step, selected interval/feature indices	deterministic biPLS parity
sklearn/PLSRegression-siPLS-selection	📐 sklearn 1.4 PLSRegression deterministic exhaustive interval combinations	pls4all C++ internal siPLS-selection kernel	selection	synergy interval PLS	1e-8	1e-8	interval partition, candidate interval matrix, RMSE by combination, best combination, selected interval/feature indices	deterministic siPLS parity
sklearn/PLSRegression-coefficient-stability	📐 sklearn 1.4 PLSRegression over deterministic Monte-Carlo subsets	pls4all C++ internal stability-selection kernel	selection	MCUVE-style coefficient stability	1e-8	1e-8	mean/std coefficients, stability scores, exact top-k indices	Monte-Carlo subset parity
sklearn/PLSRegression-UVE	📐 sklearn 1.4 PLSRegression over deterministic Monte-Carlo subsets plus artificial variables	pls4all C++ internal UVE-selection kernel	selection	UVE artificial-variable threshold	1e-8	1e-8	real/noise stability scores, max-noise threshold, exact selected indices	deterministic SplitMix64 artificial-variable parity
sklearn/PLSRegression-EMCUVE	📐 sklearn 1.4 PLSRegression over deterministic ensemble MC-UVE members	pls4all C++ internal EMCUVE-selection kernel	selection	EMCUVE ensemble vote rule	1e-8	1e-8	mean real stability scores, vote frequencies, noise thresholds, exact selected indices	deterministic ensemble MC-UVE parity
sklearn/PLSRegression-randomization-selection	📐 sklearn 1.4 PLSRegression coefficient scores with deterministic Y permutations	pls4all C++ internal randomization-selection kernel	selection	randomization-test PLS selector	1e-8	1e-8	observed scores, p-values, exceedance counts, exact selected indices	deterministic SplitMix64 permutation parity
sklearn/PLSRegression-SPA-selection	📐 sklearn 1.4 PLSRegression coefficient seed plus NumPy successive projections	pls4all C++ internal SPA-selection kernel	selection	SPA-PLS projection selector	1e-8	1e-8	coefficient scores, selection step scores, exact selected indices	deterministic projection parity
sklearn/PLSRegression-CARS-selection	📐 sklearn 1.4 PLSRegression deterministic exponential-retention CV	pls4all C++ internal CARS-selection kernel	selection	CARS-PLS competitive adaptive reweighted sampling	1e-8	1e-8	coefficient scores by iteration, RMSE path, retained counts, exact selected indices	deterministic CARS parity
sklearn/PLSRegression-RandomFrog-selection	📐 sklearn 1.4 PLSRegression deterministic Random Frog subset walk	pls4all C++ internal Random-Frog-selection kernel	selection	Random Frog PLS inclusion-frequency selector	1e-8	1e-8	global scores, inclusion frequencies, RMSE path, subset sizes, exact selected indices	deterministic Random Frog parity
sklearn/PLSRegression-SCARS-selection	📐 sklearn 1.4 PLSRegression deterministic stability-weighted subsampling CV	pls4all C++ internal SCARS-selection kernel	selection	SCARS-PLS stability competitive adaptive reweighted sampling	1e-8	1e-8	coefficient scores by iteration, stability scores, RMSE path, retained counts, exact selected indices	deterministic SCARS parity
sklearn/PLSRegression-GA-selection	📐 sklearn 1.4 PLSRegression deterministic genetic subset search	pls4all C++ internal GA-selection kernel	selection	GA-PLS population search	1e-8	1e-8	global scores, inclusion frequencies, best/mean RMSE path, best subset sizes, exact selected indices	deterministic GA-PLS parity
sklearn/PLSRegression-Shaving-selection	📐 sklearn 1.4 PLSRegression deterministic recursive coefficient shaving	pls4all C++ internal Shaving-selection kernel	selection	shaving PLS recursive elimination	1e-8	1e-8	coefficient scores by step, RMSE path, retained counts, exact selected indices	deterministic shaving parity
sklearn/PLSRegression-REP-selection	📐 sklearn 1.4 PLSRegression deterministic fixed-count recursive elimination	pls4all C++ internal REP-selection kernel	selection	REP-PLS recursive elimination	1e-8	1e-8	coefficient scores by step, RMSE path, retained counts, removed counts/indices, exact selected indices	deterministic REP parity
sklearn/PLSRegression-IPW-selection	📐 sklearn 1.4 PLSRegression deterministic coefficient reweighting	pls4all C++ internal IPW-selection kernel	selection	IPW-PLS iterative predictor weighting	1e-8	1e-8	score path, weight path, RMSE path, ranking indices, exact selected indices	deterministic IPW parity
sklearn/PLSRegression-ST-selection	📐 sklearn 1.4 PLSRegression deterministic score thresholds	pls4all C++ internal ST-selection kernel	selection	ST-PLS score-threshold selector	1e-8	1e-8	normalized coefficient scores, threshold RMSE path, masks/counts, ranking indices, exact selected indices	deterministic ST-PLS parity
sklearn/PLSRegression-BVE-selection	📐 sklearn 1.4 PLSRegression deterministic backward variable elimination	pls4all C++ internal BVE-selection kernel	selection	BVE-PLS backward elimination	1e-8	1e-8	candidate RMSE matrix, chosen RMSE path, retained counts, removed indices, exact selected indices	deterministic BVE parity
sklearn/PLSRegression-T2-selection	📐 sklearn 1.4 PLSRegression plus plsVarSel-style Hotelling T2 thresholds	pls4all C++ internal T2-selection kernel	selection	T2-PLS loading-weight selection	1e-8	1e-8	T2 scores, UCL per alpha, RMSE path, selected masks/counts, exact selected indices	deterministic T2-PLS parity
numpy/WVC-PLS-selection	📐 NumPy mirror of plsVarSel WVC-PLS numeric-regression WVC2	pls4all C++ internal WVC-selection kernel	selection	WVC-PLS weighted variable contribution	1e-8	1e-8	weights, loadings, WVC score matrix, final scores, exact top-k indices	deterministic WVC-PLS parity
numpy/WVC-PLS-threshold-selection	📐 NumPy WVC-PLS threshold/factor rule over WVC2 scores	pls4all C++ internal WVC-threshold-selection kernel	selection	thresholded/factor WVC-PLS	1e-8	1e-8	final scores, ranked indices, mean score, effective threshold, selected indices	deterministic WVC threshold/factor parity
sklearn/PLSRegression/component-coefficients	📐 sklearn 1.4 PLSRegression prefix coefficient formulas	pls4all C++ internal component coefficient kernels	validation	original-scale coefficients per latent prefix	1e-8	1e-8	component-major coefficient blocks	component-count model selection support
pls4all-python-validation-splits	📐 Python deterministic split fixture	pls4all C++ internal split generators	validation	k-fold / LOO / holdout	exact	exact	train/test index plans	splitter parity
pls4all-python-advanced-validation-splits	📐 Python deterministic split fixture	pls4all C++ internal split generators	validation	external folds / repeated k-fold / Monte-Carlo / Kennard-Stone / SPXY	exact	exact	train/test index plans	advanced splitter parity
sklearn/PLSRegression/kfold-cv	📐 sklearn 1.4 PLSRegression with deterministic k-fold splits	pls4all C++ internal CV engine	validation	NIPALS PLS regression CV	1e-8	1e-8	out-of-sample predictions, aggregate metrics, test index plan	cross-validation parity
pls4all-numpy-simpls-component-cv	📐 NumPy SIMPLS with deterministic k-fold splits	pls4all C++ internal model-selection kernel	validation	SIMPLS component-count CV	1e-8	1e-8	metrics by component, best component count	component selection parity
pls4all-numpy-simpls	📐 pls4all NumPy SIMPLS fixture	pls4all C++ N4M_SOLVER_SIMPLS	regression	SIMPLS	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
pls4all-numpy-svd	📐 pls4all NumPy SVD fixture	pls4all C++ N4M_SOLVER_SVD	regression	SVD	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
pls4all-numpy-power	📐 pls4all NumPy power-iteration fixture	pls4all C++ N4M_SOLVER_POWER	regression	power PLS	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
pls4all-numpy-randomized-svd	📐 pls4all NumPy randomized-SVD fixture	pls4all C++ N4M_SOLVER_RANDOMIZED_SVD	regression	randomized SVD PLS	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
sklearn/PLSCanonical/nipals	📐 NumPy mirror of sklearn 1.4 PLSCanonical(algorithm='nipals')	pls4all C++ N4M_ALGO_PLS_CANONICAL + N4M_SOLVER_NIPALS	canonical	NIPALS + canonical deflation	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity
sklearn/PLSCanonical/svd	📐 NumPy mirror of sklearn 1.4 PLSCanonical(algorithm='svd')	pls4all C++ N4M_ALGO_PLS_CANONICAL + N4M_SOLVER_SVD	canonical	SVD + canonical deflation	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity
sklearn/PLSSVD	📐 NumPy mirror of sklearn 1.4 PLSSVD	pls4all C++ N4M_ALGO_PLS_SVD + N4M_SOLVER_SVD	cross-decomposition	direct cross-covariance SVD score model	1e-9	1e-9	transform scores, weights, projection predictions, preprocessing stats	algorithm parity; predict is pls4all latent projection
sklearn/PLSDA-dummy/PLSRegression	📐 sklearn 1.4 PLSRegression on dummy-coded Y	pls4all C++ N4M_ALGO_PLS_DA + N4M_SOLVER_NIPALS	discriminant	PLS-DA dummy-response scores	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity; predictions are continuous class scores
sklearn/PLSRegression-scores-plus-numpy-LDA	📐 sklearn 1.4 PLSRegression scores + NumPy pooled-covariance LDA	pls4all C++ internal PLS-LDA kernel	discriminant	PLS score-space LDA	1e-8	1e-8	predictions, decision scores	classifier parity
sklearn/PLSRegression-scores-plus-numpy-logistic	📐 sklearn 1.4 PLSRegression scores + NumPy baseline multinomial logistic Newton	pls4all C++ internal PLS-logistic kernel	discriminant	PLS score-space logistic	1e-8	1e-8	predictions, decision scores, probabilities, intercepts, coefficients	classifier parity
sklearn/PLSRegression-block-weighted-MBPLS	📐 NumPy block autoscaling + sklearn 1.4 PLSRegression(scale=False)	pls4all C++ internal MB-PLS kernel	regression	block-weighted MB-PLS	1e-8	1e-8	predictions, coefficients, intercept, block weights, x preprocessing stats	multi-block parity
sklearn/PLSRegression-local-window-LWPLS	📐 Gaussian-weighted local PLS on raw rows (λ = max(1, 0.5·n_neighbors)), mirroring nirs4all lwpls.py::_lwpls_predict	pls4all C++ internal LW-PLS kernel	regression	local-window LW-PLS	1e-8	1e-8	predictions, neighbor indices	local model parity; fixture agrees with the C++ core to ~7e-16
pls4all-numpy-opls	📐 pls4all NumPy OPLS1 fixture	pls4all C++ N4M_ALGO_OPLS + N4M_SOLVER_NIPALS	orthogonal	OPLS1 + orthogonal corrections	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity; first score column is predictive, later columns are orthogonal
pls4all-numpy-opls-da-binary	📐 pls4all NumPy OPLS1 fixture on one-column dummy Y	pls4all C++ N4M_ALGO_OPLS_DA + N4M_SOLVER_NIPALS	discriminant	binary OPLS-DA dummy-response scores	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity
pls4all-numpy-opls-da-multiclass	📐 pls4all NumPy multivariate OPLS fixture on one-hot Y	pls4all C++ N4M_ALGO_OPLS_DA + N4M_SOLVER_NIPALS	discriminant	multi-class OPLS-DA common predictive score	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity; one shared predictive subspace
pls4all-numpy-kernelpls	📐 pls4all NumPy kernel PLS fixture	pls4all C++ N4M_SOLVER_KERNEL_ALGORITHM	regression	kernel PLS	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
pls4all-numpy-wide-kernelpls	📐 pls4all NumPy wide-kernel PLS fixture	pls4all C++ N4M_SOLVER_WIDE_KERNEL	regression	wide-kernel PLS	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
pls-r-oscorespls	📐 NumPy port of R pls oscorespls.fit	pls4all C++ N4M_SOLVER_ORTHOGONAL_SCORES	regression	orthogonal-scores PLS	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	solver parity
pls4all-numpy-pcr	📐 pls4all NumPy PCR fixture	pls4all C++ N4M_ALGO_PCR + N4M_SOLVER_SVD	regression	PCR	1e-9	1e-9	predictions, coefficients, intercept, x/y mean+scale, latent arrays	algorithm parity
sklearn-canonical-vs-mixomics-canonical	sklearn 1.4 PLSCanonical	mixOmics 6.28 pls(mode='canonical')	canonical	NIPALS	1e-7	1e-7	predictions, coefficients, intercept, x/y mean+scale	cross-impl — 📜 documented pair (no active fixture producer)
ropls-opls-vs-nirs4all-opls	ropls 1.34 opls	nirs4all 0.8 OPLS	orthogonal	OPLS-NIPALS	1e-5	1e-4	predictions only	OPLS sign + ordering vary; 📜 documented pair (no active fixture producer)
bench-AOM_v0-vs-pls4all-aom	📐 nirs4all/bench/AOM_v0/aompls	pls4all (Phase 6)	AOM	SIMPLS + operator bank	TBD	TBD	selection curves, selected operators/components, predictions	Source-of-truth is the bench AOM_v0 reference, not the packaged nirs4all model API
pls4all-refcpu-vs-pls4all-blas	📐 pls4all REFERENCE_CPU	pls4all BLAS	any	any	1e-10	1e-9	all	same algorithm, different SGEMM path; fixed reduction order, no FMA
pls4all-refcpu-vs-pls4all-cuda	📐 pls4all REFERENCE_CPU	pls4all CUDA	any	any	1e-9	1e-8	predictions	fp64 GPU drift envelope
pls4all-linux-vs-pls4all-macos-arm64	📐 pls4all REFERENCE_CPU (Linux x86_64)	pls4all REFERENCE_CPU (macOS arm64)	any	any	1e-11	1e-11	all	cross-platform sanity

The tolerance_table_row key in each fixture’s comparison_policy block points to a row by name. The comparator resolves missing per-field tolerances against this row.