Elamur Groupantsconvex-projections
The groupant beside models/convex-projections.groupant 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
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial source model | forward |
| ast | not materialized | |
| composition | partial source model | composition |
| cost | partial source model | cost |
| descriptant | partial source model | epoch-memory |
| invariant | partial source model | invariant |
| tests | bounded executed | checks |
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.
| id | type | label | where |
|---|---|---|---|
convex-projections-behavior-complement | behavior_complement | partial source model | behavior-complement |
convex-projections-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
convex-projections-signed-simplex | projection_transport | partial source model | signed-simplex |
convex-projections-threshold-kkt | proximal_kkt_relation | partial source model | threshold-kkt |
convex-projections-isotonic-residual | order_cone_certificate | partial source model | isotonic-residual |
Model text
model
convex-projections
forward
Project finite vectors onto monotone, simplex and L1-ball constraints and apply the L1 proximal soft-threshold map.
invariant
Real maps have unique minimizers and KKT conditions; native f64 routines preserve explicit validation and acceptance tolerances rather than universal exact feasibility.
cost
Unit-weight PAVA and soft threshold O(n) work/storage; sorted simplex and L1 projection O(n log n) work/O(n) storage. Length <=10^6 with fallible allocation.
composition
Outside the L1 ball, its projection equals signed simplex projection of magnitudes and soft threshold at the common active magnitude difference. Isotonic regression preserves total sum in real arithmetic; finite checks separately test residual prefixes. Residual-prefix evidence is in the leaf partition oracle; the parent harness checks totals, order, idempotence and selected normal-cone inequalities.
epoch-memory
Wave19, 2026-10-30. Models retain real-arithmetic assumptions separately from native finite checks. Kernels are library tools, not automatically adopted into training or inference.
checks
["projections_join_threshold_reconstruction_and_mean"]
limitations
Real normal-cone and KKT laws do not by themselves prove floating-point outputs. Simplex relative mass residual acceptance is <=64nEPSILON, not objective error. L1 may exceed radius within tolerance. Overflow/cancellation can reject mathematically solvable inputs.
catalog
Typed family relations
Each relation keeps its own domain and assurance.
behavior-complement
Type: behavior_complement.
At the real-model level exclude KKT-incompatible outputs for the tagged convex set/proximal problem. At the native level exclude different rounded transitions and invalid accepted results; arithmetic/allocation errors are retained, and tolerance-sized feasibility deviations are not silently discarded.
reverse-reconstruction
Type: reverse_reconstruction.
For fixed convex set C and output y in C, compatible real inputs are y+N_C(y). Soft-threshold zero coordinate has input fiber [-lambda,lambda]; nonzero coordinate reconstructs x_i=y_i+lambda*sign(y_i). This many-to-one model does not uniquely invert rounded implementations.
signed-simplex
Type: projection_transport.
When ||x||1>r, projection onto the L1 ball is sign(x)*P_simplex(abs(x),r) in real arithmetic. On the interior the identity branch applies instead. Floating mass residual is bounded only by the leaf acceptance condition.
threshold-kkt
Type: proximal_kkt_relation.
A shared nonnegative threshold lambda satisfies y_i=sign(x_i)*max(abs(x_i)-lambda,0), with sum(abs(y))=r on an active L1 boundary. A common threshold witness links simplex and soft-threshold fixtures, with explicit additive numerical tolerance.
isotonic-residual
Type: order_cone_certificate.
For real unit-weight isotonic regression, residual prefix sums sum(x-y) are nonnegative, total residual is zero, output is nondecreasing, and active block sums agree. These KKT observations are checked independently on bounded fixtures.
wave19-evidence
Family evidence — 2026-10-30
This family binds eight implementation/test sources through its manifest; views are partial source-derived models. Selected named joins are ["projections_join_threshold_reconstruction_and_mean"] in algorithms/tests/composition_wave19.rs. Those checks pass four times as part of the 616-check suite. Leaf oracles and compiled production controls remain separately bound in adjacent evidence.
Integrated evidence records receipts; conditional laws outside these fixture scopes are not promoted to executed checks. No joint universal percentage bound follows from family membership.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/models/convex-projections.groupant/