[Perf #478] RandomForest Digits: remove per-tree training overhead and improve scaling

[godofecht]

Parent: #478

Canonical v2 Digits: Flow fit 93.14 ms vs sklearn 28.95 ms; Flow predict 0.608 ms vs sklearn 0.919 ms. Prediction already wins; training is the entire regression. Iris end-to-end wins ~9.9x.

Profile bootstrap/sample generation, RNG, per-tree setup, tree fit, feature subsampling, allocation/free, tree storage and opportunities for parallel or batched work. Reuse #482 findings where the tree builder is shared.

Acceptance: tree-by-tree timing and allocation profile; distinguish forest orchestration from tree-core cost; scaled n_estimators/sample/feature sweeps; preserve bootstrap/RNG semantics and learned-state diagnostics; Digits fit >=0.95x first, target >=1.05x, without sacrificing the current prediction win.

[godofecht]

I found a bootstrap-specific optimization that should be semantically exact and is worth A/B testing before attacking more tree-core code.

A size-n bootstrap sample is completely represented by the per-source-row multiplicities m_i. For any classification-tree threshold, the explicit copied bootstrap class counts satisfy

N^B_{L,c}(t) = sum_{i in L(t)} m_i 1[y_i=c],

and likewise on the right. Therefore node counts, majority class, Gini/entropy, weighted child impurity and impurity decrease are identical between a materialized X_boot/y_boot and the original X/y plus multiplicities. With identical feature-subset RNG, threshold ordering and tie rules, the whole deterministic tree is identical by induction.

That lets RandomForest generate the same bootstrap RNG stream but do multiplicity[draw] += 1 rather than copying the row into X_boot/y_boot. The tree builder operates on source-row IDs + weights; node n_samples remains the sum of multiplicities. Duplicate equal feature values must be consumed as one value group before testing the next threshold boundary.

For the ordinary size-n bootstrap, E[U] = n(1-(1-1/n)^n) ~= 0.63212n unique rows. On Digits n=1797 this is ~1136 active source rows, ~661 fewer than the copied 1797-row representation. The root-level row-visit ratio is therefore ~0.632 if the weighted scan visits each active source row once. Materializing X_boot also costs at least 4nd + 4*n bytes per tree for f32 X/y, excluding allocator metadata and the bootstrap-index array.

I independently checked explicit-vs-weighted best-split equivalence over 100 randomized multiclass bootstrap cases including repeated feature values; all matched. The complete derivation and an adjacent Flow witness are now in OpenProjects as ml/multiplicity-preserving-random-forest-bootstrap.{md,flow}.

Next production test: add a multiplicity-aware RF fit path and require identical PRNG progression plus node-by-node feature/threshold/n_samples/impurity/leaf equality, then measure per-tree bootstrap time, tree time, U/n, copied bytes and row visits. This should tell us how much of #483 is still bootstrap orchestration versus the tree core.