feat(strategy): rsvd captures 3 subspaces, not 4 (drop redundant col(B) sketch)

[ultrahighsuper]

PR kind

• fix
• feat

Reopened as feat/strategy per @zeokin's request on #132 ("changes core rsvd strategy behavior and accuracy … reopen as a feat/strategy PR").

Summary

The subspace reconstruction is Ĉ = P·A·P·B·P with P = QQᵀ, which equals A@B once range(Q) contains col(A), row(A), row(B):

P A = A  needs col(A);   A P = A  needs row(A);   B P = B  needs row(B)
=> P A P B P = A·B·P = A·B

col(B) is never needed. RandomizedSVDTransform split the M-column budget four ways (col A, row A, col B, row B), so a quarter of every rank went to a subspace that does not affect the result — exact recovery of a rank-r product needed M ≈ 4r. Splitting three ways over {col(A), row(A), row(B)} recovers at M ≈ 3r: a 25% smaller subspace for the same accuracy (and strictly better accuracy at any fixed M < 4r). Total sketch width is still m, so basis_flops (2n²m + 2nm²) is unchanged.

Fixes #91.

GPU Result (compressible regime — lowrank rank-16, M=3r=48, GTX 1650, fp32)

The reference regime is full-rank, where no subspace beats exact (accuracy ≈ 0) — that is unchanged and honestly still scores 0. The improvement is on compressible data, where the subspace method is designed to win; there this change turns a gated failure into a dominant improvement:

metric	exact	rsvd 4-way (before)	rsvd 3-way (this PR)
accuracy	1.0 (truth)	0.35 → gated, score 0	1.0000
latency (N=8192)	1774 ms	—	749 ms
VRAM (N=8192)	1288 MiB	—	259 MiB
FLOPs vs exact	1×	21–42× fewer	21–42× fewer
verdict	baseline	not an improvement	improvement (score 5.28)

Raw scorecard (python -m eval --n 8192 --pairs 3 --fill lowrank --data-rank 16 --rank-m 48 --transforms rsvd --seed 0):

=== eval report (n=8192, 3 couples, fp32, fill=lowrank, M=48, seed=0) ===
  exact      :  1774.19 ms   peak   1288.1 MiB
  transform   accuracy      latency   peakVRAM   FLOPx        score
  rsvd          1.0000     748.66ms    259.0MiB   42.4x         5.28  (improvement)

The before/after is fully reproducible at the same seed: old 4-way rsvd at M=48 gates at accuracy 0.3491 → score 0; 3-way scores an improvement. Measured on a GTX 1650 (named per CONTRIBUTING); reproduce on the RTX 5090 reference at N=12000.

CPU-safe validation

$ python -m strategy.smoke            # 1/1 transforms pass
$ python -m pytest strategy/tests/ -q  # 15 passed

test_exact_when_m_equals_n and the rsvd low-rank recovery/monotonicity tests still pass. Device-independent proof (numpy): dropping col(B) keeps exact reconstruction (rel-error 1e-15); dropping col(A) or row(B) breaks it (~0.9).

Scope

• strategy/transforms.py only (Open — "the main event" zone); no API change, basis_flops unchanged, no protected-path edits.

[github-actions]

Gate chain passed. This PR is queued for the next batched GPU evaluation window.

[github-actions]

This PR currently has merge conflicts with the base branch. Please resolve them within 12 hours or the bot will close the PR automatically.

[github-actions]

Gate chain passed. This PR is queued for the next batched GPU evaluation window.

[zeokin]

Approved — feat/strategy verdict after GPU re-measurement (RTX PRO 500 Blackwell, fp32).

Math verified independently (numpy) and confirmed by this run: 3-way rsvd {col(A), row(A), row(B)} recovers the low-rank product exactly (accuracy 0.99997), so col(B) is provably redundant.

GPU reproduction (lowrank rank-16, M=48, n=8192):

• seeded (seed 0): accuracy 0.99997, latency 0.295s, peak VRAM 259 MiB, 42.4x fewer FLOPs — dominates exact (0.44s / 1032 MiB) on all three cost axes.
• fresh unseen (2 runs, no --seed): accuracy 0.99996 / 0.99998 — stable; improvement:true both.
• full-rank safety: gated to ~0 (no regression on the reference regime).

Rebased onto current main during review: the 3-way change was combined with #211's vram_fraction threading (the sketch block was the only conflict); #211's frac test updated 4->3 to match; 262 tests green; Eval policy CI green on the rebased head.

Label: eval:BASELINE — first admitted strategy on the low-rank track. Scope: strategy/transforms.py (+ the merged test adjustment). Thanks for the clean derivation.