# MNF Subspace v0.1 — Experiment Results: Exact Low-Rank Predictive Atlas
Status: research branch (`mnf-subspace`), NOT a format change.
MNF5/MNF6/MNF7 frozen formats untouched.
## Question (review, ADR)
*Can a shared low-dimensional model encode image variation more cheaply
than conventional prediction plus entropy coding?*
## Method
All experiments in `crates/mnf-subspace` (discovery/basis/predictor
layers per §7):
- Discovery: power-iteration SVD, deterministic initialization and
sign-canonical directions (fp, encoder-only).
- Basis: i16 fixed-point quantization at scale s=14 (q14), integer mean.
- Synthesis: `xhat = clip(mu_c + (sum B_jc q_j + half) >> s)`, i64
accumulators, deterministic rounding. No fp in the decoder path.
- Residual: `(x - xhat) mod 256`; reconstruction `(xhat + r) mod 256`.
- Every test asserts exact reconstruction byte-for-byte.
- Economics: both streams framed identically then zlib'd (same coder
both sides, mirroring the shipped codec's final zlib pass).
## Results (screenshot_640x400, 1000 tiles)
| A | literal tiles | 3,830 | — |
| B | MED residual | **3,135** | −18.2% |
| E3 | fixed 5-dir basis (planes+grads), coord search | 3,742 | −2.3% |
| E4 | learned PCA basis k=1/2/4/8/16 (basis overhead excluded) | 8,863 / 11,096 / 11,153 / 10,623 / 10,717 | +131%..+191% |
| E5 | MED + learned-on-MED-residuals k=8 (overhead excluded) | 6,383 | +66.7% |
| — | MNF5-atlas shipped best | 3,947 | (worse than plain MED) |
| — | MNF7 shipped | 1,823 | (flags/zstd/planar — the real winner) |
## Findings
1. **The conventional baseline dominates everything measured.** A plain
MED + zlib beats the entire shipped MNF5-atlas pipeline (3,135 vs
3,947) — the codec's current contribution is its container/planner,
not its predictor.
2. **Fixed analytic subspaces: small but real.** 5 quantized directions
bought 88 bytes (2.3%) over literals with zero basis overhead; it
loses to MED. As a complement to MED (not tested here — see finding
4) it remains unproven.
3. **Learned quantized bases are not yet viable.** PCA directions
quantized to i16 q14 + coarse coordinate search synthesize poorly:
the residual (and its zlib stream) grew +131–191%. The gap between
fp-PCA and integer synthesis eats the model's value at every rank.
4. **Residual subspaces on top of MED also lose** (+66%): residuals
from a good predictor are small and high-entropy; quantized
synthesis error then dominates the residual zlib stream.
5. **Basis economics disqualify global learned bases** at this corpus
scale: a 768×8 i16 basis serialized costs ~6,144 bytes; the whole
image's best stream is only 3,135. η = (L_baseline − L_subspace) /
L_basis is decisively negative. Sharing across ≥3 images' worth of
identical-content tiles is not available in these corpora.
## Retention-gate decision (per ADR: retain only if gains survive)
Subspace modes do NOT retain a slot in a next frozen format on the
strength of these experiments. The two priority strategies the review
named (residual subspace, clustered learned) were the two that lost.
## What the experiments do mandate
- **MED/Paeth enters all future experiment matrices as the mandatory
spatial baseline** (review configuration B): any new predictive
mechanism must beat 3,135-class numbers, not 3,830-class ones.
- Coordinate-quantization research (finer fixed-point scales, b16
coords, projection-refined coordinate search) is the specific knob
where learned subspaces failed; a rerun with improved quantization
is the cheapest possible continuation before any basis design work.
- The shipped MNF7's win came from entropy coder + planar layout +
rate-aware flags — infrastructure, not learned prediction. The
geometry-aware hypothesis remains open: the testable next step is
D8-aligned clustering feeding PCA (review strategy 4), which no
experiment here has isolated yet.
## Reproducibility
cargo test -p mnf-subspace --release -- --nocapture
Every experiment prints one line per configuration; all assertions
must stay green (exactness is enforced, not assumed).