# mnist_collapse — collapse and grounding-rescue on REAL MNIST images (external validity)

**Claim tested:** everything so far used a *synthetic* sandbox with a zero-error decoder oracle. Do
model collapse and its rescue by grounding also appear on **real images** with a **classifier**
oracle — i.e. is the effect real, not a synthetic artefact?

**Setup (Layer 1.5, real-data tier).** The generative model is a **convolutional VAE** (the model
in which generative collapse was first observed). Each generation a **fresh** VAE is trained from
scratch on the previous VAE's own generated digits, plus a fraction `g` of fresh **real** MNIST
images (grounding). `K = 30` **modes** = digit class × stroke-thickness bin (S=3), Zipf-resampled so
the rarest ~18 modes form a real tail. The **oracle** is a frozen CNN (digit class) + deterministic
thickness bin; its **mode accuracy ≈ 98.5%** (recorded in `manifest.json` with the full 30×30
confusion matrix) is the measurement-noise floor. Two arms — dry (`g = 0`) vs grounded (`g = 0.1`) —
`n = 6000` images/generation, 15 generations, 4 replicates.

### Symbols
- **mode** = (digit class, stroke-thickness bin); **`p*`** = Zipf truth over the 30 modes; **`p̂`** = the VAE's oracle-measured mode distribution.
- **`g`** = grounding fraction (share of real MNIST images each generation). **forward-KL** = distance from truth; **support** = distinct modes alive; **`H`** = diversity; **tail truth-mass alive** = fraction of the rare tail retained.

### The four panels (dry = red, grounded = green; band = 95% CI over 4 reps)
1. **Forward-KL.** Dry climbs from ~0.5 to **~18** (the VAE drifts far from truth); grounded stays
   near the floor. Collapse is real on images.
2. **Support.** Dry collapses from all 30 modes to **~1** (the VAE ends up emitting a single blurry
   mode); grounded holds all 30.
3. **Tail truth-mass alive.** Dry's rare tail is wiped out (→ 0.06); grounded keeps the whole tail.
4. **Heterozygosity.** Dry diversity → 0; grounded holds `H ≈ 0.9`.

See **`mnist_montage.png`** for the eyeball version: gen-0 digits are varied and recognisable; by
gen 12–15 the dry lineage has degenerated into one blurry blob.

### Takeaway
Model collapse and its arrest by a small dose of real data **reproduce on real MNIST images with a
learned classifier oracle** — external validity for the whole Layer-1.5 story. Note the VAE needs
~10% grounding here (vs ~5% for the synthetic histogram), consistent with the `grounding` finding
that trained neural models need somewhat more grounding than the exact operator. This is
**confirmation-only** (signs, not magnitudes; blueprint §3.5) — the exact synthetic oracle remains
the anchor for every quantitative claim, and the oracle confusion matrix is the recorded noise floor.
**Falsifier (not triggered):** if the dry VAE had shown no diversity loss, or grounding had failed to
arrest it, the external-validity claim would fail.