# collapse — model collapse in REAL neural weights, arrested by grounding

**Claim tested:** does the collapse we proved in math actually happen in a *trained neural network* —
and does a little grounding stop it?

**Setup (Layer 1.5).** The model is now a small **autoregressive GRU** (a recurrent net, ~128 hidden
units). Each generation a **fresh** GRU is trained from scratch, by ordinary next-token prediction, on
the previous GRU's own generated sequences (plus any real samples). `K = 256` modes, `n = 200`,
25 generations, grounding `g ∈ {0, 0.02, 0.05, 0.1}`, 5 repeats. A generation-0 fidelity check
confirms the GRU reproduces the truth almost perfectly (KL ≈ 0.008) before any collapse is measured.

### Symbols
- **GRU** — a small recurrent neural net that emits sequences token by token; retrained each generation on the prior generation's output.
- **forward-KL** `D(p*‖p_t)` — distance from truth; the metric that actually sees neural collapse.
- **`H`** diversity; **tail items alive** — how many rare modes still appear.

### The four panels
1. **Collapse in weights.** Forward-KL over generations, one line per `g`. The dry lineage (`g = 0`)
   **climbs** (drifts from truth) toward ~2.3; grounded lineages are held lower. Collapse is real in
   trained weights.
2. **`H` barely moves.** Diversity over generations sits near `H*` for all arms — the GRU's smoothing
   bias keeps spurious spread alive, so **diversity `H` hides the collapse**. (This is why forward-KL,
   not `H`, is the operative neural metric — see `grounding`.)
3. **Stationary divergence vs `g`.** End-state forward-KL falls as grounding rises: more real data →
   closer to truth.
4. **Tail survival vs `g`.** Fraction of rare modes alive rises with grounding.

### Takeaway
The core phenomenon transfers from math to real neural nets: **a GRU trained on its own output drifts
from truth, and grounding arrests it** — the *sign* Layer-1 predicts (blueprint §3.5). Note the
honest caveat surfaced here and developed in `grounding`: **diversity `H` is the wrong ruler for a
neural net** (smoothing keeps it high even during collapse); distance-from-truth is the right one.