# architectures — collapse and rescue are architecture-general

**Claim tested:** is model collapse (and its cure, grounding) a quirk of one model type, or does the
same signature appear across genuinely different neural architectures?

**Setup (Layer 1.5).** The identical generational loop is run with three different generative models —
an **exact histogram** (no neural net), an **autoregressive GRU** (recurrent), and a **causal-masked
MLP** (feed-forward) — each a distinct "inductive bias." `K = 256` modes, `n = 200`, 22 generations,
5 repeats, compared at **dry (`g = 0`)** vs **grounded (`g = 0.05`)**.

### Symbols
- **inductive bias** — the built-in assumptions of a model type (a histogram has none; a GRU and an MLP smooth differently).
- **forward-KL** distance from truth; **tail items alive** — how many rare modes still appear.
- **dry** = no grounding; **grounded** = 5% real data mixed in.

### The three panels
1. **Trajectories.** Forward-KL over generations, coloured by architecture; **solid = dry** (climbs,
   collapse) vs **dashed = grounded** (held down). The dry-up / grounded-down gap appears in **every**
   architecture.
2. **Stationary forward-KL (grouped bars).** For each architecture, dry (red) vs grounded (green).
   Divergence **falls with grounding across all three** — histogram, GRU, MLP.
3. **Tail-item survival (grouped bars).** Same grouping. Survival **rises with grounding across all
   three.** (Note the histogram's bars are tiny: with no smoothing it drops rare modes outright,
   whereas the GRU/MLP keep some alive — an inductive-bias difference, not a contradiction.)

### Takeaway
The Wright–Fisher collapse operator and the grounding rescue are **not artefacts of one model** — they
show up in an exact counter, a recurrent net, and a feed-forward net alike. This is the
architecture-generality claim of Layer 1.5. **Falsifier (not triggered):** if the signs had appeared
only for the histogram, collapse would be a property of the idealised operator, not of trained models.
*(A VAE was also implemented but fails the generation-0 fidelity check on this task, so it is excluded
to avoid confusing underfitting with collapse — documented as a known limitation.)*