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## 3. Where we are (results, C512, TinyStories-BPE)
- **EP gradient ≈ exact BPTT gradient** (cosine ≈ 0.92–0.99 per component when the free phase is converged) — the
learning rule is validated, not approximate.
-- **Best val cross-entropy 1.8977** (warm-started, `ep_warm_fast`, still descending pre-lr-decay as of 2026-07-05;
- previous era best 1.9313) vs a same-parameter BP transformer ~1.79; generates coherent children's stories.
+- **Best val cross-entropy 1.7065** (warm-started `ep_warm_fast`, FINISHED 2026-07-07) — **beats the tuned depth-1
+ BP reference (1.7921) by 0.086 and the parameterization-matched BP+EMA twin (1.9632, best of 8 configs) by 0.257**:
+ the equilibrium computation's iteration-depth dividend, measured. Generates coherent children's stories.
- **From scratch: 2.0119** (`ep_self_restart`, a from-scratch lineage with restart-on-abort; finished 2026-07-05) —
the old "~2.10 plateau" is broken, but the warm/scratch gap (~0.11) remains the crux (see §5).
- The recipe **trains stably and approaches BP** at this scale. Model = C512 / H16 / T256, damped DEQ block.