Depth recurrence has been tried ~45 times in this competition and never reached SOTA. I wanted to understand why, so I ran a structured ablation (12 runs total) testing five techniques against the three failure modes that kill recurrence: quantization error amplification, per-iteration identity collapse, and residual magnitude erasure.

Result: 1.2659 BPB post-quant. Config: 1 prelude + 4 shared × 3 loops + 1 coda = 14 effective layers from 6 unique blocks, 10.7 MB (well under 16MB limit). Q-gap +0.0076. Not competitive with SOTA (1.1194), but 3-loop recurrence has never worked before — PR #363 measured ~900× quantization amplification over 3 cycles.

What made it work (three techniques, none used elsewhere in the competition):

• Output-LN — moved RMSNorm from MLP input to MLP output. This was the critical piece. Without it, shared weights can't tell loop iterations apart because pre-norm erases magnitude. With it, mixing alphas learned a clear gradient (0.37→0.70) instead of collapsing to ~0.48. Based on Kim et al. (arXiv:2502.02732, §3.2).

• Birkhoff-constrained mixing — replaced the learned 2-vector residual mix with a sigmoid parameterization that guarantees spectral norm ≤ 1. Alone it actually hurts (+0.002 BPB), but paired with Output-LN it prevents the exponential quantization blowup that killed every prior 3-loop attempt. From mHC-lite (arXiv:2601.05732).

• Capped timestep scaling — per-iteration scale vectors clamped to [-4, +4], stored as float16. The surprising finding: zero effect on pre-quant BPB, but reduces Q-gap by 26–30%. It's a quantization robustness technique, not a training technique. The gammas survive quantization as float16 passthrough while everything else gets crushed to int8. From Xu & Sato (arXiv:2410.01405).

Possibly useful for non-recurrent submissions: Output-LN, Birkhoff mixing, and per-layer scaling vectors are all drop-in additions that don't require weight sharing. If anyone wants to try them on the standard stack, the code is there.

Full ablation tables and theory with citations in the README and research_notes.md.