integrate McLeish et al. + Lys et al.: reposition related work, rung-2 Muon note

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

PAPER.md

@@ -198,16 +198,38 @@ checkpoint selection likewise failed to track generation accuracy.
 
 ## 4. Related work
 
-Universal Transformers (adaptive depth); DEQ (fixed-point inference);
+Two recent papers bracket this work. **McLeish et al. (arXiv:2511.07384)**
-Huginn / recurrent-depth latent reasoning (arXiv:2502.05171) — prelude/core/
+retrofit depth-recurrence into pretrained 1B models via layer surgery +
-coda with input injection, trained from scratch; Mixture-of-Recursions
+continued pretraining (~50B tokens, all parameters, Muon, recurrence
-(arXiv:2507.10524) — learned per-token depth; Relaxed Recursive Transformers
+curriculum to r=32): the generic claims "retrofitted recurrence works and
-(arXiv:2410.20672) — uptraining tied layers with per-loop LoRA; Coconut —
+beats the non-recurrent parent" and "pretrain-then-convert" are theirs, at
-latent chain-of-thought; pause tokens (Goyal et al.) — token-space silent
+~5 orders of magnitude more training cost than ours. They name layer choice
-compute. Distinct here: the recurrence is **retrofitted onto a frozen model
+as an open problem; our lens-derived band with its causal backing (anchor
-at adapter cost**, its location is **chosen by an interpretability signal**,
+cliff at L14, tap invariance, wrong-band ≈ 0, KV-sharing hazard) is a direct
-and the same signal **verifies** the added computation. Our pause-token and
+answer to it. Unlike their surgery (which needs a healing phase), our k=0
-weights controls connect directly to that literature's baselines.
+exactly recovers the base model. **Lys et al. (arXiv:2602.14759)** loop
+frozen models training-free and show naive looping degrades (distribution
+shift) while interpolating with the un-looped state rescues it — independent
+convergent evidence for our anchor-dominant merge; their whole setting
+corresponds to the untrained cell of our attribution table (17.9% hard =
+our FF/untrained level), evaluated by likelihood rather than execution.
+
+Earlier lineage: Universal Transformers (adaptive depth); DEQ (fixed-point
+inference); Huginn (arXiv:2502.05171) — prelude/core/coda from scratch;
+Mixture-of-Recursions (arXiv:2507.10524) — learned per-token depth; Relaxed
+Recursive Transformers (arXiv:2410.20672) — uptrained tied layers; Coconut —
+latent CoT; pause tokens (Goyal et al.) — token-space silent compute, whose
+trained-adapter variant proved a near-match for our loop on MBPP (§3.2).
+
+What remains distinct here: **interpretability-derived loop placement with
+causal validation** (answering McLeish et al.'s open problem); **a 1.6M-param
+trained merge on a fully frozen base** (between Lys et al.'s free end and
+McLeish et al.'s full-retraining end, and the only one of the three where
+the base model is provably untouched); **prompt-only latent planning with
+bit-exact KV-cache write-in and zero decode cost**; **the attribution
+ladder** (untrained / weights / pause / loop / explicit plan) — neither
+bracket paper runs compute-matched token-space controls; and **difficulty-
+adaptive depth via the STaR-label gate**, named as future work in both.
 
 ## 5. Limitations
 

WORKSPACE_LOOPING.md

@@ -255,6 +255,16 @@ passing code, CE on code tokens, curriculum k=1 easy / 2 mixed / 4 hard; the
 
 ### Rung-2 design note: depth-graded band unfreezing
 
+**Optimizer note (from McLeish et al., arXiv:2511.07384):** use **Muon**, not
+AdamW, when unfreezing the band — they report AdamW loss-spikes to NaN when
+training through recurrence; adapter-only training didn't hit this, band-LoRA
+likely will. Also adopt their FLOPs convention for recurrent models
+(FLOPs = (6N₁+2N₂)D, N₁ = params with grads, N₂ = forward-only) in any
+compute-matched comparison. **Adaptive-α candidate (from Lys et al.,
+arXiv:2602.14759):** their training-free softmax auto-alignment interpolation
+is a cheap ablation against fixed α — directly relevant to the 12B α
+miscalibration.
+
 When the band itself is unfrozen (per-iteration LoRA), unfreeze
 **entrance-faded**: full trainability at L14 decaying to frozen by ~L22
 (e.g. LoRA α × max(0, 1−(ℓ−14)/8)). Rationale: the only novel inputs in the