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+# Related work — relevance to the jspace looping project
+
+Running notes on papers in this folder: what they show, where they overlap
+with our claims, and what remains ours. Update when a new PDF lands here.
+
+Our shorthand below: "our loop" = frozen gemma-4 base + 1.6M anchor-dominant
+merge adapter at L14, band L14–30, prompt-only latent planning, STaR-labeled
+difficulty→depth curriculum, frozen-prompt KV trick, attribution ladder
+(untrained / FF / pause / loop / explicit plan), gate probe.
+
+---
+
+## 2511.07384 — McLeish et al., "Teaching Pretrained Language Models to
+## Think Deeper with Retrofitted Recurrence" (UMD/LLNL/Tübingen, Nov 2025)
+
+**What they do.** Convert pretrained 1B models (TinyLlama, OLMo-2, Llama-3.2)
+into depth-recurrent models: remove middle layers, split the rest into
+prelude → recurrent block → coda; recurrent input is a **linear adapter over
+[e; s]** (prelude output ⊕ previous iterate; s₀ = random noise). Then full
+continued pretraining: ~50B tokens math-heavy data, all parameters trained,
+Muon optimizer, Poisson-Lognormal recurrence sampling with a curriculum
+ramping mean recurrence to 32, truncated BPTT (last 8 iterations), plus a
+"healing" phase (26B tokens FineWeb-Edu) to recover from layer surgery.
+Result: at matched training FLOPs the retrofit beats continued-pretraining
+the non-recurrent parent on GSM8K/MATH; accuracy scales with test-time
+recurrence; pretrained init beats random init by ≥950B tokens of training.
+
+**Overlap — must cite, cannot claim as novel:**
+- Retrofitting recurrence into a pretrained fixed-depth model works and
+  beats the non-recurrent baseline (their headline, at much larger scale).
+- Merge adapter at loop entry combining embedding-side and state-side
+  inputs ([e; s] → linear, vs our (1−α)e + α·ŝ + MLP([e;ŝ])).
+- Recurrence-depth curriculum during training.
+- "Pretrain traditional, then convert" (our rung-2 vision): they did the
+  continued-pretraining version at 1B/50B tokens. The generic claim is theirs.
+
+**What remains ours (Paper A positioning):**
+1. **Where to loop is interpretability-derived.** They pick splits by
+   benchmark search and name layer choice as an open problem ("future work
+   could identify a more optimal method for layer choice"). We derive the
+   band from the J-lens workspace regime and back it causally: anchor cliff
+   at L14, tap invariance, band-10–20 location ablation ≈ 0, KV-sharing
+   hazard. We answer their stated open problem.
+2. **Frozen base, 1.6M-param adapter, ~600 steps on a desk machine** vs all
+   parameters, 50B tokens, MI300A cluster — ~5 orders of magnitude apart on
+   the cost curve. No layer removal → no healing phase needed, and k=0
+   exactly recovers the base model (they cannot say that).
+3. **Prompt-only latent planning + frozen-prompt KV trick: zero decode-time
+   cost.** Their recurrence runs on every generated token (decode cost ×r).
+4. **Attribution controls** (untrained / FF / pause / explicit plan). They
+   have no compute-matched token-space control.
+5. **Difficulty-adaptive depth** (STaR buckets, gate probe): named in their
+   Discussion as unsolved future work. Our gate is a first result on it.
+
+**Worth stealing:**
+- **Muon > AdamW for recurrent training** (AdamW loss-spikes to NaN) —
+  directly relevant when we unfreeze the band / fade-off unfreezing.
+- s₀ init: theirs is random noise, ours the actual residual state — likely
+  why a frozen base works for us at all; expect a reviewer question here.
+- FLOPs accounting convention for recurrent models: FLOPs = (6N₁ + 2N₂)D
+  with N₁ = params with gradients, N₂ = forward-only (truncated BPTT).
+
+**Where to cite:** Paper A related work (primary contrast), Paper B
+(layer-choice open problem → our mechanistic answer), rung-2 planning notes.
+
+---
+
+## 2602.14759 — Lys et al., "Inner Loop Inference for Pretrained
+## Transformers: Unlocking Latent Capabilities Without Training"
+## (IMT Atlantique / Sony, Mar 2026)
+
+**What they do.** Training-free "middle looping" of frozen off-the-shelf
+models (Gemma-2 2B/9B, Llama-3-8B): re-apply a block range [s, e) R times at
+inference. Key findings: (1) **naive looping systematically degrades**
+(distribution shift — looped activations leave the manifold the model was
+trained on, some configs collapse to chance); (2) **regularized looping
+rescues it**: interpolate the looped state with cached states / the baseline
+state (uniform average, moving average ĥ = η·h⁽⁰⁾ + (1−η)·h⁽ᵗ⁾,
+softmax auto-alignment) → modest but consistent gains across WinoGrande,
+ARC, GSM8K, HellaSwag, MMLU (likelihood-scored, mostly multiple-choice).
+Full start×end layer-pair sweep heatmaps. Frames looping as "logits
+refinement" — depth as iterative refinement of a shared latent state.
+
+**Overlap — must cite:**
+- Their moving-average regularization η·h⁽⁰⁾ + (1−η)·h⁽ᵗ⁾ is exactly the
+  anchor term of our merge, minus the trained MLP. Independent confirmation
+  that **anchoring to the un-looped state is the thing that makes frozen-band
+  looping viable** — cite as convergent evidence for the anchor-dominant
+  design (α=0.3).
+- "Training-free looping gives modest gains on a frozen model" ≈ our
+  untrained-loop arm (17.9% hard vs 5.5 baseline on MBPP-hard, but = FF
+  control). Their whole paper lives inside one cell of our attribution table.
+- Layer-pair sweeps parallel our location ablation (theirs benchmark-driven,
+  ours interpretability-predicted then confirmed).
+
+**What remains ours:**
+1. **A trained merge** — their gains are modest by their own description;
+   our trained adapter roughly doubles the untrained/FF level on hard items
+   (17.9 → 37.4) and the pause/plan ladder bounds what the recurrence adds.
+2. **Generative evals with per-item verification** (MBPP tests, GSM answer
+   match, Rust compile-run) vs their likelihood-scored multiple choice —
+   ours measures the regime where latent planning should matter.
+3. **Prompt-only looping + frozen-prompt KV trick** (they loop everything,
+   every position; no decode-cost story).
+4. Curriculum, difficulty gating, cross-task transfer arms, KV-sharing
+   hazard (their Gemma-2 has no KV sharing; our E2B finding that
+   interventions entered ≥L15 are structurally null is a hazard their
+   sweep methodology would silently hit on models that do share).
+
+**Worth stealing:**
+- Their distribution-shift framing of *why* naive looping fails is a clean
+  citable explanation for why zero-init MLP + anchor is the right
+  parameterization (we motivate; they demonstrate the failure mode).
+- Softmax auto-alignment interpolation: a training-free adaptive α — cheap
+  ablation candidate against our fixed α=0.3 (relevant to the 12B α
+  miscalibration result).
+
+**Where to cite:** Paper A (untrained/anchor cell; convergent evidence for
+anchoring), Paper B (distribution-shift account of loop instability;
+KV-sharing hazard contrast).
+
+---
+
+## Combined positioning takeaway
+
+The two papers bracket us: McLeish et al. = full-retraining recurrence at
+scale (expensive end), Lys et al. = zero-training looping (free end). Our
+niche is the middle, and it is still open: **interpretability-chosen band +
+tiny trained merge on a frozen base + prompt-only latent planning with zero
+decode cost + a full attribution ladder + difficulty gating.** Neither paper
+touches any of the last three items; both strengthen the premise that band
+looping is a real mechanism rather than a curiosity.