# 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.

## One mechanism, three training regimes (anchoring)

All three loop-entry designs are the same idea — **re-ground the looped
state in the baseline forward pass** — differing only in how much training
supports it:

| regime | anchor form | training | outcome |
|---|---|---|---|
| Lys naive | none (α_state = 1) | zero | collapse (off-manifold drift) |
| Lys regularized | fixed inference-time interpolation η·h⁽⁰⁾ + (1−η)·h⁽ᵗ⁾ | zero | modest, consistent gains |
| **ours (Paper A)** | fixed mix (1−α)e + α·ŝ + trained zero-init MLP([e;ŝ]) | 1.6M params, frozen base | large gains at 2B-effective |
| McLeish | e concatenated every iteration through a **learned** adapter | all params, 50B tokens | gains at scale; anchor constraint absorbed by retraining |

Reading: how much off-manifold state the frozen band tolerates is bounded,
and anchor strength must make up for whatever training does not provide.
Lys's naive-looping collapse is the zero-training limit of the phenomenon;
McLeish's full retraining is the opposite limit, where the manifold itself
moves to accommodate the loop and explicit anchoring dissolves into learned
injection. Our **12B α-miscalibration** (α=0.3 tuned at 2B; untrained loop
craters 72.6→23.0 at 12B) is then not a quirk but the same stability law
seen mid-spectrum: the tolerable loop share depends on the model, and a
coefficient tuned on one substrate overdrives another. This connects
directly to Lys's distribution-shift account and predicts the queued
α∈{0.1, 0.15} 12B arm should recover much of the loss; their softmax
auto-alignment (adaptive η, training-free) is the natural fallback if no
fixed α transfers. Worth a paragraph in Paper A (design justification +
12B analysis) and Paper B (stability mechanism).

**Outcome (2026-07-14, prediction confirmed):** the `12b_adaptive` MBPP
arm (adaptive anchoring, 2×/8× H100 fleet) recovers the substrate —
k=0/2/4 = 72.4/70.8/69.4 overall vs 72.6/54.6/43.0 under fixed α=0.3,
with hard monotone 11.4→18.2→27.3. The tolerable-loop-share account
called this shape in advance: stability restored by weakening the loop
share, hard gains preserved and k-monotone, residual easy erosion
(98.9→92.2) to be handled by the gate.
