jspace/related_work/relevant_to_us.md

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.

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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.

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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).

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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.