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Transformers Stop Thinking Too Early, and a Tiny LoRA Fixes It

Zehao Jin, Ruixuan Deng, Junran Wang

arXiv:2609.36585v1cs.AIcs.CLcs.LG

TL;DR

Pretrained transformers reliably follow only short reference chains, despite longer reference-following computations being possible in principle. The paper trains a rank-8 LoRA at one layer while freezing model weights, extending the relay; Qwen3-8B exact accuracy on 24-line chains rises from 15.5% to 99%.

  • Problem

    Thirteen pretrained base models reliably follow only 1.4–3.6 lines, despite transformers being able in principle to implement longer reference-following computations.

    Source: §1 · p. 1

  • Method

    The paper trains a task-specific rank-8 LoRA at one layer while freezing every model weight, extending the program’s chain-identity relay.

    Source: §1 · pp. 1–2

  • Results

    Qwen3-8B exact accuracy on 24-line chains rises from 15.5% frozen to 99%, while longer-trained Ouro reaches at least 160 lines after eight loops.

    Source: §4 · pp. 3–4

  • Takeaways & Limitations

    Default answers understate the computation accessible under a specified intervention; for adaptation, placement determines which useful computation can follow a change.

    Source: §9 · p. 8

    Mechanistic tasks are synthetic and in-context; MuSiQue provides placement evidence with gold paragraphs, not direct evidence of the same mechanism.

    Source: §9 · p. 8

Abstract

from arXiv · show

Pretrained transformers use little of their depth to follow references in context. Thirteen base models reliably follow only 1.4-3.6 lines, and extra pretrained loops add little. A task-trained rank-8 LoRA at one early layer extends this computation with all model weights frozen. Qwen3-8B improves from 15.5% to 99% exact accuracy on 24-line chains; a longer-trained LoRA reaches 50 lines. Ouro-1.4B reaches 60 lines after four loops and at least 160 after eight. The LoRA starts a relay: program lines pass on their chain identity through a short range of middle layers. Frozen heads read progressively further up the chain, and removing parent-line attention stops the relay. A frozen-model measurement locates the last useful intervention layer within tolerance in three of four held-out models. Task-specific LoRAs also improve MuSiQue. Default answers therefore understate the computation accessible through a tiny edit. Code and an interactive demo are available at https://lunamos.github.io/stop-thinking-too-early/

1. Introduction

Pretrained models follow only short reference chains, but a one-layer LoRA with model weights frozen substantially extends chain computation and reveals a relay mechanism.

1. Introduction

  • Thirteen pretrained base models reliably follow only 1.4–3.6 lines, and extra loops add little reach.Even DeepSeek-V4-Flash (292B MoE) remains near chance on longer chains.Source: §1 · p. 1
  • Qwen3-8B exact accuracy on 24-line chains rises from 15.5% to 99% with a rank-8 LoRA, while Ouro-1.4B reaches at least 160 lines after eight loops.All model weights remain frozen; a longer-trained LoRA reaches 50 lines in one pass.Source: §1 · p. 1
  • By default, program lines pass chain identity only two or three lines; with the LoRA, each line collects earlier names and attends further up its chain.The relay advances through a short range of middle layers, repeated in each loop.Source: §1 · pp. 1–2
  • A frozen-model measurement predicts the useful intervention limit with modest precision, while early task-specific LoRAs improve MuSiQue exact match.On MuSiQue, projection LoRA restricted to early layers preserves most of the gain from adapting every layer.Source: §1 · p. 2

2. Task and intervention

The paper evaluates reference-chain following with randomized assignment programs and compares frozen models with low-rank interventions and recurrent models.

2. Task and intervention

  • Each reference-chain program has chains of assignments followed by a query; every later assignment points to a variable defined by an earlier line.Names, nouns, and queried chains are randomized, and assignments can be level-ordered or interleaved while preserving definition before use.Source: §2 · p. 2
  • Evaluation covers thirteen standard base models, DeepSeek-V4-Flash, and the looped models Ouro-1.4B, Ouro-2.6B, and Huginn-0125.The Ouro models use four loops; Huginn’s recurrent core was trained with 32 recurrences on average.Source: §2 · p. 2
  • Choice accuracy selects among chain roots, exact accuracy ranks the correct root first over the full vocabulary, and reach is the longest chain followed at 80% accuracy.Standard-model LoRA evaluations use two-chain exact accuracy; looped-model experiments generally use two-chain choice accuracy.Source: §2 · p. 2
  • The rank-8 LoRA updates the residual stream at a layer input, while frozen attention and MLP layers carry communication between tokens.The intervention acts independently at each token; looped models reuse the same LoRA in every loop unless specified.Source: §2 · p. 2
  • Only A, B, and a scalar are trained; the standard Qwen3-8B LoRA adds 65,537 parameters and enters layer 14.The standard Ouro-1.4B LoRA enters layer 6; the intervention is trained with answer cross-entropy and a WikiText-103 KL penalty.Source: §2 · p. 2

3. The default computation stops early

Across standard and looped models, the default computation extends reference chains only a little: the context relay stops early, and the query completes only a few more pointer steps.

3. The default computation stops early

  • Reliable reach across thirteen standard models is 1.4–3.6 lines; DeepSeek-V4-Flash reaches 4.0 lines but scores 42% at six and 38% at eight, near chance.Qwen3-8B choice accuracy falls from 83.5% at three lines to 54% at four and 41.5% at five.Source: §3 · pp. 2–3
  • Ouro-1.4B’s three-chain reach plateaus at 2.2 lines after three to five loops, while Huginn remains at 1.4–1.6 lines after 8–32 recurrences.Solved demonstrations improve answer format but leave reach short.Source: §3 · p. 3
  • In Qwen3-8B, the root value remains at its source until the query takes over near layer 32 of 36, while pointer effects reach the query earlier.Blocking query attention to pointer lines harms answers in the middle layers but changes accuracy by at most two points between those layers and the late value copy.Source: §3 · p. 3
  • A pointer’s effect falls from 90% to 10% over 7.1 ± 1.4 layers across models with 16–64 layers; Ouro query takeover occurs chiefly in loops three and four.The network continues computing after this interval but stops extending the chain.Source: §3 · p. 3
  • Frozen Qwen3-8B’s relay reaches line four; across thirteen models it stops at lines three to five, using a 75%-accuracy threshold for every line in the prefix.Ouro never reliably reaches line five after six loops, and Huginn never reaches line four after sixteen recurrences.Source: §3 · p. 3, Figure 2 · p. 3

4. A small LoRA makes the layers count

A rank-8 LoRA makes long-chain reference following possible with frozen model weights, and repeated loops extend the computation. Results vary with training length, loop count, and intervention schedule.

Long chains in one pass

  • 99.0% exact accuracy on 24-line chains, versus 15.5% frozen, is achieved by Qwen3-8B with the layer-14 LoRA.The longer-trained LoRA reaches 50 lines; it answers 40-line chains at 98% and 48-line chains at 88%, versus 4% and 9% frozen.Source: §4 · pp. 3–4
  • Interleaving lowers 24-line accuracy to 76.5%, and using three chains lowers 16-line accuracy to 58.0%, though both remain well above frozen performance.The longest one-pass results use level-ordered, two-chain programs.Source: §4 · p. 4

Longer chains with more loops

  • Ouro-1.4B’s longer-trained LoRA reaches 60 lines after four loops and at least 160 after eight; Huginn’s reaches 58 lines after sixteen recurrences.In Ouro, the 160-line result has 87% accuracy, and reach eventually declines when either model runs well beyond its training loop count.Source: §4 · p. 4, Figure 3 · p. 4
  • Ouro’s first-loop-only LoRA reaches 9.5 lines after two loops, 21.5 after three, and about 25 after four through eight, while unmodified loops continue the computation.This result concerns shorter programs. LoRAs trained with one, two, or four loops reach 12.5, 4.4, or 1.9 lines in the first loop, respectively.Source: §4 · p. 4

The useful layers can be run again

  • 64-line exact accuracy rises from 34% in one pass to 66% with one re-entry and 92% with two, versus 10% frozen.The re-entered segment is Qwen3-8B layers 14–22, with the LoRA applied at each re-entry.Source: §4 · p. 4

Other interventions work at the same location

  • Rank-8 projection LoRA yields 99.0% and 90.0% accuracy at 16 and 24 lines; three-step FLAS yields 99.5% and 94.0%.At layer 26, all four tested interventions select between two chains near chance; the matched comparison uses 200 programs per cell.Source: §4 · p. 4, Table 1 · p. 4

5. The LoRA starts a relay in the middle layers

A LoRA lets program lines carry chain identity through a short middle-layer relay, while frozen attention reads progressively farther up each chain. Parent-line attention supports the relay, and associated computations are detectable in the broader frozen model.

A short interval carries a much longer computation

  • With the LoRA, Qwen3-8B’s relay reaches lines 5, 6, 6, 8, 9, 13, and 16 at layers 16–22; frozen reach stops at line four.Restoring a redirected pointer’s clean state recovers its effect at progressively later lines and then at the query.Source: §5 · pp. 4–5, Figure 4 · p. 5

The same pattern repeats across loops

  • Ouro’s relay advances mainly within layers 7–15 of each loop, and the longer-trained LoRA reaches lines 4, 9, 25, and 40 after its first four loops.A first-loop-only LoRA also lets Ouro’s unmodified loops continue the relay; Ouro-2.6B and Huginn likewise advance within short middle or late-core intervals.Source: §5 · pp. 5–6

Attention reaches further as the relay advances

  • With the LoRA, Qwen attention reaches two lines up at layers 16–18, then progressively farther, to seven lines up at layers 21–22.This gradual growth differs from pointer doubling: attention overlaps several earlier lines rather than making discrete jumps that double in length.Source: §5 · p. 5, Figure 4 · p. 5

The relevant heads already exist in the frozen model

  • In Ouro, ablating seven longer-reading heads lowers reach to 12.0 versus a median 24 across matched random-head draws; in Qwen, removing ten parent-reading heads lowers choice accuracy from 89% to 53%.The heads are selected by their reads, with scoring on separate program halves; removing eight longer-reading Qwen heads leaves 65%, versus 90% after matched random-head removal.Source: §5 · p. 5

The parent line is necessary

  • Removing Qwen parent attention in layers 14–22 returns six-, eight-, and twelve-line chains to chance, while removing those edges in layers 23–29 leaves accuracy at 100%, 100%, and 98%.In Ouro, parent cuts stop the relay, while cuts to attention two or more lines up reduce reach from 17.8 to 9.4.Source: §5 · p. 5, Figure 5 · p. 6

Earlier names let a line find earlier lines

  • After the LoRA, probes decode names defined progressively farther up the chain; blocking parent attention reduces loop-two decoding of names four lines up from 0.29 to 0.18.The LoRA itself exchanges no information across tokens, and removing its eight-dimensional span from later states leaves chain-identity read-out near 95%.Source: §5 · p. 5

The ability is learned before the LoRA

  • LoRA training unlocks progressively longer chains in later OLMo checkpoints, while small looped transformers trained on programs show a similar relation between relay progress and attention distance.The checkpoint reach is 10.2 after 84 billion tokens and 23.7 after 336 billion, while frozen reach stays below two.Source: §5 · p. 6

6. Where to put the fix

Intervention placement matters: moving a LoRA past a model-specific middle-layer limit sharply reduces its benefit. A frozen-model cutoff provides a prospective estimate of that limit, while later loops can offer another opportunity for a useful intervention.

A sharp placement limit

  • Moving Qwen3-8B’s LoRA from layer 20 to 21 lowers reach from 20.5 to 5.2 lines; corresponding transitions occur at layers 12–15 in OLMo-3-7B and 13–15 in Llama-3.1-8B.The comparison holds rank, data, and optimization fixed; an early-started relay can continue beyond the limit, but a later LoRA cannot start one.Source: §6 · p. 6, Figure 6 · p. 7

Predicting placement from the frozen model

  • The frozen-model cutoff meets the preregistered held-out criterion in three of four models, with mean absolute error 2.25 layers on those models.Across all nine models its error is 2.22 layers, essentially tied with 2.27 for a post-hoc rule at 48% of depth; the table brackets the last working and next tested layers.Source: §6 · p. 6, Table 2 · p. 6

A later loop provides another opportunity

  • In Ouro, a last-loop-only LoRA at layer 6 reaches 21.6 lines after four loops, versus 2.6 at layer 20; Ouro-2.6B reaches 9.6 at layer 12 versus 4.7 at layer 24.The layer-24 intervention still has 24 layers after it, indicating that useful middle-layer computation—not simply remaining depth—distinguishes the placements.Source: §6 · pp. 6–7

7. Multi-hop question answering

Task-specific LoRAs improve multi-hop question answering in fictional-fact questions and MuSiQue, including when projection updates are restricted to early layers. The reported evaluations cover multiple models and answer settings.

Fictional facts preserve the controlled setting

  • Qwen3-8B exact match on fictional-fact questions rises from 41.2% to 97.4%, and on unseen six-hop questions from 23% to 88%.Ouro’s LoRA extends reliable answers from two hops to six after four loops and eight after six or eight loops, at 91–92% accuracy.Source: §7 · p. 7

Early layers also matter on MuSiQue

  • On 900 MuSiQue development questions, early LoRAs add 11.4, 9.4, and 17.9 exact-match points in Qwen3-8B, OLMo-3-7B, and Llama-3.1-8B.Qwen’s frozen exact match is 52.9%; its layer-6 LoRA beats layer 30 by 13.0 points, but layer selection used the same development set.Source: §7 · p. 7
  • Early projection LoRA retains most of the all-layer gain: 11.0 versus 12.8 points in Qwen, 10.6 versus 10.8 in OLMo, and 20.1 versus 20.9 in Llama.Late projection LoRA gains are 0.4, 0.9, and 10.7 points, respectively.Source: §7 · p. 7
  • In Ouro, layer-6 LoRA raises exact match on 300 development questions from 48.3% to 60.0% after four loops, with the largest gain on four-hop questions, from 40% to 58%.The benchmark supports the placement preference; the program experiments establish the relay mechanism.Source: §7 · p. 7

8. Related work

The related work connects multi-hop composition and reference tracking to questions of information flow, reusable circuits, and recurrent computation. The paper situates its contribution as measuring what frozen layers can extend after a representation edit.

Composition and information flow

  • Prior work studies multi-hop composition, layerwise access, and information flow, while this paper tests where frozen pretrained weights can extend an in-context computation (Press et al., 2023; Yang et al., 2024b; Guo et al., 2025).The paper connects these timing questions to a prospective test of intervention placement.Source: §8 · pp. 7–8

Binding and reusable circuits

Loops and adaptation

9. Discussion

A wrong answer or weak gains from additional loops do not show that pretrained weights cannot compose references. The paper limits its evidence to specified task settings and identifies unresolved mechanistic questions.

9. Discussion

  • Default behavior and computation accessible under intervention should be distinguished: placement determines which useful computation can follow an edit, while loops and re-entry repeat the layers that carry it.The mechanistic tasks are synthetic and in-context; MuSiQue tests placement with gold paragraphs, not the same mechanism.Source: §9 · p. 8
  • The evidence is bounded by task-specific LoRAs, detailed traces focused on Qwen3-8B and Ouro-1.4B, and looped results using two model families.The learned routing directions and minimum sufficient rank remain unidentified, and causal tests do not uniquely specify the algorithm.Source: §9 · p. 8

Impact Statement

The work evaluates interventions on public models, synthetic tasks, and public datasets, with deployment reliability and broader behavioral effects left for separate evaluation. Its appendix describes randomized reference-chain prompts and task-specific scoring conventions.

Impact Statement

  • The work uses public models, synthetic tasks, and public datasets; deployment reliability and effects on broader model behavior require separate evaluation.The authors do not foresee direct harmful uses beyond those of the underlying models.Source: Impact Statement · p. 9

A.1. Prompts, models, and scoring

  • Programs randomize names, root values, and queried chains, while chain order can be level-shuffled or interleaved; the model panels include thirteen standard base models and three looped families.Choice accuracy compares logits among root values, exact accuracy ranks the correct root over the full vocabulary, and reach is the interpolated first downward crossing of 80% accuracy; MuSiQue is scored by exact match and F1 after text normalization.Source: §A.1 · p. 12

A.2. Training the LoRA

A rank-8 LoRA substantially raises Qwen3-8B’s exact accuracy on 24-line chains, while frozen standard models reliably follow only a few lines. The accompanying analyses characterize the relay and locate pointer reading within a short interval of middle-layer computation.

A.2. Training the LoRA

  • The rank-8 LoRA acts independently at each token, with frozen attention and MLP layers carrying communication; Qwen uses layer 14, Ouro layer 6, and Huginn the recurrent core’s input-adapter output.Training combines answer cross-entropy with a WikiText-103 KL penalty; Ouro and Huginn use gradients through their training loops, and the scalar rescales the full residual stream while BA is rank eight.Source: §A.2 · pp. 12–13, Table 3 · p. 13
  • 198/200 correct answers were recorded for Qwen3-8B on 24-line chains, and the 48-line result was 88/100.The 24-line result had a 95% Wilson interval of 96.4–99.7%.Source: §A.2 · p. 13

A.3. Restoration, read-outs, and attention

  • Restoration traces replace a root noun or redirect a pointer, then restore a clean residual state; ridge read-outs track chain membership, and attention analyses compare parent-line reads with controls.A line is readable at 75% accuracy on two chains, and the relay extends only through the longest prefix whose lines all pass that threshold.Source: §A.3 · p. 13

B.1. A short computation in standard models

  • The default relay stops at lines 3–5 across thirteen models, while the query resolves the last one or two pointers before a late layer copies the selected root value.In Qwen3-8B, the query acquires half the root-value effect near layer 32 of 36; Figure 8 summarizes the separate computations and restoration traces.Source: §B.1 · p. 14, Figure 8 · p. 15
  • 1.4–3.6 lines was the reliable reach across thirteen standard models, with median 2.2; DeepSeek-V4-Flash reached 4.0 but was near chance at six and eight lines.Table 4 summarizes frozen reach and related measurements across the standard-model panel.Source: Table 4 · p. 14, §B.1 · p. 14

B.2. Measuring when pointer reading ends

  • 7.1 ± 1.4 layers was the 90%-to-10% pointer-effect width across 16–64-layer models; the cutoff measure averages the first loss of half the source-token effect for pointers on lines 2 and 3.For Qwen3-8B the cutoff is 20.5, the transition is largely complete by 24, and value copying follows near 32.Source: §B.2 · p. 14, Figure 8 · p. 15
  • Seven of nine threshold combinations gave slopes from −0.008 to 0.075, while the other two gave 0.116 and 0.111; using two chains shifts individual widths by up to four layers.Larger models within Qwen, Llama, and Gemma nevertheless resolve more pointers in the similarly wide range.Source: §B.2 · pp. 14–15
  • Blocking attention during the pointer-reading range reduced two-line accuracy to 0.76, 0.40, and 0.53 in Qwen3-8B, OLMo-3-7B, and Llama-3.1-8B, respectively.Blocking after reading but before value copying left accuracy nearly unchanged; sliding three-layer cuts hurt only within the measured reading range.Source: §B.2 · p. 15

B.3. Extra loops repeat the short computation

Extra pretrained loops add little to reference-following, while early task-trained interventions substantially extend chain accuracy and reach. Several intervention forms work at the same layer, but moving them past the useful region removes most of their benefit.

B.3. Extra loops repeat the short computation

  • Ouro’s reach plateaus after a few frozen loops, while pointer effects transfer to the query only in later loops and blocking query attention there costs 16–24 points.Across loops, Ouro-1.4B reaches 2.3 lines at most; Huginn reaches 1.4–1.6 lines after 8, 16, or 32 recurrences.Source: §B.3 · pp. 15–16, Figure 10 · p. 17

C.1. Accuracy, format, and model controls

  • 98.5%, 98.0%, and 99.0% exact accuracy at 16, 20, and 24 lines with the Qwen3-8B layer-14 LoRA compares with 15.5%, 14.5%, and 15.5% frozen.The LoRA also reaches 50 lines after longer training; interleaved assignments retain 76.5% exact accuracy at 24 lines.Source: §C.1 · p. 18
  • The Qwen3-8B LoRA retains much of its benefit on interleaved assignments, three-chain programs, and code-to-English assignment transfer.The supplied evaluations report 76.5% at 24 interleaved lines, 83.5% at eight lines with three chains, and 94% on English assignments after code-style training.Source: §C.1 · p. 18

C.2. Alternative interventions at the same layer

  • 99.5% and 94.0% exact accuracy at 16 and 24 lines comes from a three-step low-rank flow; projection LoRA scores 99.0% and 90.0%.At layer 26, the tested interventions choose between chains near chance, indicating that extending the chain depends on early placement.Source: §C.2 · p. 18

C.3. Loop count, training length, and transfer

Loop-trained LoRAs extend reference following far beyond frozen models, and the relay advances through middle layers as frozen attention reads farther up each chain. Parent-line attention supports that relay, while intervention placement and task-specific training shape its reach and transfer.

C.3. Loop count, training length, and transfer

  • At least 160 lines are reached by Ouro-1.4B after eight loops, while Huginn reaches 58 after sixteen; both lose reach when run for too many recurrences.Ouro’s longer-trained LoRA reaches 60 lines after four loops and about 146 after six; Huginn’s later reach falls at 32 and 64 recurrences.Source: §C.3 · pp. 19–20

D. The computation carried by the middle layers

  • The relay advances in middle layers as attention reaches farther up the chain; targeted parent-reading heads support longer reads, while matched random-head cuts have smaller effects.Ouro’s relay advances mainly in layers 7–15; in Qwen3-8B, the relay advances no farther than the corresponding attention distance.Source: §D.1 · p. 20, §D.2 · p. 21, §D.3 · p. 21

D.4. What the representations carry

  • Line representations accumulate ancestor names before chain membership is readable, and later frozen loops can continue the computation after a first-loop-only LoRA.Blocking parent attention in Ouro’s second loop keeps four- to six-line names near their loop-1 values.Source: §C.3 · p. 19, §D.4 · p. 21

E. Parent attention and longer reads

  • Removing parent attention stops the relay, and in three-chain evaluations the useful longer reads follow the line’s own chain.Removing reads at least two lines earlier reduces Ouro’s reach; the effects differ under blocked-key and renormalizing cuts.Source: §E.1 · pp. 22–23, §E.2 · p. 23, §E.3 · p. 23

F. The last useful input layer

  • The frozen-model cutoff predicts the last useful LoRA placement within the preregistered tolerance in three of four held-out models, with 2.25-layer mean absolute error.For Qwen3-8B, moving the LoRA from layer 20 to 21 lowers reach from 20.5 to 5.2 lines.Source: §F.1 · p. 23, §F.2 · p. 24, Table 7 · p. 24

F.3. A later loop can supply the needed middle layers

  • A later loop can supply missing middle layers, but a LoRA placed there in only the last loop does not initiate the relay.In Ouro-1.4B, a layer-20 last-loop LoRA reaches 2.6 lines after four loops, versus 21.6 for a layer-6 last-loop LoRA.Source: §F.3 · pp. 24–25

G.1. Fictional facts

  • Task-trained LoRAs extend multi-hop fictional-question performance beyond their training range, including six-hop answers at 88% in Qwen3-8B.The reported comparisons use matched prompts; intervals quantify question sampling rather than training-seed variability.Source: §G.1 · p. 25, §G.2 · p. 25

G.3. Standard-model MuSiQue controls

  • On MuSiQue, early LoRAs improve exact match across Qwen3-8B, OLMo-3-7B, and Llama-3.1-8B, while early projection LoRAs preserve most all-layer gains.In Qwen3-8B, early projection LoRA gains 11.0 points versus 12.8 for all-layer projection LoRA; a single-hop SQuAD-trained LoRA does not improve MuSiQue.Source: §G.3 · pp. 26–27

G.4. Ouro results by loop, hop, and intervention

In Ouro, a layer-6 LoRA improves MuSiQue exact match across loop counts, while checkpoint and controlled-model experiments examine when and how a relay develops. The section also describes training, reach-estimation conventions, connections to prior work, and reproducibility resources.

G.4. Ouro results by loop, hop, and intervention

  • 60.0% EM at four loops with the layer-6 LoRA compares with 48.3% frozen on Ouro’s 300-question development set.Across two through eight loops, the layer-6 LoRA gives 11.7–14.0 paired-gain points; at four loops, a matched-size projection LoRA gives 61.7% EM. At four loops, layer 6 gives 60.0% versus 55.3% for layer 20 when applied every loop; last-loop-only gains are 6.3 points at layer 6 and −1.3 at layer 20.Source: §G.4 · p. 28

H. When the relay appears during learning

  • Exact reach with an identically trained layer-6 LoRA rises from about 1.5 to 10.2 to 23.7 lines across OLMo-3-7B checkpoints at 21, 84, and 336 billion tokens.Frozen reach remains below two lines; a layer-12 LoRA reaches 3.3 and 8.2 lines at the two later checkpoints, versus 21.5 in the final model. The base-LoRA transfer comparison is confounded by the fixed LoRA and answer format and does not identify a causal effect of post-training.Source: H. When the relay appears during… · pp. 28–29

I.1. Training setup

  • The controlled models use a shared two-layer body repeated across 4–16 layers and train on synthetic reference-chain programs with curriculum growth up to eight or sixteen lines.The models are width 256 with eight heads; training runs 30,000 steps, and the maximum chain length grows when recent average training accuracy exceeds 0.9.Source: §I.1 · p. 29

I.2. Progress and ancestor names

  • Across 165 layer steps from 24 models, relay progress matches attention distance in 108 steps, exceeds it in 8, and falls short in 49.In the illustrated model, ancestor names arrive gradually; cutting parent attention at layer 3 delays three-line-name decoding, while removing attention beyond the parent at layers 5 and 6 leaves name decoding unchanged.Source: §I.2 · p. 29

I.3. Depth changes how far attention must reach

  • Six of ten models learn the sixteen-line curriculum, and every model that does loses about half its twelve-line accuracy when longer reads are removed.Across depths, longer curricula are associated with farther attention reads; the three-chain experiments also find both own-chain relay and, in one six-layer model, reliance on other chains’ assignments.Source: §I.3 · pp. 29–30

J. Complete looped reach estimates

  • Reach is defined at 80% choice accuracy, with 95% parametric-bootstrap intervals; estimates are capped at the longest tested length, so some entries are lower bounds.The appendix tables report Ouro reach over the first four loops and with additional inference loops, plus Huginn reach by recurrence count.Source: J. Complete looped reach estimates · p. 30, Table 11 · p. 31, Table 12 · p. 31

K. Further connections to prior work

  • Related work spans entity tracking, recurrent algorithms, and efficient adaptation; this paper focuses on how a small intervention changes reference following in frozen weights.The controlled from-scratch models test whether attention distance and relay progress are related under a controlled setting.Source: K. Further connections to prior work · p. 32

L. Reproducibility

  • The project page provides experiment and analysis scripts, including a guide linking each claim to its script and command.The experiments use synthetic prompts, public models, and public datasets.Source: L. Reproducibility · p. 32

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