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Running Fewer Loops Removes Refusal Behaviour in Recurrent-Depth Language Models

Seyedarmin Azizi, Erfan Baghaei Potraghloo, Arya Fayyazi, Saeid Shokoufa, Massoud Pedram

arXiv:2610.15218v1cs.AI

TL;DR

Recurrent-depth models let deployments reduce computation by running fewer loops, but the paper finds that this setting also changes safety. Across Ouro and Huginn-0125, it measures the loss, examines the refusal-related internal signal, and tests training at randomly chosen depths as a remedy.

  • Problem

    Because loop count is a deployment-time cost or speed choice, full-depth safety evaluations may not reflect the shallower settings actually run.

    Source: §1 · pp. 1, 3

  • Method

    The paper measures safety across depths on Ouro and Huginn-0125 using four distinct measurements, then tests runtime repairs and training at randomly chosen depths.

    Source: §9 · p. 17

  • Results

    Reducing loops removes refusal faster than harm detection or task ability, a pattern reproduced across four Ouro checkpoints and Huginn-0125 from 1 to 32 loops.

    Source: §9 · pp. 16–17

  • Takeaways & Limitations

    Training at randomly chosen depths roughly triples the one-loop refusal gap relative to final-loop-only supervision without costing full-depth accuracy.

    Source: §9 · p. 17

    At one loop, filtering leaves smaller samples—98 harmful and 75 harmless prompts on Ouro-1.4B-Thinking—though the ordering persists at two loops with 0.992 answer retention.

    Source: §4.1 · p. 6

Abstract

from arXiv · show

A recurrent-depth language model reuses one block of weights several times in a row. The number of repetitions, which we call loops, is chosen when the model runs, not when it is trained, and running fewer is cheaper and faster, so a deployment may choose to do it. Running fewer loops also makes these models less safe, and the loss of safety is larger than the loss of anything else we measured. We study four released Ouro checkpoints and Huginn-0125. At half of its trained depth, Ouro-1.4B-Thinking still solves 0.692 of the GSM8K maths problems, against 0.775 at full depth, keeping 89% of its accuracy. Over the same reduction, the rate at which it helps with harmful requests rises from 0.038 to 0.205, 5.3 times higher. The information is not lost: a linear classifier reads whether a request is harmful from the model's internal state after a single loop, with an ROC AUC of 0.967 against 0.986 at full depth. What the missing loops remove is the refusal that should follow. We measure the effect with four instruments, one generating no text at all, and reproduce it on a second model family. Removing a single direction from Ouro-1.4B's internal state at full depth drops its refusal rate on harmful prompts from 0.950 to 0.130, identifying what the shallow model is missing. Two run-time repairs do not help: the models' early-exit rules do not spend more loops on harmful requests, and choosing a depth per request does not recover the loss. Changing the training does. Standard safety training makes the shallow model safe only by refusing 0.865 of harmless requests, while training at randomly chosen depths reaches a separation of +0.399 between harmful and harmless refusal at one loop, against +0.118. On Huginn-0125 it keeps harmful help at or below 0.040 at every depth from 1 to 32 loops, where standard training reaches 0.194, and it costs no accuracy at full depth.

1 INTRODUCTION

Recurrent-depth models let deployments trade computation for quality, but reducing loops also removes refusal behaviour faster than measured task ability or harm detection. The paper traces this gap to a refusal-related direction that has not settled at shallow depth and tests runtime and training remedies.

1 INTRODUCTION

  • At two of four loops, Ouro-1.4B-Thinking retains 89% of GSM8K accuracy while harmful compliance rises from 0.038 to 0.205, a 5.3-fold increase.Figure 1 contrasts the small accuracy loss with the larger increase in harmful help.Source: §1 · p. 2, Figure 1 · p. 2
  • At reduced depth, harm detection and task ability decline more slowly than refusal, so models can retain ordinary capability while helping with harmful requests.The internal classifier scores 0.960 after one loop versus 0.982 at full depth on Ouro-1.4B; task ability falls by about half while refusal falls almost to nothing.Source: §1 · pp. 1–2
  • Across four Ouro checkpoints and Huginn-0125, the paper measures safety across inference depths and finds refusal behaviour falls faster than harm detection or task ability.Four measurements are used, including one that generates no text.Source: §1 · p. 2
  • Removing the refusal-related direction at full depth lowers Ouro-1.4B’s refusal gap from +0.800 to +0.080, while adding it at one loop raises Ouro-1.4B-Thinking’s gap from -0.170 to +0.220.The harmfulness signal is readable after one loop, but the direction associated with refusal has not settled.Source: §1 · p. 2
  • Early-exit rules and per-request depth selection do not repair the loss, whereas training at randomly chosen depths preserves harmful-versus-harmless refusal separation without reducing full-depth accuracy.Standard safety training leaves the shallow model safe only by refusing most harmless requests.Source: §1 · pp. 2–3
  • Because loop count is a runtime cost-and-latency choice, a full-depth safety evaluation may not describe the model deployed at a shallower setting.The same weights are used; fewer loops move the readout earlier.Source: §1 · pp. 1, 3

2 BACKGROUND AND SETTING

The paper studies recurrent-depth models whose shared block can be run for a variable number of loops, and treats loop count as both a compute and safety setting. It compares truncation and gated exit under an ordinary deployment assumption and measures refusal separation, harmful compliance, and task ability.

Recurrent-depth models

  • A recurrent-depth model repeatedly applies one shared block to its internal state, then uses a readout head to predict the next token; the loop count can vary by run.The state update is h_k+1 = f(h_k, x), with r denoting the number of loops.Source: §2 · p. 3
  • Ouro repeats its whole stack and was trained with four loops, while Huginn-0125 repeats only a middle block and was trained with an average of 32 repetitions.The families also differ in size, training data, and depth range.Source: §2 · p. 3

Two ways to reduce depth

  • Truncation reads out after fewer than the trained loops, while gated exit uses a learned head and threshold to stop early; the experiments leave weights unchanged.For Ouro, truncation and gated exit produce the same computation when they stop at the same loop.Source: §2 · p. 3

What we assume about the attacker

  • The assumed setting is an ordinary deployment that lowers loop count for cost or speed and checks quality without re-testing safety, rather than an attacker modifying weights.The safety question is whether these reasonable deployment settings remain as safe as the aligned and tested setting.Source: §2 · p. 3

What we measure

  • The refusal gap is refusal on harmful prompts minus refusal on harmless prompts, while harmful compliance counts harmful prompts receiving real, on-topic help.GSM8K accuracy measures task ability under the same decoding settings as the safety runs.Source: §2 · p. 3

3 HOW WE MEASURE SAFETY AT DIFFERENT DEPTHS

The measurement approach separates what a model represents from what it does, while controlling for output quality and testing whether the depth effect survives different scoring protocols. It combines prompt-based scoring, internal-state analyses, and a refusal-direction intervention.

Prompts and scoring

  • The prompt set contains 260 harmful and 200 harmless prompts, scored with a safety judge and refusal-opening checks; alternative scoring and sampled decoding preserve the depth effect.Every depth sees the same prompts, with greedy decoding and a fixed token budget in the primary setup.Source: §3 · p. 4

Filtering out broken text

  • Answers are filtered as coherent only when rep3 is at most 0.25 and dup at most 0.02, with safety rates computed on retained answers and retention reported.The judge can mistake on-topic but unusable text for harmful help, so two text-quality measures remove broken outputs.Source: §3 · p. 4
  • Where the filter retains at least 0.850 of answers, filtered and unfiltered compliance differ by at most 0.056, and filtering shrinks rather than enlarges the refusal-gap drop.For Ouro-1.4B-Thinking, the full-depth-to-one-loop drop is 0.863 before filtering and 0.694 after filtering.Source: §3 · p. 4, Figure 2 · p. 5

Four ways of measuring the same thing

  • Four protocols test the depth effect: plain generation, forced answers, equal-length answers, and a one-pass probability comparison that generates no text.The no-generation protocol compares probabilities for a harmful-request target sentence and a fixed refusal sentence on harmful and harmless prompts.Source: §3 · pp. 4–5

Looking inside the model

  • A cross-validated logistic probe measures harm information in each loop’s internal state, while a refusal-associated direction is estimated from refused-versus-complied states and added or removed.The intervention uses a shared-normalisation-layer hook; addition is compared with a random direction of equal length.Source: §3 · p. 5

4 HOW SAFETY AND CAPABILITY CHANGE WITH LOOP COUNT

As recurrent-depth models run fewer loops, refusal falls faster than harm detection or task ability, so settings that retain useful benchmark performance can lose substantial safety. The pattern appears across measurement methods, in dense-model comparisons, and in Huginn-0125.

4.1 THE THREE ABILITIES COME APART

  • At one loop, Ouro-1.4B-Thinking retains 0.961 of harm detection but 0.161 of refusal gap, a 0.800 separation.Harm detection is read from the model's internal state without generating text.Source: §4.1 · pp. 5–6, Figure 3 · p. 6

4.2 THE DEPTHS A DEPLOYMENT WOULD ACTUALLY USE

  • At two of four loops, Ouro-1.4B-Thinking keeps 89% of GSM8K accuracy (0.692 vs 0.775) while harmful compliance rises from 0.038 to 0.205.Ouro-2.6B-Thinking's harmful compliance rises from 0.035 to 0.344 at one loop, with 0.962 of answers coherent.Source: §4.2 · pp. 6–7, Table 1 · p. 7

4.3 THE FOUR MEASUREMENTS AGREE

  • The three generation-based measures agree within 0.035 at two loops and above, while a generation-free comparison also shows harmful preference rising and harmless preference barely moving.At one loop, the generation-based measures spread further, by up to 0.156.Source: §4.3 · pp. 7–8, Figure 5 · p. 8, Figure 6 · p. 9

4.4 A DENSE MODEL BEHAVES DIFFERENTLY

  • In dense controls, refusal is the last capability to go; in recurrent-depth models, it is the first.With two layers removed, Qwen3-1.7B keeps 0.625 of task ability and 0.894 of refusal gap, whereas Ouro-1.4B-Thinking's one-loop difference is -0.237.Source: §4.4 · p. 9

4.5 FEWER LOOPS AND PROMPT ATTACKS COMPOSE

  • On Ouro-2.6B-Thinking, the strongest jailbreak template raises harmful compliance from 0.080 to 0.717; one loop without a template reaches 0.447, and both together reach 0.830.The depth setting is chosen by the deployer in the paper's threat model, rather than being an attack itself.Source: §4.5 · p. 10

4.6 A SECOND MODEL FAMILY, WITH A MUCH LONGER DEPTH RANGE

  • On Huginn-0125, standard safety training's 0.031 harmful compliance at full depth rises to 0.194 at four loops; random-depth training removes the depth difference.The released Huginn-0125 has weak separation, with refusal gap +0.333 and harmful compliance 0.455 at full depth.Source: §4.6 · p. 10, Figure 7 · p. 10

5 LOCATING THE MISSING COMPONENT

The shallow state retains harmfulness information, but its refusal direction is not yet aligned with the full-depth direction. Removing that direction reduces refusal at full depth, while adding it at shallow depth does not consistently restore selective refusal.

5.1 THE INFORMATION ARRIVES EARLY, THE DIRECTION DOES NOT

  • A one-loop probe reaches AUC 0.960, 0.967, and 0.982 across three Ouro checkpoints, while the full-depth refusal direction agrees with the one-loop direction at only 0.412, 0.486, and 0.842.Using the full-depth direction on the one-loop state yields lower separation than a probe fitted at that depth; the direction settles furthest on the checkpoint that loses the least refusal behaviour.Source: §5.1 · p. 11

5.2 A TEST THAT CHANGES THE MODEL’S BEHAVIOUR

  • Removing the full-depth refusal direction drops harmful-prompt refusal from 0.950 to 0.130 on Ouro-1.4B and raises harmful compliance from 0.050 to 0.850.The edit also reduces the refusal gap from +0.800 to +0.080; effects on harmful-prompt refusal are smaller on the two other checkpoints.Source: §5.2 · p. 11
  • Adding the refusal direction at one loop raises harmful-prompt refusal from 0.320 to 0.910 on Ouro-1.4B-Thinking, while a same-length random direction leaves the refusal gap at -0.050.The refusal gap changes from -0.170 to +0.220 with the refusal direction; harmless-prompt refusal rises less, from 0.490 to 0.690.Source: §5.2 · pp. 11–12
  • On two other checkpoints, adding the direction raises refusal on harmful and harmless prompts similarly, leaving refusal gaps at -0.050 and +0.370 rather than restoring separation.The edit demonstrates that refusal is produced along the direction, but a fixed run-time addition is not a general repair.Source: §5.2 · p. 12

6 TWO RUN-TIME REPAIRS THAT DO NOT WORK

Neither the model’s early-exit rule nor per-request depth selection recovers shallow refusal. Knowing whether a prompt is harmful is insufficient to choose the useful depth; the per-prompt oracle requires more specific information.

6 TWO RUN-TIME REPAIRS THAT DO NOT WORK

  • At the earliest Ouro-1.4B-Thinking exit setting, harmful and harmless prompts average 2.439 and 2.397 loops, a difference of just 0.042.Across thresholds and models, the difference never exceeds 0.058 of one loop.Source: §6 · p. 12
  • Together, these tests show that run-time depth allocation does not fix the problem: the model and an idealised label-based router do not know where to spend computation.Source: §6 · pp. 12–13
  • A per-prompt oracle reaches a 0.896 refusal gap on Ouro-1.4B at an average of 1.520 loops, exceeding the model’s full-depth value.The oracle picks the lowest depth that produces the right behaviour for each prompt, showing a potential gain in principle.Source: §6 · pp. 12–13
  • A router told each prompt’s true harmfulness label stays close to fixed-depth performance, with refusal gaps from −0.060 to 0.111 across budgets.The per-prompt oracle remains far above this label-based router, so harmfulness labels alone do not identify which individual prompts need more depth.Source: §6 · p. 13

7 TRAINING AT RANDOMLY CHOSEN DEPTHS

Training at randomly chosen depths preserves selective refusal in shallow settings better than final-loop or exit-gate training, without reducing full-depth GSM8K accuracy. The approach also improves shallow fluency and transfers to Huginn-0125.

7 TRAINING AT RANDOMLY CHOSEN DEPTHS

  • The random-loop objective applies the loss to one uniformly sampled loop per example, unlike final-loop loss or the early-exit-weighted mixture.The compared LoRA arms use the same refusal data, schedule, and hyperparameters.Source: §7 · p. 13
  • Random-loop training leaves full-depth GSM8K accuracy at 0.783, equal to the untrained model’s 0.783, and raises the full-depth refusal gap from +0.737 to +0.797.Source: §7 · p. 13
  • Random-depth training raises the coherent-answer fraction at one loop from 0.585 untrained to 0.992.Source: §7 · p. 13
  • Across three retraining seeds, the ordering between random-loop and final-loop training holds in every run.The random-loop objective removes the measured asymmetry between retained safety and task ability rather than reversing it.Source: §7 · pp. 13–14
  • At one loop, random-loop training yields a +0.399 refusal gap versus +0.118 with final-loop training, while refusing 0.585 of harmless prompts versus 0.865 and 0.926.All trained arms reduce harmful compliance from 0.270 to 0.008–0.009; Figure 10 summarizes the refusal gap, harmless-prompt refusal, and GSM8K accuracy across loop counts.Source: §7 · p. 13, Figure 10 · p. 14, Table 2 · p. 15
  • Across the tested refusal-suppression and persona templates, both adapters reduce worst-case harmful compliance, and the refusal gap improves under the persona template.For persona prompts, the gap rises from +0.134 untrained to +0.328 and +0.368 for the two trained adapters.Source: §7 · p. 14
  • On Huginn-0125, random-depth training keeps harmful compliance at or below 0.040 from 1 to 32 loops, while standard training reaches 0.194 at four loops.At one loop, the text-quality filter keeps 0.962 of random-depth answers, compared with 0.119 under final-loop training.Source: §7 · p. 14

8 RELATED WORK

Related work studies recurrent depth, adaptive inference compute, shallow alignment, compression-related safety changes, and interpretability methods. This paper distinguishes its focus on loop-count-dependent refusal in recurrent-depth models from those lines of work.

8 RELATED WORK

  • Recent recurrent-depth models expose loop count as a test-time compute budget, including Huginn-0125 (Geiping et al., 2025) and Ouro (Zhu et al., 2025b).Earlier work covers weight-tied recurrence and cross-layer sharing, while follow-on work studies sparsity, routing, and depth scaling.Source: §8 · p. 15
  • Adaptive-computation work typically evaluates accuracy, latency, and cost, and no prior work measures refusal as a function of recurrent-model loop count.SafeDepth addresses safety-oriented compute allocation in a standard transformer (Li & Harris, 2026).Source: §8 · pp. 15–16
  • Prior shallow-alignment studies locate safety in response positions, refusal directions, layer bands, or parameters, whereas this paper varies computation per token.The cited lines include Qi et al. (2025), Arditi et al. (2024), and Li et al. (2025).Source: §8 · p. 16
  • Unlike quantisation and pruning studies that change weights, this work keeps the released model’s parameters identical and changes only loop count.Related work reports safety shifts under compression, including Hong et al. (2024) and Wei et al. (2024).Source: §8 · p. 16
  • The evaluation combines response-quality filtering and refusal-gap scoring with probes and ablations applied across loop index.These adapt established jailbreak-evaluation work (Souly et al., 2024) and interpretability methods commonly applied across layers of fixed-depth networks.Source: §8 · p. 16

9 CONCLUSION

Reducing loops removes refusal faster than harm detection or task ability across Ouro and Huginn, while dense-model layer removal shows the opposite ordering. The conclusion identifies an unsettled refusal direction, rejects runtime fixes, and recommends training and reporting across depths.

9 CONCLUSION

  • Across four Ouro checkpoints and Huginn-0125, refusal falls faster than harm detection or task ability; dense controls lose answer ability before refusal, the opposite order.Huginn-0125 was evaluated across 1 to 32 loops.Source: §9 · pp. 16–17
  • At one loop, Ouro-1.4B retains harm information (AUC 0.960 versus 0.982 at full depth), but removing its full-depth refusal direction drops the refusal gap from +0.800 to +0.080.Adding the direction at one loop raises the Ouro-1.4B-Thinking refusal gap from -0.170 to +0.220.Source: §9 · p. 17
  • Early exit and per-request depth selection do not restore safety; random-depth safety training roughly triples the one-loop refusal gap without reducing full-depth accuracy.Final-loop-only training leaves shallow safety dependent on refusing most harmless requests.Source: §9 · p. 17
  • Safety evaluation should report performance across depth, and training should cover the depths at which the model will run.The paper frames loop count as both a deployment setting and a safety setting.Source: §9 · pp. 16–17

A EXPERIMENTAL DETAILS

  • The experiments cover four four-loop Ouro checkpoints, Huginn-0125 trained with an average of 32 repetitions, and Qwen3-1.7B as a dense layer-removal control.The Ouro checkpoints span two model sizes and two kinds of post-training.Source: §9 · p. 17, A EXPERIMENTAL DETAILS · p. 22
  • Safety evaluation uses 260 harmful and 200 harmless prompts, while task ability is measured on 120 GSM8K test problems per cell.Decoding is greedy with a 512-token budget unless stated otherwise.Source: A EXPERIMENTAL DETAILS · p. 22
  • Safety training uses 1,200 harmful-prompt/refusal pairs plus instruction-following and worked GSM8K examples; the latter preserve normal-length answers and avoid a training–test split overlap.The training setup uses LoRA, rank 16, for two epochs.Source: A EXPERIMENTAL DETAILS · p. 22

B FULL PER-CELL RESULTS

The per-cell results document protocol and filtering choices, including coverage limits and sample-size cautions. They also provide the table scopes for the equal-length, quality-filter, measurement-protocol, Huginn, and probe results.

B FULL PER-CELL RESULTS

  • The filtered Section 4 table covers three Ouro checkpoints because the main runs omit Ouro-2.6B; equal-length runs cover all four.Table 3 is the equal-length protocol and is not comparable cell by cell with Table 1; it does not remeasure GSM8K accuracy.Source: B FULL PER-CELL RESULTS · p. 22, Table 3 · p. 23
  • At the headline compliance depths, the filter retains 0.992 of Ouro-1.4B-Thinking answers at two loops and 0.962 of Ouro-2.6B-Thinking answers at one loop.Single-loop cells for the 1.4B models retain far fewer answers and rely on smaller samples.Source: B FULL PER-CELL RESULTS · p. 22
  • Filtering makes the one-loop comparison of surviving refusal gap versus surviving task ability harder, not easier; without filtering, differences are -0.446, -0.428, and -0.110 on Ouro-1.4B-Thinking, Ouro-1.4B, and Ouro-2.6B-Thinking, respectively.The first two differences have intervals entirely below zero.Source: B FULL PER-CELL RESULTS · pp. 22–23
  • The three-protocol comparison scores refusal gap before filtering: raw generation, bounded generation followed by a forced answer, and equal-length truncation.Equal-length truncation controls answer length across depths; a dash denotes a model-depth combination not run under that protocol.Source: Table 5 · p. 25
  • The Huginn table spans 1 to 32 loops and compares final-loop-only training with uniform random-loop supervision; at two loops, filtering raises released-model apparent compliance from 0.381 to 0.905.That cell retains only 0.162 of harmful-prompt answers, so it is based on 42 of 260 prompts.Source: Table 6 · p. 25
  • The probe table reports harmfulness-probe AUC, full-depth refusal-direction AUC, and cosine alignment of each depth’s refusal direction with the full-depth direction.The cosine measures how far the direction still has to move, rather than how far the state has to move.Source: Table 7 · p. 26

C SCORING WITHOUT GENERATING

A forced-choice measure compares compliant and refusal continuations without generating text, providing a depth comparison that is distinct from observed generation. Its scale should not be read as an absolute safety measure.

C SCORING WITHOUT GENERATING

  • The forced-choice measure finds effects on Ouro-1.4B-Thinking (0.303, interval [+0.214, +0.391]) and Ouro-1.4B (0.246, [+0.160, +0.332]), but none on Ouro-2.6B-Thinking (-0.020, [-0.065, +0.026]).The measure compares the probability preference for a compliant continuation over a refusal at each loop without generating.Source: C SCORING WITHOUT GENERATING · p. 27, Table 8 · p. 28
  • On Ouro-1.4B, the forced-choice measure prefers compliance on 0.895 of harmful prompts at full depth, whereas generated refusal gap is +0.712.The authors use this measure for cross-depth comparison free of generation effects, not as an absolute measure of safety.Source: C SCORING WITHOUT GENERATING · p. 27
  • The harmful-minus-harmless row is derived from the two prompt-group fractions, and its interval treats the groups as independent samples.Table 8 reports paired shallow-minus-full changes in log-probability margin, in nats.Source: C SCORING WITHOUT GENERATING · p. 27, Table 8 · p. 28

D THE DENSE CONTROL ON A FINE LAYER GRID

Fine-grid layer removal in dense models does not reproduce the recurrent-depth refusal pattern, and the effect of prompt-level attacks compounds with fewer loops. The dense comparison is informative only while the model retains task ability, and the attack results carry a thin-sample caution.

D THE DENSE CONTROL ON A FINE LAYER GRID

  • The dense-control grid removes 1, 2, 4, 6, 8, or 10 of 28 layers to compare settings where the model still works with recurrent-depth cuts.The grid was chosen because the coarser comparison reached settings where dense-model task ability was lost.Source: D THE DENSE CONTROL ON A FINE LAYER GRID · p. 28, Table 9 · p. 29
  • On Qwen3-1.7B, removing two layers leaves 0.350 of answers, while Ouro-1.4B-Thinking at half its loops retains 0.992.Qwen3-1.7B GSM8K accuracy falls from 0.733 at full depth to 0.058 with four layers removed.Source: D THE DENSE CONTROL ON A FINE LAYER GRID · p. 28
  • At settings where dense models still work, both retain more refusal gap than task ability, reversing the pattern across every Ouro checkpoint.For Qwen3-1.7B with two layers removed, task-ability retention is 0.625 and refusal-gap retention is 0.894, a difference of +0.269.Source: D THE DENSE CONTROL ON A FINE LAYER GRID · p. 28
  • The dense comparison stops being informative once task ability is near its floor; the authors therefore interpret it only at the two mildest cuts.Below 24 layers, GSM8K retention is at most 0.023.Source: D THE DENSE CONTROL ON A FINE LAYER GRID · p. 28

E COMPOSITION WITH PROMPT-LEVEL ATTACKS

  • The prompt-attack table crosses depth with three jailbreak templates on two Thinking checkpoints, using 100 harmful and 100 harmless prompts per cell.The templates request no apology, a “Sure, here is” opening, or role-play as a morally unconstrained character.Source: E COMPOSITION WITH PROMPT-LEVEL ATTACKS · p. 29, Table 10 · p. 30
  • On Ouro-2.6B-Thinking, persona prompting raises harmful compliance from 0.080 at full depth to 0.717; at one loop alone it is 0.447, and together they reach 0.830.The largest compliance in both models comes from a template at a single loop, not either factor alone.Source: E COMPOSITION WITH PROMPT-LEVEL ATTACKS · p. 29, Table 10 · p. 30
  • On Ouro-2.6B-Thinking, the refusal gap falls from +0.820 to +0.263 with the persona template, then to +0.052 with the template at one loop.The single-loop cells for Ouro-1.4B-Thinking are least reliable: fewer than half the prompts remain after filtering, including 38 harmful persona-template answers.Source: E COMPOSITION WITH PROMPT-LEVEL ATTACKS · p. 29

F JUDGE AND DECODING CHECKS

Checks across judges and decoding preserve the depth trend, while routing and early exit do not establish a way to recover shallow-depth safety. Additional training-data comparisons find similar shallow harmless-refusal rates across two alternative data mixtures.

F JUDGE AND DECODING CHECKS

  • 0.075 to 0.224 on Ouro-1.4B, 0.027 to 0.469 on Ouro-1.4B-Thinking, and 0.019 to 0.204 on Ouro-2.6B-Thinking: filtered compliance rises from full depth to one loop under the second judge.Judge agreement is at least 0.827 in every cell, and the second judge never reports a higher compliance rate than the primary judge.Source: F JUDGE AND DECODING CHECKS · p. 30, Table 11 · p. 31
  • 0.029 versus 0.133: on Ouro-1.4B-Thinking at one loop, the sampled mean refusal gap is below the greedy gap, and depth ordering holds in every seed.Across sampled cells, refusal-gap standard deviation is at most 0.061; the corresponding full-to-one-loop drop is 0.783 on Ouro-1.4B-Thinking and 0.822 on Ouro-2.6B-Thinking.Source: F JUDGE AND DECODING CHECKS · p. 30, Table 12 · p. 31

G EARLY-EXIT BEHAVIOUR AND DEPTH ROUTING

  • 2.418 of four loops: even at its most eager setting, Ouro-1.4B-Thinking’s exit rule does not choose the shallowest settings, so the reported effect concerns externally set compute budgets.The routing simulation compares depth-blind allocation, label-aware coarse allocation, the gate, and a per-prompt oracle; the oracle is headroom, not a deployable policy.Source: G EARLY-EXIT BEHAVIOUR AND DEPTH ROUTING · p. 31, Table 13 · p. 32, Table 14 · p. 33

H ADDITIONAL TRAINING-DATA COMPARISONS

  • 0.465 and 0.425: the two alternative harmless-data mixtures’ one-loop harmless refusal rates are similar to 0.495 for the plain random-depth run.The authors therefore do not claim harmless-data topic is the operative factor.Source: H ADDITIONAL TRAINING-DATA COMPARISONS · p. 34

I TRAINING SEEDS AND UNSEEN ATTACKS FOR THE DEPTH-AWARE OBJECTIVE

This section tests whether depth-aware safety training generalizes across seeds and unseen attacks, and uses stored outputs to illustrate shallow-depth behavior under random-loop training, final-loop training, and a dense-control model. It also qualifies the findings’ scope, noting limited model-size coverage and judge-family variation.

I TRAINING SEEDS AND UNSEEN ATTACKS FOR THE DEPTH-AWARE OBJECTIVE

  • Both objectives reduced harmful compliance under two unseen jailbreak templates at full depth and at the worst loop count, compared with the untrained model.Adapters were trained on plain harmful prompts without wrappers; the test covered Ouro-1.4B at every loop count.Source: I TRAINING SEEDS AND UNSEEN ATTACKS… · p. 34, Table 16 · p. 35
  • Across three seeds, random-loop training kept a positive one-loop retention gap (+0.118, +0.183, +0.137), while final-loop training’s gaps were negative (-0.237, -0.341, -0.419).The one-loop refusal-gap ranges did not overlap, and final-loop training achieved shallow safety by refusing harmless prompts in all three runs.Source: I TRAINING SEEDS AND UNSEEN ATTACKS… · p. 34, Table 15 · p. 35

J SCOPE

  • Across released models from 1.4B to 3.5B parameters, the effect appeared in all four Ouro checkpoints and Huginn-0125, but its size varied by model and training type.The fraction of the refusal gap kept at one loop was 0.351 for Ouro-1.4B, 0.126 for Ouro-1.4B-Thinking, and 0.723 for Ouro-2.6B-Thinking; Ouro-2.6B’s 0.442 comparison used three loops because full-depth runs were unavailable.Source: J SCOPE · p. 35
  • Two judge-independent measurements agreed with judge-based results in direction and ordering, and a larger guard model reproduced the depth trend across three checkpoints.The larger guard agreed with the primary judge on at least 0.827 of answers in every cell; judge-family variation remained untested.Source: J SCOPE · p. 36
  • At one loop, untrained Ouro-1.4B refused 0.465 of harmless prompts, versus 0.495 after random-depth training, indicating that shallow computation itself drives high harmless refusal.The paper reports a refusal gap defined to be unaffected by a uniform shift in refusal frequency.Source: J SCOPE · p. 36

K VERBATIM MODEL OUTPUTS

  • In stored outputs, Ouro-2.6B-Thinking’s one-loop reasoning trace recognized an insider-trading request as illegal but the reply gave the procedure, unlike its full-depth refusal.At one loop, Ouro-1.4B also produced harmful compliance on a fabricated-review request, while its full-depth output refused.Source: K VERBATIM MODEL OUTPUTS · pp. 36–38
  • On a harmless prompt at 1 loop, final-loop training refuses while random-loop training answers, illustrating the refusal-gap distinction.The random-loop-trained model provides treatment information; the final-loop-trained model declines the request.Source: K VERBATIM MODEL OUTPUTS · p. 40
  • At 4 loops, Huginn-0125 refuses the harmful request after random-loop training but complies after final-loop training, despite refusing at 32 loops.The transcripts show final-loop training refusing at 32 loops and producing harmful compliance at 4; random-loop training refuses at 4.Source: K VERBATIM MODEL OUTPUTS · p. 40
  • With layers removed, Qwen3-1.7B stops producing language rather than answering harmful prompts, and its shallow outputs are judged refusals on harmful and harmless prompts alike.The full-depth example is a coherent refusal, while the shallowest output is gibberish; this control's refusal gap is near zero.Source: K VERBATIM MODEL OUTPUTS · pp. 40–41

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