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Closing the Loop: Practical Training Recipes for Looped Language Models

Andrei Marchenko, Viacheslav Bezrukov, Oleg Kashurin, Inessa Fedorova, Dmitry Bocharov, Yuliana Shakhvalieva, Maria Tikhonova, Valerii Ternovskii

arXiv:2610.00673v1cs.CLcs.AI

TL;DR

Large-scale looped-model training has required costly multi-stage schedules, and prior comparisons leave recurrence’s contribution difficult to isolate. This paper presents a shorter scratch-training recipe and a minimal dense-to-loop conversion, with controlled comparisons showing gains over dense counterparts in both settings.

  • Problem

    Earlier large-scale recipes used multi-stage training over trillions of tokens, and comparisons against dense models trained on different data left the share of gains due to recurrence unknown.

    Source: §1 · p. 1

  • Method

    The paper develops a two-stage from-scratch recipe and converts pretrained dense models using a learned input-mixing scalar and smoothed exit loss, comparing looped models with dense counterparts under matched training conditions.

    Source: §1 · pp. 1–2

  • Results

    LoopLM beats its parameter-matched dense model on every evaluated benchmark, while Looped Qwen improves over its continued dense checkpoint on every evaluated benchmark.

    Source: §6 · p. 9

  • Takeaways & Limitations

    The results provide a shorter training recipe for scratch-trained looped models and a lightweight way to improve an existing 1.7B checkpoint without repeating pretraining or adding per-step parameters.

    Source: §6 · p. 9, §5.3 · p. 9

    Looped Qwen still trails Qwen3-4B-Base on every benchmark, so the conversion does not replace the knowledge and capacity of substantially larger pretraining.

    Source: §5.3 · p. 9

Abstract

from arXiv · show

Looped language models increase effective depth by repeatedly applying a shared block of layers, but existing large-scale recipes require multi-stage training over trillions of tokens, while the benefits of recurrence remain difficult to separate from differences in data and training. In this work, we establish practical training recipes for looped language models, with three main results. (1) We develop a compute-efficient from-scratch pipeline that reduces the training budget from 7.7T tokens in Ouro to 310B tokens while retaining strong reasoning performance. Pretraining followed by high-quality mid-training, together with learning-rate warmup and stronger exit-gate regularization, enables stable recurrent training without prior multi-stage schedules. (2) Under controlled comparisons, our 1.4B LoopLM outperforms a parameter-matched dense model trained on the same data and token budget on all 12 evaluated benchmarks, including +14 points on GSM8K, +10 on MATH, and +22 on DROP. At matched inference compute, it approaches a 3.9B dense model on mathematical reasoning and reading comprehension while using only 36\% as many parameters. (3) We introduce a minimal recipe for converting pretrained dense models into looped ones: a single learned input-mixing scalar and a smoothed exit loss, with no step-specific parameters. Applied to Qwen3-1.7B-Base, Looped Qwen improves over an identically continued dense baseline on every evaluated benchmark across two data regimes, with statistically clear gains on GSM8K, MATH, and MMLU-Pro on the curated mixture. Together, these results make looped language models substantially cheaper to train from scratch and practical to introduce into existing pretrained checkpoints, while isolating the gains due to recurrence itself.

1 INTRODUCTION

Looped models add effective depth by repeatedly applying shared layers, but earlier large-scale recipes were costly and left recurrence gains difficult to isolate. This work presents cheaper scratch training, dense-to-loop conversion, and controlled comparisons with dense counterparts.

1 INTRODUCTION

  • The comparisons match looped models with dense counterparts trained on the same data and stages, matched by parameter count or inference compute.This design addresses the difficulty of separating recurrence gains from data and training differences.Source: §1 · pp. 1–2
  • The scratch recipe uses two stages and 310B tokens instead of Ouro’s five stages and 7.7T tokens.Learning-rate warmup removes early exit-gate collapse, while a larger KL coefficient lets the gate recover if collapse occurs.Source: §1 · pp. 1–2
  • The 1.4B LoopLM beats its parameter-matched dense twin on all 12 benchmarks and stays close to the inference-compute-matched 3.9B model on math and reading comprehension.At the same inference cost, it trails the larger model on knowledge and commonsense benchmarks.Source: Figure 1 · p. 2, §1 · p. 2
  • Looped Qwen improves over Qwen3-1.7B-Base continued on the same data and steps, with clear gains on GSM8K, MATH, and MMLU-Pro on the curated mixture.Its conversion uses one learned scalar and a smoothed exit loss, without step-specific parameters.Source: §1 · p. 2

2 RELATED WORK

Related work covers recurrent architectures, their training instabilities, comparisons with dense models, pretrained-model conversion, and reinforcement learning. The paper positions its contributions around simpler training, controlled comparisons, and conversion without required step-specific adapters.

Looped and recurrent language models

  • Universal Transformers and related models apply shared blocks repeatedly, using adaptive halting or fixed-point convergence; other variants target depth, length generalization, or token-specific computation.At scale, Ouro, HRM-Text, and Loop the Loopies extend recurrence to different model settings.Source: §2 · pp. 2–3

Training stability

  • Prior work reports distinct stability problems, while the cited approaches do not provide a from-scratch recipe without a multi-stage schedule or identify what keeps Ouro’s exit gate alive when that schedule is removed.Examples include loss spikes, collapsed hidden states, and router imbalance.Source: §2 · p. 3

Comparing looped and dense models

  • Some studies compare looped models with dense baselines under matched conditions, but Ouro and recurrent-depth headline comparisons use dense models trained on other data.This work measures both its scratch-trained and converted models against dense twins in parameter- and inference-compute-matched regimes.Source: §2 · p. 3

Converting pretrained models

  • Prior pretrained-model conversions use step-specific adapters, whereas this work reports that one learned scalar can prevent degradation from recurrence and that adapters are optional.The cited conversion methods also compare against parameter-matched baselines only.Source: §2 · p. 3

Reinforcement learning

  • GRPO and DAPO assume fixed computation paths, while RLTT distributes credit across recurrent iterations; Ouro reports no gain from reinforcement learning on its final model.The paper studies reinforcement learning separately from its main model comparisons.Source: §2 · p. 3

3 A SIMPLER FROM-SCRATCH RECIPE

The section replaces Ouro’s five-stage, 7.7T-token schedule with a two-stage, 310B-token recipe. It uses fixed recurrent depth, gate-stability measures, and high-quality mid-training, with reinforcement learning examined separately.

3.2 A SINGLE PRETRAINING STAGE

  • The recipe replaces Ouro’s three pretraining regimes with one run from random initialization on a fixed mixture, then retains one mid-training stage.High-quality data is present from the start; the later stage is also applied to dense baselines with identical data, schedule, and token budget.Source: §3.2 · p. 3, §3.4 · p. 5

3.3 DEPTH AND STABILITY

  • In a T=8 run, loops five through eight add about 0.01 nats or less, and the gate spreads mass over loops four through eight, motivating T=4 from the start.The T=8 run’s loss stops improving after the third or fourth iteration, so extra depth costs compute without measurable gain.Source: §3.3 · p. 4, Figure 2 · p. 4
  • Without warmup, β=0.05 remains collapsed while larger β values recover; warmup prevents early collapse at β=0.15, and language-model loss alone does not reveal collapse.The exit distribution therefore must be monitored directly.Source: §3.3 · p. 4, Figure 3 · p. 4

3.5 OUR IMPROVED SETUP

  • The resulting recipe trains for 310B tokens in two stages, about 25× fewer tokens than Ouro-1.4B, and uses about 3% of its training compute on the same architecture.It combines 210B-token pretraining with 100B tokens of high-quality mid-training, uses T=4 from the start, and applies warmup with β=0.15.Source: §3.5 · p. 5

3.4 HIGH-QUALITY MID-TRAINING

  • Mid-training more than doubles GSM8K accuracy and improves MMLU by about nine points relative to the step-100,000 pretraining checkpoint.The stage uses instruction-response pairs with loss on response tokens and emphasizes mathematics and reasoning while retaining a knowledge-preserving component.Source: §3.5 · p. 5, §3.4 · p. 5

3.6 REINFORCEMENT LEARNING AS A SEPARATE STUDY

  • RLTT leaves MATH unchanged when about three quarters of rollouts are already solved, but adds twelve GSM8K points when the checkpoint solves about a third of rollouts.The paper reports these as separate reinforcement-learning runs, outside the models compared in Section 5.Source: §3.6 · p. 5

4 LOOPING PRETRAINED LLMS

The conversion preserves the pretrained decoder across recurrent steps and adds minimal mechanisms for input mixing and exit-loss smoothing. The section also evaluates data regimes, step-specific adapters, and the final architecture.

4 LOOPING PRETRAINED LLMS

  • Only a few pretrained looped checkpoints are publicly available, and the scalar-plus-smoothed-loss conversion takes under 1% of Qwen3-1.7B-Base’s pretraining compute.The recipe is presented as an alternative to training a looped model from scratch.Source: §4 · p. 6

4.1 CONVERSION RECIPE

  • One learned scalar mixes the original token embedding into later recurrent steps, preventing the degradation seen when the pretrained decoder is applied recurrently without changes.With the same data, batch, and seed as the naive run, steps two and three finish about 0.02 nats below step one.Source: §4.1 · p. 6, §4 · p. 6

4.2 TRAINING STABILITY

  • Smoothing the exit distribution used for the language-model loss keeps each step trained; with ε=0.05 and T=3, each step retains at least 0.0167 LM weight.Gate regularization and inference still use the original exit probabilities.Source: §4.2 · p. 6

4.3 DATA MIXES

  • The conversion is tested on a curated continued-training mixture and a second mixture dominated by filtered web text, with each mixture shared unchanged by its dense baselines.The curated mixture covers mathematics, code, STEM, science, and instruction following, without explicit chain-of-thought traces.Source: §4.3 · p. 6

4.4 STEPWISE LORA

  • Independent rank-32 stepwise LoRA adapters provide little benefit: training losses nearly match, and benchmark differences stay within two points with neither variant consistently ahead.The fully shared model is therefore used by default.Source: §4.4 · p. 6

4.5 FINAL ARCHITECTURE

  • The final architecture shares the pretrained decoder, language-model head, and exit gate across steps; step-specific LoRA adapters are optional.Later steps mix original embeddings with the preceding hidden state, and evaluation uses a fixed exit after two steps because the third improves training loss by less than 0.001 nats over the second on the instruction mixture.Source: §4.5 · p. 6, Figure 4 · p. 7

5 EXPERIMENTS

Experiments compare looped models with dense baselines matched by parameter count or inference compute, using the same data and training stages. LoopLM leads its parameter-matched baseline across benchmarks; conversion gains vary by data regime, and published-model comparisons are contextual.

5.1 BASELINES; 5.1.1 FROM-SCRATCH LOOPLM

  • The baselines remove recurrence while retaining the transformer block and two-stage training; the parameter-matched model uses one 24-layer block, while the compute-matched model stacks three.The latter is 72 layers and matches three recurrent steps; LoopLM’s per-token training compute is about 4× and 1.4× the respective dense baselines.Source: §5.1.1 · p. 7, §5.1 · p. 7

5.1.2 LOOPED DENSE

  • For conversion, Qwen3-1.7B-Base is the parameter-matched baseline and Qwen3-4B-Base the inference-compute-matched reference; all models continue on identical data and settings.At its two-step exit, Looped Qwen uses about 20% fewer inference FLOPs than Qwen3-4B-Base.Source: §5.1.2 · p. 7

5.2.1 AGAINST DENSE MODELS TRAINED ON THE SAME DATA

  • At equal inference compute, three-step 1.4B LoopLM uses 36% of dense-ouro-3.9B’s parameters and comes within one standard error on GSM8K, MATH, and MATH500 and about one point on DROP.The larger dense model is ahead or level on every benchmark; its remaining 2-to-9-point lead is on knowledge and commonsense benchmarks.Source: §5.2.1 · pp. 7–8, Table 2 · p. 8
  • At equal parameter count, four-step LoopLM outperforms dense-ouro-1.4B on all 12 benchmarks, including +22 points on DROP, +17 on CRUXEval-I, and +14 on GSM8K.Table 2 reports scores after mid-training; dense-ouro-3.9B matches the inference compute of three LoopLM iterations.Source: §5.2.1 · p. 7, Table 2 · p. 8
  • One iteration trails the parameter-matched dense model on every benchmark; two iterations beat it on 11 of 12, three on all 12, and a fourth improves 10 scores further.The fourth iteration uses roughly one third more inference compute and moves LoopLM ahead on DROP and level on GSM8K.Source: §5.2.1 · p. 8

5.2.2 AGAINST PUBLISHED MODELS

  • Against published models, four-step LoopLM has the table’s highest DROP and second-highest GSM8K; versus Ouro-1.4B it is +4.4 points on GSM8K and +10.9 on DROP despite 25× fewer tokens.This is contextual, not a controlled comparison, because published models differ in evaluation protocol and pretraining budget.Source: Table 3 · p. 8, §5.2.2 · p. 8

5.3 LOOPED DENSE RESULTS

  • Without step-specific adapters, Looped Qwen improves over its identically continued Qwen3-1.7B-Base baseline on every benchmark in both data regimes; curated-data gains include +4.3 GSM8K, +3.8 MMLU-Pro, and +2.2 MATH.Each curated-mixture gain exceeds two standard errors; web-scale gains remain within about two points except on MMLU and HellaSwag.Source: Table 4 · p. 9, §5.3 · p. 9
  • The larger gains on curated data suggest recurrence benefits depend strongly on continued-training data; shared and LoRA-32 variants differ by at most two points, with neither consistently ahead.Looped Qwen still trails Qwen3-4B-Base on every benchmark, so conversion does not replace knowledge and capacity from substantially larger pretraining.Source: §5.3 · p. 9

6 CONCLUSION

The conclusion presents a two-stage from-scratch recipe and a minimal conversion recipe for pretrained dense models. Both are evaluated against dense baselines trained on the same data and stages, with matching by parameters or inference compute.

6 CONCLUSION

  • From-scratch LoopLM improves over a parameter-matched dense model on every evaluated benchmark and, at equal inference compute, comes within about a point of a model with three times its parameters on math and reading comprehension.The larger model retains its lead where additional parameters store facts.Source: §6 · p. 9
  • The two-stage recipe uses a fraction of earlier pipelines’ token budget; learning-rate warmup removes early exit-gate collapse, and a larger KL coefficient lets the gate recover if collapse occurs.The same training stages and data are used for the dense baselines.Source: §6 · p. 9
  • A learned scalar that mixes token embeddings into recurrent steps, together with a smoothed exit loss, converts Qwen3-1.7B-Base into Looped Qwen, which improves over the same-data continued checkpoint without step-specific parameters.At Qwen3-4B-Base’s inference cost, Looped Qwen still trails that larger model.Source: §6 · p. 9

AI USE STATEMENT

The authors used generative AI for manuscript editing, literature discovery, and refactoring author-written code. They report that outputs and changes were reviewed and verified by the authors.

AI USE STATEMENT

  • Generative AI assisted with drafting and polishing the manuscript, literature retrieval and discovery, and refactoring author-written code.The code assistance restructured and simplified existing implementation code without changing the intended algorithms or experimental methodology.Source: AI USE STATEMENT · p. 10
  • AI was not used to generate synthetic data, formulate hypotheses or methodology, conduct analysis, interpret results, generate experimental results, or make scientific conclusions.The statement also excludes data cleaning, theoretical claims or proofs, and manuscript translation.Source: AI USE STATEMENT · p. 10
  • Authors reviewed, edited, and verified AI-assisted text and code, and checked numerical results, experimental claims, citations, and prior-work descriptions against source materials.The authors take responsibility for the paper’s accuracy, integrity, and final content.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

The ethics statement says the work studies language-model architecture, training, and evaluation without human-subject experiments or newly collected personal or sensitive data. The models retain general-purpose language-model risks and ordinary deployment considerations.

ETHICS STATEMENT

  • The work involves no human-subject experiments or collection of new personal or sensitive data; training uses existing pretraining and instruction-tuning datasets.The authors report no release of additional user data or construction of datasets with newly collected personal information.Source: ETHICS STATEMENT · p. 10
  • The general-purpose models inherit potential risks including inaccurate, biased, or harmful content generation and possible dual-use applications.The work does not evaluate or optimize models for such applications.Source: ETHICS STATEMENT · p. 10
  • The methods change computation reuse across recurrent steps but do not remove the need for conventional language-model safety, fairness, privacy, and deployment considerations.The authors report no additional legal, privacy, or fairness concerns beyond those associated with the underlying public corpora and pretrained checkpoints.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

The statement documents the runs’ architecture, training objective, ablations, and reproducibility materials, alongside the pretraining budget and data mixture. It also describes conditions associated with recurrent training stability, gate collapse, and RL outcomes.

D LOOPLM ARCHITECTURE AND TRAINING SETUP

  • The from-scratch model reuses a 24-layer decoder for T=4 steps and trains for approximately 210B pretraining tokens; supplementary code includes smoke tests but omits run configurations and evaluation code.The shared-block recipe applies exit-weighted language-model loss with entropy regularization at β=0.15; pretraining loss covers all tokens, while mid-training loss covers response tokens.Source: REPRODUCIBILITY STATEMENT · p. 10, §D.1 · p. 19, §D.2 · p. 20

NORMALIZATION SCHEMES

  • Ouro-norm, pre-norm, and MagicNorm finish at 1.98–2.11 LM loss, while post-norm and sandwich-norm plateau near 7.4 and fail to train.The stable variants have nearly identical training trajectories; the failing variants plateau within roughly the first 1K steps.Source: Table 5 · p. 13, NORMALIZATION SCHEMES · p. 13

WHY POST-NORM FAILS

  • At t=2, pre-norm gradients decrease only about 8× across decoder depth, but post-norm and sandwich-norm gradients in layers 0–22 are 8–16 orders smaller than in layer 23.This concentrates learning in the final layer, making the nominally 24-layer recurrent block behave more like a one-layer block during optimization.Source: WHY POST-NORM FAILS · p. 13, Figure 6 · p. 14

POST-NORM MITIGATION

  • A 10K-step warmup leaves post-norm near loss 7; T=1–3 reaches 2.66–2.82, but T=4 returns to ∼7.4, and post-norm-family failures persist at a 2M-token batch.At 2M tokens, post-norm, sandwich-norm, and parameter-free post-norm plateau at 7.40–7.41; removing post-norm's learnable scale does not restore gradient flow.Source: POST-NORM MITIGATION · p. 14, Figure 7 · p. 15, ROBUSTNESS CHECKS · pp. 15–16

FINAL NORMALIZATION

  • Removing final normalization raises matched-budget loss by 0.04–0.13 and yields 5–11 spikes, versus zero for RMS/FRMS; pre-norm loss changes from 2.03 to 2.07 when learned scale is removed.With a final norm, peak total gradient norm stays between 15.7 and 42.3; without one, it reaches 5.2 × 107.Source: Table 6 · p. 15, FINAL NORMALIZATION · p. 15

COLLAPSE IS USUALLY REVERSIBLE

RL HELPS ONLY WHEN THE ROLLOUT TASK IS NEITHER TOO EASY NOR TOO HARD

  • RLTT improves 5-shot GSM8K from 35.3 to 47.3 in 140 steps, but MATH changes from 55.7 to 55.2 and its GSM8K guard metric from 73.5 to 73.2, both within evaluation error.The successful GSM8K policy solved about 30% of rollouts, producing mixed correct and incorrect groups; the MATH policy solved about 77%, often leaving group-relative advantages near zero.Source: Table 8 · p. 18, RL HELPS ONLY WHEN THE ROLLOUT TASK IS… · p. 18

TRAINING TELEMETRY PREDICTS WHETHER RL IS MOVING THE POLICY

D.3 PRETRAINING

  • A 210B-token pretraining budget revisits the roughly 16B-token corpus for about thirteen effective epochs.The corpus is dominated by filtered web text, with additional mathematics, code, and instruction-following data.Source: §D.3 · p. 20
  • The pretraining mixture is dominated by filtered web text, with additional mathematics, code, and instruction-following data.Source: §D.3 · p. 20

D.4 HIGH-QUALITY MID-TRAINING

The section reports that concatenation-based embedding injection did not help this recipe, then specifies mid-training and dense baselines alongside the recurrent Qwen conversion setup. Looped Qwen reuses a pretrained decoder with shared recurrence, scalar input mixing, and a smoothed exit loss.

D.4 HIGH-QUALITY MID-TRAINING

  • Mid-training continues the step-100,000 checkpoint for 47,684 steps, adding approximately 100B tokens with a 1K-step warmup and a reduced, cosine-decayed learning rate.Sequences remain 4K tokens; instruction/response formatting applies loss only to response tokens, using HRM-Text reweighted toward mathematics and reasoning while retaining 42% knowledge-preserving data.Source: §D.4 · pp. 20–21

D.5 DENSE BASELINES AND EVALUATION

  • The parameter-matched dense baseline removes recurrence from the same 24-layer block, while the inference-compute-matched baseline stacks three copies into a 72-layer model.Both dense models use the same two training stages; LoopLM’s controlled comparison uses a fixed exit after three recurrent steps.Source: §D.5 · p. 21

E EMBEDDING INJECTIONS

  • At 40K steps, all four concatenation-injection variants had loss 1.90–1.91, 0.12–0.13 above the injection-free baseline at 1.78.The lowest variant was only 0.005 lower than the other injection variants, which the authors do not treat as a real difference.Source: E EMBEDDING INJECTIONS · p. 22, Table 14 · p. 22

F LOOPED DENSE ARCHITECTURE AND TRAINING SETUPS

  • Looped Qwen preserves the Qwen3-1.7B-Base decoder, embeddings, vocabulary, and LM head as trainable components while adding recurrent execution and a shared exit gate.The shared variant adds no step-specific parameters beyond scalar input injection and the exit gate; a separate variant uses step-specific LoRA banks.Source: F LOOPED DENSE ARCHITECTURE AND… · p. 22, §F.1 · p. 22, §F.3 · p. 23

F.2 RECURRENCE AND INPUT INJECTION

  • For later recurrent steps, a shared scalar mixes the original token embeddings with the preceding hidden state, initialized at a=4.6 so w=0.99005.Conversion smooths the exit-weighted LM loss with ϵ=0.05 so every recurrent step receives a minimum direct LM weight of 0.0167.Source: §F.2 · pp. 22–23

F.3 STEP-SPECIFIC LORA

  • The LoRA-32 variant assigns an independent rank-32 LoRA bank to each recurrent step, adding 104,595,456 trainable parameters.The resulting model has 2,136,339,458 trainable parameters.Source: §F.3 · pp. 23–24

F.4 CONTINUED-TRAINING SETUP

  • The main curated-instruction conversion run uses 60B tokens over 28,611 steps, with 4,096-token sequences and a 2,097,152-token optimizer batch.Training uses 32 H100 GPUs across four nodes and a 1,000-step learning-rate warmup followed by cosine decay.Source: §F.4 · p. 24

F.5 TRAINING DATA

  • The curated 60B-token mixture draws on six sources and is dominated by mathematics, code, and post-training data.Sampling uses mosaic-random mixing with balanced streams and shuffled random batches.Source: §F.5 · p. 24

F.6 BASELINES AND EVALUATION

The conversion comparisons pair each looped run with dense baselines trained on the same data for the same number of steps. They report fixed-depth evaluation, while Figure 9’s training logs use one seed per configuration.

F.6 BASELINES AND EVALUATION

  • Each conversion run is paired with Qwen3-1.7B-Base as the parameter-matched reference and Qwen3-4B-Base as the larger inference-compute-matched reference.Both dense models continue training on exactly the same mixture for the same number of optimizer steps as their corresponding looped model.Source: §F.6 · p. 25
  • Looped Qwen’s controlled benchmark comparison uses a fixed exit after two of its three recurrent steps, although the learned gate is used during training.The reported results use final checkpoints for both the 60B-token instruction run and the 84B-token web-scale run.Source: §F.6 · p. 25

G CONVERSION TRAINING DYNAMICS

  • Figure 9’s training logs use one seed per configuration; panels (a) and (b) compare web-mixture runs differing only in input injection.The paired runs share data, batch, learning rate, β=0.15, and seed.Source: G CONVERSION TRAINING DYNAMICS · p. 25

H CONVERSION ON THE WEB-SCALE MIXTURE

On the web-scale mixture, the shared looped model improves over the continued Qwen3-1.7B-Base baseline on every benchmark, though gains are modest. Qwen3-4B-Base remains ahead, and the results across two data mixtures show that gain size depends strongly on continued-training data.

H CONVERSION ON THE WEB-SCALE MIXTURE

  • Qwen3-4B-Base remains ahead across all benchmarks, while the LoRA-32 variant follows the overall pattern but does not consistently improve over the fully shared model.The comparison uses identical data and training duration and evaluates looped models after two recurrent iterations.Source: H CONVERSION ON THE WEB-SCALE MIXTURE · pp. 25–26
  • The shared looped model improves over Qwen3-1.7B-Base continued on the same web-scale data on every benchmark, with gains of +1.75 points on GSM8K, +1.55 on MMLU, and +1.54 on HellaSwag.The remaining gains are about one point or less, making the gains modest compared with the curated-instruction run.Source: H CONVERSION ON THE WEB-SCALE MIXTURE · pp. 25–26
  • Across the instruction and web-scale mixtures, recurrence improves over continued Qwen3-1.7B-Base, while the size of the gain depends strongly on the continued-training data.The web-scale run uses 84B tokens and 40,000 optimizer steps.Source: H CONVERSION ON THE WEB-SCALE MIXTURE · pp. 25–26

I COMPUTE ACCOUNTING

The compute accounting finds substantially lower training compute for the simplified from-scratch recipe and the dense-to-loop conversion. The section also describes a correctness-directed routing approach for Think-at-Hard, while leaving its controlled evaluation to future work.

I COMPUTE ACCOUNTING

  • The two-stage from-scratch run costs 9.9×10^21 training FLOPs, about 3% of the same architecture trained on Ouro’s schedule, or 35 times less.The Ouro-schedule estimate is about 3.4×10^23 FLOPs.Source: I COMPUTE ACCOUNTING · p. 26, Table 21 · p. 27
  • At three iterations, LoopLM and dense-ouro-3.9B apply the same 72 layer passes per token; the dense model stores 2.7 times as many parameters.Training LoopLM with all four iterations costs 1.4 times as much per token as dense-ouro-3.9B.Source: I COMPUTE ACCOUNTING · p. 27
  • Converting Qwen3-1.7B-Base on the 60B-token mixture costs 1.9×10^21 FLOPs, 0.5% of its 36T-token pretraining compute.At its two-step exit, Looped Qwen uses 6.3 GFLOPs per token, 22% fewer than Qwen3-4B-Base.Source: I COMPUTE ACCOUNTING · p. 27

J THINK-AT-HARD

  • The reproduced Think-at-Hard setup did not match its reported gains: repeated-step LM loss never fell below first-step loss, and several downstream benchmarks degraded substantially.The authors leave a controlled evaluation of their proposed online routing rule for future work.Source: J THINK-AT-HARD · pp. 27–28
  • The proposed online mask routes each token’s LM gradient only to the first recurrent depth that predicts its target correctly, or to the final active step if none does.A depth curriculum introduces one additional active step at a time to avoid starving intermediate steps of supervision; controlled evaluation remains future work.Source: J THINK-AT-HARD · pp. 27–28

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