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Small Models Scout Bottleneck Order for Large-Model Data Control

Seungmin Choi, Jiwon Sung, Muhammad Umer, Abhiram Rao Gorle, Guijin Son, Youngjae Yu, John M. Cioffi

arXiv:2608.14936v1cs.AI

TL;DR

The paper asks whether small-model training trajectories can guide larger models in resolving skill bottlenecks under first-passage training. It introduces LogFloor and finds that phase-ordered bottleneck paths reduce token costs and transfer across model scales.

  • Problem

    First-passage skill training requires every monitored skill to reach its floor, raising whether small-model trajectories can guide larger models’ bottleneck priorities.

  • Method

    LogFloor observes per-skill scores, computes floor pressure, and allocates each training round toward the bottleneck skills exerting greatest pressure.

  • Results

    Across bAbI and 70M-to-12B transfer, bottleneck-resolving paths reduce first-passage cost, with LogFloor saving 56.2% on average across five bAbI slices.

  • Takeaways & Limitations

    Phase-ordered bottleneck resolution is a transferable curriculum structure whose signal is not captured by static mixtures alone.

  • Takeaways & Limitations

    The evidence concerns monitored first-passage training with explicit floors and skill-associated data slices, and replay across architectures is not guaranteed.

Abstract

from arXiv · show

Small proxy models are commonly used to identify data mixtures for larger-scale training. We ask whether their training trajectories reveal another transferable structure: the order in which larger models should resolve skill bottlenecks. We formulate first-passage skill training, where each monitored skill has a target floor and the objective is to minimize the tokens required to reach all floors. We introduce LogFloor, a closed-loop controller that directs each round toward current bottlenecks, producing phase-ordered resolution trajectories. Across five bAbI skill slices on Qwen2.5-1.5B, LogFloor reduces token cost by 56.2% on average. In 70M-to-12B transfer, three-round replay of a 70M scout path reaches every floor in all eight target runs, saving 30.9% by pair mean, 39.4% in pooled training tokens, and 37.6% under source-cost accounting. On MMLU-control, a frozen scout path succeeds across all eight 12B runs. Collapsing a path to its static marginal mixture or reversing its phase order removes most benefits, while bottleneck labels alone remain partially useful. These results identify phase-ordered bottleneck resolution as a transferable curriculum structure for monitored skill-targeted training.

Introduction

The introduction frames training as a first-passage problem: every monitored skill must reach its floor, so data control should resolve bottlenecks rather than optimize average validation performance. It introduces LogFloor and argues that phase-ordered bottleneck-resolving trajectories, rather than static mixtures alone, can transfer from a 70M scout to 12B targets.

  • Problem formulation: First-passage skill training requires every monitored skill to reach its floor before training can terminate.This exposes bottleneck-limited data control when one skill remains below its required threshold.
  • Method: LogFloor observes per-skill monitor scores, computes floor pressure, and allocates each round toward the bottleneck skills exerting the largest pressure.The resulting allocation path is called a bottleneck-resolving trajectory.
  • Transfer: A 70M scout can reveal a phase-ordered bottleneck path that remains useful for a 12B target after a short target-side phase probe.The claimed transferable structure is specifically a bottleneck-resolving trajectory in monitored first-passage training, not a universal claim about small models determining curricula.
  • Results: 56.2% training-token savings were achieved on average across target floors from 2.8 to 3.3 on five controlled bAbI skill slices with Qwen2.5-1.5B.Skill-It and Online Data Mixing did not robustly improve this first-passage objective because they do not use target information.
  • Transfer: Order-destruction controls show that the transferred signal is not reducible to a static data mixture.The paper isolates the contribution of bottleneck order rather than treating bottleneck labels alone as the complete transferable signal.

Related Work

Prior work uses small proxy models for static mixture selection, example selection, regression-based mixing, and dynamic proxy-policy transfer. Other studies examine curriculum order, online data allocation, and skill-acquisition order, whereas this work replays source paths to reduce target first-passage cost.

  • Proxy-guided data control: Proxy-model methods guide larger runs through static domain mixtures, supervised-finetuning example selection, regression-based mixtures, and dynamic policy transfer.The cited examples are DoReMi, SmallToLarge, RegMix, and AC-ODM.
  • Proxy-guided data control: The study audits AC-ODM as a dynamic proxy-policy baseline and RegMix as a static proxy-mixture baseline under the same monitored first-passage protocol.RegMix-D uses proxy trajectories for dynamic scheduling but evaluates fixed-budget schedules rather than minimizing tokens to reach all monitored skill floors.
  • Ordering and online allocation: Curriculum-ordering research shows that data order can affect training trajectories, while Skill-It, ODM, Aioli, and related work adapt allocation online using losses, bandits, optimization, or influence signals.These approaches study evolving data allocation and domain preferences during training.
  • Skill-acquisition order: Liu et al. (2026) find regularities in skill-acquisition order across pretrained checkpoints, whereas this work intervenes by replaying a realized source path for a new target model.The intervention tests whether replay reduces first-passage training cost.

First-Passage Control with LogFloor

LogFloor formalizes first-passage training as reaching every monitored skill floor while minimizing consumed tokens, then allocates training toward current floor-pressure bottlenecks. On five controlled bAbI slices, it substantially reduces token cost and usually corroborates route first-passage on heldout monitors.

  • Objective: First-passage training stops at the first round when every monitored skill reaches its target floor, unlike fixed-budget objectives based on average endpoint performance.Scores determine stopping and controller updates; heldout data serves only as an external audit.
  • Controller: LogFloor allocates more of each next round to skills with larger remaining deficits, using exponential bottleneck emphasis, smoothing, and fixed allocation caps.Greedy LogFloor is evaluated as a hard-bottleneck variant.
  • Results: Round 11 versus round 42: LogFloor clears all target floors far earlier than uniform training in a representative run by repeatedly prioritizing the current bottleneck skill.The red boxes identify the bottleneck selected at each round.
  • Results: 56.2% pooled token savings: LogFloor beats matched uniform training across five bAbI slices and six target floors, reaching all 30 route targets.Greedy LogFloor achieves 51.1% pooled savings, while Skill-It and ODM achieve −7.8% and −0.9%, respectively.
  • Heldout audit: 28 out of 30 runs: heldout audits clear all target floors at the route first-hit round, with a mean minimum heldout margin of +0.260 above targets.The exact 95% Clopper–Pearson interval for heldout confirmation is [77.9%, 99.2%].

Cross-Scale Transfer by Replaying LogFloor · Trajectories

The section evaluates whether small-model bottleneck-resolving trajectories can guide larger target models. It defines ordered trajectory replay schemes that localize target phases and then traverse the source path monotonically, with H = 3 used in main target-probe experiments.

  • Trajectories: The transfer question is whether bottleneck-resolving trajectories learned by small models can guide larger target models.
  • Trajectory Replay Schemes: The transferable object is the source run’s ordered before-hit allocation sequence, indexed from wS_0 through wS_{T_S−1}.
  • Trajectory Replay Schemes: Because source and target models may traverse bottleneck phases at different rates, phase-indexed replay monotonically traverses the ordered source path after phase localization.
  • Trajectory Replay Schemes: Raw round-indexed replay applies source allocation wS_r at target round r, assuming equal source-target bottleneck-phase speeds.It serves as a baseline for testing literal source-round copying without phase localization.
  • Trajectory Replay Schemes: H = 3 is the common probe length for all main target-probe experiments, selected after sensitivity checks over H ∈ {1, 3, 5}.In the MMLU source-seed-2 sweep, H = 3 reaches all 8/8 targets.
  • Trajectory Replay Schemes: Target-probe replay matches the target’s three-round normalized probe to a same-length window in a 70M uniform calibration trace using normalized mean squared distance.Similarity uses relative skill scores within each round and the trend of the worst skill.
  • Trajectory Replay Schemes: After phase matching, replay advances monotonically from the matched source phase and clamps to the final logged allocation if the target outlasts the source trajectory.After the probe, it uses no further target scores, first-passage horizon, updating, interpolation, or rematching.
  • Trajectory Replay Schemes: Oracle phase-aligned replay length-normalizes the source trajectory using the observed target before-hit length and matches relative progress r/(T_L −1).Because T_L is available only after observing the target trajectory, this scheme is not replayable at deployment.

70M-to-12B Transfer

Replayable LogFloor trajectories transfer from 70M scouts to 12B targets, outperforming static mixtures and retaining substantial savings after scout-cost accounting. The ordered source path adds value beyond a fixed probe-derived mixture, while static proxy search transfers non-monotonically.

  • Cross-scale transfer: 51.0% unweighted mean target training token savings came from trajectory replay across six Pythia transfer settings, versus 42.3% for cumulative static mixtures and 36.9% for final static mixtures.These results test replayable target-probe replay across models with different scales.
  • 70M-to-12B transfer: Replay of the 70M trajectory was nearly as effective as 12B online LogFloor, which saved 34.4% by pair mean and 39.4% pooled savings.The comparison uses eight seed-matched 70M–12B bAbI source–target pairs.
  • Ordered trajectory value: All eight targets were reached by replaying the 70M trajectory, whereas a constant mixture from the same three-round probe reached only seven.The missed target’s aggregate cost and savings were undefined.
  • Cost accounting: 37.6% scout-inclusive saving remained after adding the 70M source-training cost, scaled by the 70M/12B parameter ratio, to replay’s 12B target cost.This accounts for the cost of scouting the trajectory.
  • Proxy-based baselines: 35.3% savings remained for trajectory replay under proxy-search cost accounting, compared with 23.8% for RegMix after including its 70M search cost.RegMix saved 40.1% when only target training was counted.
  • Proxy-based baselines: Increasing static proxy-search budget improved the 70M proxy score but transferred non-monotonically to 12B, so the small-model-best mixture need not be large-model-best.This exposes a limitation of static proxy search.

Understanding Replay-Based Transfer

Replay transfers phase-ordered bottleneck information rather than merely a static mixture, with aligned source–target trajectories exhibiting similar deficit geometry and controller pressure. Across MMLU and bAbI controls, preserving temporal order delivers the largest gains, while bottleneck identities alone retain partial value.

  • Phase Geometry: 0.814 off-diagonal versus 0.807 diagonal deficit cosine, while top-2 bottleneck overlap is 0.935 versus 0.930 after normalized-phase alignment.Off-diagonal source–target seed pairs are at least as similar as diagonal pairs in the phase geometry audit.
  • Phase Geometry: 98.5% of target-online pressure progress is retained by logged source actions, with a mean one-step surrogate gap of 0.0236.This is a local MMLU matched-target audit, not a proof of full first-passage transfer.
  • Order Controls: 60.3% pooled-round savings come from correct replay across eight MMLU targets, whereas static collapse yields 10.3% and reversal 6.0%.The same correct path saves 46.8% by pair mean and 59.8% in pooled tokens.
  • Order Controls: 25.0% pooled-round savings remain when replay retains only bottleneck identities in correct order, versus −11.2% for the reversed sequence.The full path’s 60.3% savings indicates additional value from allocation strength and secondary domain structure.
  • Replication: 35.1% pooled-token savings result from correct bAbI replay, compared with 20.1% for static mean replay; reversal reaches six targets with −1.9% savings.Current-bottleneck mass correlates positively with token saving (ρ = 0.589), while mass on cleared skills correlates negatively (ρ = −0.704).

Robustness, Scope, and Limitations

The method remains robust when scout and target floors differ and across several settings, but the evidence supports an empirical scope rather than a universal curriculum law. Its claims are limited to monitored first-passage training with explicit floors and skill-associated data slices, and cross-architecture replay is not guaranteed.

  • Floor robustness: 28 out of 30 targets are reached when trajectories scouted at floors 2.8, 3.0, and 3.3 are replayed at different target floors.Four out of six scout–target floor pairs reach all five target seeds, including cases where the scout floor is lower or higher than the target.
  • Scope across settings: Robustness extends across target levels, skill counts, model sizes, pretraining stages, benchmarks, and architectures, including SuperGLUE, Mamba, and 72B settings.Skill-count and model-size results establish robustness rather than monotonic improvement; gains are weak at the earliest pretraining stage but consistently positive later.
  • Scope across settings: The results define the method’s empirical scope rather than a universal curriculum law.The evidence broadens beyond the main bAbI and Pythia settings but does not establish monotonic scaling behavior.
  • Operating modes and limitations: Online LogFloor and small-model replay are operating modes of one control principle for monitored first-passage training with explicit floors and skill-associated data slices.Target probe replay is deployable, whereas oracle phase-aligned replay is used only as a mechanism diagnostic.
  • Operating modes and limitations: Cross-architecture replay is not guaranteed: replay from Qwen to Mamba transfers well, whereas replay from Qwen to another architecture is not established here.The supplied passage explicitly contrasts successful Qwen-to-Mamba transfer with the absence of a general guarantee.

Conclusion

The paper introduces first-passage skill training and LogFloor to expose bottleneck-resolving trajectories, showing that phase-ordered paths can transfer across model scales. A 70M scout path helps a 12B target reach all monitored floors faster after a short target probe.

  • Conclusion: First-passage skill training and LogFloor expose trajectories that resolve training bottlenecks.LogFloor is described as a floor-pressure controller.
  • Conclusion: A 70M model can scout a phase-ordered bottleneck path that helps a 12B target reach all monitored floors faster after a short target probe.The conclusion identifies cross-scale transfer as the key takeaway.
  • Conclusion: In bAbI-control, replaying the scout trajectory nearly matches direct 12B online control.The passage presents this as evidence that the transferred path remains effective at target scale.
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