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arxiv: 2508.05015 · v2 · submitted 2025-08-07 · 💻 cs.LG · cs.AI

SPaCe: Unlocking Sample-Efficient Large Language Models Training With Self-Pace Curriculum Learning

Dai Do , Manh Nguyen , Svetha Venkatesh , Hung Le This is my paper

Pith reviewed 2026-05-19 00:16 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords sample-efficient trainingcurriculum learninglarge language modelsreasoning tasksmulti-armed banditdata reductionreinforcement learning
0
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The pith

SPaCe trains large language models for reasoning with up to 100 times fewer samples than standard methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces SPaCe to make reinforcement learning fine-tuning of LLMs practical under tight data budgets. It first reduces the training set by clustering examples according to semantics and difficulty, then uses a multi-armed bandit to pick which clusters to sample from at each step based on how well the current model solves them and how much progress the cluster shows. A sympathetic reader cares because uniform sampling wastes samples on easy or redundant items while current approaches need enormous datasets that few labs can afford. The experiments claim this curriculum matches or exceeds baseline accuracy on reasoning tasks despite the drastic cut in data volume.

Core claim

SPaCe first applies cluster-based data reduction to partition training examples by semantics and difficulty and extract a compact yet diverse subset. It then runs a multi-armed bandit that treats clusters as arms and allocates samples according to the model's solve rates on each cluster plus measured learning progress within the cluster. This self-paced selection produces training curricula that deliver comparable or superior accuracy to state-of-the-art baselines on multiple reasoning benchmarks while using up to 100 times fewer samples.

What carries the argument

Cluster-based data reduction followed by multi-armed bandit allocation that selects training samples according to the current model's solve rates and cluster-level learning progress.

If this is right

  • LLMs reach comparable reasoning accuracy on standard benchmarks with far smaller training sets.
  • Adaptive allocation driven by model performance outperforms uniform sampling across epochs.
  • Semantic and difficulty clustering can shrink data volume without erasing essential reasoning patterns.
  • Both the reduction step and the bandit step are required for the observed efficiency gains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same clustering-plus-bandit pattern could be tested on non-reasoning tasks such as code generation or instruction following to see if sample savings transfer.
  • If clustering introduces hidden selection bias, an alternative progress signal that avoids explicit clusters might be needed for robustness.
  • Lower sample counts would directly reduce the compute and energy cost of producing capable reasoning models.

Load-bearing premise

Solve rates on the current model plus cluster-level progress give an unbiased signal for which future samples will deliver the most learning value.

What would settle it

Re-run the reported benchmarks with the clustering step removed or the bandit replaced by uniform sampling and check whether the 100-fold sample reduction and accuracy parity both disappear.

Figures

Figures reproduced from arXiv: 2508.05015 by Dai Do, Hung Le, Manh Nguyen, Svetha Venkatesh.

Figure 1
Figure 1. Figure 1: SPaRFT Architecture. Top: Initial training data is annotated with difficulty, and each [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Multi-arm Bandit Cluster Selection and its Impact on Cluster Solve Rates During Training. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top: Difficulty distribution of training examples in SPaRFT. Middle: Difficulty of training [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of selection strategies across datasets. Selecting diverse examples with [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results for 1 seed with Qwen3-0.6B and different number of clusters. [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Results for 1 seed with Qwen3-0.6B and different number of samples per cluster. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effect of Removing Difficulty in Clustering on Performance. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: DeepScaleR subsets’ difficulty distributions. [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: System prompt used in our experiments. Models/Datasets URL Qwen3-Embedding-0.6B https://huggingface.co/Qwen/Qwen3-Embedding-0.6B Qwen2.5-0.5B-Instruct https://huggingface.co/Qwen/Qwen2.5-0.5B-Instruct Llama3.2-1B-Instruct https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct Falcon3-1B-Instruct https://huggingface.co/tiiuae/Falcon3-1B-Instruct Alibaba-NLP/gte-Qwen2-1.5B-instruct https://huggingface.co/Al… view at source ↗
read the original abstract

Large language models (LLMs) have shown strong reasoning capabilities when fine-tuned with reinforcement learning (RL). However, such methods require extensive data and compute, making them impractical under many realistic training budgets. Many existing pipelines sample training examples uniformly across steps or epochs, ignoring differences in difficulty, redundancy, and learning value, which slows learning and wastes computation. We propose \textbf{SPaCe}, a self-paced learning framework that enables efficient learning based on the capability of the model being trained through optimizing which data to use and when. First, we apply \emph{cluster-based data reduction} to partition training data by semantics and difficulty, extracting a compact yet diverse subset that reduces redundancy. Then, a \textit{multi-armed bandit} treats data clusters as arms, allocating training samples based on the model's solve rates and learning progress. Experiments across multiple reasoning benchmarks show that SPaCe achieves comparable or better accuracy than state-of-the-art baselines while using up to \(100\times\) fewer samples. Ablation studies and analyses further highlight the importance of both data clustering and adaptive selection. Our results demonstrate that carefully curated, performance-driven training curricula can unlock strong reasoning abilities in LLMs with minimal resources.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces SPaCe, a self-paced curriculum learning framework for efficient fine-tuning of LLMs on reasoning tasks. It first performs cluster-based data reduction to partition training examples by semantics and difficulty and extract a compact diverse subset, then employs a multi-armed bandit that treats clusters as arms and allocates samples according to the current model's solve rates and cluster-level learning progress. The central empirical claim is that SPaCe matches or exceeds state-of-the-art baselines on multiple reasoning benchmarks while using up to 100× fewer training samples.

Significance. If the reported gains prove robust, the work would meaningfully advance sample-efficient LLM training by demonstrating that a combination of semantic/difficulty clustering and performance-driven adaptive allocation can preserve accuracy under severe data budgets. Such a result would be of immediate practical value for resource-constrained fine-tuning pipelines.

major comments (2)
  1. [Ablation studies] Ablation studies: the reported ablations isolate the contributions of clustering and adaptive selection but omit a uniform-allocation control trained on the same reduced cluster subset. Without this baseline it remains possible that the observed sample-efficiency gains are largely attributable to the initial cluster-based reduction rather than the bandit mechanism.
  2. [Experiments] Experiments section: the performance claims (comparable or better accuracy with up to 100× fewer samples) are presented without details on baseline implementations, number of independent runs, statistical significance tests, or variance across random seeds. These omissions make it impossible to judge whether the central efficiency claim is supported by the evidence.
minor comments (1)
  1. [Abstract] The abstract refers to “multiple reasoning benchmarks” without naming them; listing the concrete datasets (e.g., GSM8K, MATH) would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and outline the revisions we will make to improve the manuscript.

read point-by-point responses

  1. Referee: Ablation studies: the reported ablations isolate the contributions of clustering and adaptive selection but omit a uniform-allocation control trained on the same reduced cluster subset. Without this baseline it remains possible that the observed sample-efficiency gains are largely attributable to the initial cluster-based reduction rather than the bandit mechanism.

    Authors: We agree that this control is necessary to isolate the bandit's contribution. In the revised manuscript we will add an ablation that applies uniform sampling over the identical reduced cluster subset produced by the cluster-based data reduction step. This will allow direct comparison with the adaptive bandit allocation and clarify whether the efficiency gains stem primarily from clustering or from the performance-driven selection. revision: yes

  2. Referee: Experiments section: the performance claims (comparable or better accuracy with up to 100× fewer samples) are presented without details on baseline implementations, number of independent runs, statistical significance tests, or variance across random seeds. These omissions make it impossible to judge whether the central efficiency claim is supported by the evidence.

    Authors: We acknowledge these omissions. In the revision we will expand the Experiments section with: (i) precise implementation details and hyper-parameters for all baselines, (ii) results averaged over at least five independent runs using different random seeds, (iii) statistical significance tests (e.g., paired t-tests) comparing SPaCe against baselines, and (iv) standard deviations or error bars to report variance. These additions will provide the necessary rigor to support the sample-efficiency claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity in SPaCe derivation or claims

full rationale

The paper describes a two-stage method of first applying cluster-based data reduction on semantics and difficulty to obtain a compact subset, followed by a multi-armed bandit that allocates samples using observed solve rates and learning progress signals from the model under training. These steps rely on standard unsupervised clustering and bandit algorithms driven by empirical performance metrics rather than any fitted parameter that is then renamed as a prediction of the same metric. No equations are presented that define the target accuracy or sample-efficiency gains in terms of the clustering or bandit outputs by construction. Ablations are cited to isolate the contributions of clustering versus adaptive selection, and the headline results are framed as experimental outcomes on external reasoning benchmarks rather than internal consistency checks. The derivation chain remains self-contained against external benchmarks with no load-bearing self-citations or uniqueness theorems imported from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract relies on the unstated premise that semantic-difficulty clusters remain stable and informative throughout training and that bandit rewards based on solve rates accurately predict future learning value.

axioms (2)
  • domain assumption Cluster-based partitioning by semantics and difficulty produces a compact yet diverse subset without losing critical learning signals.
    Invoked in the first step of the method description.
  • domain assumption Model solve rates on clusters provide a reliable, non-circular signal for allocating future training samples.
    Central to the multi-armed bandit component.

pith-pipeline@v0.9.0 · 5751 in / 1344 out tokens · 35865 ms · 2026-05-19T00:16:14.543003+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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  1. A Survey of Reinforcement Learning for Large Reasoning Models

    cs.CL 2025-09 accept novelty 3.0

    A survey compiling RL methods, challenges, data resources, and applications for enhancing reasoning in large language models and large reasoning models since DeepSeek-R1.

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