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

arXiv: https://arxiv.org/abs/2508.05015 · HTML: https://mlsanity.com/paper/2508.05015/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 18 of 18)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Aligner: Efficient Alignment by Learning to Correct](https://mlsanity.com/paper/2402.02416/) (2024)
- [SPAM: Spike-Aware Adam with Momentum Reset for Stable LLM Training](https://mlsanity.com/paper/2501.06842/) (2025)
- [AdaGC: Enhancing LLM Pretraining Stability via Adaptive Gradient Clipping](https://mlsanity.com/paper/2502.11034/) (2025)

## Built on by (most cited first, 4 of 4)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Self-Improvement of Large Language Models: A Technical Overview and Future Outlook](https://mlsanity.com/paper/2603.25681/) (2026)
- [Uncertainty-Guided Checkpoint Selection for Reinforcement Finetuning of Large Language Models](https://mlsanity.com/paper/2511.09864/) (2025)
- [Manifold Bandits: Bayesian Curriculum Learning over the Latent Geometry of Large Language Models](https://mlsanity.com/paper/2606.19750/) (2026)

## Abstract (arXiv)

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 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 cluster-based data reduction to partition training data by semantics and difficulty, extracting a compact yet diverse subset that reduces redundancy. Then, a textitmulti-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×) 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.