ZPD Detector: Data Selection via Capability-Difficulty Alignment for Large Language Models

TL;DR

The paper tackles data efficiency in domain-specific instruction tuning for large language models under limited data budgets. It introduces ZPD Detector, a plug-and-play framework that aligns sample difficulty with current capability via difficulty calibration, Rasch-based ability estimation, and a ZPD scoring mechanism. The Rasch 1PL model uses item difficulty $b_i$ and ability $\theta$, with predicted probability $P_i = \sigma(\theta - b_i)$ and ZPDScore $= p_i(1 - p_i)$. Results across MedQA, GSM8K, and synthetic AgriQA demonstrate that ZPD-selected subsets can match or exceed full-data training with substantially fewer samples, offering practical data efficiency and insights for curriculum-style training strategies.

Abstract

As the cost of training large language models continues to increase and high-quality training data become increasingly scarce, selecting high-value samples or synthesizing effective training data under limited data budgets has emerged as a critical research problem. Most existing data selection methods rely on static criteria, such as difficulty, uncertainty, or heuristics, and fail to model the evolving relationship between the model and the data. Inspired by the educational theory of the Zone of Proximal Development (ZPD), we propose ZPD Detector, a data selection framework that adopts a bidirectional perspective between models and data by explicitly modeling the alignment between sample difficulty and the model's current capability. ZPD Detector integrates difficulty calibration, model capability estimation based on Item Response Theory (IRT), and a capability-difficulty matching score to dynamically identify the most informative samples at each learning stage, improving data utilization efficiency; moreover, this dynamic matching strategy provides new insights into training strategy design. All code and data will be released after our work be accepted to support reproducible researc

Figures (5)

• Figure 1: Motivation of ZPD-based approach. The most informative training samples lie between what a model can already solve and what is beyond its current capability.
• Figure 2: Overview of the ZPD Detector pipeline.(A) Estimate raw sample difficulty using average token-level NLL. (B) Adjust underestimated errors via model correctness feedback. (C) Normalize calibrated difficulty scores as item parameters. (D) Input difficulty into the Rasch model. (E) Use model correctness records as responses. (F) Estimate model ability via maximum likelihood. (G) Predict the probability of correctness for each sample. (H) Compute ZPDScores to reflect model uncertainty. (I) Rank samples by ZPDScores. (J) Select the top-$k\%$ most informative samples for fine-tuning.
• Figure 3: MedQA performance under a 15% data budget comparing base training, static ZPD selection, and curriculum refresh (E2), demonstrating the benefit of capability-aware sample re-alignment during training.
• Figure 4: Gradient norm distributions of samples from different difficulty regions on Qwen3-8B. Each bucket contains an equal number of samples. Gradient norms are computed on LoRA-adapted layers in the transformer blocks.
• Figure 5: Difficulty distributions of ZPD-selected samples across different backbone models. From left to right: LLaMA3-8B-Instruct, Qwen3-8B, and Mistral-7B-Instruct.