# CDS: Knowledge Component-Driven Data Synthesis Guided by Cognitive Diagnosis Theory

arXiv: https://arxiv.org/abs/2501.07674 · HTML: https://mlsanity.com/paper/2501.07674/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Synthetic reasoning data and bootstrapping, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [Principle-Driven Self-Alignment of Language Models from Scratch with Minimal Human Supervision](https://mlsanity.com/paper/2305.03047/) (2023)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [Benchmarking Foundation Models with Language-Model-as-an-Examiner](https://mlsanity.com/paper/2306.04181/) (2023)
- [Orca 2: Teaching Small Language Models How to Reason](https://mlsanity.com/paper/2311.11045/) (2023)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [Synthetic Data (Almost) from Scratch: Generalized Instruction Tuning for Language Models](https://mlsanity.com/paper/2402.13064/) (2024)
- [Neural Cognitive Diagnosis for Intelligent Education Systems](https://mlsanity.com/paper/1908.08733/) (2019)
- [LLM2LLM: Boosting LLMs with Novel Iterative Data Enhancement](https://mlsanity.com/paper/2403.15042/) (2024)
- [Maybe Only 0.5% Data is Needed: A Preliminary Exploration of Low Training Data Instruction Tuning](https://mlsanity.com/paper/2305.09246/) (2023)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [In-Context Principle Learning from Mistakes](https://mlsanity.com/paper/2402.05403/) (2024)
- [MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data](https://mlsanity.com/paper/2402.08957/) (2024)
- [LogiCoT: Logical Chain-of-Thought Instruction-Tuning](https://mlsanity.com/paper/2305.12147/) (2023)
- [LLMs-as-Instructors: Learning from Errors Toward Automating Model Improvement](https://mlsanity.com/paper/2407.00497/) (2024)
- [Neural-Symbolic Collaborative Distillation: Advancing Small Language Models for Complex Reasoning Tasks](https://mlsanity.com/paper/2409.13203/) (2024)
- [CEM: A Data-Efficient Method for Large Language Models to Continue Evolving From Mistakes](https://mlsanity.com/paper/2404.08707/) (2024)

## Abstract (arXiv)

Large Language Models (LLMs) have achieved significant advancements, but the increasing complexity of tasks and higher performance demands highlight the need for continuous improvement. Some approaches utilize synthetic data generated by advanced LLMs based on evaluation results to train models. However, conventional evaluation methods fail to provide detailed, fine-grained profiles of LLMs, limiting their guidance for data synthesis. In this paper, we introduce the Cognitive Diagnostic Synthesis (CDS) method, which incorporates a diagnostic process inspired by Cognitive Diagnosis Theory (CDT) to refine evaluation results and characterize model profiles at the knowledge component level. Based on these diagnostics, we propose two diagnosis-synthesis strategies for weakness-targeted data synthesis. Additionally, we present an enhanced data augmentation and selection pipeline to improve the quality and diversity of synthesized data. Our experiments with several open-source models show significant improvements across multiple benchmarks, achieving up to 6.00% improvement in code generation, 13.10% in mathematical reasoning, and 5.43% in academic exams. Code and data are available on GitHub.