# MulDimIF: A Multi-Dimensional Constraint Framework for Evaluating and Improving Instruction Following in Large Language Models

arXiv: https://arxiv.org/abs/2505.07591 · HTML: https://mlsanity.com/paper/2505.07591/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 22 of 22)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [A Comprehensive Capability Analysis of GPT-3 and GPT-3.5 Series Models](https://mlsanity.com/paper/2303.10420/) (2023)
- [Label Words are Anchors: An Information Flow Perspective for Understanding In-Context Learning](https://mlsanity.com/paper/2305.14160/) (2023)
- [Benchmarking Complex Instruction-Following with Multiple Constraints Composition](https://mlsanity.com/paper/2407.03978/) (2024)
- [Multi-IF: Benchmarking LLMs on Multi-Turn and Multilingual Instructions Following](https://mlsanity.com/paper/2410.15553/) (2024)
- [On the Multi-turn Instruction Following for Conversational Web Agents](https://mlsanity.com/paper/2402.15057/) (2024)
- [IOPO: Empowering LLMs with Complex Instruction Following via Input-Output Preference Optimization](https://mlsanity.com/paper/2411.06208/) (2024)
- [CIF-Bench: A Chinese Instruction-Following Benchmark for Evaluating the Generalizability of Large Language Models](https://mlsanity.com/paper/2402.13109/) (2024)
- [TL-Training: A Task-Feature-Based Framework for Training Large Language Models in Tool Use](https://mlsanity.com/paper/2412.15495/) (2024)

## Built on by (most cited first, 15 of 15)

- [MiniCPM-V 4.5: Cooking Efficient MLLMs via Architecture, Data, and Training Recipe](https://mlsanity.com/paper/2509.18154/) (2025)
- [LongCat-Flash Technical Report](https://mlsanity.com/paper/2509.01322/) (2025)
- [Feedback-Driven Tool-Use Improvements in Large Language Models via Automated Build Environments](https://mlsanity.com/paper/2508.08791/) (2025)
- [Auditing Data Membership in Reinforcement Learning With Verifiable Rewards](https://mlsanity.com/paper/2511.14045/) (2025)
- [Replay Failures as Successes: Sample-Efficient Reinforcement Learning for Instruction Following](https://mlsanity.com/paper/2512.23457/) (2025)
- [MedXIAOHE: A Comprehensive Recipe for Building Medical MLLMs](https://mlsanity.com/paper/2602.12705/) (2026)
- [ImpRIF: Stronger Implicit Reasoning Leads to Better Complex Instruction Following](https://mlsanity.com/paper/2602.21228/) (2026)
- [Experience is the Best Teacher: Motivating Effective Exploration in Reinforcement Learning for LLMs](https://mlsanity.com/paper/2603.20046/) (2026)
- [FMBench: Adaptive Large Language Model Output Formatting](https://mlsanity.com/paper/2602.06384/) (2026)
- [LLM Swiss Round: Aggregating Multi-Benchmark Performance via Competitive Swiss-System Dynamics](https://mlsanity.com/paper/2512.21010/) (2025)
- [UNSPECIFIC: General Constraint Synthesis for Breaking Copy-and-Paste Shortcut in LLM Instruction Following](https://mlsanity.com/paper/2608.09154/) (2026)
- [ScopeIF: Improving Scope-Aware Precise Instruction-Following in Large Language Models via Graded Reward Modeling](https://mlsanity.com/paper/2609.32189/) (2026)
- [When Verifiable Counts Depend on Wording: Auditing Wording Robustness in Instruction Following](https://mlsanity.com/paper/2610.05278/) (2026)
- [Policy Alignment: New Signals for Membership Auditing in On-Policy Distillation](https://mlsanity.com/paper/2610.11423/) (2026)
- [Rubrics from the Task, Verdicts from Evidence: Pointwise Rubric Rewards with Tool-Augmented Judges](https://mlsanity.com/paper/2610.18766/) (2026)

## Abstract (arXiv)

Instruction following refers to the ability of large language models (LLMs) to generate outputs that satisfy all specified constraints. Existing research has primarily focused on constraint categories, offering limited evaluation dimensions and little guidance for improving instruction-following abilities. To address this gap, we introduce MulDimIF, a multi-dimensional constraint framework encompassing three constraint patterns, four constraint categories, and four difficulty levels. Based on this framework, we design a controllable instruction generation pipeline. Through constraint expansion, conflict detection, and instruction rewriting, we construct 9,106 code-verifiable samples. We evaluate 18 LLMs from six model families and find marked performance differences across constraint settings. For instance, average accuracy decreases from 80.82% at Level I to 36.76% at Level IV. Moreover, training with data generated by our framework significantly improves instruction following without compromising general performance. In-depth analysis indicates that these gains stem largely from parameter updates in attention modules, which strengthen constraint recognition and adherence. Code and data are available in https://github.com/Junjie-Ye/MulDimIF.