# Bridging Auxiliary Constraints to Resolve Instruction Following in Large Reasoning Models

arXiv: https://arxiv.org/abs/2606.03624 · HTML: https://mlsanity.com/paper/2606.03624/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 41 of its 49 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 41)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Instruction Induction: From Few Examples to Natural Language Task Descriptions](https://mlsanity.com/paper/2205.10782/) (2022)
- [Benchmarking Complex Instruction-Following with Multiple Constraints Composition](https://mlsanity.com/paper/2407.03978/) (2024)
- [Fact-Checking Complex Claims with Program-Guided Reasoning](https://mlsanity.com/paper/2305.12744/) (2023)
- [InFoBench: Evaluating Instruction Following Ability in Large Language Models](https://mlsanity.com/paper/2401.03601/) (2024)
- [FollowBench: A Multi-level Fine-grained Constraints Following Benchmark for Large Language Models](https://mlsanity.com/paper/2310.20410/) (2023)
- [Did You Read the Instructions? Rethinking the Effectiveness of Task Definitions in Instruction Learning](https://mlsanity.com/paper/2306.01150/) (2023)
- [Distilling an End-to-End Voice Assistant Without Instruction Training Data](https://mlsanity.com/paper/2410.02678/) (2024)
- [LLM Self-Correction with DeCRIM: Decompose, Critique, and Refine for Enhanced Following of Instructions with Multiple Constraints](https://mlsanity.com/paper/2410.06458/) (2024)
- [Prompt Optimization via Adversarial In-Context Learning](https://mlsanity.com/paper/2312.02614/) (2023)
- [LIFBench: Evaluating the Instruction Following Performance and Stability of Large Language Models in Long-Context Scenarios](https://mlsanity.com/paper/2411.07037/) (2024)
- [MathFusion: Enhancing Mathematical Problem-solving of LLM through Instruction Fusion](https://mlsanity.com/paper/2503.16212/) (2025)
- [Answer is All You Need: Instruction-following Text Embedding via Answering the Question](https://mlsanity.com/paper/2402.09642/) (2024)

## Abstract (arXiv)

Large Reasoning Models (LRMs) have demonstrated impressive capabilities in many tasks, yet they struggle with reliably following multiple instructions, either by failing to satisfy individual constraints or by struggling to balance competing constraints simultaneously. We formalize this challenge as the Constraint Adherence Problem (CAP). This paper introduces a novel framework that addresses CAP by representing instructions as a structured knowledge graph of constraints. Our approach, Constraint Relationship Graph Completion (CRGC), explicitly models relationships between constraints, identifies adherence challenges, and discovers ``bridge constraints'' that help the model better focus on and reconcile requirements. Bridge constraints act as auxiliary instructions that make primary constraints more salient and compatible. Unlike existing approaches that enhance instruction following through general training methods, CRGC specifically improves constraint satisfaction by leveraging the model's own knowledge to create better pathways for generation. Experiments across three popular instruction following datasets demonstrate that our approach reduces constraint violations by 39% compared to standard prompting while maintaining reasoning abilities of large reasoning models.