# Call Neighbours Yourself: Graph Walks with Destination-Conditioned On-Policy Self-Distillation

arXiv: https://arxiv.org/abs/2608.29588 · HTML: https://mlsanity.com/paper/2608.29588/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 32)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [One for All: Towards Training One Graph Model for All Classification Tasks](https://mlsanity.com/paper/2310.00149/) (2023)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [OpenClaw-RL: Train Any Agent Simply by Talking](https://mlsanity.com/paper/2603.10165/) (2026)
- [ZeroG: Investigating Cross-dataset Zero-shot Transferability in Graphs](https://mlsanity.com/paper/2402.11235/) (2024)
- [UniGraph: Learning a Unified Cross-Domain Foundation Model for Text-Attributed Graphs](https://mlsanity.com/paper/2402.13630/) (2024)
- [GOFA: A Generative One-For-All Model for Joint Graph Language Modeling](https://mlsanity.com/paper/2407.09709/) (2024)
- [CaT: Balanced Continual Graph Learning with Graph Condensation](https://mlsanity.com/paper/2309.09455/) (2023)
- [When Do LLMs Help With Node Classification? A Comprehensive Analysis](https://mlsanity.com/paper/2502.00829/) (2025)
- [CaseLink: Inductive Graph Learning for Legal Case Retrieval](https://mlsanity.com/paper/2403.17780/) (2024)
- [CaseGNN: Graph Neural Networks for Legal Case Retrieval with Text-Attributed Graphs](https://mlsanity.com/paper/2312.11229/) (2023)
- [PUMA: Efficient Continual Graph Learning for Node Classification with Graph Condensation](https://mlsanity.com/paper/2312.14439/) (2023)
- [Graph-R1: Incentivizing the Zero-Shot Graph Learning Capability in LLMs via Explicit Reasoning](https://mlsanity.com/paper/2508.17387/) (2025)
- [NPG-Muse: Scaling Long Chain-of-Thought Reasoning with NP-Hard Graph Problems](https://mlsanity.com/paper/2508.20373/) (2025)
- [Text Meets Topology: Rethinking Out-of-distribution Detection in Text-Rich Networks](https://mlsanity.com/paper/2508.17690/) (2025)
- [LEXA: Legal Case Retrieval via Graph Contrastive Learning with Contextualised LLM Embeddings](https://mlsanity.com/paper/2405.11791/) (2024)
- [TRN-R1-Zero: Text-rich Network Reasoning via LLMs with Reinforcement Learning Only](https://mlsanity.com/paper/2604.19070/) (2026)

## Built on by (most cited first, 1 of 1)

- [GraphEcho: Structural Redundancy and Evidence Provenance in LLM Graph Agents](https://mlsanity.com/paper/2609.17695/) (2026)

## Abstract (arXiv)

Reasoning over text-attributed graphs (TAGs) requires large language models (LLMs) to combine a node's text with evidence distributed across its neighbourhood. Existing methods fix the set of accessible neighbours before generation, forcing reasoning to operate over a static context and preventing the model from acquiring missing evidence during inference. We argue that neighbour selection should itself be part of the reasoning process. To this end, we propose Call Neighbours Yourself (CNY), a framework that enables LLMs to proactively explore graph neighbourhoods through topology-constrained graph-walk actions. Instead of reasoning over a pre-selected neighbour set, CNY exposes lightweight neighbour previews and learns when to expand candidate neighbours for additional evidence. To address the delayed-credit challenge of neighbour exploration, we introduce destination-conditioned on-policy self-distillation, which retrospectively evaluates a selected neighbour after its content is revealed and converts the resulting change in action preference into an action-level training signal. Experiments on standard TAG reasoning benchmarks under a unified raw-text setting show that CNY consistently outperforms fixed-context post-training baselines. Furthermore, the learned exploration policy transfers to unseen graphs and to a graph-level task not encountered during training. Code is available at https://github.com/superallen13/CNY.