# Graph-based Target Back-Propagation for Context Adaptation in Multi-LLM Agentic Systems

arXiv: https://arxiv.org/abs/2606.14155 · HTML: https://mlsanity.com/paper/2606.14155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 72 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 19 of 19)

- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Optimizing Instructions and Demonstrations for Multi-Stage Language Model Programs](https://mlsanity.com/paper/2406.11695/) (2024)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Language Model Fine-Tuning on Scaled Survey Data for Predicting Distributions of Public Opinions](https://mlsanity.com/paper/2502.16761/) (2025)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [Learning without training: The implicit dynamics of in-context learning](https://mlsanity.com/paper/2507.16003/) (2025)
- [The Closeness of In-Context Learning and Weight Shifting for Softmax Regression](https://mlsanity.com/paper/2304.13276/) (2023)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Self-Evolving Multi-Agent Systems via Textual Backpropagation](https://mlsanity.com/paper/2506.09046/) (2025)
- [TextResNet: Decoupling and Routing Optimization Signals in Compound AI Systems via Deep Residual Tuning](https://mlsanity.com/paper/2602.08306/) (2026)

## Abstract (arXiv)

Context adaptation automates prompt engineering in LLM-based systems by iteratively revising tunable prompts from task feedback, without modifying model weights. Extending this paradigm to multi-LLM agentic systems is crucial: existing methods suffer from inaccurate credit assignment and lack convergence guarantees. We propose Graph-based Target Back-Propagation (GTBP), a context adaptation framework for agentic workflows modeled as directed acyclic graphs. GTBP propagates local target outputs backward through the workflow graph and uses target--output discrepancies to guide a stage-wise prompt update mechanism. Theoretically, we show that GTBP's stage-wise prompt updates become stable over iterations, and that a sufficiently capable LLM optimizer can decrease the overall objective. Empirically, GTBP consistently outperforms strong baselines across three benchmarks while maintaining comparable computational cost.