# GIF: Locally Sound Geometric Information Flow Control for LLMs

arXiv: https://arxiv.org/abs/2606.23277 · HTML: https://mlsanity.com/paper/2606.23277/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Agent threats, guardrails and governance, one of 16 directions in LLM agents and tool use.
- Builds on 30 of its 53 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Placed in

- LLM agents and tool use / [Agent threats, guardrails and governance](https://mlsanity.com/agents/agent-threats-guardrails-and-governance/)

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

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Not what you've signed up for: Compromising Real-World LLM-Integrated Applications with Indirect Prompt Injection](https://mlsanity.com/paper/2302.12173/) (2023)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Defeating Prompt Injections by Design](https://mlsanity.com/paper/2503.18813/) (2025)
- [Defending Against Indirect Prompt Injection Attacks With Spotlighting](https://mlsanity.com/paper/2403.14720/) (2024)
- [Progent: Securing AI Agents with Privilege Control](https://mlsanity.com/paper/2504.11703/) (2025)
- [Adaptive Attacks Break Defenses Against Indirect Prompt Injection Attacks on LLM Agents](https://mlsanity.com/paper/2503.00061/) (2025)
- [Securing AI Agents with Information-Flow Control](https://mlsanity.com/paper/2505.23643/) (2025)
- [PromptArmor: Simple yet Effective Prompt Injection Defenses](https://mlsanity.com/paper/2507.15219/) (2025)
- [System-Level Defense against Indirect Prompt Injection Attacks: An Information Flow Control Perspective](https://mlsanity.com/paper/2409.19091/) (2024)
- [AgentDAM: Privacy Leakage Evaluation for Autonomous Web Agents](https://mlsanity.com/paper/2503.09780/) (2025)
- [Design Patterns for Securing LLM Agents against Prompt Injections](https://mlsanity.com/paper/2506.08837/) (2025)
- [RTBAS: Defending LLM Agents Against Prompt Injection and Privacy Leakage](https://mlsanity.com/paper/2502.08966/) (2025)
- [Hutch++: Optimal Stochastic Trace Estimation](https://mlsanity.com/paper/2010.09649/) (2020)
- [MCP Security Bench (MSB): Benchmarking Attacks Against Model Context Protocol in LLM Agents](https://mlsanity.com/paper/2510.15994/) (2025)
- [AgentSentry: Mitigating Indirect Prompt Injection in LLM Agents via Temporal Causal Diagnostics and Context Purification](https://mlsanity.com/paper/2602.22724/) (2026)
- [Simple Prompt Injection Attacks Can Leak Personal Data Observed by LLM Agents During Task Execution](https://mlsanity.com/paper/2506.01055/) (2025)
- [Systems Security Foundations for Agentic Computing](https://mlsanity.com/paper/2512.01295/) (2025)
- [Mechanistic Data Attribution: Tracing the Training Origins of Interpretable LLM Units](https://mlsanity.com/paper/2601.21996/) (2026)
- [Mitigating Indirect Prompt Injection via Instruction-Following Intent Analysis](https://mlsanity.com/paper/2512.00966/) (2025)
- [DATE-LM: Benchmarking Data Attribution Evaluation for Large Language Models](https://mlsanity.com/paper/2507.09424/) (2025)
- [Jacobian Scopes: token-level causal attributions in LLMs](https://mlsanity.com/paper/2601.16407/) (2026)

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

- [Certified Mechanistic Edits: Behavioral Guarantees for Skill Removal and Preservation](https://mlsanity.com/paper/2610.03502/) (2026)

## Abstract (arXiv)

Large language models increasingly mediate interactions between sensitive data, untrusted inputs, and privileged actions in agentic systems, creating security and privacy risks. These range from prompt injections that manipulate downstream tool use to leakage of confidential information through model outputs. Recent Information Flow Control (IFC)-based defenses show promise but lack a principled semantic foundation for reasoning about information flow through the model itself. Since any input token may influence any output token in an autoregressive LLM, existing approaches suffer from severe taint explosion. We present Geometric Information Flow (GIF), a semantic framework for tracking information flow from input tokens to outputs. GIF uses the LLM Jacobian and local output geometry to upper-bound the Shannon mutual information between perturbed input spans and model outputs, yielding a scalable measure computable on large models via automatic differentiation and low-rank approximation. Unlike attention-based or correlational attribution heuristics, GIF satisfies local geometric soundness, and we provide a fully mechanized Lean 4 proof that it upper-bounds the true information flow induced by a given prompt under local regularity assumptions. We evaluate GIF on integrity and confidentiality tasks across multiple prompt-injection and privacy-leakage benchmarks. GIF achieves near-perfect recall even without a downstream declassifier, outperforming attention-based baselines. Combined with lightweight LLM-based declassifiers, it matches or exceeds the F1 of direct LLM-as-judge baselines such as GPT-5.5 xhigh reasoning while using up to 81x lower token cost. GIF flows detected with small surrogate models transfer to larger state-of-the-art models and other model families, even when the surrogate is up to 200x smaller, suggesting black-box deployment without gradient access.