# Geometry-Lite: Interpretable Safety Probing via Layer-Wise Margin Geometry

arXiv: https://arxiv.org/abs/2605.20241 · HTML: https://mlsanity.com/paper/2605.20241/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 23 references that are in the map.
- First posted on arXiv 18 May 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations](https://mlsanity.com/paper/2312.06674/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models](https://mlsanity.com/paper/2308.01263/) (2023)
- [A Holistic Approach to Undesired Content Detection in the Real World](https://mlsanity.com/paper/2208.03274/) (2022)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [ToxicChat: Unveiling Hidden Challenges of Toxicity Detection in Real-World User-AI Conversation](https://mlsanity.com/paper/2310.17389/) (2023)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [On Second Thought, Let's Not Think Step by Step! Bias and Toxicity in Zero-Shot Reasoning](https://mlsanity.com/paper/2212.08061/) (2022)
- [Safety Layers in Aligned Large Language Models: The Key to LLM Security](https://mlsanity.com/paper/2408.17003/) (2024)
- [When Benchmarks Lie: Evaluating Malicious Prompt Classifiers Under True Distribution Shift](https://mlsanity.com/paper/2602.14161/) (2026)
- [Truth as a Trajectory: What Internal Representations Reveal About Large Language Model Reasoning](https://mlsanity.com/paper/2603.01326/) (2026)

## Abstract (arXiv)

Prompt-level safety probes for large language models use hidden-state representations to separate safe from unsafe prompts, but strong average detection performance does not explain the geometry of this separation. In particular, it remains unclear how safety evidence is formed across layers, which aspects of that layer-wise geometry support low-false-positive decisions, and which geometric biases remain stable under benchmark shift. We study this as an empirical decomposition problem and introduce Geometry-Lite, a compact prompt-level probe that maps each layer's final prompt-token representation to signed margins under centroid, local-neighborhood, and supervised linear-boundary readouts, then summarizes the resulting margin profiles by boundary position, layer-to-layer change, and coarse shape. Across nine instruction-tuned backbones (1.2B--70B) and seven safety benchmarks, Geometry-Lite improves over single-layer probes while remaining close to raw multi-layer score stacking, making it a useful instrument for analyzing the multi-layer safety signal. The decomposition shows that safety evidence is expressed primarily through persistent boundary-position geometry: final or extremal margins and unsafe-side layer occupancy dominate aggregate detection performance. In contrast, finite-difference drift and structural summaries add little to pooled AUROC, although drift can provide small recall-oriented corrections under shifted low-FPR thresholds. Under benchmark shift, optimized linear boundaries are sharp on the training mixture, whereas class-conditional mean geometry retains separation more reliably on a predefined hard held-out subset. Overall, prompt-level safety evidence is not primarily a layer-to-layer motion signal, but a persistent layer-wise margin geometry whose useful components and readout-level biases become visible in decision-critical regimes.