# Alignment Quality Index (AQI) : Beyond Refusals: AQI as an Intrinsic Alignment Diagnostic via Latent Geometry, Cluster Divergence, and Layer wise Pooled Representations

arXiv: https://arxiv.org/abs/2506.13901 · HTML: https://mlsanity.com/paper/2506.13901/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 32 of its 121 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)
- LLM safety and security / [Safety alignment, refusal and guardrails](https://mlsanity.com/safety/safety-alignment-refusal-and-guardrails/)

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

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [Alignment faking in large language models](https://mlsanity.com/paper/2412.14093/) (2024)
- [Recursively Summarizing Books with Human Feedback](https://mlsanity.com/paper/2109.10862/) (2021)
- [ViP-LLaVA: Making Large Multimodal Models Understand Arbitrary Visual Prompts](https://mlsanity.com/paper/2312.00784/) (2023)
- [Auditing large language models: a three-layered approach](https://mlsanity.com/paper/2302.08500/) (2023)
- [GrIPS: Gradient-free, Edit-based Instruction Search for Prompting Large Language Models](https://mlsanity.com/paper/2203.07281/) (2022)
- [LLM-PQ: Serving LLM on Heterogeneous Clusters with Phase-Aware Partition and Adaptive Quantization](https://mlsanity.com/paper/2403.01136/) (2024)
- [Layer by Layer: Uncovering Where Multi-Task Learning Happens in Instruction-Tuned Large Language Models](https://mlsanity.com/paper/2410.20008/) (2024)
- [AI-Generated Images as Data Source: The Dawn of Synthetic Era](https://mlsanity.com/paper/2310.01830/) (2023)
- [Time-Varying Gaussian Process Bandits with Unknown Prior](https://mlsanity.com/paper/2402.01632/) (2024)
- [Value Imprint: A Technique for Auditing the Human Values Embedded in RLHF Datasets](https://mlsanity.com/paper/2411.11937/) (2024)
- [AT4CTR: Auxiliary Match Tasks for Enhancing Click-Through Rate Prediction](https://mlsanity.com/paper/2312.06683/) (2023)
- [Diffusion-Generative Multi-Fidelity Learning for Physical Simulation](https://mlsanity.com/paper/2311.05606/) (2023)

## Built on by (most cited first, 8 of 8)

- [How Semantically Stable Are LLM Refusals? Measuring Confusion in Local Safety Boundaries](https://mlsanity.com/paper/2512.01037/) (2025)
- [When Behavioral Safety Evaluation Fails: A Representation-Level Perspective](https://mlsanity.com/paper/2606.08044/) (2026)
- [SPINAL -- Scaling-law and Preference Integration in Neural Alignment Layers](https://mlsanity.com/paper/2601.06238/) (2026)
- [SafeConstellations: Mitigating Over-Refusals in LLMs Through Task-Aware Representation Steering](https://mlsanity.com/paper/2508.11290/) (2025)
- [PermaFrost-Attack: Stealth Pretraining Seeding(SPS) for planting Logic Landmines During LLM Training](https://mlsanity.com/paper/2604.22117/) (2026)
- [HyperLens: Quantifying Cognitive Effort in LLMs with Fine-grained Confidence Trajectory](https://mlsanity.com/paper/2605.05741/) (2026)
- [MENTIS: What Belief Changes Under Alignment? Measuring Multi-Scale Latent Torsion in Language Models](https://mlsanity.com/paper/2606.01060/) (2026)
- [Reproducing FACTER: Fairness via Conformal Thresholding and Prompt Repair](https://mlsanity.com/paper/2606.28620/) (2026)

## Abstract (arXiv)

Alignment is no longer a luxury, it is a necessity. As large language models (LLMs) enter high-stakes domains like education, healthcare, governance, and law, their behavior must reliably reflect human-aligned values and safety constraints. Yet current evaluations rely heavily on behavioral proxies such as refusal rates, G-Eval scores, and toxicity classifiers, all of which have critical blind spots. Aligned models are often vulnerable to jailbreaking, stochasticity of generation, and alignment faking. To address this issue, we introduce the Alignment Quality Index (AQI). This novel geometric and prompt-invariant metric empirically assesses LLM alignment by analyzing the separation of safe and unsafe activations in latent space. By combining measures such as the Davies-Bouldin Score (DBS), Dunn Index (DI), Xie-Beni Index (XBI), and Calinski-Harabasz Index (CHI) across various formulations, AQI captures clustering quality to detect hidden misalignments and jailbreak risks, even when outputs appear compliant. AQI also serves as an early warning signal for alignment faking, offering a robust, decoding invariant tool for behavior agnostic safety auditing. Additionally, we propose the LITMUS dataset to facilitate robust evaluation under these challenging conditions. Empirical tests on LITMUS across different models trained under DPO, GRPO, and RLHF conditions demonstrate AQI's correlation with external judges and ability to reveal vulnerabilities missed by refusal metrics. We make our implementation publicly available to foster future research in this area.