Alignment Quality Index (AQI) : Beyond Refusals: AQI as an Intrinsic
  Alignment Diagnostic via Latent Geometry, Cluster Divergence, and Layer wise
  Pooled Representations
Authors: name: Abhilekh Borah, name: Chhavi Sharma, name: Danush Khanna, name: Utkarsh Bhatt, name: Gurpreet Singh, name: Hasnat Md Abdullah, name: Raghav Kaushik Ravi, name: Vinija Jain, name: Jyoti Patel, name: Shubham Singh, name: Vasu Sharma, name: Arpita Vats, name: Rahul Raja, name: Aman Chadha, name: Amitava Das

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.