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.

The rapid advancement of large language models (LLMs) has revolutionized numerous applications, but presents significant challenges in aligning these models with diverse human values, ethical standards, and specific user preferences. Direct Preference Optimization (DPO) has become a cornerstone for preference alignment but is constrained by reliance on fixed divergence measures and limited feature transformations. We introduce DPO-Kernels, an innovative enhancement of DPO that integrates kernel methods to overcome these challenges through four key contributions: (i) Kernelized Representations: These representations enhance divergence measures by using polynomial, RBF, Mahalanobis, and spectral kernels for richer feature transformations. Additionally, we introduce a hybrid loss that combines embedding-based loss with probability-based loss; (ii) Divergence Alternatives: Beyond Kullback–Leibler (KL), we incorporate Jensen-Shannon, Hellinger, Rényi, Bhattacharyya, Wasserstein, and other f-divergences to boost stability and robustness; (iii) Data-Driven Selection: Choosing the optimal kernel-divergence pair among 28 combinations (4 kernels × 7 divergences) is challenging. We introduce automatic metrics that analyze the data to select the best kernel-divergence pair, eliminating the need for manual tuning; (iv) Hierarchical Mixture of Kernels (HMK): Combining local and global kernels for precise and large-scale semantic modeling. This approach automatically selects the optimal kernel mixture during training, enhancing modeling flexibility. DPO-Kernels achieve state-of-the-art generalization in factuality, safety, reasoning, and instruction following across 12 datasets. While alignment risks overfitting, Heavy-Tailed Self-Regularization (HT-SR) theory confirms that DPO-Kernels ensure robust generalization in LLMs. Comprehensive resources are available to facilitate further research and application of DPO-Kernels.

Precise alignment in Text-to-Image (T2I) systems is crucial for generating visuals that reflect user intent while adhering to ethical and policy standards. Recent controversies, such as the Google Gemini-generated Pope image backlash, highlight the urgent need for robust alignment mechanisms. Building on alignment successes in Large Language Models (LLMs), this paper introduces YinYangAlign, a benchmarking framework designed to evaluate and optimize T2I systems across six inherently contradictory objectives. These objectives highlight core trade-offs, such as balancing faithfulness to prompts with artistic freedom and maintaining cultural sensitivity without compromising creativity. Alongside this benchmark, we propose the Contradictory Alignment Optimization (CAO) framework, an extension of Direct Preference Optimization (DPO), which employs multi-objective optimization techniques to address these competing goals. By leveraging per-axiom loss functions, synergy-driven global preferences, and innovative tools like the Synergy Jacobian, CAO achieves superior alignment across all objectives. Experimental results demonstrate significant improvements in fidelity, diversity, and ethical adherence, setting new benchmarks for the field. This work provides a scalable, effective approach to resolving alignment challenges in T2I systems while offering insights into broader AI alignment paradigms.