Post-training quantization (PTQ) has become a key approach for large language model (LLM) compression. Existing methods commonly adopt block-level reconstruction as a surrogate to calibrate each quantized Transformer block. However, our analysis shows that this loose objective can admit cancellation patterns, where the aggregated block-level reconstruction error is small even though the per-head errors remain large. We therefore revisit the PTQ formulation from a variational perspective. By treating per-head representations as latent variables and the block output as the observed variable, we find that conventional block-level reconstruction corresponds to optimizing only the observation-level term, while omitting a latent alignment term that captures head-level quantization error. Motivated by this finding, we propose HEAL, a Latent HEad ALignment framework that turns block-level reconstruction calibration into joint observation-latent calibration with stop-gradient head alignment. Experiments on LLaMA-2/3 and Qwen2.5 families under low-bit weight-activation quantization show that HEAL generally improves perplexity and zero-shot accuracy over block-level reconstruction baselines.

Multiperspective Fusion (MPF) is a novel posttraining alignment framework for large language models (LLMs) developed in response to the growing need for easy bias mitigation. Built on top of the SAGED pipeline, an automated system for constructing bias benchmarks and extracting interpretable baseline distributions, MPF leverages multiperspective generations to expose and align biases in LLM outputs with nuanced, humanlike baselines. By decomposing baseline, such as sentiment distributions from HR professionals, into interpretable perspective components, MPF guides generation through sampling and balancing of responses, weighted by the probabilities obtained in the decomposition. Empirically, we demonstrate its ability to align LLM sentiment distributions with both counterfactual baselines (absolute equality) and the Human Resource baseline (biased for Top Univeristy), resulting in small KL divergence, reduction of calibration error and generalization to unseen questions. This shows that MPF offers a scalable and interpretable method for alignment and bias mitigation, compatible with deployed LLMs and requiring no extensive prompt engineering or finetuning.