Data-aware post-training quantization (PTQ) minimizes a per-token reconstruction loss on a small calibration corpus—an objective natural for average-token preservation, but one that implicitly weights positions by their empirical frequency. For **Automatic Speech Recognition (ASR)**, this weighting is misaligned with tail-sensitive recognition risk: names, numerals, technical terms, and domain-specific words are practically important but receive proportionally little calibration mass.

We propose **Tail-Aware Reconstruction Quantization (TARQ)**, a label-free PTQ framework that shifts calibration toward the lexical tail. **TARQ** introduces **rareBAL**, a closed-form per-Linear-layer rule that equalizes the calibration mass contributed by common and tail positions, plus a metric-consistent residual correction that aligns the sequential PTQ sweep with the reweighted objective. **TARQ** requires no entity labels, no curated calibration set, no validation decoding, and no additional training.

Across eight ASR backbones and eight datasets under 4-bit weight-only quantization, **TARQ** improves mean rare-WER, the **Word Error Rate (WER)** restricted to rare-word reference positions, while maintaining competitive aggregate WER. It achieves the lowest cross-corpus rare-WER swing, **0.63 percentage points (pp)**, among compared methods, and transfers without modification to entity-rich evaluation on ProfASR and ContextASR-Speech-En with no entity supervision.

Path planning is a fundamental scientific problem in robotics and autonomous navigation, requiring the derivation of efficient routes from starting to destination points while avoiding obstacles. Traditional algorithms like A* and its variants are capable of ensuring path validity but suffer from significant computational and memory inefficiencies as the state space grows. Conversely, large language models (LLMs) excel in broader environmental analysis through contextual understanding, providing global insights into environments. However, they fall short in detailed spatial and temporal reasoning, often leading to invalid or inefficient routes. In this work, we propose LLM-A*, an new LLM based route planning method that synergistically combines the precise pathfinding capabilities of A* with the global reasoning capability of LLMs. This hybrid approach aims to enhance pathfinding efficiency in terms of time and space complexity while maintaining the integrity of path validity, especially in large-scale scenarios. By integrating the strengths of both methodologies, LLM-A* addresses the computational and memory limitations of conventional algorithms without compromising on the validity required for effective pathfinding.