Response-Margin Defects in LLM Quantization: Descriptive Divergence without Invariant Optimization

This paper develops a response-margin framework for studying quantization in large language models. The central distinction is between output distortion and response-margin damage. Conventional quantization audits often measure how much a quantized model deviates from the full-precision model at the level of outputs, logits, activations, or loss. This paper instead asks whether the quantized representative preserves specified response margins: the margins that support decision-relevant or task-relevant responses under a chosen readout family and calibration domain. The paper separates two claims that are often conflated. The first, ARQ-D, is descriptive: response-margin salience may differ from output salience and may better predict held-out response collapse. The second, ARQ-O, is optimizing: such response information may be converted into a stable and reproducible allocation improvement under a fixed bit budget, objective, oracle, trial budget, and admissible search class. The main conclusion is that ARQ-D is meaningful, but it does not by itself imply ARQ-O. Response-margin defects can expose real and predictive vulnerabilities that are not captured by output-side distortion. However, this diagnostic information does not automatically determine an invariant bit-allocation rule. Optimization requires additional structure: a feasible quantizer class, an objective, an observation oracle, a trial budget, admissible search rules, and a validation discipline. The empirical audits study weight, activation, and true sequential KV quantization. Weight and activation quantization show strong output-response divergence and strong held-out predictive advantage of response salience over output-side controls. The KV axis is weaker and more power-dependent. Across axes, the tested routes from descriptive divergence to invariant optimization fail: residual allocation is not robust, response-primary allocation gains are partial rather than reproducible, positive Type-II interaction is not supported, apparent absorption is metric-dependent, and true sequential KV accumulation is not detected. The contribution of the paper is therefore not a new quantization algorithm, but a structural clarification. Response-aware quantization is valuable as a diagnostic and audit framework: it reveals where output-based criteria fail to see response collapse. But the step from diagnosis to optimization is a separate, non-invariant allocation claim. In short, response-margin divergence is a diagnostic fact; optimization is an additional claim that must be separately specified and validated.