Discovering the Hidden Role of Gini Index In Prompt-based Classification

Large language models are increasingly used for ordinal classification, yet semantically equivalent changes to prompt organization can alter their predictions. We conduct systematic experiments to characterize positional bias from label order, demonstration order, and demonstration placement. First, we apply the three probes to ten frontier LLMs on a common ordinal-classification task; every model is sensitive to all three positional sources, showing that the problem is pervasive. Second, we vary eight prompt-, task-, and model-level factors across five datasets; accuracy and stability are often misaligned, and only lower scale cardinality consistently improves both. Third, we compare pointwise, pairwise, and listwise inference, alternative aggregation and debiasing methods, and joint configurations; the tested corrections do not provide a reliable remedy, while a comparison-based listwise formulation offers the best balance but transfers unevenly across models and bias sources. These findings show that positional robustness depends on the full system configuration rather than the model alone. Ordinal-classification systems should therefore be selected jointly for predictive performance and stability.

We revisit the foundations of fairness and its interplay with utility and efficiency in settings where the training data contain richer labels, such as individual types, rankings, or risk estimates, rather than just binary outcomes. In this context, we propose algorithms that achieve stronger notions of evidence-based fairness than are possible in standard supervised learning. Our methods support classification and ranking techniques that preserve accurate subpopulation classification rates, as suggested by the underlying data distributions, across a broad class of classification rules and downstream applications. Furthermore, our predictors enable loss minimization, whether aimed at maximizing utility or in the service of fair treatment. Complementing our algorithmic contributions, we present impossibility results demonstrating that simultaneously achieving accurate classification rates and optimal loss minimization is, in some cases, computationally infeasible. Unlike prior impossibility results, our notions are not inherently in conflict and are simultaneously satisfied by the Bayes-optimal predictor. Furthermore, we show that each notion can be satisfied individually via efficient learning. Our separation thus stems from the computational hardness of learning a sufficiently good approximation of the Bayes-optimal predictor. These computational impossibilities present a choice between two natural and attainable notions of accuracy that could both be motivated by fairness.

Safety-critical perception systems must reliably detect rare object classes within small label spaces, a setting that long-tailed detection methods, designed for hundreds of classes with dense annotation, fundamentally do not address. Open-vocabulary detectors offer a promising alternative, as they use natural language queries at inference time, making prompt quality a first-class lever for detection performance. We exploit this property to address class imbalance: rather than retraining models or collecting additional annotations, we ask whether iteratively refining the language prompts, fed to frozen detectors, can improve minority class detection. We introduce C-GAP Caption-Guided Augmentation and Prompting), a detector-agnostic, annotation-free framework that operates in two phases. First, we establish a composite caption baseline combining per-image scene descriptions with class-quantity context, which we show outperforms scene-description only or class-quantity-only prompts across multiple open-vocabulary architectures and benchmarks. Second, an LLM iteratively refines each image's caption individually, with trials triaged into accept, tentative, or regenerate buckets based on minority-class [email protected] against a dynamic threshold derived from the composite baseline. Refinement terminates early once sufficient [email protected] gain is achieved. No detector weights are updated at any stage. Our experiments shows that C-GAP improves minority-class average precision up to 53% over the baselines. On COCO, C-GAP improves minority-class [email protected] by ~81% relative over the composite baseline (17.69 -> 32.09). Experiments confirm that composite captions provide the critical foundation for effective refinement: using scene-description-only or class-quantity-only prompts as the refinement starting point yields diminishing returns, supporting both stages of C-GAP as necessary contributions.