DEVELOPING NOVEL STATISTICAL METHODS FOR DETECTING AND MITIGATING BIAS IN LARGE LANGUAGE MODELS.

Abstract

Large Language Models (LLMs) have achieved remarkable performance across a wide range of natural language processing tasks; however, they systematically encode and amplify societal biases ncluding gender, racial, religious, and socioeconomic biases inherited from their pre-training corpora. Existing bias detection approaches are predominantly heuristic, template-based, or benchmark-constrained, offering limited statistical rigour and generalisability across diverse linguistic contexts. This paper introduces a novel statistical framework, designated the Multi-Dimensional Bias Detection and Mitigation System (MDBDMS), for the comprehensive, theoretically-grounded assessment and reduction of bias in LLMs. The framework integrates three novel methodological contributions: (i) a Distributional Semantic Disparity (DSD) measure a non-parametric, rank-based test for detecting systematic directional asymmetries in token embedding distributions across demographic groups; (ii) a Counterfactual Bias Amplification Score (CBAS) a causal inference-based metric quantifying the marginal increase in biased output probability attributable to specific demographic attribute perturbations; and (iii) a constrained fine-tuning procedure employing Lagrangian optimisation to enforce bias fairness constraints while preserving downstream task performance. Comprehensive evaluation is performed on GPT-4, LLaMA-3-70B, Mistral-7B, and Falcon-40B across seven bias dimensions using six established benchmark datasets (WinoBias, StereoSet, CrowS-Pairs, BBQ, TruthfulQA, and HolisticBias). The MDBDMS achieves state-of-the-art bias reduction across all evaluated models, with mean Bias Score reductions of 41.8% and preservation of task accuracy within a 2.3% degradation tolerance. These results advance the field of responsible AI and provide a practically deployable toolkit for enterprise-grade LLM governance.