Fairness-Aware Mixture-of-Experts via Subgroup Reweighting and Gate Regularization

Ensuring fairness is essential as machine learning increasingly informs consequential decisions. However, many fairness-aware methods focus on the outputs of individual predictors, without directly controlling sensitive information retained in the underlying representations. We propose Deep Fair Learning (DFL), which combines distance covariance regularization with predictive loss to jointly learn representations and downstream predictors, promoting fairness at both levels while preserving task-relevant information. Its marginal and class-conditional formulations target independence and separation, respectively. Under suitable regularity conditions, we establish non-asymptotic joint excess-risk rates and convergence of the learned representation up to natural invariances. We further derive fairness-inheritance bounds linking representation-level dependence to downstream disparities over suitable predictor classes, extending fairness guarantees beyond the jointly trained predictor. Experiments on tabular, text, and image benchmarks show that DFL achieves lower fairness gaps than competing methods in many evaluated settings while maintaining competitive predictive accuracy, with fairness gains largely preserved after downstream retraining.

Demographic prompts are routed differently from neutral prompts in Mixture-of-Experts (MoE) language models, motivating tests of routing-level stereotype control. We introduce Fairness-Aware Routing Equilibrium (FARE), a diagnostic framework combining demographic routing profiles, empirical layer selection, and fixed inference-time reweighting, and evaluate five MoE architectures in English. At the selected operating points, CrowS-Pairs preference changes by at most 1.3 percentage points; DeepSeekMoE selects no intervention. Paired 95% confidence intervals exclude decreases larger than 2.2 points on each intervened model, and the only nominally significant change (Qwen1.5, p = 0.015) does not survive multiple-comparison correction. OLMoE and Qwen3 nevertheless change nearly every top-k expert set. Noise controls, random and truncated synthetic profiles, and hard masking also move preference by at most 1.5 points. Four generation protocols on OLMoE, Mixtral, Qwen1.5, and Qwen3 show no consistent change in the measured toxicity, lexical, or reference-overlap metrics. Selection and evaluation items overlap, so these comparisons are not independent evaluations. The tested reweighting procedure offers limited stereotype control.

Mixture-of-Experts (MoE) models provide a flexible framework for partitioning complex prediction problems into simpler local learning tasks through an input-dependent gating mechanism. Existing interpretable MoE approaches, such as Mixture of Decision Trees (MoDT), achieve transparency by employing homogeneous decision-tree experts, but this restricts the model to a single inductive bias across all regions of the feature space. We extend the MoDT framework by introducing heterogeneous expert families comprising decision trees, linear support vector machines, and quadratic discriminant analysis under a common probabilistic gating mechanism. To ensure coherent likelihood-based inference, non-probabilistic experts are calibrated to produce conditional class probabilities, allowing parameter estimation within the generalized Expectation-Maximization framework of MoDT. We further establish theoretical monotone ascent guarantees for the proposed heterogeneous gating updates, providing a justification for the optimization procedure. Experiments on a diverse collection of synthetic and real-world benchmark datasets demonstrate that the proposed framework adaptively specializes experts according to local data geometry, yielding interpretable expert assignments while achieving predictive performance competitive with homogeneous MoDT and Random Forests. The proposed approach combines interpretability, adaptive inductive bias selection, and probabilistic coherence within a unified mixture-of-experts framework.