Learning Fair Representations with Kolmogorov-Arnold Networks

TL;DR

This work tackles fairness in high-stakes college admissions by integrating Kolmogorov-Arnold Networks (KANs) into an adversarial debiasing framework to produce fair, interpretable representations. The authors prove that KANs are Lipschitz and $\beta$-smooth, enabling stable adversarial optimization, and they introduce an adaptive penalty mechanism to balance fairness and accuracy during training. Empirical results on two real-world admissions datasets show that KAN-based debiasing with adaptive $\lambda$ consistently improves fairness metrics (Demographic Parity and $p\%$-Rule) while preserving or enhancing predictive performance relative to state-of-the-art baselines, with ADOPT often delivering the best trade-off. The work highlights the practical potential of spline-based, interpretable architectures for fairness-aware decision-making and suggests future directions for feature-level bias detection and broader fairness definitions.

Abstract

Despite recent advances in fairness-aware machine learning, predictive models often exhibit discriminatory behavior towards marginalized groups. Such unfairness might arise from biased training data, model design, or representational disparities across groups, posing significant challenges in high-stakes decision-making domains such as college admissions. While existing fair learning models aim to mitigate bias, achieving an optimal trade-off between fairness and accuracy remains a challenge. Moreover, the reliance on black-box models hinders interpretability, limiting their applicability in socially sensitive domains. To circumvent these issues, we propose integrating Kolmogorov-Arnold Networks (KANs) within a fair adversarial learning framework. Leveraging the adversarial robustness and interpretability of KANs, our approach facilitates stable adversarial learning. We derive theoretical insights into the spline-based KAN architecture that ensure stability during adversarial optimization. Additionally, an adaptive fairness penalty update mechanism is proposed to strike a balance between fairness and accuracy. We back these findings with empirical evidence on two real-world admissions datasets, demonstrating the proposed framework's efficiency in achieving fairness across sensitive attributes while preserving predictive performance.

Figures (4)

• Figure 1: Schematic overview of the proposed adversarial debiasing framework using KANs. The classifier (KAN), $f$, learns predictive representations from input features, $x$, while an adversary (also a KAN), $g$, attempts to infer the sensitive attribute, $z$, from the classifier’s output, $y$, using a min-max objective. Fairness parameter, $\lambda$, is updated adaptively after every training epoch in an attempt to balance accuracy and fairness scores.
• Figure 2: Ablation study to compare predictive performance and fairness scores across proposed frameworks with different spline knot complexities, and baseline models under varying optimization strategies, evaluated on dataset $D_{(1)}$. (a) Illustrates metrics of the proposed KAN-based adversarial frameworks using three different optimizer techniques ($o_1$: Adam, $o_2$: OAdam, $o_3$: ADOPT). Similarly, (b) depicts the Baseline model performance across varying optimizers.
• Figure 3: Training Loss convergence of the KAN-based adversarial learning framework across three different spline knot orders ($k \in \{3,4,5 \}$), under three different optimization techniques. Each plot illustrates the convergence behavior of the model, highlighting the impact of optimizer choice and KAN model's spline complexity on training stability.
• Figure 4: The Kernel Density Estimate (KDE) plots for KAN-based adversarial debiasing model, using adaptive $\lambda$ policy. It uses the $k=3$ spline knot complexity of KAN models (for both classifier and adversary models), and is trained on $D_{(1)}$ dataset. It depicts the pre-trained and post-trained models, highlighting the bias present in the model predictions.

Theorems & Definitions (12)

• Lemma 1
• proof
• Lemma 2
• proof
• Proposition 1
• proof
• Proposition 2
• proof
• Definition B: Wasserstein-1 distance
• Proposition 3