Learning Fair Representations with Kolmogorov-Arnold Networks

AI summary

Overview

Research area: Fairness-aware machine learning / algorithmic fairness, with a focus on adversarial debiasing using Kolmogorov-Arnold Networks (KANs).

Technical level: Advanced. The paper combines a min-max adversarial training objective, spline-based function approximation theory, Lipschitz and smoothness proofs, and empirical benchmarking, but the core intuition is summarized here in accessible terms.

Scope in one sentence: The paper proposes and evaluates an adversarially trained KAN classifier with an adaptive fairness penalty for mitigating socioeconomic bias in college admissions decisions, tested on two real University of California Irvine admissions datasets.

What This Paper Is About

Machine learning models used in high-stakes decisions such as college admissions can amplify historical bias against marginalized groups, and current fairness methods struggle to balance fairness against predictive accuracy while remaining interpretable. The authors replace the standard neural network inside an adversarial debiasing framework with a Kolmogorov-Arnold Network, whose learnable spline functions are argued to give both adversarial stability and structural interpretability. They also add an adaptive mechanism that automatically tunes the fairness penalty during training instead of relying on manual tuning.

Key Contributions

1. A KAN-based adversarial debiasing framework. The classifier and the adversary are both KANs trained in a min-max (zero-sum) objective; the authors state this is the first work to elaborate on a KAN-based adversarial debiasing framework, to the best of their knowledge.

2. Theoretical guarantees for adversarial stability. Lemma 1 shows each univariate spline function is Lipschitz continuous on a bounded range and therefore the overall KAN function f is L-Lipschitz continuous on a bounded domain. Lemma 2 shows that because the constituent splines are twice differentiable with bounded second derivatives, f is β-smooth. Two appendix propositions show that finite sums of spline functions preserve smoothness and that composition of smooth functions in a KAN preserves smoothness.

3. An adaptive fairness penalty (λ) update mechanism. Instead of manually tuning the fairness coefficient λ, the algorithm computes the fairness gap at each epoch and updates λ with a linear rule, clipped into the range [0.1, 1.0].

4. Empirical validation on two real admissions datasets. The framework is evaluated on two UCI Computer Science freshman applicant datasets with two binary sensitive attributes (low-income status and first-generation flag), under three optimizers and against three baselines.

Main Findings

• KAN models beat the baselines on the fairness–accuracy trade-off. The authors report that the KAN-based adversarial debiasing framework, regardless of optimizer choice, consistently outperforms the baseline models across both datasets, which they attribute largely to the adaptive λ policy.

• On dataset D₁ (4,442 records, Fall 2021), optimizer choice shifted the balance. The Adam-based KAN model offered stronger predictive power (an increase of 0.45% in Accuracy and 3.41% in AUROC) compared to OAdam, while OAdam enhanced fairness outcomes significantly; the ADOPT-trained model exhibited a balanced performance across fairness and accuracy. Concretely, K₁ with Adam scored 74.92 Accuracy, 80.27 AUROC, 85.79 p%-Rule₁, 89.65 p%-Rule₂, with DP₁ = 0.028 and DP₂ = 0.035.

• On the larger dataset D₂ (26,243 records, Fall 2018–Fall 2024), performance improved notably. All setups trained on D₂ showed significant improvement, and the ADOPT-based model stood out with accuracy increases of 0.15% and 0.82% over the Adam setup, plus increases of 15.14% and 18.48% in p%-Rule over the Adam setup. K₂ with ADOPT reached 82.51 Accuracy, 86.68 AUROC, 99.25 p%-Rule₁, 99.70 p%-Rule₂, DP₁ = 0.032 and DP₂ = 0.037.

• MLP baselines under-performed the KAN models. B₁ and B₁′ under-performed relative to the KAN models, especially on D₂.

• The two state-of-the-art baselines behaved differently across datasets. B₂ achieved high fairness on D₁ but suffered a drop on D₂, whereas B₃ started with lower fairness on D₁ but improved substantially on D₂ with proper fine-tuning.

• Higher spline knot orders improved fairness in the ablation. In the ablation using spline orders k = {3, 4, 5} on D₁, accuracy stayed relatively stable across k setups while the p%-Rule fairness metrics tended to improve with higher spline orders. Higher k (k = 4, 5) may introduce convergence instability; the ADOPT-trained model showed comparatively stable training dynamics versus Adam or OAdam.

• KAN training loss showed instability. The K₁ model's training loss curve exhibits pronounced spikes, which the authors attribute to the smoothness–dimension trade-off in KANs, described as inherent to preserving universal approximation.

• Interpretability motivation. Standard adversarial debiasing leaves the predictor as a black-box function lacking interpretability, which the authors identify as a key limitation in sensitive settings; KAN's spline-based architecture and explicit functional decomposition are offered as the alternative.

Methodology in Plain English

The authors frame admissions as a binary classification problem: given a feature vector x (about 140 features covering demographics, academic records, high school information, and essay responses), a binary sensitive attribute z, and a binary label y (the final read score), predict the label. A classifier and an adversary play a zero-sum game: the classifier tries to predict the label while preventing the adversary from inferring the sensitive attribute from its output, governed by the fairness coefficient λ.

The key change from prior work is that both the classifier and the adversary are Kolmogorov-Arnold Networks rather than multilayer perceptrons. KANs use learnable univariate spline functions instead of scalar weights and fixed activations, parameterized as B-spline curves h(x) = Σᵢ cᵢ Bᵢ(x) with learnable coefficients. The authors argue the smoothness and Lipschitz continuity of these splines stabilize the adversarial optimization dynamics, which they prove in Lemma 1 and Lemma 2 and support with two appendix propositions.

Rather than hand-tuning λ, they compute the fairness gap each epoch as δ = (τ − p%-Rule)/τ and update λ ← clip(λ + η·δ, 0.1, 1.0). Training proceeds over grid levels, initializing each new grid from the previously trained models, first training the adversary with the classifier frozen, then training the classifier with adversarial debiasing. Experiments use a fixed B-spline order of k = 3 in the main comparison (chosen as striking an effective balance between expressiveness, smoothness, and training stability, consistent with Liu et al. 2024), with the ablation sweeping k ∈ {3, 4, 5}. Three optimizers (Adam, OAdam, ADOPT) and two fairness metrics (p%-Rule and DP, where a higher p%-Rule closer to 100% indicates better fairness) are used, with Accuracy and AUROC for predictive performance. Baselines are B₁ (an FFNN-based standard adversarial debiasing framework), B₂ (an exponential gradient-based debiasing model), and B₃ (a ROAD-based robust optimization for adversarial debiasing method).

Why This Matters

Impact on research: The paper connects a recent architecture (KANs) to an established fairness technique (adversarial debiasing), supplying proofs of Lipschitz continuity and smoothness as the justification for using KANs in a min-max setting rather than only demonstration by experiment. It also contributes evidence on which optimizers suit spline-based adversarial training and on how spline knot complexity interacts with fairness metrics.

Real-world applications:

• College and university admissions, the paper's direct case study, where decisions must be equitable across socioeconomic groups and are subject to public scrutiny and interpretability requirements; the authors cite the University of California's Non-Discriminatory Policy and the reduction of standardized testing as context.
• Healthcare, listed among the high-stakes domains where fairness-aware AI is needed.
• Hiring, also listed as a high-stakes domain where discriminatory model behavior is a concern.
• Educational access programs more broadly, such as supporting marginalized applicants who face resource and support disparities that affect academic performance.

Industry relevance: Organizations deploying models in regulated or socially sensitive decisions need methods that preserve predictive quality while satisfying group-fairness criteria and offering some transparency into decision logic. The paper notes that enforcing strict criteria such as Demographic Parity leads to a provable loss in accuracy — citing Zhao and Gordon 2022 that any predictor satisfying exact DP incurs an average classification error lower-bounded by half the base rate gap between groups — plus reduced robustness to data perturbations or distribution shifts. An adaptive penalty that trades off these pressures automatically is directly useful for teams that otherwise must spend costly manual effort tuning a fairness coefficient.

Future Directions

• Feature-level bias detection via reweighting. The authors propose incorporating explicit feature-level bias detection through a reweighting mechanism, which could improve overall fairness while helping to adhere to data privacy constraints.

• Fairness definitions beyond Demographic Parity. Extending the framework to incorporate alternative fairness definitions beyond DP is described as a way to provide new insights.

• Addressing convergence instability. The paper observes pronounced spikes in KAN training loss, attributed to the smoothness–dimension trade-off, and notes that higher spline orders may introduce convergence instability — leaving open how to stabilize adversarial KAN training at higher complexity.

• Broader KAN-based fairness-aware systems. The authors frame this work as a step toward aligning algorithmic performance with social responsibility and encourage future exploration of KAN-based fairness-aware systems that uphold both ethical and performance standards in critical decision-making.

Target Audience

This paper suits researchers and graduate students working on algorithmic fairness, adversarial learning, and interpretable machine learning; practitioners building decision systems for admissions, hiring, or healthcare who need evidence on accuracy–fairness trade-offs; and readers with a background in neural network training or optimization theory who want to understand how spline-based architectures behave under min-max debiasing. Readers seeking a purely applied walkthrough should note that the theoretical arguments and appendix proofs form a substantial portion of the contribution, while the empirical comparison is concentrated on two admissions datasets.

Authors’ 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.