Learning Fair Representations with Kolmogorov-Arnold Networks

Conference: AAAI 2026 arXiv: 2511.11767 Code: N/A Area: Fairness in Machine Learning / Explainable AI Keywords: Kolmogorov-Arnold Networks, adversarial debiasing, fairness, adaptive penalty, college admissions

TL;DR

This paper proposes integrating Kolmogorov-Arnold Networks (KAN) into an adversarial debiasing framework, leveraging KAN's spline-based architecture to provide theoretical guarantees of Lipschitz continuity and smoothness. An adaptive \(\lambda\) update mechanism is introduced to dynamically balance fairness and accuracy. The approach achieves significant improvements on fairness metrics on the UCI college admissions dataset.

Background & Motivation

Background: Machine learning models are widely deployed in high-stakes decision-making scenarios such as college admissions and healthcare, yet historical biases embedded in training data frequently lead to discriminatory predictions against marginalized groups. In college admissions specifically, students from low-income families and first-generation college students systematically face resource inequalities.

Limitations of Prior Work:

Pre-processing methods: Modify the input data distribution to remove bias, but alter data integrity and are ill-suited for admissions scenarios requiring comprehensive evaluation.

Post-processing methods: Adjust model outputs after prediction, with limited influence on internal representations.

In-processing methods (adversarial debiasing): Incorporate fairness constraints directly during training, making them the most appropriate choice. However, existing MLP-based adversarial debiasing frameworks suffer from two core problems: - Instability in the fairness–accuracy trade-off: Zhao et al. proved that the error lower bound of a classifier satisfying exact Demographic Parity (DP) is half the difference in base rates between the two groups, rendering the fairness–accuracy competition during training unstable. - Black-box opacity: Standard neural networks cannot explicitly express feature contributions, undermining trustworthiness in sensitive contexts such as admissions.

Key Challenge: In adversarial debiasing frameworks, the selection of the fairness penalty coefficient \(\lambda\) is highly dependent on manual tuning, and a fixed \(\lambda\) throughout training cannot adapt to the dynamically shifting fairness–accuracy trade-off.

Key Insight: Replace MLP with KAN as both the classifier and adversary in the adversarial debiasing framework. KAN, grounded in the Kolmogorov-Arnold representation theorem, substitutes fixed activation functions with learnable B-spline functions, inherently providing Lipschitz continuity and \(\beta\)-smoothness to stabilize adversarial training. An adaptive \(\lambda\) update strategy is further introduced to eliminate manual tuning.

Method

Overall Architecture

The framework adopts the classical adversarial debiasing structure (min-max game), replacing both the classifier \(f\) and the adversary \(g\) with KAN networks:

• Classifier \(f\): Takes input features \(x\) and predicts label \(y\) (admitted/not admitted).
• Adversary \(g\): Takes the classifier output \(f(x)\) and attempts to infer the sensitive attribute \(z\) (low-income/non-low-income, first-generation/non-first-generation).
• Optimization objective: \(\min_{\theta_f} \max_{\theta_g} \mathcal{L}_{\mathcal{Y}}(f(x), y) - \lambda \cdot \mathcal{L}_{\mathcal{Z}}(g(f(x)), z)\)

The classifier minimizes prediction loss while maximizing the adversary's loss (preventing the adversary from inferring the sensitive attribute from predictions); the adversary attempts to minimize its own loss. \(\lambda\) controls the strength of the fairness constraint.

Key Designs

1. KAN Architecture Replacing MLP:

   • Function: Replace conventional fully connected networks with B-spline-based KAN as the classifier and adversary.
   • Mechanism: KAN represents any multivariate function as a finite superposition and composition of univariate functions: \(f(x_1, ..., x_n) = \sum_{q=1}^{2n+1} \Phi_q(\sum_{r=1}^n \phi_{q,r}(x_r))\), where each \(\phi\) is parameterized by B-splines.
   • Design Motivation: (1) Each spline function \(h(x)\) is a piecewise polynomial that is twice continuously differentiable, guaranteeing Lipschitz continuity (Lemma 1) and robustness to input perturbations. (2) The \(\beta\)-smoothness of spline functions (Lemma 2) bounds gradient variation, ensuring stable convergence in adversarial training. (3) The visualization and decomposition of spline functions provide model interpretability.

2. Adaptive \(\lambda\) Update Mechanism:

   • Function: Dynamically adjust the penalty coefficient \(\lambda\) after each training epoch based on the current fairness status.
   • Mechanism: Compute the fairness gap \(\delta = (\tau - p\%\text{-Rule}) / \tau\) (where \(\tau\) is the target fairness threshold), then update \(\lambda \leftarrow \text{clip}(\lambda + \eta \cdot \delta, 0.1, 1.0)\).
   • Design Motivation: \(\lambda\) is increased to strengthen the constraint when fairness is insufficient, and decreased to recover accuracy headroom when the target is already satisfied. The clip operation keeps \(\lambda\) within a safe range, preventing extreme values from destabilizing training.

3. Multi-Optimizer Exploration:

   • Function: Compare Adam, Optimistic Adam (OAdam), and ADOPT optimizers within the KAN framework.
   • Mechanism: OAdam uses gradient extrapolation from past steps to accelerate convergence in the min-max game; ADOPT adaptively adjusts the learning rate for non-stationary environments.
   • Design Motivation: KAN's high complexity makes training sensitive to the choice of optimizer, and different optimizers exhibit distinct behaviors in the fairness–accuracy trade-off, necessitating empirical exploration.

Loss & Training

Training alternates between two phases: 1. Freeze the classifier and train the adversary to minimize \(\mathcal{L}_{\mathcal{Z}}(g(f(x)), z)\). 2. Train the classifier to minimize \(\mathcal{L}_{\mathcal{Y}}(f(x), y) - \lambda \cdot \mathcal{L}_{\mathcal{Z}}(g(f(x)), z)\).

KAN uses B-spline order \(k=3\) (cubic splines) and supports grid refinement to progressively increase model capacity.

Key Experimental Results

Main Results (Fairness and Accuracy Comparison)

Model	Optimizer	Acc	AUROC	p%-Rule (Low-income)	p%-Rule (First-gen)	DP Gap (Low-income)	DP Gap (First-gen)
KAN(D₁)	Adam	74.92	80.27	85.79	89.65	0.028	0.035
KAN(D₁)	ADOPT	74.58	81.45	89.21	90.92	0.047	0.055
KAN(D₂)	OAdam	81.69	86.26	99.25	99.55	0.026	0.030
KAN(D₂)	ADOPT	82.51	86.68	99.25	99.70	0.032	0.037
MLP-B₁(D₁)	Adam	72.55	72.53	98.32	99.61	0.009	0.011
MLP-B₁'(D₂)	Adam	74.87	71.77	93.97	97.79	0.010	0.004
ExpGrad-B₂(D₁)	Adam	72.44	76.12	95.22	97.59	0.024	0.012
ROAD-B₃(D₁)	Adam	74.92	80.95	83.10	83.91	0.085	0.080

On the larger dataset D₂, the KAN+ADOPT configuration simultaneously achieves the highest accuracy (82.51%) and near-perfect fairness (p%-Rule 99.25%/99.70%).

Ablation Study (Effect of Spline Order)

Configuration	Key Performance	Notes
KAN \(k=3\)	Most stable convergence	Optimal balance between expressiveness and smoothness
KAN \(k=4\)	Slight improvement in p%-Rule	Higher-order splines better model the fairness boundary
KAN \(k=5\)	Convergence fluctuations	Smoothness–dimensionality trade-off; training loss spikes observed
MLP baseline	High fairness but low accuracy	Fixed \(\lambda\) strategy excessively sacrifices accuracy for fairness

Key Findings

• KAN's advantage is more pronounced on the larger dataset D₂: accuracy exceeds the MLP baseline by approximately 7.6% (82.51 vs. 74.87), while simultaneously achieving higher p%-Rule (99.25 vs. 93.97).
• The ADOPT optimizer is best suited to KAN's spline architecture, achieving the optimal balance between accuracy and fairness.
• The adaptive \(\lambda\) strategy is one of the key factors differentiating KAN from MLP baselines; the fixed \(\lambda\) used in MLP baselines tends to over-sacrifice accuracy in pursuit of fairness.
• Training loss spikes observed in KAN are an intrinsic characteristic of KAN's universal approximation property (smoothness–dimensionality trade-off) and do not affect final convergence.

Highlights & Insights

• This work is the first to introduce KAN into an adversarial debiasing framework. Beyond an architectural substitution, it provides theoretical analysis (Lipschitz continuity + \(\beta\)-smoothness) explaining why KAN is well-suited for adversarial training.
• The adaptive \(\lambda\) design is concise and practical: linear adjustment based on the gap between the p%-Rule and the target threshold, with clip-based stabilization, avoids expensive hyperparameter search.
• Validation on real admissions data rather than synthetic datasets enhances practical relevance.

Limitations & Future Work

• Only binary classification (admitted/not admitted) and binary sensitive attributes are evaluated; multi-class and intersectional sensitive attribute settings remain unexplored.
• The fairness definition is limited to Demographic Parity; conditional fairness criteria such as Equalized Odds are not considered.
• KAN's training complexity exceeds that of MLP due to B-spline coefficient learning, raising scalability concerns on large-scale data.
• Comparisons with more recent fairness methods (e.g., FairMixup, LAFTR) are absent.
• Experiments are conducted solely on the UCI admissions dataset; validation across additional domains is needed.

Related Work & Insights

• The Lipschitz continuity and smoothness analysis of KAN can be generalized to other scenarios requiring stable adversarial training, such as GAN training and robust classification.
• The adaptive penalty coefficient approach parallels the augmented Lagrangian method in constrained optimization, though the proposed mechanism is simpler and more direct.
• Combining KAN's interpretability (spline function visualization per edge) for fairness auditing is a promising research direction.

Rating

• Novelty: ⭐⭐⭐⭐
• Experimental Thoroughness: ⭐⭐⭐
• Writing Quality: ⭐⭐⭐⭐
• Value: ⭐⭐⭐⭐

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