Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias

Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs. Existing approaches are MLP- or flow-based and lack per-edge functional transparency; the only Kolmogorov--Arnold Network (KAN) variant with monotonicity, MonoKAN, enforces the constraint only on a restricted parameter subset and requires a projection-style training procedure. We close this gap with \textbf{MKAN}, a KAN with hard monotonicity guaranteed for \emph{all} parameter values via exponential reparameterization of B-spline coefficients, positive edge weights, and a monotone base activation. Training reduces to standard unconstrained gradient descent. Our headline theoretical contribution is a \emph{representation-cost} theorem: any $C^K, K >0$ feature extractor inducing a ball-shaped semantic-neighborhood partition admits a monotone realization of the equivalent neighborhood structure at $N' = N^* + k \le 2N^*$, where $k$ is the number of non-monotone coordinates of the original. The bound is architecture-agnostic and gives a principled sizing rule for monotone encoders. Empirically, MKAN is competitive with state-of-the-art monotone NNs on the SMM/ICML-2024 benchmark while being the only method that combines hard unconstrained monotonicity with KAN's per-edge functional transparency; the $2N^*$ prediction is validated in a self-supervised feature-size sweep on four real datasets, and on a controlled monotone-generative dataset MKAN recovers ground-truth factors with substantially higher Spearman alignment than KAN, MLP, and linear baselines.

Design Principles of Zero-Shot Self-Supervised Unknown Emitter Detectors

The proliferation of wireless devices necessitates more robust and reliable emitter detection and identification for critical tasks such as spectrum management and network security. Existing studies exploring methods for unknown emitters identification, however, are typically hindered by their dependence on labeled or proprietary datasets, unrealistic assumptions (e.g. all samples with identical transmitted messages), or deficiency of systematic evaluations across different architectures and design dimensions. In this work, we present a comprehensive evaluation of unknown emitter detection systems across key aspects of the design space, focusing on data modality, learning approaches, and feature learning modules. We demonstrate that prior self-supervised, zero-shot emitter detection approaches commonly use datasets with identical transmitted messages. To address this limitation, we propose a 2D-Constellation data modality for scenarios with varying messages, achieving up to a 40\% performance improvement in ROC-AUC, NMI, and F1 metrics compared to conventional raw I/Q data. Furthermore, we introduce interpretable Kolmogorov-Arnold Networks (KANs) to enhance model transparency, and a Singular Value Decomposition (SVD)-based initialization procedure for feature learning modules operating on sparse 2D-Constellation data, which improves the performance of Deep Clustering approaches by up to 40\% across the same metrics comparing to the modules without SVD initialization. We evaluate all data modalities and learning modules across three learning approaches: Deep Clustering, Auto Encoder and Contrastive Learning.