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.

The Ringelmann Effect in Multi-Agent LLM Systems: A Scaling Law for Effective Team Size

Inference-time multi-agent LLM scaling lacks a shared unit: counting nominal agents conflates cost with independent evidence. We derive a two-parameter scaling law $R(N) = N_\text{eff}/N = 1/(1+c(N-1)N^{-β})$ where the regime exponent $β$ classifies any configuration into one of three asymptotic regimes -- hard-ceiling at $1/c$ ($β= 0$), sublinear at $N^β/c$ ($0 < β< 1$), or linear ($β\ge 1$), and a mean-field theorem predicts that peer count $k$ and rounds $τ$ during agent debate enter the dynamics only through their product $kτ$. The law applies at two levels: answer diversity and correctness redundancy. Across 44 (model $\times$ task $\times$ condition) cells spanning peer debate, self-correction, random-noise placebo, self-consistency, three open-weight families (Qwen, Llama, Ministral) at scales from 7B to 32B with a frontier API check (Gemini), thinking models, heterogeneous teams, and sparse communication, the functional form fits every condition at $R^2 > 0.99$; only $(c, β)$ shifts. On free-form math, dense peer influence collapses the answer-level regime from sublinear into hard-ceiling; correctness-level fits remain hard-ceiling throughout. Three findings have practical implications. \emph{(i)}~Thirty dense debating agents produce no more answer diversity than one on MMLU-Hard. \emph{(ii)}~A noise placebo tracks self-correction on free-form math and at $4\times$ scale, so within homogeneous teams the gain commonly attributed to ``debate'' comes from re-evaluation, not peer content. \emph{(iii)}~A single $N \le 5$ pilot predicts the $N=30$ structural ceiling, and within the configurations tested only architectural diversity (heterogeneous teams) lowers $c$ and escapes the hard-ceiling regime, communication-mode interventions do not.

Learned Elevation Models as a Lightweight Alternative to LiDAR for Radio Environment Map Estimation

Next-generation wireless systems such as 6G operate at higher frequency bands, making signal propagation highly sensitive to environmental factors such as buildings and vege- tation. Accurate Radio Environment Map (REM) estimation is therefore increasingly important for effective network planning and operation. Existing methods, from ray-tracing simulators to deep learning generative models, achieve promising results but require detailed 3D environment data such as LiDAR-derived point clouds, which are costly to acquire, several gigabytes per km2 in size, and quickly outdated in dynamic environments. We propose a two-stage framework that eliminates the need for 3D data at inference time: in the first stage, a learned estimator predicts elevation maps directly from satellite RGB imagery, which are then fed alongside antenna parameters into the REM estimator in the second stage. Across existing CNN- based REM estimation architectures, the proposed approach improves RMSE by up to 7.8% over image-only baselines, while operating on the same input feature space and requiring no 3D data during inference, offering a practical alternative for scalable radio environment modelling.

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.

SABER: Symbolic Regression-based Angle of Arrival and Beam Pattern Estimator

Accurate Angle-of-arrival (AoA) estimation is essential for next-generation wireless communication systems to enable reliable beamforming, high-precision localization, and integrated sensing. Unfortunately, classical high-resolution techniques require multi-element arrays and extensive snapshot collection, while generic Machine Learning (ML) approaches often yield black-box models that lack physical interpretability. To address these limitations, we propose a Symbolic Regression (SR)-based ML framework. Namely, Symbolic Regression-based Angle of Arrival and Beam Pattern Estimator (SABER), a constrained symbolic-regression framework that automatically discovers closed-form beam pattern and AoA models from path loss measurements with interpretability. SABER achieves high accuracy while bridging the gap between opaque ML methods and interpretable physics-driven estimators. First, we validate our approach in a controlled free-space anechoic chamber, showing that both direct inversion of the known $\cos^n$ beam and a low-order polynomial surrogate achieve sub-0.5 degree Mean Absolute Error (MAE). A purely unconstrained SR method can further reduce the error of the predicted angles, but produces complex formulas that lack physical insight. Then, we implement the same SR-learned inversions in a real-world, Reconfigurable Intelligent Surface (RIS)-aided indoor testbed. SABER and unconstrained SR models accurately recover the true AoA with near-zero error. Finally, we benchmark SABER against the Cram\'er-Rao Lower Bounds (CRLBs). Our results demonstrate that SABER is an interpretable and accurate alternative to state-of-the-art and black-box ML-based methods for AoA estimation.

Deep Temporal Graph Networks for Real-Time Correction of GNSS Jamming-Induced Deviations

Global Navigation Satellite Systems (GNSS) are increasingly disrupted by intentional jamming, degrading availability precisely when positioning and timing must remain operational. We address this by reframing jamming mitigation as dynamic graph regression and introducing a receiver-centric deep temporal graph network that predicts, and thus corrects, the receivers horizontal deviation in real time. At each 1 Hz epoch, the satellite receiver environment is represented as a heterogeneous star graph (receiver center, tracked satellites as leaves) with time varying attributes (e.g., SNR, azimuth, elevation, latitude/longitude). A single layer Heterogeneous Graph ConvLSTM (HeteroGCLSTM) aggregates one hop spatial context and temporal dynamics over a short history to output the 2D deviation vector applied for on the fly correction. We evaluate on datasets from two distinct receivers under three jammer profiles, continuous wave (cw), triple tone (cw3), and wideband FM, each exercised at six power levels between -45 and -70 dBm, with 50 repetitions per scenario (prejam/jam/recovery). Against strong multivariate time series baselines (MLP, uniform CNN, and Seq2Point CNN), our model consistently attains the lowest mean absolute error (MAE). At -45 dBm, it achieves 3.64 cm (GP01/cw), 7.74 cm (GP01/cw3), 4.41 cm (ublox/cw), 4.84 cm (ublox/cw3), and 4.82 cm (ublox/FM), improving to 1.65-2.08 cm by -60 to -70 dBm. On mixed mode datasets pooling all powers, MAE is 3.78 cm (GP01) and 4.25 cm (ublox10), outperforming Seq2Point, MLP, and CNN. A split study shows superior data efficiency: with only 10\% training data our approach remains well ahead of baselines (20 cm vs. 36-42 cm).

Data Model Design for Explainable Machine Learning-based Electricity Applications

The transition from traditional power grids to smart grids, significant increase in the use of renewable energy sources, and soaring electricity prices has triggered a digital transformation of the energy infrastructure that enables new, data driven, applications often supported by machine learning models. However, the majority of the developed machine learning models rely on univariate data. To date, a structured study considering the role meta-data and additional measurements resulting in multivariate data is missing. In this paper we propose a taxonomy that identifies and structures various types of data related to energy applications. The taxonomy can be used to guide application specific data model development for training machine learning models. Focusing on a household electricity forecasting application, we validate the effectiveness of the proposed taxonomy in guiding the selection of the features for various types of models. As such, we study of the effect of domain, contextual and behavioral features on the forecasting accuracy of four interpretable machine learning techniques and three openly available datasets. Finally, using a feature importance techniques, we explain individual feature contributions to the forecasting accuracy.

Automated Modeling Method for Pathloss Model Discovery

Modeling propagation is the cornerstone for designing and optimizing next-generation wireless systems, with a particular emphasis on 5G and beyond era. Traditional modeling methods have long relied on statistic-based techniques to characterize propagation behavior across different environments. With the expansion of wireless communication systems, there is a growing demand for methods that guarantee the accuracy and interoperability of modeling. Artificial intelligence (AI)-based techniques, in particular, are increasingly being adopted to overcome this challenge, although the interpretability is not assured with most of these methods. Inspired by recent advancements in AI, this paper proposes a novel approach that accelerates the discovery of path loss models while maintaining interpretability. The proposed method automates the model formulation, evaluation, and refinement, facilitating model discovery. We evaluate two techniques: one based on Deep Symbolic Regression, offering full interpretability, and the second based on Kolmogorov-Arnold Networks, providing two levels of interpretability. Both approaches are evaluated on two synthetic and two real-world datasets. Our results show that Kolmogorov-Arnold Networks achieve R^2 values close to 1 with minimal prediction error, while Deep Symbolic Regression generates compact models with moderate accuracy. Moreover, on the selected examples, we demonstrate that automated methods outperform traditional methods, achieving up to 75% reduction in prediction errors, offering accurate and explainable solutions with potential to increase the efficiency of discovering next-generation path loss models.

A Network Science Approach to Granular Time Series Segmentation

Time series segmentation (TSS) is one of the time series (TS) analysis techniques, that has received considerably less attention compared to other TS related tasks. In recent years, deep learning architectures have been introduced for TSS, however their reliance on sliding windows limits segmentation granularity due to fixed window sizes and strides. To overcome these challenges, we propose a new more granular TSS approach that utilizes the Weighted Dual Perspective Visbility Graph (WDPVG) TS into a graph and combines it with a Graph Attention Network (GAT). By transforming TS into graphs, we are able to capture different structural aspects of the data that would otherwise remain hidden. By utilizing the representation learning capabilities of Graph Neural Networks, our method is able to effectively identify meaningful segments within the TS. To better understand the potential of our approach, we also experimented with different TS-to-graph transformations and compared their performance. Our contributions include: a) formulating the TSS as a node classification problem on graphs; b) conducting an extensive analysis of various TS- to-graph transformations applied to TSS using benchmark datasets from the TSSB repository; c) providing the first detailed study on utilizing GNNs for analyzing graph representations of TS in the context of TSS; d) demonstrating the effectiveness of our method, which achieves an average F1 score of 0.97 across 59 diverse TSS benchmark datasets; e) outperforming the seq2point baseline method by 0.05 in terms of F1 score; and f) reducing the required training data compared to the baseline methods.

MRM3: Machine Readable ML Model Metadata

As the complexity and number of machine learning (ML) models grows, well-documented ML models are essential for developers and companies to use or adapt them to their specific use cases. Model metadata, already present in unstructured format as model cards in online repositories such as Hugging Face, could be more structured and machine readable while also incorporating environmental impact metrics such as energy consumption and carbon footprint. Our work extends the existing State of the Art by defining a structured schema for ML model metadata focusing on machine-readable format and support for integration into a knowledge graph (KG) for better organization and querying, enabling a wider set of use cases. Furthermore, we present an example wireless localization model metadata dataset consisting of 22 models trained on 4 datasets, integrated into a Neo4j-based KG with 113 nodes and 199 relations.