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arxiv: 2505.23383 · v4 · submitted 2025-05-29 · 💻 cs.LG

Automated Modeling Method for Pathloss Model Discovery

Ahmad Anaqreh , Shih-Kai Chou , Bla\v{z} Bertalani\v{c} , Mihael Mohor\v{c}i\v{c} , Thomas Lagkas , Carolina Fortuna This is my paper

Pith reviewed 2026-05-19 13:11 UTC · model grok-4.3

classification 💻 cs.LG
keywords path loss modelingautomated model discoveryKolmogorov-Arnold NetworksDeep Symbolic Regressionwireless propagation5G networksinterpretable machine learning
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The pith

Automated methods using Kolmogorov-Arnold Networks and Deep Symbolic Regression discover path loss models with up to 75 percent lower prediction error than traditional statistical techniques.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that two AI techniques can automate the creation of path loss models for wireless signals while keeping the models interpretable. Traditional approaches depend on fixed statistical formulas that often fall short as wireless networks expand into new environments for 5G and beyond. Deep Symbolic Regression produces compact, fully readable equations, and Kolmogorov-Arnold Networks deliver high accuracy with partial interpretability at two different levels. Tests on both synthetic data and real measurements indicate that these automated models achieve coefficients of determination near one and cut errors substantially.

Core claim

Kolmogorov-Arnold Networks reach a coefficient of determination close to one with low prediction error, Deep Symbolic Regression yields compact models of moderate accuracy, and both automated approaches outperform conventional statistical methods by reducing prediction errors by as much as 75 percent on the examined cases.

What carries the argument

Kolmogorov-Arnold Networks and Deep Symbolic Regression, which automate the formulation, evaluation, and refinement of path loss models to deliver both accuracy and interpretability.

If this is right

  • Path loss models can be generated and updated automatically rather than derived by hand for each new environment.
  • Wireless system designers gain access to models that are both more accurate and more transparent than standard statistical fits.
  • The 75 percent error reduction on tested data would directly improve link-budget calculations and network planning.
  • Two levels of interpretability from Kolmogorov-Arnold Networks allow users to inspect both local and global behavior of the model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same automation pipeline could be applied to related propagation problems such as delay spread or interference modeling.
  • Combining the compact equations from Deep Symbolic Regression with the accuracy of Kolmogorov-Arnold Networks might produce hybrid models that are both small and precise.
  • Wider adoption would reduce the time required to characterize new frequency bands or urban scenarios for future wireless standards.

Load-bearing premise

The synthetic and real-world datasets used for training and evaluation are representative of the target propagation environments and the observed performance gains extend beyond the specific cases shown.

What would settle it

Apply the models discovered by the two methods to a fresh collection of real-world propagation measurements from an unseen environment and check whether the error reduction stays near 75 percent.

Figures

Figures reproduced from arXiv: 2505.23383 by Ahmad Anaqreh, Bla\v{z} Bertalani\v{c}, Carolina Fortuna, Mihael Mohor\v{c}i\v{c}, Shih-Kai Chou, Thomas Lagkas.

Figure 1
Figure 1. Figure 1: The flow diagram of AutoPL modeling method. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The flow diagram of developing a PL model using KANs. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: KAN model performance as a function of grid size, steps and lambda. The conclusions for indoor and outdoor models [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The flow diagram of developing a PL model using DSR. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: DSR model performance as a function of policy and samples. The conclusions for indoor and outdoor models are [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The predicted values by the KAN model vs the actual [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: The learned KAN [4,4,1] network for approximating [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: The predicted values by the KAN model vs the actual [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: The predicted values by the KAN model vs the actual [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The learned KAN [4,1] network for approximating [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The predicted values by the KAN model vs the actual [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The learned KAN [3,1] network for approximating [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
read the original abstract

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 interpretability 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 formulation, evaluation, and refinement of the model, facilitating the discovery of the model. We examine 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 the coefficient of determination value R^2 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an automated approach to pathloss model discovery for wireless propagation (with emphasis on 5G) that employs Deep Symbolic Regression for fully interpretable models and Kolmogorov-Arnold Networks for two-level interpretability. Both methods are evaluated on two synthetic and two real-world datasets; the central claims are that KAN reaches R² values close to 1 with minimal error, DSR yields compact models of moderate accuracy, and the automated techniques outperform traditional statistical methods by up to 75% error reduction while preserving interpretability.

Significance. If the performance and generalization claims prove robust, the work would offer a practical, interpretable alternative to black-box neural models for propagation modeling, potentially accelerating accurate model discovery for next-generation wireless systems. The explicit focus on interpretability and the demonstration of error reduction on both synthetic and measured data are strengths that align with needs in the field.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Experimental Evaluation): the headline performance figures (R² near 1, 75% error reduction) are reported without any description of train/test splits, cross-validation procedure, baseline implementation details, or statistical significance testing. Because the methods are supervised fitting procedures, the absence of these controls creates a moderate risk that the reported gains are inflated by overfitting or selection effects.
  2. [§3 and §4] §3 (Datasets) and §4: only four datasets (two synthetic, two real-world) are used, with no cross-environment validation, sensitivity analysis to frequency or scenario choice, or external hold-out sets. The claim that automated methods generalize and outperform traditional approaches therefore rests on the untested assumption that these particular cases are representative of the broader range of propagation environments.
minor comments (2)
  1. [§4] Clarify the exact traditional baseline models (e.g., which empirical formulas or statistical fits) and their parameter-fitting procedure so that the 75% error-reduction figure can be reproduced.
  2. [Figures in §4] Add error bars or confidence intervals to any prediction plots and report the number of independent runs for the stochastic components of DSR and KAN training.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help improve the clarity and rigor of our experimental presentation. We address each major comment below and outline the planned revisions.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experimental Evaluation): the headline performance figures (R² near 1, 75% error reduction) are reported without any description of train/test splits, cross-validation procedure, baseline implementation details, or statistical significance testing. Because the methods are supervised fitting procedures, the absence of these controls creates a moderate risk that the reported gains are inflated by overfitting or selection effects.

    Authors: We agree that explicit details on data partitioning, validation procedures, baseline implementations, and significance testing are necessary to allow readers to assess potential overfitting. The current manuscript emphasizes the model discovery process and resulting accuracy metrics but omits these methodological specifics. In the revised version we will expand §4 with a dedicated subsection describing the train/test split ratios applied to each dataset, the cross-validation approach, the exact parameter settings and implementations used for the traditional statistical baselines, and the outcomes of appropriate statistical tests (e.g., paired t-tests) on the error reductions. These additions will directly address the concern about inflated performance claims. revision: yes

  2. Referee: [§3 and §4] §3 (Datasets) and §4: only four datasets (two synthetic, two real-world) are used, with no cross-environment validation, sensitivity analysis to frequency or scenario choice, or external hold-out sets. The claim that automated methods generalize and outperform traditional approaches therefore rests on the untested assumption that these particular cases are representative of the broader range of propagation environments.

    Authors: We acknowledge that the evaluation is confined to four datasets and that broader cross-environment testing would strengthen generalization statements. The selected datasets were chosen to span controlled synthetic cases and measured urban/suburban scenarios at relevant 5G frequencies. In the revision we will augment §3 with additional characterization of each dataset (frequency, distance ranges, environment types) and insert a sensitivity analysis subsection in §4 that varies frequency and scenario parameters within the existing data. We will also add an explicit limitations paragraph discussing the representativeness of the chosen environments and the value of future multi-environment studies. Expanding to entirely new external hold-out sets or large-scale cross-validation campaigns, however, would require substantial new measurement campaigns that lie beyond the scope of the present work. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected in the derivation or evaluation chain

full rationale

The paper applies established Deep Symbolic Regression and Kolmogorov-Arnold Network techniques to discover pathloss models, then reports empirical performance (R^2, error reduction) on two synthetic and two real-world datasets. No equations, self-definitional steps, or load-bearing self-citations appear in the provided abstract or described workflow that would reduce a claimed prediction or result back to the input data or prior author work by construction. The methods are treated as black-box or symbolic fitting procedures whose outputs are evaluated against the same data sources, but without explicit reduction of the reported metrics to the fitting process itself or any uniqueness theorem imported from self-citation. The derivation chain remains self-contained: model discovery follows from the cited AI algorithms, and performance claims rest on standard supervised evaluation rather than tautological re-labeling of inputs as outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard machine-learning assumptions about data representativeness and the ability of symbolic or network-based approximators to capture propagation physics; no new physical entities are introduced.

free parameters (1)
  • network hyperparameters and regression search parameters
    Architecture depth, width, and symbolic regression hyperparameters are chosen or tuned to achieve the reported fits on the given datasets.
axioms (1)
  • domain assumption Path loss behavior can be adequately captured by a deterministic function of distance and environmental variables that is discoverable from finite measurement sets.
    This underpins both the symbolic regression and network-based modeling pipelines.

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