Dataset for "A Guarded Trainable Exponent Operator: Identifiability, Numerical Robustness, and Parameter-Efficient Extrapolation"

Published: 22 September 2026| Version 1 | DOI: 10.17632/s94zjz6tps.1
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Description

Dataset for "A Guarded Trainable Exponent Operator: Identifiability, Numerical Robustness, and Parameter-Efficient Extrapolation" Overview: This dataset provides complete experimental logs, numerical audit traces, benchmark results, real-world evaluations, and Python reproduction scripts for the article "A Guarded Trainable Exponent Operator: Identifiability, Numerical Robustness, and Parameter-Efficient Extrapolation" (Chang et al., 2026). It supports full empirical auditability for the guarded exponent operator (ε = 10^-8, L = 30). Directory Contents: 1. synthetic_benchmarks/ - primary_fits/: Results comparing individual, shared, and fixed exponents (n ∈ {32..256}, σ ∈ {0.0..0.20}) across 10,368 primary fits. - diagnostic_fits/: 3,096 diagnostic fits analyzing structural misspecifications. - metrics_summary.csv: Aggregated RMSE, nMAE, and Log-OLS loss metrics. 2. numerical_audits/ - precision_audits/: Traces of 93,312 forward test cases across FP64, FP32, and FP16 modes, demonstrating 100% finite-value execution reliability (zero NaN/Inf crashes). - safeguard_ablation/: Grid evaluations for floor (ε ∈ [10^-12, 10^-4]) and cap (L ∈ [1, 2]). 3. real_world_evaluations/ - yacht_hydrodynamics/: Inputs and Leave-One-Hull-Out (LOHO) cross-validation outputs for 308 observations across 22 hulls. - nist_chwirut2/: Ultrasonic benchmark data (54 observations across 22 distances). 4. baseline_comparisons/ - mlp_baselines/: Benchmarks for 16-unit and 64-unit MLPs (L-BFGS-B and Adam up to 2,000 epochs). - ginn_lp_baselines/: Comparisons against GINN-LP (AAAI 2024), including boundary stability logs. 5. code_and_scripts/ - guarded_exponent_core.py: Standalone Python/PyTorch guarded operator core. - reproduce_synthetic_experiments.py: Script to re-run primary synthetic fitting tasks. - reproduce_numerical_audit.py: Script executing the 93,312-case forward numerical audit. - reproduce_real_world_benchmarks.py: Script running LOHO validation on Yacht and NIST benchmarks. Protocol & Reproduction: - Optimization: Trained via L-BFGS-B (max 300 steps, func tol 10^-12, grad tol 10^-8). - Safeguards: Input floor ε = 10^-8, log-linear bounds clipped to [-30, 30] (L = 30). - Requirements: Python 3.12+, NumPy, SciPy, PyTorch. - Execution: Unzip archive, run `pip install numpy scipy torch pandas`, then execute: `python code_and_scripts/reproduce_numerical_audit.py` `python code_and_scripts/reproduce_synthetic_experiments.py` `python code_and_scripts/reproduce_real_world_benchmarks.py` Associated Manuscript: Title: A Guarded Trainable Exponent Operator: Identifiability, Numerical Robustness, and Parameter-Efficient Extrapolation Authors: Jen-Hsiang Chang, Der-Shan Sun, Hsin-Hou Chang (hhchang@mail.tcu.edu.tw)

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Steps to reproduce

Steps to Reproduce the Experimental Findings and Audits 1. Environment Setup & Dependencies Ensure Python 3.12 or higher is installed on a standard CPU or workstation. Install the required Python packages using pip: pip install numpy scipy torch pandas matplotlib 2. Data Archive Unpacking Download and extract the dataset ZIP archive. Ensure the extracted folder maintains the following directory structure: - code_and_scripts/ (Reproduction Python scripts & core operator logic) - synthetic_benchmarks/ (Synthetic power-law fitting raw logs & metrics) - numerical_audits/ (93,312-case forward execution trace logs) - real_world_evaluations/ (Yacht Hydrodynamics & NIST Chwirut2 datasets) - baseline_comparisons/ (MLP and GINN-LP baseline execution logs) 3. Reproducing Forward Numerical Stability Audits To re-run the 93,312-case forward numerical audit testing execution reliability across FP64, FP32, and FP16 precision modes: python code_and_scripts/reproduce_numerical_audit.py - Expected Outcome: Verifies 100% finite-value execution without non-finite (NaN/Inf) overflows or zero-crossing crashes under the guarded floor (ε = 10^-8) and log-linear cap (L = 30). 4. Reproducing Synthetic Benchmark Experiments To re-execute the primary synthetic fitting benchmark tasks across varying sample sizes (n ∈ {32, 64, 128, 256}) and noise levels (σ ∈ {0.0, 0.05, 0.10, 0.20}): python code_and_scripts/reproduce_synthetic_experiments.py - Expected Outcome: Generates primary fit metrics comparing individual, shared, and fixed exponents, producing an OOD normalized MAE of ~0.089 for individual trainable exponents. 5. Reproducing Real-World Physical Benchmarks To run the Leave-One-Hull-Out (LOHO) cross-validation on Yacht Hydrodynamics (22 hulls) and NIST Chwirut2 (22 distances): python code_and_scripts/reproduce_real_world_benchmarks.py - Expected Outcome: Outputs cross-validation loss metrics and out-of-fold predictions matching the main text figures. 6. Output Verification & Comparison All generated output logs, fitted parameters, and figure plots will be saved to an automatically created `reproduction_outputs/` folder. Compare the generated summary CSV files against `synthetic_benchmarks/metrics_summary.csv` to confirm exact statistical replication. Hardware / Execution Time Note: All reproduction scripts run on a single-threaded standard CPU architecture. Complete execution of all reproduction steps takes approximately 1–2 minutes.

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Computer Science, Artificial Intelligence

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