Marginal Magnitude Rather than Temporal Structure: An Empirical Reassessment of Multi-Generator Chaos-Based Robustness Testing for IoT Intrusion Detection
4 affiliations
- 1School of Computer Science, UPES, Dehradun 248007, Uttarakhand, India
- 2Data Science Cluster, School of Computer Science, UPES, Dehradun 248007, Uttarakhand, India
- 3Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
- 4Department of Archives and Communication, Center of Documentation and Administrative Communication, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Abstract
Chaos injection–perturbing numerical flow features with a sequence drawn from a chaotic system–has been proposed as a robustness stress test for IoT intrusion detection, but published instances fix a single generator, a single train/test split, and a small classifier pair. We generalize the injection framework to an arbitrary chaotic source and evaluate six generators (logistic, tent, Hénon, Lorenz, Rössler, Chua) against six classifier families across four injection-severity scenarios and eight train/test splits, on a class-balanced working set of 239,981 flows (sub-sampled from 303,082 flows drawn per directory) from all 34 class directories of the public CICIoT2023 corpus. Across 1152 evaluation cells, three findings emerge. First, generator choice produces a statistically decisive but small effect: pooled F1 degradation spans only 5.57–6.11% across the six generators (a factor of 1.10), and the discrete-versus-continuous distinction has no explanatory value. Second, lag-1 autocorrelation does not predict degradation (r=+0.209, p=0.692), whereas the marginal magnitude of the shaped perturbation does (mean |ψ|: r=+0.974, p=0.001). Because the operator applies its sequence index-wise to randomly enumerated test rows, we prove that, averaged over that random enumeration, the distribution of the evaluation outcome depends on the sequence only through its empirical marginal (Proposition 1); for the single fixed enumeration of a given split, no such invariance holds in general, and the claim there is empirical. Under the protocol tested, chaos injection therefore behaves as an amplitude stress test rather than a test of chaotic structure. A 4608-cell control grid provides the empirical evidence: permuting the chaotic sequence, or replacing it with i.i.d. noise of matched marginal, changes mean degradation by −0.002 and +0.005 percentage points, inside a pre-declared equivalence bound of ±0.25 pp; matching all six generators to a common empirical CDF collapses the between-generator spread by 71.6% but leaves a small, statistically detectable residual generator effect. Third, the three tree ensembles are the least robust family (7.75% versus 3.81%; Wilcoxon p=0.0078, paired t-test p=2.9×10−8), reversing the prior single-generator ranking, and the ranking is itself conditional on injection severity. This family ordering is not a threshold artifact: it reproduces on threshold-free AUC degradation (6.80% versus 3.44%) and on absolute F1 loss in percentage points (6.56 versus 3.10), and a cluster-respecting reanalysis that treats the eight seeds and six classifiers as clustered rather than independent reduces the generator effect to a single high-amplitude generator separating from the other five. Code, seeds, and raw logs are released openly.
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BibTeX
@article{sinha2026marginal,
title = {{Marginal Magnitude Rather than Temporal Structure: An Empirical Reassessment of Multi-Generator Chaos-Based Robustness Testing for IoT Intrusion Detection}},
author = {Keshav Sinha and Sanoj Kumar and Musrrat Ali and Abdul Rahaman Wahab Sait},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193596},
url = {https://www.mdpi.com/2227-7390/14/19/3596},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Marginal Magnitude Rather than Temporal Structure: An Empirical Reassessment of Multi-Generator Chaos-Based Robustness Testing for IoT Intrusion Detection
AU - Keshav Sinha
AU - Sanoj Kumar
AU - Musrrat Ali
AU - Abdul Rahaman Wahab Sait
PY - 2026
DA - 2026/10/03
JO - Mathematics
DO - 10.3390/math14193596
UR - https://www.mdpi.com/2227-7390/14/19/3596
AB - Chaos injection–perturbing numerical flow features with a sequence drawn from a chaotic system–has been proposed as a robustness stress test for IoT intrusion detection, but published instances fix a single generator, a single train/test split, and a small classifier pair. We generalize the injection framework to an arbitrary chaotic source and evaluate six generators (logistic, tent, Hénon, Lorenz, Rössler, Chua) against six classifier families across four injection-severity scenarios and eight train/test splits, on a class-balanced working set of 239,981 flows (sub-sampled from 303,082 flows drawn per directory) from all 34 class directories of the public CICIoT2023 corpus. Across 1152 evaluation cells, three findings emerge. First, generator choice produces a statistically decisive but small effect: pooled F1 degradation spans only 5.57–6.11% across the six generators (a factor of 1.10), and the discrete-versus-continuous distinction has no explanatory value. Second, lag-1 autocorrelation does not predict degradation (r=+0.209, p=0.692), whereas the marginal magnitude of the shaped perturbation does (mean |ψ|: r=+0.974, p=0.001). Because the operator applies its sequence index-wise to randomly enumerated test rows, we prove that, averaged over that random enumeration, the distribution of the evaluation outcome depends on the sequence only through its empirical marginal (Proposition 1); for the single fixed enumeration of a given split, no such invariance holds in general, and the claim there is empirical. Under the protocol tested, chaos injection therefore behaves as an amplitude stress test rather than a test of chaotic structure. A 4608-cell control grid provides the empirical evidence: permuting the chaotic sequence, or replacing it with i.i.d. noise of matched marginal, changes mean degradation by −0.002 and +0.005 percentage points, inside a pre-declared equivalence bound of ±0.25 pp; matching all six generators to a common empirical CDF collapses the between-generator spread by 71.6% but leaves a small, statistically detectable residual generator effect. Third, the three tree ensembles are the least robust family (7.75% versus 3.81%; Wilcoxon p=0.0078, paired t-test p=2.9×10−8), reversing the prior single-generator ranking, and the ranking is itself conditional on injection severity. This family ordering is not a threshold artifact: it reproduces on threshold-free AUC degradation (6.80% versus 3.44%) and on absolute F1 loss in percentage points (6.56 versus 3.10), and a cluster-respecting reanalysis that treats the eight seeds and six classifiers as clustered rather than independent reduces the generator effect to a single high-amplitude generator separating from the other five. Code, seeds, and raw logs are released openly.
SN - 2227-7390
ER -