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arxiv: 2509.09758 · v4 · submitted 2025-09-11 · 📊 stat.AP

A Path Signature Framework for Detecting Creative Fatigue in Digital Advertising

Charles Shaw This is my paper

Pith reviewed 2026-05-18 17:25 UTC · model grok-4.3

classification 📊 stat.AP
keywords creative fatiguepath signatureschange detectiondigital advertisingrough path theoryCTR monitoringperformance trajectoriesgeometric features
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The pith

Path signatures detect creative fatigue in digital advertising by capturing geometric changes in performance trajectories.

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

The paper introduces a framework that embeds daily advertising performance data, such as click-through rates, as continuous paths in a geometric space. It then uses truncated log-signatures from rough path theory to represent these paths and detect when fatigue sets in through shifts in trend, volatility, or non-linear patterns. This approach aims to provide earlier warnings than traditional statistical methods focused only on averages or variances. A sympathetic reader would care because faster detection of declining ad effectiveness can reduce wasted spending on underperforming creatives. The evaluation uses synthetic data mimicking real impression and CTR noise to test lead times and alert accuracy.

Core claim

The paper claims that advertising performance trajectories can be embedded as paths and represented by truncated (log-)signatures, allowing detection of creative fatigue as geometric change in trend, volatility, and non-linear dynamics beyond simple mean or variance shifts, with an explicit quantification of performance loss relative to a benchmark and evaluation on synthetic panel data using an operational ground truth based on sustained deterioration from a recent-best baseline.

What carries the argument

The truncated log-signature of the embedded performance path, which serves as a geometric feature representation that encodes iterated integrals to capture the shape and dynamics of the trajectory for change detection.

If this is right

  • Changes in non-linear dynamics of CTR can be detected in addition to mean shifts.
  • Lead-time and alert-burden metrics can be reported for practical monitoring.
  • Performance loss can be quantified relative to a benchmark period.
  • The method scales linearly with time-series length for fixed signature depth.
  • Sensitivity analysis over tuning parameters shows robustness.

Where Pith is reading between the lines

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

  • Applying this geometric method to other marketing metrics like conversion rates could improve overall campaign monitoring.
  • Integration with automated creative testing platforms might enable dynamic rotation based on signature-detected fatigue.
  • Future work could compare signature features against standard time-series anomaly detection algorithms on real datasets.
  • Extending the paths to include multiple dimensions like impressions and costs simultaneously could capture more complex fatigue patterns.

Load-bearing premise

The synthetic panel dataset accurately mimics realistic impression volumes and noisy day-to-day CTR dynamics, and the operational ground truth for fatigue onset based on a noise-robust CTR estimate and sustained deterioration relative to a recent-best baseline is a valid proxy for actual fatigue.

What would settle it

Running the detector on a real-world proprietary dataset with marketing team-confirmed fatigue events and measuring whether it provides statistically significant earlier alerts or lower false positive rates compared to mean-shift detectors.

Figures

Figures reproduced from arXiv: 2509.09758 by Charles Shaw.

Figure 1
Figure 1. Figure 1: Classic Wear-Out: A period of stable performance followed by a long, gradual decline. [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Sharp Drop: A sudden, significant drop in performance after a stable period. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fatigue and Recovery: A period of decline followed by a partial performance recovery. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Volatile Decline: A general downward trend characterised by high day-to-day volatility. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Multi-Stage Decline: A stepped decline with multiple distinct change points and periods of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Non-Continuous Data (Sharp Drop): Demonstrates the method’s robustness to significant gaps [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Non-Continuous Data (Gradual Decline): The signature method correctly identifies the change [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

This paper introduces a signature-based framework for detecting advertising creative fatigue using path signatures, a geometric representation from rough path theory. Creative fatigue -- the degradation of creative effectiveness under repeated exposure -- is operationally important in digital marketing because delayed detection can translate directly into avoidable opportunity cost. We reframe fatigue monitoring as a geometric change detection problem: advertising performance trajectories are embedded as paths and represented by truncated (log-)signatures, enabling detection of changes in trend, volatility, and non-linear dynamics beyond simple mean or variance shifts. We further connect statistical detection to managerial decision-making via an explicit quantification of performance loss relative to a benchmark period. Because proprietary production data cannot be released, we evaluate the proposed framework on a synthetic panel dataset designed to mimic realistic impression volumes and noisy day-to-day CTR dynamics. We define observed CTR as the realised binomial rate $CTR_t := C_t/I_t$ using daily clicks $C_t$ and impressions $I_t$. The accompanying CSV also contains a pre-computed CTR field (e.g., due to rounding or upstream derivation), but all modelling and evaluation in this paper use $C_t/I_t$. Crucially, the dataset does not include injected changepoints; we therefore define an operational ground truth for ``fatigue onset'' based on a noise-robust CTR estimate and a sustained deterioration relative to a recent-best baseline. We report lead-time (early warning) and alert-burden metrics under this operational definition, and provide a sensitivity analysis over the detector's primary tuning parameters. The methodology scales linearly in time-series length for fixed signature depth and is suitable for monitoring large creative portfolios.

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 paper introduces a path signature framework from rough path theory to detect creative fatigue in digital advertising. Performance trajectories are embedded as paths and represented by truncated (log-)signatures to identify changes in trend, volatility, and non-linear dynamics. Evaluation uses a synthetic panel dataset mimicking noisy CTR dynamics (with observed CTR defined as C_t/I_t), an operational ground truth based on noise-robust CTR estimates and sustained deterioration relative to a recent-best baseline, and reports lead-time and alert-burden metrics plus sensitivity analysis over tuning parameters. The approach is claimed to scale linearly in time-series length.

Significance. If the geometric features can be shown to add value beyond mean-shift detectors, the framework could offer a scalable tool for monitoring large creative portfolios and quantifying performance loss, with potential to reduce opportunity costs in digital marketing. Credit is due for the explicit sensitivity analysis over detector tuning parameters, the linear scalability claim, and the use of synthetic data with an operational ground truth definition to enable evaluation where proprietary data cannot be shared.

major comments (2)
  1. [Abstract] Abstract: the central claim that truncated (log-)signatures enable detection of changes in trend, volatility, and non-linear dynamics 'beyond simple mean or variance shifts' is not supported by the evaluation. The operational ground truth for fatigue onset relies on a noise-robust CTR estimate and sustained deterioration relative to a recent-best baseline, which primarily encodes mean/trend shifts in the C_t/I_t series; this setup means the reported lead-time and alert-burden metrics do not test the claimed incremental value for volatility or higher-order path effects.
  2. [Data and ground truth definition] Section describing the synthetic dataset and ground truth definition: the dataset contains no injected changepoints for volatility or non-linear dynamics, and the paper lacks specific details on the noise-robust CTR computation method. This leaves gaps in demonstrating robustness to realistic day-to-day noise and undermines support for the geometric change detection advantage over standard detectors such as CUSUM or EWMA.
minor comments (2)
  1. [Methods] Clarify in the methods section how the signature truncation depth interacts with the detector tuning parameters, and whether any cross-validation was used to select them.
  2. [Data description] The distinction between the pre-computed CTR field in the accompanying CSV and the modelled C_t/I_t should be stated more explicitly to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for acknowledging the potential of the framework, the sensitivity analysis, and the use of synthetic data with an operational ground truth. We address each major comment below and describe the specific revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that truncated (log-)signatures enable detection of changes in trend, volatility, and non-linear dynamics 'beyond simple mean or variance shifts' is not supported by the evaluation. The operational ground truth for fatigue onset relies on a noise-robust CTR estimate and sustained deterioration relative to a recent-best baseline, which primarily encodes mean/trend shifts in the C_t/I_t series; this setup means the reported lead-time and alert-burden metrics do not test the claimed incremental value for volatility or higher-order path effects.

    Authors: We agree that the current operational ground truth is defined via sustained deterioration in a noise-robust CTR estimate relative to a recent-best baseline and therefore primarily reflects mean and trend shifts. Consequently, the reported metrics do not directly quantify any incremental benefit of the signature features for volatility or higher-order effects. The theoretical motivation for using truncated log-signatures remains their ability to encode iterated integrals that capture such dynamics, but we accept that this is not empirically demonstrated in the present evaluation. In the revised manuscript we will add a new subsection containing synthetic experiments in which controlled volatility shifts and non-linear path perturbations are injected into the performance trajectories. On these augmented datasets we will report lead-time and alert-burden for the signature detector alongside CUSUM and EWMA baselines, thereby providing direct evidence for the claimed geometric advantage. revision: yes

  2. Referee: [Data and ground truth definition] Section describing the synthetic dataset and ground truth definition: the dataset contains no injected changepoints for volatility or non-linear dynamics, and the paper lacks specific details on the noise-robust CTR computation method. This leaves gaps in demonstrating robustness to realistic day-to-day noise and undermines support for the geometric change detection advantage over standard detectors such as CUSUM or EWMA.

    Authors: We will expand the synthetic-data section to include an explicit algorithmic description of the noise-robust CTR estimator (a rolling-window median filter with outlier rejection, followed by a local linear trend fit). We will also augment the data-generation procedure with additional panels that contain injected volatility changes and non-linear drift perturbations while preserving the same marginal impression and click statistics. These new panels will be used to recompute all detection metrics and to compare the signature-based detector against CUSUM and EWMA. The existing sensitivity analysis over tuning parameters will be extended to the new scenarios, directly addressing robustness to day-to-day noise and the relative performance versus standard detectors. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies independent geometric features to an explicitly chosen operational proxy

full rationale

The paper derives its detector from truncated (log-)signatures of performance paths, a construction taken from rough path theory and applied to the observed CTR series C_t/I_t. The operational ground truth is separately defined in the abstract as a noise-robust CTR estimate plus sustained deterioration relative to a recent-best baseline; this proxy is used only for reporting lead-time and alert-burden metrics and is not obtained from the signature transform itself. No equation or step equates the signature features to the ground-truth definition by construction, no self-citation chain is load-bearing, and the methodology is presented with explicit scaling and sensitivity analysis over its own tuning parameters. The evaluation therefore tests the chosen detector against a stated benchmark rather than reducing the claimed geometric advantages to the benchmark by definition.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The paper rests on domain assumptions from rough path theory for path embeddings and the representativeness of synthetic data plus operational ground truth definitions, with tuning parameters for signature depth and detector settings but no new invented entities or heavy self-citation.

free parameters (2)
  • signature depth
    Truncation level for (log-)signatures is a primary tuning parameter controlling captured dynamics.
  • detector tuning parameters
    Primary tuning parameters for the change detector, subject to sensitivity analysis.
axioms (2)
  • domain assumption Performance trajectories can be meaningfully embedded as paths whose geometric features capture fatigue-related changes in trend, volatility, and non-linear dynamics.
    Invoked when reframing fatigue monitoring as a geometric change detection problem.
  • domain assumption Rough path theory and truncated signatures provide a suitable representation for detecting changes beyond mean or variance shifts in CTR time series.
    Central to the proposed methodology using path signatures.

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Reference graph

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