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arxiv: 2604.20122 · v1 · submitted 2026-04-22 · 💻 cs.LG · cs.AI

Recognition: unknown

Adaptive Conformal Anomaly Detection with Time Series Foundation Models for Signal Monitoring

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Pith reviewed 2026-05-10 01:16 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords anomaly detectionconformal predictiontime seriesfoundation modelsadaptive calibrationsignal monitoringfalse alarm control
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The pith

A post-hoc adaptive conformal method produces an interpretable anomaly score directly as a false alarm rate p-value from any time series foundation model.

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

The paper introduces an adaptive conformal anomaly detection technique that works directly with pre-trained time series foundation models without fine-tuning. It generates an anomaly score that can be read as a p-value representing the false alarm rate. By adaptively weighting conformal prediction bounds based on past predictions, the method maintains calibration even when the underlying data distribution changes. This approach requires no model fine-tuning and preserves theoretical guarantees on error rates while enabling use in resource-constrained settings.

Core claim

The proposed method employs weighted quantile conformal prediction bounds whose weighting parameters are learned adaptively from past predictions, yielding an interpretable anomaly score equivalent to a false alarm rate (p-value) that remains valid under distribution shifts while preserving out-of-sample guarantees.

What carries the argument

Weighted quantile conformal prediction bounds with adaptive learning of weighting parameters from past predictions, which dynamically adjusts the anomaly scoring for time series signals.

If this is right

  • Integrates as a model-agnostic post-hoc step with any pre-trained foundation model.
  • Maintains stable false alarm control during distribution shifts in time series data.
  • Enables rapid deployment without additional training or fine-tuning expertise.
  • Produces directly actionable decisions via the p-value interpretation of anomaly scores.

Where Pith is reading between the lines

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

  • The adaptive weighting step may reduce manual calibration effort when applying foundation models to new monitoring tasks.
  • This approach could be tested on non-time-series sequential data to check if similar adaptivity holds.
  • Combining the method with different foundation model architectures would show how much the guarantees depend on the base predictor quality.

Load-bearing premise

That learning optimal weighting parameters adaptively from past predictions preserves the exchangeability and coverage guarantees of the underlying conformal prediction framework.

What would settle it

A dataset with strong distribution shifts where the observed false alarm rate for a nominal p-value level deviates substantially from the target rate.

Figures

Figures reproduced from arXiv: 2604.20122 by Dhaval C. Patel, Fearghal O'Donncha, Natalia Martinez Gil, Nianjun Zhou, Roman Vaculin, Wesley M. Gifford.

Figure 1
Figure 1. Figure 1: Illustration of our proposed W1-ACAS method. (a) Anomaly scoring pipeline: conformal p-values are computed across forecast horizons from forecaster errors and aggregated. The mapping is adapted online by weighting past nonconformity scores, with weights evolving to capture distri￾butional shifts or recurring patterns. (b) Example signal (blue) with ground-truth anomaly labels, where detected outliers (red … view at source ↗
Figure 2
Figure 2. Figure 2: Performance across univariate datasets for a subset of anomaly detection meth￾ods. Heatmaps show the average per-dataset performance for PA-F1, Affiliation-F, AUC-PR, and Calibration Error (CalErr) across a selected subset of methods. Higher values indicate better perfor￾mance for PA-F1, Affiliation-F, and AUC-PR, while lower values are preferred for CalErr. Overall, the proposed W1-ACAS combined with Chro… view at source ↗
Figure 3
Figure 3. Figure 3: FPR vs. threshold in the low-FPR regime. Curves shows the mean false positive rate (FPR) across datasets for a given method, with shaded inter-quartile range (IQR) bands. The dashed gray line indicates ideal calibration (F P R = β). Curves above the line reflect over-confident scoring (FPR larger than threshold), while curves below the line reflect conservative scoring. In most cases, W1-ACAS (blue) yields… view at source ↗
Figure 4
Figure 4. Figure 4: Example signals (blue) with ground-truth anomaly labels (red shading) are shown in the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Figures (a) and (d) show an example of a generated signal under the random shift and [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Example signals (blue) with ground-truth anomaly labels (red areas), detected outliers (red [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Trade-offs between false positive rate and detection performance across datasets. Left column: PA-F1 vs FPR (log scale). Right column: Affiliation-F vs FPR (log scale). Each point uses color for AD method and marker for forecast model. The operating points of W1-ACAS (blue), in most cases, achieve both the highest F1 score and lowest FPR, especially for PA-F1. Within the same TSFM model, W1-ACAS is better … view at source ↗
Figure 8
Figure 8. Figure 8: Performance of W1-ACAS when aggregating different forecast steps. Rows correspond to datasets (NAB, NEK, MSL, YAHOO, Stock, WSD) and columns to metrics (PA-F1, Affiliation-F, AUC-PR, VUS-PR). limited gains beyond this point [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Performance of W1-ACAS when aggregating different learning rate. Rows correspond to datasets (NAB, NEK, MSL, YAHOO, Stock, WSD) and columns to metrics (PA-F1, Affiliation-F, AUC-PR, VUS-PR). cast errors are properly calibrated online using W1-ACAS. Notably, the slightly higher forecasting error of TTM on YAHOO corresponds to its lower anomaly-detection performance in [PITH_FULL_IMAGE:figures/full_fig_p022… view at source ↗
Figure 10
Figure 10. Figure 10: Performance of W1-ACAS when aggregating different batch size update nb. Rows correspond to datasets (NAB, NEK, MSL, YAHOO, Stock, WSD) and columns to metrics (PA-F1, Affiliation-F, AUC-PR, VUS-PR). (1 sequence with 18 features and over 16k samples), and LTDB (Goldberger et al., 2000) (5 curated sequences, each with 2 features and approximately 100k samples). We evaluate our multivariate extensions, W1-ACA… view at source ↗
Figure 11
Figure 11. Figure 11: Performance of W1-ACAS when aggregating different critical alarm rate αc. Rows correspond to datasets (NAB, NEK, MSL, YAHOO, Stock, WSD) and columns to metrics (PA-F1, Affiliation-F, AUC-PR, VUS-PR). 24 [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
read the original abstract

We propose a post-hoc adaptive conformal anomaly detection method for monitoring time series that leverages predictions from pre-trained foundation models without requiring additional fine-tuning. Our method yields an interpretable anomaly score directly interpretable as a false alarm rate (p-value), facilitating transparent and actionable decision-making. It employs weighted quantile conformal prediction bounds and adaptively learns optimal weighting parameters from past predictions, enabling calibration under distribution shifts and stable false alarm control, while preserving out-of-sample guarantees. As a model-agnostic solution, it integrates seamlessly with foundation models and supports rapid deployment in resource-constrained environments. This approach addresses key industrial challenges such as limited data availability, lack of training expertise, and the need for immediate inference, while taking advantage of the growing accessibility of time series foundation models. Experiments on both synthetic and real-world datasets show that the proposed approach delivers strong performance, combining simplicity, interpretability, robustness, and adaptivity.

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 a post-hoc adaptive conformal anomaly detection method for time series signal monitoring that uses predictions from pre-trained foundation models without fine-tuning. It applies weighted quantile conformal prediction with weighting parameters learned adaptively from past predictions to handle distribution shifts, claims that the resulting anomaly scores are valid p-values interpretable as false-alarm rates, and asserts that out-of-sample coverage guarantees are preserved.

Significance. If the coverage guarantees are rigorously established under adaptive weighting, the work would offer a practical, model-agnostic way to deploy foundation models for interpretable anomaly detection in industrial settings with limited data and distribution shifts, combining simplicity with stable false-alarm control.

major comments (2)
  1. [theoretical analysis / §3] The central claim that out-of-sample guarantees are preserved rests on the adaptive learning of weighting parameters from past predictions. The manuscript must supply an explicit derivation (likely in the theoretical analysis section) showing that the data-dependent weights maintain the exchangeability or martingale property required for the weighted quantile to deliver marginal coverage at level 1-α; standard weighted conformal results assume fixed weights and do not automatically extend to this adaptation rule.
  2. [experiments section] The abstract states that experiments demonstrate strong performance and preserved guarantees, yet the experimental protocol (including how adaptive weights are updated on the data stream and how coverage is verified under shifts) is not detailed enough to confirm that the empirical results support the validity claim rather than merely showing competitive detection rates.
minor comments (2)
  1. [method description] Clarify the precise update rule and loss function used to learn the weighting parameters from past residuals or predictions.
  2. [related work] Add a short discussion of how the method differs from existing adaptive conformal prediction techniques for non-stationary data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. We address each major comment below and will revise the manuscript to strengthen the theoretical justification and experimental documentation.

read point-by-point responses
  1. Referee: [theoretical analysis / §3] The central claim that out-of-sample guarantees are preserved rests on the adaptive learning of weighting parameters from past predictions. The manuscript must supply an explicit derivation (likely in the theoretical analysis section) showing that the data-dependent weights maintain the exchangeability or martingale property required for the weighted quantile to deliver marginal coverage at level 1-α; standard weighted conformal results assume fixed weights and do not automatically extend to this adaptation rule.

    Authors: We agree that an explicit derivation is required. In the revised manuscript we will expand Section 3 with a formal proof that the adaptive weights, computed exclusively from past observations, are predictable with respect to the natural filtration. This predictability preserves the martingale property of the weighted conformal p-values, yielding marginal coverage at level 1-α under the maintained exchangeability assumption on the underlying time series. The derivation will explicitly contrast the fixed-weight case with our online adaptation rule and state the precise conditions under which validity holds. revision: yes

  2. Referee: [experiments section] The abstract states that experiments demonstrate strong performance and preserved guarantees, yet the experimental protocol (including how adaptive weights are updated on the data stream and how coverage is verified under shifts) is not detailed enough to confirm that the empirical results support the validity claim rather than merely showing competitive detection rates.

    Authors: We acknowledge the need for greater transparency. The revised experimental section will include: (i) the precise online update rule for the weighting parameters together with the chosen learning rate and window size; (ii) pseudocode for the streaming procedure; and (iii) additional figures and tables reporting empirical coverage rates over time, both on stationary segments and under controlled distribution shifts. These diagnostics will directly verify that the observed false-alarm rates remain consistent with the nominal level, thereby supporting the validity claim beyond detection performance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external conformal theory

full rationale

The paper proposes a post-hoc adaptive conformal anomaly detection method using weighted quantile bounds with weights learned from past predictions, claiming preservation of out-of-sample guarantees and p-value interpretability. No quoted equation or step reduces the claimed validity or anomaly score to a self-definition, a fitted input renamed as prediction, or a self-citation chain. The adaptation is presented as an extension of standard conformal prediction (external to the paper), with experiments providing empirical support. The derivation chain is self-contained against the stated assumptions rather than tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method depends on standard conformal prediction theory holding for foundation model outputs and on the adaptive weighting mechanism not invalidating coverage; no new entities are postulated.

free parameters (1)
  • weighting parameters
    Adaptively learned from past predictions to optimize quantile bounds under shifts.
axioms (1)
  • domain assumption Conformal prediction assumptions (e.g., exchangeability or appropriate coverage conditions) hold for the weighted quantiles derived from foundation model predictions.
    Invoked to ensure the anomaly score remains a valid p-value with out-of-sample guarantees.

pith-pipeline@v0.9.0 · 5476 in / 1372 out tokens · 38808 ms · 2026-05-10T01:16:48.681896+00:00 · methodology

discussion (0)

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Reference graph

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    22 Published as a conference paper at ICLR 2026 (a) NAB — PA-F1 (b) NAB — Affiliation-F (c) NAB — AUC-PR (d) NAB — VUS-PR (e) NEK — PA-F1 (f) NEK — Affiliation-F (g) NEK — AUC-PR (h) NEK — VUS-PR (i) MSL — PA-F1 (j) MSL — Affiliation-F (k) MSL — AUC-PR (l) MSL — VUS-PR (m) Y AHOO — PA-F1 (n) Y AHOO-Affiliation-F (o) Y AHOO — AUC-PR (p) Y AHOO — VUS-PR Fig...

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