Adaptive Conformal Anomaly Detection with Time Series Foundation Models for Signal Monitoring.
Authors: Natalia Martinez
Fearghal O'Donncha
Wesley M. Gifford
Nianjun Zhou
Dhaval C Patel
Roman Vaculin
Venue: ICLR 2026 Poster (2026)
Keywords: time series anomaly detection; conformal prediction; anomaly detection; monitoring sequential signals
Primary area: learning on time series and dynamical systems

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.

Published as a conference paper at ICLR 2026
ADAPTIVE CONFORMAL ANOMALY DETECTION WITH TIME SERIES FOUNDATION MODELS FOR SIGNAL MONITORING
Natalia Martinez Gil
Fearghal O'Donncha
Wesley M. Gifford
Niajjun Zhou
Dhaval C. Patel
Roman Vaculin
IBM Research
natalia mwrtmaaaea..... .ireeez.giii gil.lbilllliig. com
ABSTRACT
We propose post-hoc adaptive conformal anomaly detection method for mon- itoring time series that leverages predictions from pre-trained foundation mod- els without requiring additional fine-tuning. Our method yields an interpretable anomaly score directly interpretable as false alarm rate (p-value), facilitating transparent and actionable decision-making. employs weighted quantile confor- mal prediction bounds and adaptively learns optimal weighting parameters from past predictions, enabling calibration under distribution shifts and stable false alarm control, while preserving oft-ol-sample guarantees. As a aggnotic solution, it integrates seamlessly with foundation models and supports rapid de- ployment in cesstrce-constrainedd enviromments. 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 ac- cessibility 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.
INTRODUCTION
A common challenge in industrial applications such as predictive maintenance and signal monitoring
is the scarcity of sufficient quality data and infrastructure to train robust models Cook et al. (011);
Ajami Daneshvar (2012); Kanawaday Sane (017): Beghi et al. (016); Shah & Tiwari 2018);
Moghaddass & Wang (201)). This limitation can hinder the ability to make accurate and reliable
predictions, which are essential to detect anomalies and ensure operational efficiency. Foundation
models, particularly in the time series domain Liang al. (202)), offer a promising solution. These models excel at leveraging prior knowledge and historical observations, enabling them to provide good enough initial estimates of expected values and statistical characteristics of monitored signals, even in data-scarce environments. This capability is invaluable for industries aiming to enhance their monitoring systems without the need for extensive datasets.
In the context of time series anomaly detection, adaptive approach is crucial for monitoring and maintaining the reliability of signals. Anomalies, or deviations from expected behavior, can manifest in different forms, such as point anomalies, where an individual observation significantly deviates from normal patterns, and contextual anomalies, where value only considered anomalous within a specific temporal context Boniol et al. (2024). Detecting these effectively requires models that capture underlying temporal dependencies and adapt to non-stationary data distributions.
A prominent class of anomaly detection methods relies on predictive modeling, where forecast- ing model learns normal time series behavior, and deviations between predicted and actual values could indicate anomalies in operations or shifts in operational modes that require expert attention Basseville (1 Choudhary et al. (2017); Gama al. (2014); (auura et al. (018). However, many existing approaches assume access to large amounts of training data, making them impractical in settings where only few samples are initially available. This motivates the use of pretrained
hfdemo/acaa cee.ipptie__ooooorm.. tsad

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2024); Ansari al. (2024); Liang Time Series Foundation Models (TSFMs) Rasul et al. 2003
et al. (024). which have been trained on large-scale datasets and can generalize to new time series with minimal adaptation. Furthermore, existing anomaly detection systems often lack interpretabil-
ity, relying on thresholding mechanisms that assume fixed data distribution (Schmidl et al. (022);
Paparrizos et al. (022b); Goswami et al. (2022), which limits their adaptability to evolving time series data. In this setting, robust system must balance sensitivity and adaptabilitty, minimizing false alarms while effectively defecting significant behavioral transitions. This ensures timely iden- tification of suspicious patterns without overwhelming experts with noise, fostering a more efficient and reliable monitoring framework Cook et al. (2019).
To address these limitations, we propose a conformal- -based anomaly detection method that inte- grates the predictions of pretrained TSFMs with conformal prediction techniques Vovk et al. (205);; Angelopoulos & Bates (02T) to produce an interpretable, adaptive anomaly score directly linked to desired alarm rate. Conformal methods offer model-agnostic and distribution-free uncertainty quantification with finite-sample guarantees, making them highly suitable for real-world anomaly detection. However, standard conformal approaches rely the assumption of exchangeability, which often violated in time series due to temporal dependencies. Furthermore, existing con- formal methods for anomaly detection primarily focus on thresholding arbitrary anomaly scores derived from non-anomalous data while assuming exchangeability Angelopoulos & Bates (2021);
Guan 2019); Bates et al. 2023), limiting their applicability in dynamic, non-stationary settings.
Main Contributions We propose W1-ACAS, a post-hoe adaptive conformal anomaly detection framework that leverages predictions from pretrained forecasters (e.g., TSFMs) to monitor signals without requiring fine-tuning. This is particularly valuable in industrial settings, where users of- ten lack sufficient data, data-cleaning pipelines, or specialized expertise Cook et al. (2019). Our approach provides a practical solution for immediate anomaly monitoring. Figure Iillustrate the method: (a) anomaly scores are derived as conformal p-values from forecaster errors across multiple horizons and aggregated into a single score; (b) anomalies are flagged when adaptive p-values fall below a threshold on real signals; and (c) the learned adaptive weights emphasize past errors with similar distributions, capturing recurring patterns such as periodicity, thereby improving detection while offering direct control over the alarm rate. Our framework offers the following properties:
Interpretability:
The anomaly score corresponds directly to an alarm rate (p-value), pro- viding a transparent and probabilistic basis for decisions.
Distribution-Agnnsst Built on quantile conformal prediction, the method is robust to heavy-tailed and complex error distributions.
Adaptivity: By weighting past nonconformity scores via the Wasserstein distance, the framework adapts online to distribution shifts, redueing false alarms while preserving cali- bration Barber et al. (023).
The method applies directly to pretrained TSFMs or any anomaly score, requiring no retraining while inheriting the guarantees of weighted confor- mal prediction. Its effectiveness is proved through integration with TSFM forecasters.
Post-Hoc and Model-Agnostic:
RELATED WORK
Time Series Anomaly Detection Prediction- methods detect anomalies by comparing ob- served values against forecasts (Gannoni et al. 2018 Boniol et al.) (024). Recent TSFMs (Rasul
al. 2023 2024 Ansari et al. 2024 et al. 2024g well suited for online detection in data-
scarce scenarios,
offering accurate zero-shot forecasting performance. Recent benchmark studies
(Paparrizos et al.]
2022b Liu & Paparrizos 2024) show that classical distance- and density-based
2007 Ramaswamy et al. 2000 2000 Aggarwal & Aggarwal| 2017 Paparrizos Gra- Bontol et al. 2021) often outperform more complex models, but they typically require access to the full dataset (non-causal), lack robustness across temporal patterns, and are un- suitable for streaming settings. Moreover, many anomaly scores lack clear probabilistic meaning, and common thresholding strategies rely on full-dataset statistics (Ahmad et al. 2017), limiting real- time applicability. In practice, anomaly detection systems must not only achieve high accuracy but also provide interpretable confidence scores while maintaining low false alarm rates (Cook et all 2019). Our work addresses these challenges by combining TSFMs with adaptive conformal scoring, yielding interpretable and calibrated thresholds for reliable streaming anomaly detection.
methods (Li et al.
vano 2015 2017
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Input Sequence
24 tire Anomaly Overview
Sliding Window
y teat Acomaty Label
Ourteer Detected
Input
Y ++1
(Vo 1 neil
[Ye
nbsorvedd
value
Forecaster h
10
Prediction fort+1 offset
Prediction for at offseet
300
1000
1500 Time
2000
2300
3000
Yd
...
(h) Anomaly Detection Example.
024 NAB 24 tire Fast Scores Conformal Weights
Adaptive Conformal Anomaly Score
Scores (Prediction Emrer
100-
0.0
Conformal Wegglts
60
p-value
p-value at offset
at offeet
0.4
p
Pt+1
0.2
0.0
Score @t+1 B++1 medianccia (
-2500
-2000
-1500
-1000
-500
Past time
(a) Adaptive Anomaly Score Pipeline.
(c) Non-conformity Scores vs Conformal Weights.
Figure 1: Illustration of proposed Wi-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 recurring patterns. (b) Example signal (blue) with ground-truth anomaly labels, where detected outliers (red dots) occur when adaptive p-values (orange) fall below threshold. (c) Converged adaptive weights (orange) over past errors (blue), averaged across horizons, shows how WI-ACAS captures error patterns with similar distributions, here reflecting its periodic behavior.
Conformal Prediction. Conformal prediction provides distribution-free uncertainty quantifica- tion with finite-sample guarantees (Vovk et al. [2005] Shater & Vovk (2088 Angelopoulos & Bates
2021. A widely used variant, split conformal prediction (SCP) (Papadopoulos et al., 2002). is post-hoc and model-agnostic. relying only on model predictions and a calibration set. While ef-
fective under exchangeability
P this assumption is often violated in time series settings, motivating
adaptive extensions. Recent works (Gibbs Candes 2021; Zaffran et al., 2022, Gibbs & Candès, 2024) adjust conformal quantiles online to handle distribution shifts, but typically optimize for
single error rate. Weighted conformal methods offer adaptation by reweighting calibration or past
scores based on some notion similarity to new observations (Lei & Wasserman 2014 Guan
2019
Tibshirani et al. 2019 Sesia & Romano, 2021 Han et al.) 2022; Guan 2023] Ghosh et al.
2023
Mao et al. 2024) improving local coverage. Bounds for non exchangeable sequences (Barber
ct al.
2023) further suggest emphasizing calibration samples that are nearly exchangeable with the
test point. This motivates approach, which leverages weighted adaptive conformal quantiles
to remain calibrated across time. Conformal prediction has also been applied to anomaly detec- tion by thresholding arbitrary anomaly scores under exchangeability (Angelopoulos & Bates) 2021]
Guan 2019 Bates et al. 2023). However, existing methods do not simultancously provide inter- pretable, cearrbutionnaggoste anomaly scores, directly control alarm rates, and adapt robustly to non-exchangeable time series. Our work addresses this gap by developing a conformal anomaly detection framework that both interpretable and resilient to real-world distribution shifts.
innformllyy, sequence of observations exchangeable if any permutation of the observations has the joint probability
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3 BACKGROUND
Consider S E IR a nonconformity score variable that quantifies the performance of a predictive model X + y on a joint distribution Px.y using nonconformity function e : y x 5 I. The input X E X' represents the model's input space, Y E Y denotes the true target variable, and Y corresponds to the output space of the model, which may include predictions or derived statistics over Y. The nonconformity function measures the degree of disagreement between the true target and the model's ' predictions, enabling S = e(Y, h(X) to capture how atypical a prediction is within the given distribution. An example of nonconformity function for a point prediction model is absolute emror e(Y, Y) = -Y.
3.1 CONFORMAL. OUTLIER DETECTION.
In the context of anomaly detection we characterize the distribution of the non-conformity score variable S Ps where
<(Y, l(X)) E I under non-anomalous conditions X, Y Px,y- Observations are flagged as outliers (or anomalies) when the composition of the nonconformity I Given significance level a, which controls the tolerated false positive rate, an anomaly detection Tunction C. : XX + {0, should satisfy the following property:
function and the predictive model h produces unusually high scores
PCCa (XC,(XX,,, = 1) S a
(1)
where P is the probability over unseen test data sampled from the non-anomalous distribution, X Yn-1 ~ Px,.. In the standard split-conformal setting, we observe s Si,..., S, non- conformity scores derived from non non-anomalous data, S, h(X,)) with X,, Non-conformity scores need not be independent of each other; the following conformal anomaly detection funetion satisfies, under echangeability conditions the false positive bound in equation
Px.y.
(X Yn+1) [[Sn+1 > qn), ạa Qi - + 600)
Here 9. is the empirical conformal quantile, conservatively adjusted with point at infinity.
Conformal Outlier Detection Beyond Exchangeability To account for heterogeneity in the non- conformity scores across the input space or potential temporal drift, we consider the generalized weighted conformal quantile estimate d Q1-a(s, w) defined as:
Qs w) = Q1-a
w;
5s.
+
+1 5,0)
(3)
+1
w
where w We E [0, 1]} is weighting vector applied to the calibration points. The standard result in Eq. is recovered when w; = 1, 1,... .n.
This weighted conformal quantile estimate produces a generalization of the conformal anomaly detector from equation 2 This conformal anomaly detection has false alarm rate guarantees even in non-exchangeable settings described in the following proposition 3.1
Proposition 3.1. (Direct application of Theorem 2 and 3 in Barber et al. (023)) Given (0, 1), = | a set of non-conformity scores where S corresponds to the test point, and vector of weights w {w; [0, 1 for the previous observations the detector
An+1 = (.n+1.X Yn+1) = 1[S > [M]
(4)
based the weighted conformal quantile estimate in Eq 3 satissies the false alarm rate guarantees
P(An+1=) =)
<a >R
i= [w]]++1 dsv(s,s"
(5)
2a+
[ dsy(s,s")
[W||++T
Here d is the distance in total variation between the sequence (n previously observed point and the test point n + 1) and sf which denotes the sequence of non-conformity scores after swapping the test point n + 1 with the i-th previously observation. The lower bound is valid under the assumption that the non-conformity scores take equal values with probability 0.
Although X and y are treated as separate spaces, they may overlap, as in reconstruction-emmr-bbeedd scores where Y X.
"Unusually low scores can he handled similarly, nonconformity scores need not be positive $ "The sequence $ is exchangeable if P..t..... ..41)) P(S.()).... So(n+1)) for any per- mutation
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Intuitively, Proposition] 3.1 indicates that one would like to assign higher weights previous obser- vations that are. pairwise, most exchangeable with the test sample (i.e., P(S)...... S.......... SS++) S,,...,,..:1 ~ P(S Sut1...., S.), and lower weights otherwise. Additionally, the lower bound encourages the maximization of |/w/11 and therefore keeping the weights close to one possible. One could decide w given access to prior knowledge about the values or reasonable upper bounds of (s) In the context of time series. previous works such as Barber et al. (2023) have set w to exponentially decay with time (w; = )) in non-time-serie series settings, other works such as (Lei & Wasserman 2014 Guan 2019 Sesia & Romano 2021 Han al. 2022 Guan 2023 Ghosh al. 2023 Mao et al. 2024) decide the weights based on criteria such as distance in covariate space, or optimize them to guarantee particular false positive rate coverage o, (Han et al. 2022) Amoukou & Brunel ) Next, we present our adaptive conformal score method, which learns with the objective of providing scores that are calibrated for every feasible false alarm across time.
4 ADAPTIVE CONFORMAL ANOMALY SCORE
The conformal outlier detection framework provides a principled way to define a binary anomaly decision variable based on a preselected a with generalization guarantees. However, the underlying nonconformity score S may not itself be an interpretable indicator of anomaly, particularly in se- quential settings where its distribution may drift over time. To address this, we aim to learn an adap- tive mapping that assigns each score approximate probability of observing more extreme value under prior (ideally normal) conditions, yielding distribution-agnosiicc p-value estimate, Formally, we consider a time series setting with a sequence of nonconformity scores Si...., St. In prediction- based anomaly detection, these are derived from a forecasting model h RTeeXy - ydd which maps The nonconformity score for sample t ++1 1 at horizon d is St = |Y++1 Yd 1- For clarity, we omit the index d in the following section, since the analysis applies independently each prediction horizon, and reintroduce it later when needed.
a context of length n. with n features to a d-step-ahead forecast Yıd =
4.1 CONFORMAL ANOMALY SCORE
We wish to learn a parametric mapping Bw R. + 10 I] of the previous nonconformity scores s = [S and the test sample S1+1i this mapping 3, should be such that it can be directly com- pared to any a threshold to produce an anomaly detector with the same false alarm rate guarantees D and equation
2 Given set of non-conformity scores derived from past, ideally non-anomalous data f their associated weights / = (w; E [0, I]}
as the one described in equations equation
and non-conformity score test sample S:+1 we propose the following score normalization
(S++1) sup(a E j0, S.+1 S Qs-a w)).
(6)
Here (S(+1) can be interpreted as the weighted, conformalized p-value, Sw = BB+1 (we omit the explicit dependence on s for clarity). The proposed function automatically maps an anomaly score S, which can take arbitrary real values, into a normalized score that directly relates to the desired false alarm rate. The decision of anomaly detection threshold becomes interpretable for the end user (it directly translates into the desired false alarm level) and preserves the guarantees of the original conformal outlier detector as shown in Proposition I.
Proposition 4.1. Given a E [0, 1). ( set of exchangeable non-conformity scores, and their weights (w; = [0, 11} the detector Cz, (Xt+1, = ([++1)++1) < ax) based on the (.) mapping defined in equation is equivalent to equation ann therefore satisfies the conformal
false alarm rate guarantees presented in equation 5 in Proposition 3.7 Proof in Appendix
4.2 ADAPTIVE WEIGHTED ANOMALY SCORES UNDER NON-EXCHANGEABILIIY
Our proposed conformal anomaly score mapping (-(+) in equation 6 depends on the weights w assigned to the previously observed scores. Therefore, given new observation S441 the mapping can be directly expressed as a function of w, (w(SS+)) = (:+1(W) such that
1+
Be+1 (w)
j+1 E 1[ S S.].
w|+1
'For sequences containing known fraction of anomalous samples below some upper bound a', the deriva- tion follows similarly, but the interpretation of 3w (S.+)) is a + a' where is the lower bound of the p-value of the sample.
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Where [n] + [n]] represents sorted mapping of the previous n nonconformity scores such that T()) = k E [n], vi E [n] where (i)) < T() if S & Sj. vi * j. π T=)(k) is the inverse sorting operation, mapping k to the index of the observation corresponding to the k largest value.
We want our proposed conformal score to be well calibrated across time, meaning (S,3() < a) Re a, for all a E [0, 1] and t. In lieu of that, we require Sw (S(+1) to be a conservative estimate such that ((+3(()+1) effectively to distributional shifts over time. The ideal condition under non-andn non-anomalous distributions for S1+1, (Sew() a) = Va E [0. 1] is achieved when A, (S++1) ~ Ujo.1j- We also note that (S(-)) cannot produce non-trivial quantile estimates below its effective sample size a. |w/+1- We therefore seek learn set of feasible weights w satisfying these conditions by minimizing the 1-Wasserstein distance (Wi) between the cumulative density function (CDF) of the proposed score variable (w)) where (w+1(w)= 3w (S(+1) as in equation 7 and the CDF of the uniform distribution Fv, subject to an effective sample size constraint determined by our critical false alarm rate Og.. Namely
ax) S a. Such calibration ensures that the conformalized scores adapts
s.t. Here ae is the user-defined critical false alarm rate. From the dual definition of W1 we have
minw (F (w)), Fu)
w 1 - 1, wi E [0, 1]. Vi E [n]]
(8)
(F Pu) So P=1 (e (p) F (p)ldp
[ FR (a) Fu (a)
Bo-UUp. I S a) - aa,
which indicates that minimizing Wi (F Fi) is equivalent to minimizing the calibration gap [P(3 1 (w) S ax) al uniformly across all false alarm rates. We next approximate the objective in equation & uuing finite samples and give the corresponding algorithm.
OPTIMIZATION
In practice, we need to approximate P' (ar) in equation with finite number of samples na. which results in the following empirical CDF based the scores {3e-s1721
f Bots (w) (a)
(B++5(W) S a).
(10)
nhb
Then, the W1 objective in equation g can be empirically approximated as follows
WI Fú)
1 (c)(w) alda,
(11)
where Å is the sort mapping of {Br+g (w) 3 scores such that 36- (w)) S Be+*-1 (w). Note that the expression in equation I is a sum of integrals of piecewise linear functions. Therefore, it is differentiable w.r.t. each B (w). and consequenlty w.r.t. to each (see equation 4 and also computable closed form. Then the weights can updated using projected gradient descent
BW, (8
Wt+na+1 We+na
83
das
k=1
(12)
Woeng+1 -I
II |w|>
Wr4ny+1
Note that here w, denotes our current estimate of the entire weighting vector w at time The partial derivatives can be expressed in closed form as
if B14i < #(1)-1
aw1
2 2,
28(0-1
if #(i)-1 < Bets S #(1)
(13)
0,445
+ ny
if Be4+
a(i) n6
and
@B(+((w)
(w) + 1 S (A:)
(14)
Owk
|||| +1

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The derivatives themselves have simple interpretation. The derivative of aWi pushes normalized 8p score Bi+s to lie within the ranges of its empirical quantile bucket [ {
and is minimized Bwk establishes that one can increase Se+z by decreasing
T, no
when Bi+1 = The derivative 0Bcl:(w)
2ns
the weight of scores higher than the currently-oberveed score S141 or by globally decreasing the
overall sample size ||]]--
Algorithm 1- W-ssesrsteiin Adaptive Conformal Anomaly Score
Require: [S 1: Scores, dei min false alarm rate, max past samples, 7i, min batch size Output: B E [0, normalized score vector
ng - 1, W [w; = 1i S M=) 1- # Compute critical samples and init weights
J.3(W) (w) + {0] [0] in 0. 3 <- 0 Initialize score Jacobian, batch counter and output
for t ne
ne do
S mmax(((nnn)))) w = {uē = - |
# Get past scores and corresponding weights
T + ARGSORT(S) # sort past scores in ascending order
J++1 = E.es 1[ < <s), Bet1 > +1
# Compute p-value score for Se+1
|6]1+1
B + BU B1+1, i is +1
JJ3(w in.nk = { (0 } for lo 1,... |s], using equation 14
Compute partial derivatives
if in n6 then म f- ARGSORT(B2+1--0
#Sort last ny normalized scores and compute gradient
Compute { 03 1== using î., equation 13
aW, 186
(W)(w) = f 33
Th awh
J,3(3)
w [I w VVI
in 40
end if end for
We propose W1-ACAS (Algorithm Dp. which operates by sequentially estimating normalized scores 3, using the current weight estimates. The weights w are then periodically updated minimize the objective in Eq. g based on the online sample buffer and the update rules in Eqs. 12 13
and 14
Aggregation Across Multiple Forecast Horizons We extend Algorithm to operate across multi- ple forecast horizons. Specifically, we run D parallel instances of the algorithm, each associated with a d-step ahead prediction error, S = V++1 y with V ha(Ytnn, d:t-d+)) 1), d E (D). This produces a set D conformal p-values for each observation + 1, denoted {se ]ej[)) The final anomaly score is the median across horizons,
3 medianaeio: 344 -4,1 (St
(15)
This requires observation to be identified as significant outlier by more than half of the horizon- specific detectors. In the streaming setting, maintain a buffer of forecasts different horizons. When a new sample Y2+1 observed, we collect its aligned forecasts 1 compute the corresponding errors { JE(D), and update each horizon-specific instance of Algorithm to obtain the adaptive p- p-values, to multivariate time series anomaly detection in a similar manner. We also outline several standard p- value combination techniques, which can also be applied to aggregate the horizon-specific p-values.
In Appendix C.2.4 we describe how Algorithm 1 eextnnss
EXPERIMENTS
We evaluate the proposed conformalized anomaly score Wi-ACAS (Algorithm) M by analyzing its calibration and anomaly detection performance time series data. Synthetic experiments (Ap- pendix C.T) validate ability to remain calibrated under both gradual and abrupt distribution shifts, where ground-truth p-values are available. Our main empirical study focuses on real-world anomaly detection datasets, where we assess detection accuracy using both fireshold-independee and thresholdddependentt metrics.
Anomaly Detection Datasets. We evaluated the performance of our proposed method (W1 ACAS, Algorithm | for unsupervised univariate time series anomaly detection when applied to
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pre-trained time series foundation model. Experiments conducted on seven benchmark datasets: YAHOO Laptev et al. 2015). NEK (Si et al.
2024). NAB (Ahmad et al. 2017). MSL (Lai et al. 202T), IOPS (IOPS p. STOCK TTan et al. 2016), and WSD (Zhng et al. 2022), all part of the curated anomaly detection benchmark of Liu & Paparrizos (2024). For the muluvariate experiments,
we additionally use the curated subsets of TAO (Laboratory] 2024), GECCO (Rehbach et al. 2018). LTDB (Goldberger et al. 2000), and Genesis (von Birgelen & Niggemann 2018) released as part of the benchmark Liu & Paparrizos (2024). Each dataset consists of an initial segment without anomalies used for training or calibration, tollowed by a test split that may contain anomalies.
WI-ACAS TSFM. We integrate WI-ACAS with three pre-trained TSFMs: Tiny Time Mix- ers (TTM) (Ekambaram et al. 2024), Chronos-Bolt-Sman (Chronos) (Ansari et al. 2024 and TiRex (Aurr et al. 2025). All models use context length of 52 and forecast horizon of D 15. For Algorithm | we set the critical false alarm rate to ag 0.01, batch size ny = 10, and learning rate 7 0.001. We use ADAM Kingma & Ba 2013 to perform an adaptive gradient descent Appendix
on the weights
C.2.3 Fig. analyzes the impact of aggregating forecast horizons, 15 provides a reasonable balance between performance and sample efficiency. Figures 9 L0 and [ show the sensitivity of Wi-ACAS to the learning rate 7, batch size ngg and Qg- The method shows low variability for small y and ny. The parameter ag controls the maxi- mum acceptable p-value resolution: smaller values require a larger number in-distribution past observations ne. but do not impose a lower bound on the detectable anomaly level.
showing that D=
Baseline Methods We compare W1-ACAS against two TSFM- baselines: a Gaussian model that fits the mean absolute forecast error across d steps using calibration data, and a Confor- mal offline approach that learns p-value mappings per horizon and aggregates them by the median.
We also include sop-performing classical methods from Liu & Paparrizos 2024]: KShape (Paparri-
zos & Gravano 2015 2017 [onnill et al. 1021 POLY (L et al. 2007). Sub-PCA (Aggarwal & Aggarwal| 2017 Sub-KNN (Ramaswamy at. 2000), SAND (oonoll al. 2021). We further include strong semi-supervised deep learning seeniing-bssed anomaly detection methods (Audibert et al., 2022). namely CNN (Munir al. 2018), USAD (Audibert al. 2020). and OmniAnomaly (Su ct al. 2019), as well as the recent general purpose TSFM MOMENT (Goswami et al. 2222)). which
provides zero-shot anomaly scoring. Additional details are provided in Appendix C.2.1
Evaluation Metrics. We report both point-wise (AUC, PA-FI) (wu et al.
2022 Wang et al.
2024 [Luu & Paparrizos, 2024) and range- wise metrics (VUS (Paparrizos et al. 2022a). Affliition- Fl (Huee et al. (022)). For threshold-dependent scores (PA-F1, Affiliation-F1),
follow the oracle strategy of Liu & Paparrizos (204)), selecting the best threshold in Jo, 1] and reporting the associated False Positive Rate (FPR) and calibration error (CallEr). Further details are in Appendix C.2.2
Results Table D reports the average performance of WI-ACAS, applied to different TSFM mod- els, compared against the described baselines on the univariate datasets. Our method achieves the strongest performance on threshold-dependenl metrics (PA-F1, Affiliation-F), including when com- pared with semi-supervised methods such as CNN, USAD, and OmniAnomaly, while remaining competitive on pareshold-independee metries (AUC, VUS). When conditioned on the same TSFM model, WICACSS shows clear improvements over the Gaussian and Conformal baselines. Fig- ure shows the average performance per univariate dataset for subset of the methods, extended per-dataset results are provided in Tables and in Appendix C2 Table shows that TSFM models have similar prediction errors across datasets, consistent with their comparable anomaly de- tection performance. Results for the multivariate datasets are presented in Table Appendix C.2.4 where we demonstrate how our approach naturally extends the multivariate setting via p-value ag- gregation, achieving top performance relative to the corresponding baselines.
Figure g shows the FPR FPR-threshold curves in the low-FPR regime, where Wi-ACAS (blue) yields the most conservative thresholds, staying closer to or below the identity line compared to compet- ing methods, while also exhibiting the lowest variance. Figure 4 shows representative detection examples along with the final learned weights. We observe that W1-ACAS is adapted to capture underlying temporal patterns errors if present. Moreover, our method effectively identifies a tran- sition in score distributions (e.g., in the vicinity of an anomalous region) but then quickly adapts to the new anomalous distribution; this helps minímize the number of alarms in the end-to-end system.
Additional examples are provided in Appendix C.2.3 Figure 6 shows more detection cases, and Figure Z illlustrates the trade-off's between FPR and Fl scores (PA-FI. Affiliation-F) across datasets. The operating points of ACAS (blue), in most cases, achieve both the highest F1 score and
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Published as a conference paper at ICLR 2026
Table 1: Performance Summary across univariate datasets. Entries indicate the mean standard deviation computed by first averaging within each dataset group, then averaging across groups (equal weight). Higher numbers are better for PA-F1, Affiliation-FF AUC-PR, VUS-PR; lower numbers are better for FPR, and calibration error (CalErr). Underlined results indicate best post-hoc methods applied to the same base forecaster, while bold indicate best results overall. Methods marked with denote deep learning semi-supervised approaches.
Forecaster
AD Method
PA-FI
Affiliatio-FI1 f
FPR 4
CalErr
AUC-PR
VUC-PR
Chromes
-CCACAS
0.912 0.066
0.893 0.060
0.077 0.114
0,025 0.029
0.355 0.261
0.440 a 0.272
Chrones
Conformal
0.863 0 109
0.891 + 0.063
0.111 0.130
0.038 = 0.055
0.310 + 0.240
0.420 + 0.248
Chronos
Gaussian
0,716 0.260
0.842 0.066
0.123
0.075 0.061
0.265 + 0.250
0.438 0.245
TTM
W1-ACAS
0,889 108
0.886 0.058
0.082 0.120
0.029 0.031
0.342 0
0.449 0.245
TTM
Conformal
0.851 0.12 124
0.062 0.885
0.120 = 0,145
0.044 = 0.056
0.317 # 0.247
0.448 + 0.250
TTM
Gaussian
0.733 + 0.240
0.849 0.067
0.128 0.115
0.081 0.065
0.270 + 0.261
0.450 0.249
TiRex
Wi-ACSS
0,925 0.048
0.897
0.064
0.084 0.113
0.025 = 0.031
0.344 + 0.269
0,438 0.272
TiRex
Conformal
0.878 + 0.085
0.890 0.063
0.107 0.137
0.038 = 0.055
0.308 + 0.257
0.429 + 0.256
TiRex
Gaussian
0.714 à 0.264
0.837 0.068
0.119 0.103
0.090 = 0.071
0.270 a: 0.264
0.432 0,250
POLY
0.527 + 0.276
0.848 0.072
0.334 0,269
0,282 0.130
0.044 + 0.031
0.377 + 0.207
Sub KNN
0.479 a: 0.291
0.786 0.074
0.451 0.276
0.174 = 0.124
0.118 # O. 106
0.321 # 0.234
KShape
0,533 0.299
0,789 0.096
0.508 0,291
0.176 0.132
0.125 a 0.135
0.303 0.262
PCA
0.536 0,332
0.826 0.097
0.374 0.297
0.248 0.131
0.100 + 0.093
0.417 = 0.274
SAND
0,460 + 0,339
0.790 0.079
0,511 0.296
0,134 0.048
0.101 + 0.1117
0.289 + 0. 190
CNN
0,858 0.138
0,881
0.059
0.083
0,103
0.643
0.227
0.269 1 0.292
0.423 = 0,289
OmniAnnomll
0.674 0.282
0.855 0.068
0,209 0.171
0.571 0.187
0.166 + 0.087
0.429 + 0.317
USAD
0.498 0.333
0.809 0.099
0.425 0,298
0.324 0,161
0.088 + 0.088
0.398 + 0.262
MOMENT.25
0.596 0.305
0.867 0.088
0.292
0.198
a 0.461 =
PL per Dataset
Cwllir DJstaset
10P5
0:50
88
KAA
0.49
0.546
0.:4
0:46
6:44
5:40
3.46
0.56
0.44
0.5
0.07
0:99
1.0
1.00
1.28
2.09
8.09
2:5
-44
332
932
010
0:42
0:22
0:27
6:39
0:39
9:30
MSD
0.90
5.03
2.02
10
30
+2
231
0000
0.27
M22
5.52
2:50
200
0.0
0.24
0.55
M33
0:20
2.04
2:
23
2.00
Clonest preckasee
pilee ploctann
TEM geccsiio
Cheenss Wi atCas
Mates Wi ACAS
KDhapeii
TIM geusiisi
Dimoos siaas
Hikes AGAS
mi rtas
MONEST
(a) PA-FI per dataset
(b) CalErr + per dataset
AUC PR per Dataset
0.23
5:70
SET
0.52
B:77
0.55
0:00
2.01
0.EE
0.31
D:0T
0:10
0.32
6:55
6L13
6.26
522
326
322
023
30
0:33
6.79
4.65
NAB
337
020
0.36
0.2
6:35
0.33
0.00
2:00
320
320
320
0.2
SEX-
0.75
6:00
356
0.27
0.55
0:35
2
3:5
0:31
330
2.00
600
2/7
W3D
0.99
0:02
094
922
022
W0100-
0:38
6:75
345
6.23
6:2
263
0.55
032
2
0.77
2.0
870
W--00
300
000
2:0
823
MOMENT
Ni Chonasay 4Go0
ma ACA-
EDhapsoo
MOMeRT
Tiece pluctien
Chomos 4CAS
Wile AGAS
mwwre AGAS
TVM
AD oz
Mathol
(c) Affiliation-F t per dataset
(d) AUC-PR per dataset
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 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 WI-ACAS combined with Chronos, TiRex or TTM yields consistently low calibration error while remaining among the nor-perfonming approaches. Note that CNN, OmniAnomaly and USAD are semi-supervised methods trained on the non-anomalous training datasplit.
Figure 2:
lowest FPR, especially for PA-FI. Within each TSFM model, our method dominates its Gaussian (green) and Conformal (orange) counterparts in nearly all cases. Furthermore, it produces better- calibrated scores (low CalErr), making threshold selection more reliable in practice.

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Published as a conference paper at ICLR 2026
1.90
6.100
6.00
1.14
4.5
100
1004
(a) NEK
(b) YAHOO
(c) IOPS
(d) NAB
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- range (IQR) bands. The dashed gray line indicates ideal calibration (FPR 3) Curves above the line reflect over-confident scoring (FPR larger than threshold), while curves below the line reflect conservative scoring. In most cases, WCAAAS (blue) yields the most conservative thresholds, staying closer or below the identity line compared to competing methods, while also having the lowest variance.
NEK-Detection
(b) WSD-Detection
(c) YAHOO-Detection
(d) JEK-WI-ACAS-WE
(c) WSD-WIL WI-ACAS -eiights
(f) YAHOO BERDOO-W-AAGE WI-ACAS -eightss
Figure 4: Example signals (blue) with ground-truth anomaly labels (red shading) are shown in the first row, where detected outliers (red dots) occur when adaptive p-values (orange) fall below threshold under our proposed Wi-ACAS method. The second row shows the final adaptive weights (orange) over past eπгоrs (blue), averaged across horizons, illustrating how W1-ACAS adapts to and captures underlying error patterns
7 CONCLUSION
In this paper, we presented -ICASSS, a post-hoc adaptive conformal anomaly detection framework that leverages predictions from pretrained TSFMs to provide interpretable, distribution-agnosiicc and well-calibrated anomaly scores without requiring retraining or large datasets. Experiments bench- mark datasets show that our method consistently outperforms competing baselines. WI-ACAS yields more conservative and stable thresholds, its a principled and easily applicable approach that adapts online to temporal erгor patterns, and minimizes false alarms by adjusting to distributions shifts. These properties make it especially suited for online monitoring in industrial and data-scarce environments. Future work will explore refining conformal weighting with contextual features, with straightforward extensions multivariate anomalies via horizon-style aggregation.
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14


Reviews:
[{"review_id": "yjQyeJQ9zn", "reviewer": "Reviewer_dKjt", "summary": "This work introduces a post-hoc adaptive conformal anomaly detection method for time series data, while combining predictions from pre-trained foundation models without fine-tuning.", "questions": "- Table 1 provides a summary of the performance of the proposed method over all the datasets. While the full table appears in the appendix, it would be helpful to include a per-dataset analysis in the main text to provide readers with insights into which scenarios the proposed method performs best/worst.\n- It is surprising to see that the baselines have a drop in performance when using point-adjusted F1. Usually, this is not the case. Methods tend to have a higher PA-F1 than a standard one. Could you explain?\n- From the results, it seems there is no clear best foundation model to be coupled with the proposed method. It would be nice to discuss this. Where do the differences in performance metrics stem from? A per-dataset analysis, as previously suggested, could provide insights.\n- How sensitive is the proposed method to the different hyperparameters that need to be adjusted?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- Sound approach that builds on the conformal prediction for non-exchangeable scenarios formulation (Barber, 2023) for a concrete application in time series anomaly detection\n- A good number of datasets considered in the evaluation\n- Promising results", "weaknesses": "Within the baselines, the paper could consider a broader number of competitors, encompassing classical and deep learning based. All the considered baselines report very poor results, although there are well-established and well-performing AD methods in the literature. One gets the impression that the evaluation is not fully fair. The authors may consider [1] for a starting point. \n\n[1] https://doi.org/10.1016/j.patcog.2022.108945", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JFXaIOnxuB", "reviewer": "Reviewer_n5Nx", "summary": "This paper presents **W1-ACAS** (1-Wasserstein Adaptive Conformal Anomaly Score), a post-hoc adaptive conformal anomaly detection method for monitoring time series using pre-trained foundation models without requiring fine-tuning. The key contributions include: (1) producing interpretable anomaly scores directly linked to false alarm rates (p-values), enabling transparent threshold selection; (2) using weighted quantile conformal prediction that adapts online to distribution shifts by learning optimal weights via Wasserstein distance minimization; (3) providing a model-agnostic solution that works seamlessly with any time series foundation model while preserving theoretical guarantees; and (4) addressing practical industrial challenges such as limited data availability, lack of training expertise, and need for immediate deployment. Experiments on synthetic and real-world benchmark datasets demonstrate that W1-ACAS achieves strong detection performance with better calibration and lower false positive rates compared to baseline methods, while maintaining robustness to temporal distribution shifts.", "questions": "1. What is the fundamental difference between this paper and [1]\n2. Does this also work on fine-tuned non-FM anomaly detection model?\n3. The TSFMs are forecasting models. They are not idea for contextual anomalies. Does this method help to alleviate that disadvantage?\n4. Is this applicable to reconstruction-based models.\n\n\n\n\n[1]  Margaux Zaffran, Olivier Féron, Yannig Goude, Julie Josse, and Aymeric Dieuleveut. Adaptive conformal predictions for time series. In Proceedings of the ICML. PMLR, 2022.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Interesting idea of improving TSFMs' performances on anomaly detection (even if the TSFMs are trained for forecasting)\n2. Solid mathematical derivations", "weaknesses": "1. Missing LLM usage section\n2. The baselines mainly consist of TSFM-based baselines. Some of these TSFMs are not specifically trained for anomaly detection, so it's easy to improve their performances.\n3. Should also include more recent (after 2023) deep-learning based baseline.\n4. Improvement not that impressive give the high standard deviation", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3CKhEA3zns", "reviewer": "Reviewer_2NiA", "summary": "This paper proposes a post-hoc, model-agnostic adaptive conformal anomaly detection framework that leverages pre-trained Time Series Foundation Models without additional fine-tuning.  Experiments on a total of seven benchmark datasets exhibit consistent superior performace over existing methods.", "questions": "Can the proposed method be extended to deal with multi-dimensional time series data?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper focuses on key pain points in industrial time series anomaly detection such as limited high-quality data, lack of training expertise, and non-stationary data distributions. These are critical challenges in fields like predictive maintenance.  Experiments are comprehensive and well-designed that cover a total of seven benchmark datasets.", "weaknesses": "One caveat is that this paper focuses exclusively on univariate time series anomaly detection, without extending it to multivariate time series scenarios, despite multivariate time series are common in industrial monitoring and predictive maintenance.  In addition, it provides no details on computational overhead or scalability of the proposed method. For practical scenarios requiring real-time monitoring, computational costs are critical and could limit practical deployments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)