UniOD: A Universal Model for Outlier Detection across Diverse Domains
Authors: Dazhi Fu
Jicong Fan
Venue: ICLR 2026 Poster (2026)
Keywords: outlier detection
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: A universal model that can be used for outlier detection on datasets with different feature dimension and heterogeneous feature space across diverse domains.

Abstract: Outlier detection (OD), distinguishing inliers and outliers in completely unlabeled datasets, plays a vital role in science and engineering. Although there have been many insightful OD methods, most of them require troublesome hyperparameter tuning (a challenge in unsupervised learning) and costly model training for every task or dataset. In this work, we propose UniOD, a universal OD framework that leverages labeled datasets to train a single model capable of detecting outliers of datasets with different feature dimensions and heterogeneous feature spaces from diverse domains. Specifically, UniOD extracts uniform and comparable features across different datasets by constructing and factorizing multi-scale point-wise similarity matrices. It then employs graph neural networks to capture comprehensive within-dataset and between-dataset information simultaneously, and formulates outlier detection tasks as node classification tasks. 
As a result, once the training is complete, UniOD can identify outliers in datasets from diverse domains without any further model/hyperparameter selection and parameter optimization, which greatly improves convenience and accuracy in real applications. More importantly, we provide theoretical guarantees for the effectiveness of UniOD, consistent with our numerical results. We evaluate UniOD on 30 benchmark OD datasets against 17 baselines, demonstrating its effectiveness and superiority.

Published as a conference paper at ICLR 2026
UNIOD: A UNIVERSAL MODEL FOR OUTLIER DETEC- TION ACROSS DIVERSE DOMAINS
Dazhi Fu Jicong Fan"
School of Data Science The Chinese University of Hong Kong, Shenzhen dazhi fuul inn. www.cuckkccoo .ddu.cn, Fanjiicong@cuhk.edu edu. cn
ABSTRACT
Outlier detection (OD), distinguishing inliers and outliers in completely unlabeled datasets, plays vital role in science and engineering. Although there have been many insightful OD methods, most of them require troublesome hyperparameter tuning (a challenge in unsupervised learning) and costly model training for every task dataset. In this work, propose UniOD, universal OD framework that leverages labeled datasets to train a single model capable detecting outliers datasets with different feature dimensions and heterogeneous feature spaces from diverse domains. Specifically, UniOD extracts uniform and comparable features across different datasets by constructing and factorizing multi-scale point-wis wise sim- ilarity matrices. It then employs graph neural networks to capture comprehensive within-dataset and hetween-datasee information simultaneously, and formulates outlier detection tasks as node classification tasks. As a result, once the training is complete, UniOD can identify outliers in datasets from diverse domains without any further model/hyperparanme greatly improves convenience and accuracy in real applications. More importantly, we provide theoretical guarantees for the effectiveness of UniOD, consistent with our numerical results. We evaluate UniOD on benchmark OD datasets against 17 baselines, demonstrating its effectiveness and superiority. Our code is available at Ittttts:: lnttps://githhbl com/ wwwa//aaaaaaaauiiia...
selection and parameter optimization, which
INTRODUCTION
Outliers observations that deviate substantially from other normal data in dataset, indicating they likely arise from distinct generative process. In data-driven applications, detecting and removing outliers is vital, since their presence can severely degrade the accuracy and robustness of downstream analyses. The problem of identifying such
termed outlier detection (OD) (Hodge Austin 2004 Chandola et al. 2009 Ruff al. (02T), anomaly detection (Pang et al.) 2021), or novelty detection (Pimentel et al. 2014)) has attracted extensive research. OD techniques
serve a variety of purposes (Singh Upadhyaya| 2012 Ahmed et al. 2016 Breier Branišová 2017), including preprocessing for supervised learning to eliminate aberrant samples, healthcare diagnostics and monitoring. fraud detection financial transactions and cybersccurity, and beyond.
divide them into two categories: traditional methods and deep-learning (neural network) based methods. Traditional methods often employ kernel functions (Pazenn 1962 Schölkopf et al. 2001). nearest neighbors (Ramaswamy et al. 2000), and decision trees (Liu et al. 2008). among others, to build their models. For instance, local outlier factor (LOF) (Breunig al. 2000) compares the local density of an observation to the local densities of its neighbors and identifies observations that have a substantially lower density than their neighbors outliers. Isolation Forest (Liu et al. 2008) assumes that outliers are more susceptible to isolation than normal observations and uses random decision trees recursively to partition the feature space, where outliers tend be separated into leaf nodes far fewer splits. Deep learning based OD methods use neural networks for feature extraction, dimensionality reduction, or other purposes. For instance, DeepSVDD (Ruff et al. 2018b) uses neural network to project
In the past few decades, many OD methods have been proposed. Basically,
"Corresponding author

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Published as a conference paper at ICLR 2026
Conventional OD Dataset Specific Models
Fit Infer
OD Tasks
UniOD Universal Model
Train
Infer
Inliers
Historical Labeled Dataset
Outliers
Unlabeled Data
Figure 1: Pipeline comparison between UniOD and conventional OD methods. These approaches
train a separate model per dataset, while UniOD) leverages a collection of historical labeled datasets train single universal model.
Sproed nd puly Inoor
Spaaed add poly Iawee
35
AURUC
AUROi
AUROC
AUROC
bendwidth
bandwidth
(a) OCSVM on Cardioto
(b) OCSVM on fault
(c) KDE on breastw
(d) KDE on optdigits
0.5
AUROC
AUROR
D.55
10
15
24
15
20
0.81
0.1
11.5
4.
8.5
NAD breastw
(f) NAD satellite
(g) DPAD Cardioto
(h) DPAD Pima
Figure 2: Examples of the performance sensitivity of OD methods to their hyperparameters.
samples into a hypersphere and uses the distance to the center of the hypersphere as an outlier score. data and maps the augmented data and original data into space where the embedding of the augmented data remains similar to that of the original data. PLAD (Cai & Fan 2022) jointly learns a perturbator perturb each normal data and a classifier to distinguish between the normal data and the perturbed counterpart, where the latter is regarded as a pseudo-abnorms sample. ImAD (Xiao & Fan 2024) is an end-to-end deep anomaly detection method for data with missing values 2025b). Note that there are more deep learning based OD methods (Shenkar & Wolf 2022 Livernoche et al. 2023a Xu et al. 2023 Fu et al.) 2024 Zhang
NeutralAD QQu al. 2021) uses augmentations
al. 2024), and some of them focus specific data types, such as tabular data (Dai et al. 2025 and
graph-structured data (Fan 2025a Cai et al. 2025 Wang et al. (025). or consider special settings such semi-supervised learning (Ruff al. 1019
9 Xiao al. (025b) and fairness (Xiao et al.)
2025a). Due to space limitations, we will not detail them in this work.
The OD methods mentioned above, especially those based deep learning, dataset-specific as shown in Figure [] That means, for a new dataset, especially when it from a different domain, we have train OD model from scratch, which has the following limitations:
High effort on model selection and hyperparameter tuning Particularly, for deep learning based OD methods, need determine the network depth, width, learning rate,
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and method-specific hyperparameters.. As shown in Figure 2 the optimal hyperparameter combinations vary considerably across different datasets, leading to considerable challenges.
High computational cost and waiting time before deployment The training or fitting process often conecconumnnn, especially when the model and data sizes are large.
Waste of knowledge from historical datasets Historical datasets often contain useful and transferable knowledge about inlier and outlier patterns, which cannot be effectively used by the conventional OD methods.
In this work, we aim to address the three limitations above by constructing a universal outlier detec- tion model, called UniOD. The main idea is to use labeled historical datasets (widely available) to train a universal model capable of detecting outliers for all other tabular datasets without retraining. Specifically, extract uniformly dimensioned features for different datasets by building and factor- izing multi-scale similarity matrices. We then use graph neural networks to capture comprehensive within- dataset and between-dataset information simultancously, and formulate outlier detection tasks as node classification tasks, so as to distinguish inliers from outliers. After training, UniOI) can be applied to any newly unseen tabular datasets without further hyperparameter tuning and parameter optimization. An overview of UniOD is shown in Figure 3 Our contributions are as follows.
We propose a novel outlier detection method UniOD, that is able to leverage knowledge from historical datasets and directly classify outliers inside a newly unseen dataset without training.
UniOD has much lower model complexity compared to other deep learning based methods since outlier detection on all datasets can be done using single model. Additionally, UniOD is computationally cheaper for outlier detection because it skips retraining.
We provide theoretical guarantees for the effectiveness of UniOD, which is consistent with the numerical verification.
We conduct experiments on 30 datasets and compare UniOD against 17 baseline methods, where UniOD outperforms most of them.
2 RELATED WORK
OD Methods without Model Training Several nonparametric OD methods, e.g. k-nearest neighbor (kNN) (Ramaswamy et al. 2000), avoid explicit training. For instance, kernel density estimation (KDE) (Parzen 1962) detects low-density data. Local outlier factor (LOF) (Breunig et al.) 20000 estimates the local density of each sample and compares local density to that of its neighbors. More recently, ECOD (Li et al. 2022) leverages empirical cumulative distribution functions to capture tail probabilities, highlighting samples that are extreme along one or more feature dimensions.
Model//Hyperpprameeee Selection for OD OD methods often sensitive hyperparameter changes (Goldstein & Uchida, 2016 Ding et al., 2022). ). To address this, recent approaches leverage prior knowledge from historical datasets for automated hyperparameter model selection. For exam- ple, MetaOD (Zhao et al., 2020) and HPOD (Zhao & Akoglu 2022) exploit past performance records for prediction, while ROBOD Ding et 2022 ensembles models with different configurations to bypass manual tuning. ELECT (Zhao et al. 2022 incorporates dataset similarity. PyOD2 (Chen et al.
2024 and MetaOOD Qin et al. (024) employ large language models to reason about models and datasets. Despite their effectiveness, these methods typically require exhaustive evaluation of hyper- parameter combinations on historical datasets, leading to substantial computational cost espeecilll for deep OD models. Dai & Fan (025) proposed an inductive anomaly detection approach, which does not apply to the transductive OD setting.
Transfer Learning for OD Transfer learning (Van Haaren et al.) 2015 Weiss et al.) 2016) has been explored in outlier and anomaly detection to alleviate the scarcity of labeled data by reusing knowledge across related tasks (Andrews et al. 2016: Vercruyssen et al. 2017 Vincent et al. 2020). For instance, LOCIT (Vincent et al. (020) transfers labeled instances from source to target tasks, and detects anomalies using both unlabeled target and transferred labeled source instances. Although effective some cases, these methods face two major limitations: (1) they require strong similarity between source and target domains, which is often unmet in practice, especially for heterogeneous
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Labels
Loss:
Similarity Matrices
Feature Unification
GIN
Aa
X
GT
Historical
Labeled Datasets
D DHi
A Azz
X
GIN
MLP
Outlier Score
GT
Training
Aog
Xax
GIN
Testing Training & Testing
GT
OD Tasks D
Figure 3: Framework of UniOD. UniOD utilizes multiple labeled datasets to train a universal GNN- based classifier that generalizes across data dimensions and domains for OD.
tabular data; and (2) they require matched feature spaces, excluding the use of source datasets with differing dimensionalities or semantics.
3 METHODOLOGY
3.1 PROBLEM STATEMENT
(nT,)) be set of du, dirmmmmiiii Formally, let T; denote "task i",, and let Dr, = [x T. XT, ,.. I;
data and assume that it be partitioned into two subsets, Z. and Dequlier where |Dipller| > [Dyplier] and the data points Dip, are drawn from an unknown distribution with density function Pinlier such that Pinlier (x) > Pinlier(x') holds for any x E 'Dinlier and x' E DDgutlerr The primary task of outlier detection (OD) is to identify Doptier from Dr:- Notably, suppose there are B datasets, from B different domains, corresponding to independent OD tasks, existing OD methods train one model on each dataset independently, which implies B times of hyperparameter tuning and model training or fitting. In addition, the knowledge from datasets across different domains overlooked. For dataset Dra+1 need to train OD model from scratch.
Dr. Dr...... DTg.
3.2 PROPOSED METHOD
To tackle the challenges faced by previously proposed OD methods, we propose UniOD, which able use labeled historical datasets from different domains, easily available in this big data era, to train general model that can detect outliers in dataset from any unseen domain without conducting any retraining. Specifically, let 2H = (DH, D be set of M historical labeled datasets, which means:
(1) DH. {xx)) y ( (XH y )....... (xH, YHH (1)
(2)
(m#g) (nHe) }}, 1= M
(1)
x E RA:: yH. 1),
1.2...... ,
where n.,, and dis, denotes the number and dimension of data in historical dataset DH, respectively. y = (0, 1) indicates that the sample is an outlier. Also, let 2 = {Dr, Dr...... Dr } be a set of B unlabeled test datasets. The primary goal of UniOD is to train universal deep-learning based model using these historical datasets 2n, which can directly detect outliers these test datasets Dr without any further training or tuning.
3.2.1 MULTI-SCALE HIMILARIY-BASED DATA UNIFICATION OF UNIOD
Considering that datasets often differ in dimensionality, feature semantics, and sample size, we first apply preprocessing to harmonize their feature spaces staadardizzinngg both the number of dimensions and the semantic interpretation of each feature. Our key idea is to represent the datasets as point-wiss similarity matrix (graph), since a well-designed graph can capture the local and global structures of dataset, and graph-based methods, such spectral clustering, provide promising performance
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in solving various machine learning problems. Specifically, for each dataset DH, calculate similarity matrix AH,o, which induces a weighted graph, using a Gaussian kernel function with hyperparameter o, i.c.
| (a)
11 xH. 2
A (a.b) Hi. exp
Va, E
nH.
(2)
Here, we encounter two problems. The first one is how to select an appropriate a for (2) The other is that converting whole dataset into one single similarity matrix will result in too much loss of information. To solve the two problems, we choose K different 6, denoted as 01 ................................ and each is determined by o 35. where BA takes a value around and ē is set as the average distance between the data points in DH., i.e., σ TH; EXEDm, ΣXED,, ||x x||. Consequently,
we generate multiple similarity matrices Ah, {AH.oo matrix A o we use singular value decomposition (SVD) to generate uniformly dimensioned features across different datasets:
1K k= for each dataset. For each similarity
A H =(u;, .,, mn Idiag(A1, A2..... Ann, [V1, . Vong
(3)
X Xn.om =[ui, U2, u. dij 1/2
x//² ;..., 1//3 1/2)
where 0 < d < nH,, is the unified feature dimension. For convenience, we write X XHi (nn,) [& (2) .....,,H.oo HH
1T E R",, xd, which is the uniformly dimensioned feature matrix of sim- ilarity matrices A A h = 1,2,... K. As result, for the whole 2H = (DH,, DH DHu h. we obtain
2n (Xm, X iig..... &H E qan,xKo Rd
(4)
where Xn.. (X (iioo........ (Dr,, Drz..... Drg we have
X (l.ok)
Similarly, for the whole 2y
= XI,..... X
(5)
The role of converting each dataset into multiple similarity matrices and extracting SVD-based features twofold. First, constructing similarity matrices and applying SVD embeddings removes dependence the original feature dimensionality and semantics, thereby enabling a unified rep- resentation across heterogeneous datasets. Second, by applying a simple subsampling technique (introduced later) to each historical dataset, can generate diverse collection of training data for UniOD, which substantially enhances its generalization capability.
3.2.2 MODEL DESIGN OF UNIOD
After generating uniformly dimensioned features LH, one straightforward option is to train a classifier with an MLP to detect outliers in 24. However, this approach discards valuable information contained in the similarity matrices AH.oo. To fully exploit such point-wise similarity information, we treat each dataset as a collection of graph-structured data, where the adjacency matrices {A 1K define the graph structure and xH define the corresponding node features. In this way, the outlier detection tasks for the historical datasets 2H are reformulated as binary node classifications over graph-structure
data. To deal with graph- structured data, we use K graph isomorphism networks (GINs) (Xu et al. 2018) and K graph transformers (GTs) build our model, where each GIN is composed of 7,1 layers and each GT is composed of L2 layers. Specifically, we let
GIN
KGIN,, (XH,, AH.), i Z KGT,, (XH), i i 1., M
(6)
(7)
where 02 and 0g denote the parameters of the GINs and GTs, respectively. The details provided in Appendix|C Then the final embedding is the following concatenation
ZH
GT
R xd
(8)
where dss the dimension of final embedding. Then we apply an L3-layer MLP with parameters 0g followed by softmax function to predict the labels:
Y H1 softmax (MLP (Zn,),, i= 1,2, .... M
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where MLPp; 03 Rd RR? Then, minimize cross entropy loss [()) train our proposed UniOD:
M nug
1 M
((0)
log y H.
(10)
where 0 = (01,02, 02, }3} denote all parameters of our model.
After training, for each specific testing dataset Dr; E !r, we can use (2) and to construct multiple graph-structured data and obtain and GTss to obtain Zr, and finally use the trained classifier ML.Po oz to obtain the outlier score for each data point:
and then
input these graphs into our trained GINs
Outlier Score (x?..
[
(32 T:
(11)
where [ la denotes the second element a vector (16) In UniOD, a larger outlier score indicates higher probability for data point to be outlier.
In summary. for each historical dataset [T]. we construct multiple graph-structured representations via (2) and (3), and reformulate the outlier-detcctoon problem node-classffication task. These graphs are then used to train our GNN-based classifier 6 and 9 using (TO). After training, any new dataset is processed through the same graph-construuctinn pipeline and fed into the pretrained model to assign outlier scores according to II. thereby identifying outliers in the newly unseen datasets.
3.2.3 ALGORITHM AND IMPLEMENTATION OF UNIOD
We provide detailed algorithm including both the training and testing stages of UniOD in Algorithm D which is in Appendix due to space limitations. Note that to enhance the generalization capability create synthetic datasets by randomly subsampling 60% samples from each Di.-
of UniOD, where the outlier (anomaly) ratio remains unchanged from the original dataset. This operation is denoted as Subsampling( Pr,)) in Algorithm 1
THEORETICAL ANALYSIS
4.1 TIME COMPLEXITY ANALYSIS
We compare the time complexity of detecting outliers new dataset Dr (with samples) between the proposed UniOD and other deep-learning methods. To simplify the comparison, all neural networks assumed to share the same maximum hidden dimension For the deep- learning baselines (excluding UniOD), we fix the number of training epochs to Q and the MLP depth to L. For UniOD, we denote its total MLP layers by L and its atten- tion layers by L'. Table 1 shows the comparison among UniOD, ICL, and DPAD, while the complete comparison for all deep learning methods is in Appendix [
Table 1: Time complexity comparison (partial)
Time Complexity
DPAD
(Q of (QuiLdd)
ICL
UniOD
of + Kd) nd M+FL+o n
Previously proposed deep learning OD methods require training for each specific dataset, resulting in an increasing training time as the number of datasets grows. In contrast, UniOD uses only one model for all datasets, and its training phase is entirely decoupled from Dr, eliminating any need for per-dataset retraining. This decoupling enables UniOD to perform online outlier detection, yielding greater efficiency compared to methods that require both training and testing stages for each dataset.
Also, we compare the number of hyperparameters of different deep learning methods in Appendix E
4.2 GENERALIZATION ABILITY ANALYSIS
In this section, provide theoretical guarantee for the effectiveness of the proposed model. Particularly, we analyze that once the model is well-trained, it is able to provide high detection accuracy unseen datasets. This is nontrivial due to the following challenges:

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Given that are training universal model for outlier detection across diverse domains, the training data is not a single dataset. Instead, is composed of multiple different datasets, which makes the analysis more complex than the traditional analysis single dataset.
Because of the graph construction and SVD embedding (see and (3)) in each dataset, the data points are no longer mutually independent, which makes some classical tools in learning theory inapplicable.
The model consists of GINs, K GTs, and one MLP, making a very complex structure, which complicates the theoretical analysis.
For convenience, we use W to denote the set of all weight matrices of our deep learning model f. and use || II., Il 1l2.. and -122,1 to denote the Frobenius norm, spectral norm (largest signular value), and 62,1 norm (sum of lg norms of columns) of matrix, respectively. To simplify the notation and analysis, without loss of generality, we let: 1) Iry, n7; have a common layer number L, all MLPs (including those in GINs and GTs and the one following their concatenation) have common depth L', and every multi-heads attentions in the GTs have H heads; 3) GT's the layer normalization and residual connection are omitted since they have tiny impact the derivation and result; 4) d is the maximum of the widths of all layers in f. Although in (10) we used the cross enosspy loss, other loss functions, such as mean square error, mean absolute error, and hinge loss, also applicable. Therefore, for theoretical analysis, we consider general loss function denoted as E(y, 9). Then the average training error (empirical risk) on the M historical datasets denoted as [(f) = मे EM - E(y (f) H. sli)). The expected error (true risk) is denoted as L(f) y Σド ( (61)], where ly| denotes the number of samples in y. We are going to analyze the gap between L(f) and L(f). Note that we let l be 1 + y), L(f) will be the expected detection accuracy on test datasets.
TTM ni; 2) All GINs and all GT's
Theorem 4.1. Let ba
maxi, [|A ll,, cx maxk
H IF bw
maxwew | By maxwew | Suppose all activation functions are 1-Lipschitz, and È is Lipschiitz and bounded by B. Then, with probability at least - 5 over the randomness of
H, the following inequality holds
C(F) = +(f)+ 83
24V
K Kubly (CaIN + CCT) (n() +331
In (2/5)
(12)
M
2M
ble LLU T. 3/2 (/2 (Bw/bw)V/n((2 Vnn(dd), dex H1/22 I 8(1-1) /nn (2d), and s(1-1) = by (6-1) (1-1) + Vo. Particularly,
where
CGN
Car
assuming -ipischhit for self-attentions yields Cat = t 12 An(2dd).
The proof of the thcorem in Appendix A Note that (1-1) is too complex and is detailed in the proof. The assumptions made in the theorem mild. For example, regarding the loss functions, ReLU, Sigmoid, and Tanh are 1-Lipschitz continuous. The theorem has the following important implications:
When there are more training datasets, namely, M larger, the bound is tighter. This is consistent with our numerical result shown by Figure 4a
Due the V K in the bound, increasing the number K of parallelized GINs and GTs has tiny impact on the gap between L(J) and Ż(ʃ) but it can reduce the training error, thereby increasing the testing accuracy. This is consistent with the results shown by Figure 4b
When the layer numbers and L' are too large, the generalization ability of UniOD weak, especially when the spectral norms of the weight matrices are larger than 1. However, we can use spectral normalization to ensure the small bw in real applications.
NUMERICAL RESULTS
5.1
EXPERIMENTAL. SETTINGS
Datasets Our experiments are conducted on ADBench (Han et al.) 2022). which is a popular benchmark in outlier (anomaly) detection, containing widely used real-world datasets in multiple
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domains, including healthcare, audio, language processing, and finance. Detailed descriptions and statistical information about these datasets are provided in the Appendix F]]
Baselines and Hyperparameter Settings UniOD is compared with 17 widely-used bascline methods.
including traditional methods: KDE (Parzen 1962), ANN (Ramaswamy et al., 2000). LOF [Breunig
et al. 2000). VC-SVM (Schölkopf et al. 2001p. IF (Liu et (008)) LODA (Pevn 2016). ECOD
(Li et al.][2022] deep-learning based methods: AE (Hinton & Salakhutdinov 2006), DSVDD (Ruff
al.] 2018a), NeutralAD (Qiu al. 2021). ICL (Shenkar & Wolli (022), SLAD (Xu al. 2023),
DTE-NP (Livernoche et al. 2023b), DPAD (Fu et al. (0024) KPCA MMPP (Schölkopt et al. 1998).
MLP+TF, and one model selection method: MetaOD (Zhao et al. 2020). It is noteworthy that methods such as ELECT (Zhao et al,, (022) and HPOD (Zhao & Akoglu 2022) are not included.
since their meta-feature construction processes are not publicly available. MetaOOD (Qin al. 2024) is designed for out-of-distribution detection, and AutoUAD (Dai & Fan, (025) is limited to inductive anomaly detection. For DTE-NP,, DPAD, SLAD, ICL., and NeutralAD, we use the code provided by the authors. As for other methods, use the code from the Python library PyOD (Zhao ct al, 2019). For both traditional and deep methods, we use grid search to obtain the best-performing set of hyperparameters in the historical datasets, which is then used in our experiments The detailed hyperparameter configuration for grid search and MetaOD is provided in Appendix [ KPCA+MLP and MLP+TF are two baseline methods that uses historical labeled datasets for training. More details are provided in Appendix H.T
Implementation In our experiments, we consider 30 datasets and partition them into two equal groups (Group I and Group II). We use Group II as the historical datasets to train UniOD and use Group as the testing datasets. We also exchange the roles of the two sets, More implementation details are provided in Appendix H.2
Performance Metrics We use two metrics to evaluate the performance of UniOD and other baseline methods: Area Under the Receiver Operating Characteristic Curve (AUROC) and the Area Under the Precision- Curve (AUPRC), following (Xu al., [023] Livernoche et al.) [202b]] Kim et al.) 2024). The two metrics are threshold-free and hence can avoid the uncertainty and unfairness in determining the thresholds for the OD methods.
Table 2: Average AUROC (%) and AUPRC (%) of each method over 5 runs. including both training and testing, on Group datasets. The best and second-best results are highlighted in red and orange, respectively.
KDE (1962)
INN
AE
DSVDD (2018)
NatsIAD (2021)
ECOD (2022)
JCL
SLAD (2023)
DPAD (2024)
DTE-NP (2024)
KPCA +MLP
MI.P +TF
MetaOD (2021)
UniOD Ours
AUROC
(2000)
(2006)
(2022)
breastw
98.43
98.47
95.12
82.88
$4.92
99.14
82.57
$1.35
86.29
97.89
$8.16
97.21
97.71
99.10
Cardio.
50.27
51.91
55.55
71.36
38.63
78.53
40.82
32,60
30.62
49.23
97.21
74.41
60.51
51.20
fuult
73.05
66.25
46.87
90.55
57.21
IntemetAds
61.79
62.36
53.71
62.
67.77 67.70
42.73
66
65.
58.
63.50
landsot
62.46
61.58
29,87
42.59
61.92 92
36.78
69.91
24
52.72
50.
39.04
40.08
$6,80
69.10
optdigits
32.32
39.91
45.11
40.74
69.38
60:45
54.18
55.29
50.63
36, 36.38
56.63
44.04
87.22
73.50
PageBlocks
90.66
92.08
91.63
89.72
84.17
91.39
62.34
74.08
52,70
89.
76.26
71.41
75.99
88.20
pendigits
79.16
77.51
60.11
Pima
72.28
72.53
63.86
63.21
61.19
39.4
51.15
47.75
61.46
71.54
63.17
68.76
70.89
72.30
satellie
76.03
73.13
68.52
$7.25 25
62. 32
5% 30
59.017
68:21
64.76
68.91
55.30
61.50
65 20
86.90
catimage-2
96.44
99.88
95.71
96.69
79.71
96..9
64.50
95.97
81.22
96.59
59.62
96.74
91.51
99.70
SpamBase
49.52
$5.99
56.82
$1.09
65.56
18.68
$2.66
47.14
$3.14
$3.39
$1.36
66.20
$6.30
thyroid
95.83
91.35
60.25
97.71
42.61
82.68
Wavefomm
75.12
75.35
60.25
64.70
69.31
60.35
62.36
44.54
55.22
73,89
62.01
51.44
69.10
84.30
WDBC
95.01
98.43
84,37
97.00
30.17
97.06
86.33
70.20
93.63
97.97
89. 10
94.86
96.30
98.40
Average
74.55
76.00
70.78
70.22
61.29
73.90
55,48
64.77
62.29
73.75
66.13
69.24
75:45
78.93
AUPPCC
breastw
87.90
61.29
71:74
Cardio.
27.54
35.64
30.86
43.89
20.17
50.54
18.55
21.78
16.69
31.00
29:47
52.40
36.96
35.30
fauk
$4.57
52.08
48.16
33.39
43.69
32.57
39.
53.04
47.89
53.77
S4L08
36.42
42.77
49.10
IntemetAds
23.80
29.76
19.33
29.83
31.68
50.89
16.07
29.35
21.11
29.39
28.39
26.59
52.50
32,80
landsai
26.03
19.02
42.66
15,95
opidigits
1.97
2.19
2,43
2.35
5.13
3.37
2.91
2.93
2.95
2.09
3,09
2.36
5,00
PageBlocks
53.98
$6.83
$2.12
$1.98
32.69
51.90 1..99
31.58
36.85
11.82
$1.11
30.61
$4.55 49
29.08
46.20
pendigits
12.11
13.66
6.70
14.47
5.14
26.56
1,63
2.75
5.68
8.05
2.89
15 39
7.02
6.00
Pima
53.69
52.64
45.43
46.13
41.15
46.42
35,63
34.64
45.46
$2.07
46.80
50.01
57.18
$2.90
satelline
59.28
$1.63
40.74
52.61
43.85
45.81
47.16
41.56
salimage-2
31.80
94.52
28.47
78.87
2.85
65.97
1.59
37.66
8.42
40.75
43.99
86.93
29:83
95.70
SpumBaae
3W.29
41.36
41.91
43.23
38.63
51.83
26.72
40.66
38.42
40.38
40.41
39.71
$1.20
42.50
mhyood
28.60
40.22
35.72
26.02
4.23
46.78
2.16
27.23
14.58
32.36
50.68
40.81
49.56
44, 30
Wiveform
11.44
13.26
4.25
4.61
33.56
4.05
6.19
2.41
11.35
5.78
WDBC
25.49
53.35
2.02
50.53
9.73
8.61
54.07
47.17
48.51
22.88
31.99
Average
36.34
44.31
32.99
38.79
26:55
43.26
23.35
29.70
28.03
38.16
34.67
38.57
38.71
45.43
8

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Published as a conference paper at ICLR 2026
Table Average AUROC (%) and AUPRC (%) of each method over runs, including both training and testing, on Group II datasets. The best and second-best results are highlighted in red and orange, respectively.
KDI: (1962)
INN (2000)
DSVDD (2018)
ECOD (2022)
ICL (2022)
SLAD (2023)
DPAD (2024)
DTE-NP (2024)
KPCA +MLP
MLP +TF
MetoOD>> (2021)
UniOD
AUROC
(2005)
(2021)
ALOI
54.85
56.72
campaign
74.19
74.21
71.54
67.28
69.06
76.24
71.41
70.22
49.79
74.28
46.46
36.08
76.21
73.23
cardio
83.90
90.99
89.81
88.91
47.68
93.50
26.99
47.82
73.23
74.34
66.37
79.59
56.41
93.77
colcba
74.70
79.71
73:67
67.28
$4.49
75.25
64.90
66.13
51.73
74.60
58.31 34
39.47
69.73
81.21
wilt
34.02
57.57
59.83
12.03
hip
99,57
99.57
99.87
99. 70
91.71
98.27
35.05
99.95
51.61
12.54
99.90
65.
99.95
100.00
magic
70.00
76.39
72.80
67.
65.
64.78
65.82
63.91
55,39
30.60
73.48
63.95
70.99
70.10
87.17
84.92
86.95
62.21
56.47
85.23
shurtle
99.26
73.58
95.85
skin
51.25
76.04
49.55
59.51
78.65
48.86
33.57
83.12
64.64
71.43
57.39
62.75
65.19
76.12
sperch
52,02
47.83
47.49
45.70
$3.61
46.97
43.22
52.41
50.98
49.99
48.30
45.96
$1.88
46.97
smap
100,00
100.00
99.95
100.00
99.
100,00
99.91
100.00
74.25
100.00
99.99
78.85
97.81
100.00
letter
57.46
58.20
55.51
54.35
90.09
vowels
82,91
91.23
76.25
41.54
97.64
59.2 29
82.17
93.65
72.66
97:37
70.29
61.56
94,99
85.01
Average
75,80
78:45
73.93
70,50
70.99
72.67
57,90
73,18
59.43
72.92
67.24
61.99
73.28
78.52
AUPRC:
3,96
4.76
3,09
campaign
28.03
24.55
20.93
23,95
10.89
12.64
cardio
36.47
51.18
43.13
46.35
11.93
56.74
6.14
19.69
30.85
35.49
23.86
38.04
18.95
57.63
celeha
5.86
9.27
5:59
6.24
2.31
10.76
4.99
5.29
2.37
6.33
3.63
4,21
5.37
11.71
15.60
3,85
11:97
3.477
9.59
3.94
1,94
wilt
3.61
13.01
5.73
3.58
4.98
hmp
44.32
44.32
70.08
59.04
3.85
15.95
0.61
86.79
1.80
1.13
79.31
L.02
96.56
100.00
magic_g.
63.52
69.83
61.36
56.21
50,11
$1.50
55.26
$2./15
40.51
73.16
641266
$2.87
62.51
62.18
20.98
15,98
12:14
21.19
3,05
41.16
3.95
4,10
6.07
16.69
26.42
10.41
21.87
19.50
shurtle
skin
19.08
31,60
19.17
24.13
33.92
18.24
14.92
46.87
21.57
28.48
23.99
35.12
21,53
31.65
speach
1.77
1.88
1.84
1,99
2.28
1.96
1.39
2.48
2.0%
2.01
1.47
1.96
3.87
1.84
smop
100,00
100.00
58.33
100,00
27.63
100100
61.11
100.00
14,09
100.00
83.33
0.22
1.12
100.00
letter
35,42
15.30
9,44
42.13
17.99
30.41
6.64
9.32
$2.40
10.54
vowels
23.17
21.48
4.02
56.95
18.11
56.06
6.44
35.61
Average
32.24
29.92
28.82
31.20
19:41
30.66
15.73
30.92
12.39
27.92
23.99
15.69
25.72
36,09
5.2 RESULTS OF OD
The average AUROC and AUPRC performance on 15 datasets from Group I is shown in Table 2 In AUROC and AUPRC, UniOD) achieves the best average performance, which is 3% higher than the second-best method-KNN. Compared with KPCA+MLP and MI.P-TF, which also use historical datasets, UniOD significantly outperforms them.
Another interesting phenomenon is that simple traditional methods, such as ANN and KDE, out- perform most deep learning methods in various datasets. One reason is that in tabular data with low-dimensional features, even a simple Euclidean distance reflects semantic differences between different samples. However, the dimension of datasets increases, deep-learning based methods will be more powerful since methods like &NN and KDE provide implicit prediction results for high-dimensional datasets as discussed in (Jiang 2017
Gu et al. 2019).
Table 4: Time costs (seconds) comparison of different deep methods on 15 datasets.
AE (2006)
DSVDD (2018)
NeutralAD
ICL (2022)
SLAD (2023)
DPAD (2024)
UniOD Ours
(2021)
384
511
664
1391
485
788
240
To mitigate the influence of specific historical datasets, we conduct cross-vale vooss-validtion experiments. In this setting, the 15 datasets in Group are treated as historical datasets, and evaluation performed on datasets from Group II. For datasets containing more than 6,000 samples, we subsample them to 6,000 while preserving the original anomaly ratio, due to computational resource constraints. As reported in Table 3 the superior performance of UniOD demonstrates its robustness and effectiveness, indicating that its performance does not depend on specific historical datasets. Meanwhile, we provide TSNE visualization results of the learned representations Zr, on several datasets in Figure and observe that most outliers tend to gather into a small, dense cluster while a smaller portion of outliers appear as isolated nodes.

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Published as a conference paper at ICLR 2026
100
80
Performance (%)
80
Performance (%)
70
60
60
40
20
5
15
Number of Historical Datasets
Number of Bandwidths
AUROC (%)
AUPRC (%)
AUROC (%)
AUPRC (%)
(a)
(b)
Figure 4: Ablation study: (a) Average performance using different numbers of historical datasets; (b)
Average performance using different number of bandwidths for similarity matrices.
Also, we compare the time costs of different deep learning OD methods in detecting the outliers the 15 datasets from Group I, the results are shown in Table Note that the reported results exclude hyperparameter tuning time. UniOD achieves lower time cost than those dataset-specific deep OD methods.
5.3 ABLATION STUDIES
In this subsection, we conduct experiments investigate how each component our proposed UniOD affects its outlier detection performance. We first evaluate the performance of UniOD with 3. 5, 10, 15 training historical datasets (with sub-sampling augmentation) shown Figure 4a is obvious that the number of historical datasets expands, its generalization performance improves correspondingly. In Figure 4b we analyze how the number bandwidths affects the performance of UniOD. A larger K results in less information loss, which improves the generalization ability. These results are consistent with Theorem 4.1 For more detailed results, please refer to Appendix
CONCLUSION
This work proposed a novel and efficient outlier detection method called UniOD. The core idea of UniOD is leverage historical datasets to train deep universal model that can detect outliers in newly unseen datasets from diverse domains without retraining. By converting each dataset into graph-structure data and generating uniformly dimensioned node features, UniOD enables single model to handle heterogeneous datasets. We provide de both theoretical analysis and empirical results to demonstrate effectiveness and efficiency. Although UniOD primarily designed for transductive anomaly detection, it can also be applied to inductive anomaly detection by converting the training set and each test point into graph-structured data and computing their outlier scores.
ACKNOWLEDGMENTS
The work was partially supported by the National Natural Science Foundation China under Grant No.62376236, the General Program of the Natural Science Foundation of Guangdong Province under Grant No.2002441555011777 1771, and the Shenzhen Stability Science Program 2023.
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A PROOF FOR THEOREM 4.
Recall that our model f E F composed of K GINs and K GTs followed by an MLP. For convenience, in the main paper, have let each GIN have L layers and each layer has an MLP of depth L'. The GTs have the same sizes, The depth of the MLP following the concatenation of GINs and GTs is also L'. We have also let ba = max,, || H,,a, 22 ex maxk v E KH, 1 bw maxwew [ By maxwew |W]]a 12,11 Suppose all activation functions are L-Lipschitz, and f is μr p-piischitz and bounded by 3.
The main idea of our analysis composed of the following steps: 1) derive the covering number bound of F; 2) derive the Rademacher complexity bound of the loss function; 3) establish the generalization bound of f.
First, we analyze the complexity of the imput data X2 E R R.Madd, which is composed of (XH,,o J ==1,2 1,2,.... K. We show the following lemma (Lemma 3.2 in (Bartlett et al. (017)).
Lemma A.1. Let conjugate exponents (p, q) and (r, be given with p S 2, well positive reals (a, b, e) and positive integer m. Let matrix E RR" be given with |X||p I b. Then
a m22r
IN ((XA: A E dd || S a) e, 1111-115)=
<
In (2dm)
2²
For convenience, we drop the index of X. Denote := (X: || S cx}. According to the lemma, letting A be an identity matrix (a virtual parameter matrix), and letting p 9 2, 1, 00, have
dx 6²
I (X, 11e)
In (2d2)
(13)
The Lipschitz constant Ter of one GT is given by the following lemma (proved in Section B.I. Lemma A.2. Suppose the CT, the layer normalization is p-Lipschitz. Let Zp-1 be the imput of layer p. 1pp-lll2 S bl2 and
(p-1), 1), Then the Lipschitz constant of the GT is
S c2
L
TGT
II
11-1) + +v)
(14)
s=1
where u pbw VII self-attentions are n-Lipschitz then
vd and = pbl (1 + v Hbb m) and b/2 111-1) S cz
(1-1)
(6-2) afll
s -
LLL. Prorm (1+VHH) TGT = bW
(15)
According to Lemma
A.3
well-known result), we can bound the covering numbers of the GT:
RGT
In (FGr,
(16)
2
where Ror = c In (2d2).
Lemma A.3. Suppose ub is a t-Lipschitr,funccion then In F,P S InN((/R,FFF))
The following lemma (proved in Section B.2) provides an upper bound for the covering number of GIN model:
Lemma A.4. Consider the L-layer GIN, where each layer has an MLP of L' layers. For any > 0, it has
RGI
In (G. <
2
where RGIN = 62f 2x
22LL' L3L (KWssW/W)))))) In(2d))
Since model is concatenation of K independent GINs and K independent GT's the covering number bound of their combination is
K K(RGIN RCT)
In (FK, (l)) <
(17)
e²
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The K-GINs and K-GTs are followed by an MLP with L' layers, and the Lipschitz constant of the MLP is TMPP by- Consequently,
K KTML RGIN RCT)
IN 6, 11x) _
(18)
() the loss on one dataset is T(y, Since the overall loss is ε(f) = +/ E Ej= MyB. y H. 2ز=1 f(y,, 0z). Suppose l is p-Lipschitz with respect to Then according Lemma B.3 is
vn Lipschitz. Then the covering number of our model with loss is bounded
MO RAN RcT)
hN (f (1p) v
(19)
nE²
The Dudley entropy integral bound used by Bartlett et al. (2017) is shown below.
Lemma A.5 (Lemma A.5 of Bartlett al. (2017)). Let F be real-valued function class taking values in [0, 11, and assume that 0 E F. Then
4a
12
VM
RD(F) S inf az0
+
M
M
our method, |4] S 8. We let F = e o where <bx) - Jæ, then F is real-valued function class
taking values in [0, 1]. Using Lemma
A.5
we obtain
RD( < inf
4a
12
VM
In (
(5)
d( B)
a>0
VM
M
BVM
inf a>0
4a
12
JIM
9 (g.00..P)) de
E
(20)
v M
MB
Ba
(BVM
4a
S inf
(inM(cFF,p)de
a>0
VM
MB
Ba
Multiplying both side by 3 yields
4a,8 v M
12
PBVM
RD(F) S inf
VIN (p
(21)
as0
M
Letting Ku² Thar RoN Rea)
it follows that
,BN
4x,3
12
Rg(F) < inf
V ez
de
a>0
VM
M.
Sa
4a,3
12
VM
(22)
inf a>0
VM
In
48
12 (nM)
+
where we have chosen 1/VM.
Then, using the following lemma (a standard tool in Rademacher complexity (Mohri et al. 2018)).
the generalization bound of our UniOD can be derived.
Lemma A.6. Given hypothesis function space F and loss function tg bounded by O, define F8 == {(Z + (z(f y) E F}. Then, with probability at least 1 over a sample D of
size M, every f FF satisfies Cf( < Lo(f) + 2RD(Fo) 3,3 Ia (2/8)
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Specifically, we have
L() SL0)+ 83 24v 24v2222K/ KUTMLVVROm ROIN + Rot In(M)
In (2/6)
+ =38V
M
2M
(23)
si()+ 83 24v K ( /RRIN + /RoT) (M()
In (2/6)
+ +/81
Myn
2M
where RGIN 13 b 12LE' ( (bw/)w)) In(2d)) RGT = ox In (2d)), TGT
IT (ub2 (i-1)
+U)
pbw
Vd
VH
pblf- + VHbw vn), and b2
2
(i-1)
S
TGT; Cz
r ex. Dropping the terms related to the residual connections and layer normalizations in the GTss we complete the proof.
(1-2) 11
ub 2
If we assume that all self-attentions are n-Lipschitz then Tar bI phorm (1+ VHn)
B LEMMAS AND PROOFS
B. PROOF FOR LEMMA A.2
Proof. We denote ft the i-th layer of a GT. is composed of multi-head self-attention, residual connection, layer normalization, and MIP. To analyze the covering number bound of single GT, first present the following lemma for the Lipschitz continuity of self-attention.
Lemma B.1. Consider the following self- atffeattentoon mechanism
((Z) Softmax (ZWo(ZWK) K)
ZWv
Vd
where E Raxd and WQ: W Wy E Rd'xd, Suppose max [ [Wlll,, (Wvlee bott, then for any and Z' satisfying |Z[l22 S by and [|'|l2 I b,, it holds that
s
1
(I - S(Z')l S
1/3 Vamb + bau 1 Z'1l
(24)
Vd
Then, according the concatenation Lipschitz lemma (Lemmal B.4. the Lipschitz constant of the multi-head (H heads) attention is
L Lmulti-att = VH bbbnab + bur
(25)
Assume that the Lipschitz constant of the layer normalization is Pnorm: and the feedforward network has L' layers. Then the Lipschitz constant of the transformer layer
(1+ VHI
( + balevvi))
LGT. bby Pnorm
(26)
=ub(i-1) (t-1) 1) +
biy 13 Paorn and v Pnrrn (1 + / HHaee n). As 12,12 < (0 and Zz l2 <
where u
[1, we bound I2 |F instead, where |Zol| = ||||| S ex. That means, we let b be the upper bound of ZZ- F. It follows that
8 < LOT._, 8/-2
(27)
We have L layers in the GIN. Therefore,
Lor
(ubl (i-) +
(28)
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If all self-attentions 77 1--iisccitzz i.e.
(2 f(z') 5n 1F
(29)
then the Lipschitz constant of the transformer layer i is
LGT; -bW (1+ (1+V VHn)
(30)
which makes
LGT =by Pnorm (1+VHI))
(31)
B.2 PROOF FOR LEMMA A.4
Since the lemma simple variant of Lemma F.8 in (Wang & Fan 2024), we will not detail the proof here. For convenience, we show the original lemma (with modified notations) below:
Lemma B.2 (Covering number bound of GIN). Let || and d = maxi, de" Given
L-layer GIN message passing network For any
Rg
(c, < 2
(Et=l (n))) and kt = IT 83 = ( Rt)
where
RG =
24| ln
2/3
3/2
Σ 1=
In the lemma, let = Lt, c= ba.
by and Ki ( b.) b,.
-bw. we obtain Lemma A.4
B.3 PROOF FOR LEMMA B
Lemma B.3. Ler e(y) = ! Ej= ElVig Vtj)li Suppose is p-Lipschitz, then ē is J Lipschitz.
Proof. It can be proved by the following derivations:
| e(y')l
Σ (l(gig) v1s)
Elvig v15))
(Cly2g) V22)
ElV5g B2g))
Σ - (eluieg: UNi)
ElUNyy v'v,))
Mlyno vigl
MlU2) 1221
(32)
En pluNs - V/Kz
V -y |I
1
Vnl Y2 - 8-21
7
JYN - M/
y'1l
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B.4 PROOF FOR LEMMA
B.1
Proof. Let g()) 2W (ZW
We calculate
vd
lf( f(Z') 1 (g - Softmax(g(Z")
W v (5oftmax(((Z))22 (oftmax()(Z)))2'),
Wvlla
[|/Softma(((Z)))) Softmax(g(Z"))24 {/ 3
[|Softmax(sZZ))z
|
[SSottma((g()) Softmax(g(Z"))1 |Z
|| Z' Z'1l= |Sootmax(s(2"))1
Ti
(33)
For Ti, we have
Ti (l)( g(Z')llF
2/d
(lZWq Z
Z'W W x z + ZWWWW -z'Wo w
2vd
<
(IZ 1
Well W<ll 1 + 1 Z [Wll Wxll Z'
2vd
1
62
by
|| Z'l) 1
Vdl
(34)
For T2, have
T2 < |Sotmaa (a (Z
Softmax(t:)IP
(35)
Softmax (f:))l
m
where t; denotes g: (Z). Combining the results above, we obtain
[l((Z) - (Z S (1abieee + beermm 11 1z- Z'll
(36)
B.5 PROOF FOR LEMMA B.4
Lemma B.4 (Concatenation Lipschitz). For K matrix functions with the same input X, suppose each of them has Lipschitz constant Lx- Then the concatenation of these functions has a Lipschitz constant max Lgv / K with respect to X.
Proof. Given K matrix functions fi, fa.....fff fx with the same input X. the row-wise concatenation of the output is denoted Y, given by F F(X) (x) fx (X)). Suppose the Lipschitz
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constant of each fa is LR, k 1,2..... ..... K. We obtain
(i fi(X)
fa(X) f2(X')
[F(X) F(X)I|
(x(X) fK(X')
K
[lx(X) Ln (X')
(37)
K
X-
k=
K
< max Lk
Σ
X
k=1
= La
-XXIp
C ALGORITHM DETAILS C.I KGIN,, AND KGT,,
KGIN,, and KGT, 83 combinations of K GINs and GT's respectively. For the k-th GIN GIN and GT of parametered by 02, 02. their outputs follows:
Z GIN, GIN (H..
i= 1;,,,.,,M
(38)
GT GT #3 (XH.): i 1=,...,, M
Then, we have GGI and Z follows: H.
ZGIN
[ZGIN
GIN
ZGINK] B,NNK],C 01 (0) K
H..
(39)
GT
[ZAt
GT2
ZGT O2 10
H: 1
C.2 GIN
The details about GIN are as follows:
Vi E [1,2, 11, 11)++1 Socnn (1+c))oN
Σ
AhOoa
(40)
MEN()
where 11),++1 is the output from 1 1 GIN layer, 100,0 denotes the neighbor set of node j. fear is multi layer perceptrons (MLP) parameterized by ((+1), Eg is a learnable parameter.
())
H..ov is the input node feature, N(j)
C.3 DETAILED TRAINING AND TESTING ALGORITHM
The detailed training and testing procedures of UniOD provided in Algorithm
D DETAILED COMPLEXITY COMPARISON FOR DEEP-LEARNING BASED OD METHODS
In this section, we analysis the time complexity on conducting outlier detection for each deep-lcarning based methods. For all these methods which primarily MI.P in the form of encoder, assume
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Algorithm 1 Training and Testing Stages of UniOD
Training stage of UniOD:
Require: historical datasets 2H = (DH, DH....... D J. training epoch Q, LT 0, 2
Output:8"
1: for each historical dataset DHr E IH do
2: (Dny: Dnz, D n1. DHp, Dnp} = Subsapmling (Dı,))
3: Obtain dH = oH U {m l 1m= LH LH U (X Im= using 2 and respectively.
4: end for
5: Initialize the parameters of UniOD: 0
6: for 1......Q do
7: for each X म: E H. dH do
8: Obtain node classification prediction using 6 and
9: Update parameters 8 using (TO)
10:
end for
11:
end for
Testing stage of UniOD:
Require: newly unseen test dataset Dr, trained model parameters 0* Output:(Outiznn Score (5) pr; j=1 12: Obatain graph structured data XT, Ar, using 2nnd
13: Obtain outlier score Outlier Score (x7, pr,
using 6 }=
and 9)
that the largest hidden dimension is d, the training epoch is Q and the layer of this encoder is La for those methods using decoder as well, we assume the layer encoder is equal to L4. The time complexity comparison of conducting outlier detection learning based methods is shown in T Note that here we assume Several specific parameters for these models are:
new dataset Dz; between several deep-
SLADD: SLAD includes two hyperparamters r,c which defines the repeat time for data tmasfooration and the number of sub-vectors.
ICL: ICL includes a hyperparamter S dı; which splits each data into dy; + pairs.
NeutralAD: NeutralAD includes hyperparamter which determines the number of learn- able transformations.
DSVDD: DSVDD requires using AE to pretrain its encoder.
Table 5: Time complexity comparison of UniOD and classical deep learning based methods in detecting the outliers of new dataset Dr,-
Time Complexity
SLAD
Qurelaad
DPAD
Qnd(Ldd n))
ICL
QudLaF
NeutralAD
QueLid
DSVDD
QuL
AE
o Que, Lnd?
UniOD
(d Kd) + nd L + n dL'
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E HYPERPARAMETER COMPARISON OF OD METHODS
Most deep-learning based OD methods have several hyperparameters which can sigmificantly affect their performance. In Table 6 compare the number of hyperparameters of different deep- learning based methods. Notably, classical deep-learning methods require careful tuning of these hyperparameters when applied to newly unseen datasets. In contrast, when applied to newly unseen datasets, UniOD involves no hyperparameters to be tuned.
Table 6: The number of hyperparameters in recent deep-learning based methods and UniOD when applied to newly unseen datasets.
Methods DTE-NP
Hyperparameters
Number
k T h h, 7 Y, X, k T, T, K. m
2
SLAD
5
DPAD
3
ICL
4
NeutralAD
3
UniOD
0
F. STATISTICS OF DATASETS
In our experiments, we train our model using 15 historical datasets and evaluate the performance of 16 methods 15 widely used real-world datasets spanning multiple domains, including healthcare, audio, language processing, and finance, in popular benchmark for anomaly detection Han et al. (2022). The statistics of these datasets are shown Table These datasets encompass a range of samples and features, from small to large, providing comprehensive metrics and evaluations for the methods.
G HYPERPARAMETER COMBINATION OF OD METHODS
In our experiments, we perform a grid search on the historical datasets to identify the best hyper- parameter configuration for each traditional and deep OD method, and these configurations in subsequent evaluations. MetaOD further leverages these hyperparameter settings in traditional methods to train a model that predicts the optimal hhrrparamte pair for each testing dataset. The specific hyperparameter configurations for different methods are summarized in Table g
H DETAILED EXPERIMENTAL SETTINGS AND RESULTS
In this section, we provide more detailed experimental settings and results.
H.1 INTRODUTION OF KPCA+MLP AND MLP+TF
For KPCA+MLP, KPCA Schōlkopl et al. 1998) is first applied to obtain uniformly dimensioned
data across historical datasets. These transformed datasets are then used to train MLPs as classifiers. The main difference from UniOD is that similarity matrices are not directly utilized. Inspired by meta-learning approaches (Iwata & Kumagai 2020 2023: Hollmann et al. 2025), we also introduce another baseline, MLP+TF. In this method, each feature is first projected into a higher dimension using an MLP, then each sample can be represented as sequence whose length equals the number of features. and whose token dimension is the MLP output size. A transformer is then applied to extract embeddings from these sequences, followed by a sum readout function to obtain a representation for each sequence (sample), which is subsequently fed into another MI.P for classification.
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Table 7: Statistics of 30 real-world datasets in ADBench.
Data
Samples
# Features
# Outlier
% Outlier Ratio
Category
Historical
ALOI
49534
27
1508
3.04
Image
campaign
41188
62
4640
11.27
Finance
cardio
1831
21
176
9.61
Healthcare
celeba
202599
39
4547
2.24
Image
cover
286048
10
2747
0.96
Botany
Wilt
4819
257
5.33
Botany
http
567498
2211
0.39
Web
letter
1600
32
100
6.25
Image
magic.gamma
19020
10
6688
35.16
Physical
mammography
11183
260
2.32
Hcaltheare
shuttle
49097
7.15
Astromautics
skin
245057
3
50859
20.75
Image
smtp
95156
3
30
0.03
Web
speech
3686
400
61
1.65
Linguistics
vowels
1456
12
50
3.43
Linguistics
breastw
683
239
34.99
Hcalthcare
x
Cardiotocography
2114
21
466
22.04
Hcalthcare
x
fault
1941
27
673
34.67
Physical
InternetAds
1966
1555
368
18.72
Image
landsat
6435
36
1333
20.71
Astronautics
X
optdigits
5216
64
150
2.88
Image
X
PageBlocks
5393
10
510
9.46
Document
X
pendigits
6870
16
156
2.27
Image
X
Pima
768
268
34.90
Healthcare
satellite
6435
36
2036
31.64
Astronautics
X
SpamBase
4207
57
1679
39.91
Document
x
satimage-2
5803
36
71
1.22
Astronautics
x
thyroid
3772
93
2.47
Hcalthcare
Waveform
3443
100
2.90
Physics
X
WDBC
367
30
10
2.72
Healtheare
X
Table 8: Hyperparameter combinations of traditional and deep OD methods used for grid search and MetaOD.
Method
Hy perpaaraaeerr
Hsperparamderr 2
Total Methods
LOP
neighhons::
[1 10, 20, 15, 50, 60,
80, 100)
distance: mmmhhttan "uclldeun" "mankowski'
36
n. neighhoons: 1,,,,
50,
largest mean
OCSVM
nu (rain encor toll: [0.1. 0.2. 0.3, 0.4.0.5 U.,.0.,............ 0.91
kemael lincar poly Boly. db"" Sigunodd"
36
KDE
3.3.0.311,33..
mamnaatinn 'euclidean" 'minkowski"
13
n. cslimmiors:: [10, 20, 30,
100, 150, 200)
max [oatures: [0.1,
0,4, 0.5,06 U.7, D:9
81
LODA
hins: [10, 20, 30, 40, 50, 75, 100, 150, 200)
random cues: [5, 10, 15, 20, 25, 30)
54
Home: [10,501000]
[256,312]
DSVDD
12 regullario [1e-1.l-1]
spoch_nume num: [10,50,10]
NeuraaAD
Iruns: [5,10.15..00 15,20
Temp: [0.3.015.1.3]
ICL
max, negatives: 100,,000500,.0000
lemperaure: (0.30.5.0.8]
SLAD
n. slad. ensemble: [10,20.30,40
hiddeen dims: [32,64128]]
DPAD
[0..)..110...]]. K: (5,00,5,200
lamisda: 00.01.01111
DTTENP
2200,500010000200000
H.2 IMPLEMENTATION DETAILS
All of our experiments this paper are implemented using Pytorch (Paskke et al., 2017 on system equipped with an NVIDIA Tesla A40 GPU and an AMD EPYC 7543 CPU. In UniOD, we set the dimension of unified feature d = 256, the number a is determined as K 5, with { = (0.3, 0.5, 3, 5). Our KGIN,, comprises L1 4 layers with successive hidden- dimensionalities [1024, 1024, 1024, 64). As for KGTg2, the dimension of the feedforward network model is set to 1024 and the layer is set to L2 6. Classifier MLPp, e,, is 3-layer MLP with successive dadden-dimensionalltiess [128, 64. 2]. We use AdamW (Loshchilov Hutter 2017) as our optimizer with learning rate being 10-5 and weight decay being 10 to train UniOD for 50 epochs.
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H.3 EXPERIMENTAL RESULTS WITH MORE OD METHODS
The experimental results on more OD methods with hyperparameter tuning including the cross validation experiments shown in Table Tablegand and Table I0
Table 9: Complete average AUROC (%) and AUPRC (%) of each method on 15 tabular datasets of ADBench. The best results are marked in bold.
KDB
LOP
1BS
OC-SVM
.1E
LOBX
DSVEOO
NestrsAA
ECC0
JCL
SL.D
DRAD
DTE-SP
KPC.A.
XeteOO
05:43
65.20
98-21
19.01
95:12
96:16
92.41
$2.95
64.22
09.16
$1.57
51.30
15.29
V7.00
55.16
47.71
99.00
Cachhtloogmppty
30.22
55.56
31:91
66:18
61997
71:64
71.36
19.61
18.55
40-81
10.53
31.93
08:31
51.30
AniemetAde
09:79
02.55
02.36
61.00
53.71
06.57
45.52
08.42
42273
53.35
55.15
09.62
53.30
tankkt
62.45
52.86
0:335
41.16
09337
52:18
42.95
42.59
01.92
78:18
09911
67
52722
58.30
3934
36.8
56.10
apditri
32.32
39:91
51:18
13-12
52.41
40.14
09:38
50.45
34.13
29
30.33
35.03
13:80
pastiyii
99.15
48.11
99221
05.51
79.45
91.95
$7.87
71.55
92.14
35.64
53.33
72.06
04.61
12.11
11.50
Piasa
72.28
$6.10
72.53
67.45
03:39
57.06
52.35
55.21
61.19
59.44
51.15
47.75
61.46
71.54
63.17
70.09
12:30
saicline
06.03
65.43
63.33
69.50
73.85
51:35
62.31
55.10
5983
21
54.36
08.91
35.30
$6.90
SpuzeBacc
49.52
38.79
55.14
$4.15
55.99
62.92
45.47
56.92
$1.09
68.56
21.65
52.09
47.4
53.14
$3.39
05.20
$6.30
dreasd
05.23
16.54
95.43
15.40
05.27
58.10
94.81
91.35
68.25
99.31
41.81
83. 12
73.53
16.37
92.65
05.01
94.10
Wasclort
70.18
70.22
63.85
69.31
63.35
55:31
62.04
$4.30
Anerage Valle
74.55
85.10
16.00
14.06
70.76
17.35
59.68
10.12
64.29
15.40
53:46
66.77
62.29
73.75
65.13
73:4b
18:95
03.25
31.54
03.64
97:18
97.18
$9:30
K5.10
61:29
09.19
71:34
69.33 30
19.45
V1.15
-2:35
03.54
05:30
Cacketloogrmpty
21.54
11.64
41:12
33.30
41:11
41:15
43.89
20:17
18:33
21: 1/
18.59
31.00
29.41
35.96
15:10
Inserne
23.90
34.28
25.05
20.47
19.33
42.55
25.04
29.33
34.65
30.59
15.01
29.3
21.33
25.39
52.50
12.80
landka
26.03
23.44
25-72
12:15
20:23
21.15
15:31
19.02
28:33
16.15
41.64
20 21
22:04
25.13
15:55
34.29
28:10
apdiazia
3.71
2.43
4.57
2.19
1.35
5.15
2.91
1.93
2.05
2.09
3.09
pasdiyii
12.11
3.85
13.05
25.62
6.70
30.55
11.59
14.47
5.14
16.56
1.53
2.25
5.58
5,05
2.59
1,02
6.00
Pizza
$3.40
47:27
$2.64
49.58
43.43
40.10
45.35
46.15
41.15
46-42
35.63
36.66
45.45
$2.00
46.90
57.18
$2.90
veacliie
65.93
59:34
51.83
46:44
43.85
81
41..6
72
41.50
SpunBucc
38.29
33.72
4.33
40.51
41.91
48.15
31:91
43.23
39,63
51.53
25.72
401
38.82
40.38
40.41
53.20
42.50
dreasl
23.00
14.56
40.2
10.56
35.72
59.76
11.05
26.02
4.25
46.18
2.16
27
14.58
30.65
49.56
44.30
3.64
4.25
5.00
4.6
33.36
6.19
3.41
4.32
11.35
5.75
WBBC
55.35
57.80
Anergee Value
36.34
25.30
44.31
42.7
32.99
47.99
35.78
38.99
25.55
45.26
23.35
29.00 (1
28.03
16
34.67
35.71
40:43
Table 10: Complete average AUROC (%) and AUPRC (%) of each method on the 15 historical datasets described above, where the 15 test datasets described above are used as historical datasets. The best results are highlighted in bold.
KDD (1962)
LUF (2000)
LNN (2000)
DC-SVM (2/01)
AB
LUIDA
DISYLD (201.)
NeatralAl)
15.003
[C.1
SLAD
DPAD (20124)
DEEE-N
SIPCA
MesalD (28011
AUROO
(2000)
(2006)
(2016)
(2021)
(2002)
(2002)
(2003)
(2004)
+M7.7
Ouars
ALOI
55.25
55.27
53.57
55.21
55.00
53.33
54,33
54.35
56.16
51.60
52.11
56.72
$2.86
$4,39
campaan
14.19
70.52
74.21
13.58
71.54
13.26
$5.50
67.23 17.28
09.05
76.24
71.41
70.22
40.79
14.25
45.45
76,21
73.23
conbi
63.00
83:00
60.90
94.30
$9.51
01.25
$8.48
13:94
07.68
95 50
26 59
0282
73.23
16.3
65.11
16.50
93:77
odeabo
14.10
16.81
79.71
79.05
73.87
A6/31
39:43
25
18.34
$1:21
xtll
34.02
$2.30
44.96
41.31
43.35
52.22
19 41
59.85
51.05
55.00
57.13
51.12
$1.61
sip
09.57
19. 47
09.57
99.00
09.87
09.79
04.64
99.30
91.21
98
11
99.00
51.61
12:54
98.00
99.95
100100
10.000
56
72:80
12.99
11.37
$3.91
$0.50
33.45
10.00
merrography
67:17
56.36
shunle
44.50
02.06
59.05
$7.05
73.56
142.7
79.55
skin
$1.25
35.29
76.06
63.66
19.55
06.53
50.37
51.51
79.65
05.95
33.57
53.12
64.64
71.43
57.30
06.19
76.12
speech
45.00
47.80
47.53
16.87
46.57
44.7
05.70
53.61
66.97
50.41
50.95
19:00
45.30
58.88
46:57
sepp
$7.00
50
74.44
$7.17
57.
50.00
voneda
$2.91
05.14
91.23
76.91
76.25
27.00
75.99
41.54
97.64
59.29
62.
93.65
72.66
97.37
70.29
04.99
85.01
Average Vilee
15.80
71.88
18:45
15.36
73.05
15.55
70.31
20.30
70.99
12.87
50,
011
13.15
50.43
12.02
67.34
15.25
78.52
ALOI
4.26
4.33
3.95
4.25
4.26
3.54
4.31
3.56
4.35
3.30
3.09
3.79
3.65
4.76
3.41
2.79
3.62
compaign
16:03
36.47
26.77
51.18
57.10
$3.50
11555
56.74
30.85
15.00
16.55
odlibe
5.80
2.50
5.37
11:37
5.59
5.91
3.30
6.34
2.31
11.76
4.50
1.39
2.37
0.34
3.63
5.37
11.71
517
16.37
1.21
7.6
11.16
7.35
25.06
15:00
1.85
11.02
1.54
1.45
3.67
9.50
3.94
9.64
5.9
will
3.61
38.61
7.58
15.95
63.52
55.71
09.53
63.70
54.36
65.22
62.34
$6.21
50.11
$4.50
$5.26
$2.45
40.51
13.46
64.35
$2.54
62.45
20.06
12.99
15.06
12.22
12:14
24.44
25.55
21.19
3.55
41.16
3.05
4.10
6,07
16.00
25.42
21.87
19:50
skuile
91.86
9.50
$4.51
98.90
91.32
14:77
91.10
19.36
95.15
13.91
speach
1.77
2,13
1.54
1.84
1.07
1.45
1.59
2.76
1.96
2.48
2.06
3.01
1.47
186
smip
100.00
K3.53
100.00
100.00
96.15
3.49
$3.05
100120
27.67
100.00
61 11
100.00
14.00
100.00
$1.11
1.13
190100
viter
15.42
54.27
10.09
11:10
8:9
3.66
9:44
7.60
19996
16.07
6.50
10.41
6.54
10:54
31.46
34.43
15.10
4.03
8.14
Anerage Wilee
38.34
24.66
20.92
51.42
36.83
33.85
31.89
31
19.01
30.66
15.75
3032
13.39
37.90
33.99
35.73
36.69
H.4 EXPERIMENTAL RESULTS WITH OD METHODS USING THEIR DEFAULT IYYPERPARAEETER COMBINATIONS
In this subsection, evaluate the effectiveness of our hyperparameter selection strategy by comparing the performance of OD methods under their default settings versus our selected hyperparameters. The results with default hyperparameters are shown in Figure 11 Several methods, including &NN, LOF,
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Published as a conference paper at ICLR 2026
OC-SVM, DSVDD, and NeutralAD, achieve better performance under our simple tuning strategy, while others exhibit slight performance degradation. This outcome is reasonable for two reasons: (i) the default recommended hyperparameters in the original papers are already designed to be effective in most scenarios; and (ii) the randomly selected historical datasets may differ substantially from the test datasets in domain, feature semanties, and dimensionality, making it difficult to transfer well-tuned hyperparameters, such optimal hyperparamter different in different datasets can also be observed from Figure 2 This also explains that the performance of MetaOD is not as good as the most effective OD methods. Nevertheless, the fact that UniOD outperforms both default and tuned baselines highlights its robustness, even when historical datasets are not closely related to the test datasets.
Table 11: Average AUROC (%) and AUPRC (%) of each method using their default hyperparameter combinations on 15 tabular datasets of ADBench. The best results are marked in bold.
KDU
LD3 (2000)
JNNN (2000)
(USSVM (2001)
All
II (2008)
DSVID (2015)
NeuIiAAD (2021)
BU00
X1 (2022)
SEAD (2023)
DRAD (2024)
DTEEN (2004)
KPC.A
UnID
AUROC
(1952)
(2005)
44.90
07.20
$5.70
78.10
76.40
58.60
Candorocograpto
55.30
68.10
68:70
42.30
75.50
57.30
38.70
47.00
49..30
Intereehds
59.50
04.50
57.39)
62.20
62.90
05.40
59.20
61.55
0,3.00
53.50
landaat
62.50
54.70
$7.60
42:40
$2.60
46.20
38.00
70.90
36.50
64.30
67.50
55.70
60.20
49.50
$9.10
opidiees
$7.50
55:70
37.30
50.70
41.33 20
09.00
33.80
$4.70
60.50
53.10
54.00
45.50
35.00
14.80
73,50
Pageillnaks
W0.00
71 m0
33.40
91.50
85.3
88. 71
413 013.00
71
91.40
74.20
75.55 50
$4.00
501.00
66.40
63.70
peidiatt
72.30
59.10
94.70
74,30
93. 10
49.90
77.50
70,40
92.70
67.30
56.60
64.90
75.00
62.40
72.30
Pine
72.30
00.10
70.90
62.40
02.32 80
67.4 40
65.
57.10
59.40
51,50
$1.30
$5.40
70.70
53.70
72.30
satzllic
50:50
60.10
70.20
satmmage
53.60
50.50
Spomllon
50
94.10
91.40
73.20
50.90
Wassffrm
75:10
701 6m
90
67.20
67.40
70.70
63.00
77.10
63.30
44.80
73.90
$1.30
64.30
WDRC
95.00
98 00
47.4 40
98.80
94.40
98.58
97.70
26.90
97.10
75.10
57 60
$3.70
97.50
$8.50
99.10
Ascrige Value
74.40
59.77
72.11
73.43
71.53
76.62
68.73
60.05
73.90
63.70
66.87
66.97
74.07
53.50
78.93
AUPPC
beeasnw
05.50
29:70
92..90
91.70
90.55
06.20
$4.60
53.50
75,71
73.40
17.70
92.10
20.90
96,90
31:20
Intemssdda
30
33.90
39.70
51.90
53.20
20:30
opidiipi
25:10
24.70
22.30
19.20
25.50
BaceBlocks
5.00
3.50
2.50
4.70
2.00
3.02
29.00
2.10
1.90
$3.00
39.40
-6 90
$3.50
15.00 13.00
43.00
$4.40
26,
$1.90
29.
30.00
47.10
53.00
20:10
46.70
Fina
5.00
4.30
7.50
22.70
5.50
26.00
9.20
58. 50
66.40
$6.40
36.50
46.10
52,
$3.40
79.20
saneline
60.30
55.40
$1.90
65.50
55.00
54.90
55.10
40.30
52.50
46,50
51.00
50.00
55.30
29.30
95.70
2
$1.30
3.30
34.70
95.50
32.20
01.60
$6.30
2.19
63.90
10.30
27.80
4.50
$0.70
1,40
95.70
SpunBine
58.20
35.00
39.40
40.20
40.00
43.70
39.70
$7,40
$1.50
31.30
37.60
38.20
40.70
49.30
42.50
Hyydd
29.50
7:30
13.20
41
05. 10
701.0
3.40
00.71
5.00
17.75 77200
14.90
35,00
11:10
64,30
Wavefom
11:4
4.70
5.30
7,50
5.00
27.30
7.60
3.40
10.00
2.70
WDBC
57.50
47.80
41.60
49.30
30.70
55.30
53.40
1.90
50.50
5.70
23.50
18.10
46.50
3.40
57,80
Avenge Value
36.36
24.55 30
12
36.15
05.50 39
$7.50
24.71
83.20
25. 29.58
30.33
38.01
39.30
18.79
45.43
H.5 RESULTS OF USING MULTIPLY BAND WIDTH FOR SIMILARITY MATRICES CONSTRUCTION
Table 12 provides the OD performance results of UniOD 15 tabular datasets of ADBench using different numbers K of bandwidth for similarity matrices construction, the detection performance and generalization ability increase significantly, which mainly stems from less information loss of these datasets.
H.6 RESULTS OF USING DIFFERENT NUMBERS OF HISTORICAL DATASETS
Table 13 presents the outier-detection (OD) performance of UniOD on 15 tabular datasets from ADBench when it is trained with varying numbers of historical datasets, denoted by M. Even with M = 1, UniOD already achieves competitive performance on the "breastw" dataset. This early success is largely attributable to the structural resemblance between the single historical dataset and 'breastw' after both of them are converted into graphs. As M increases, UniOD is exposed to more diverse set of graph-structured training examples, which enables the model to learn richer, structure- trructur-invariantt representations of normal and anomalous patterns, thereby improving both its detection performance and its generalization ability to previously unseen datasets.
H.7 RESULTS OF USING ORIGINAL HISTORICAL DATASETS
In the training of UniOD, we use a subsampling strategy on each historical dataset to create more data for training, which enhances the generalization capability of UniOD. In this subsection,
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Published as a conference paper at ICLR 2026
Table 12: Complete average AUROC (%) and AUPRC (%) UniOD on 15 tabular datasets of ADBench using different numbers K of bandwidth for similarity matrices construction.
AUROC K = 1
K
K = 3
K = 4
K =
breastw
96.73
96.83
77.35
98.36
99.10
Cardiotocography
44.49
41.76
49.69
47.21
51.20
fault
55.73
71.06
66.86
66.15
69.60
InternetAds
60.50
60.56
62.84
62.19
63.50
landsat
66.20
61.47
63.53
63.93
69.10
optdigits
81.61
71.68
60.58
58.88
73.80
PageBlocks
93.46
94.55
85.88
87.48
88.20
pendigits
53.94
78.17
88.41
85.06
77.50
Pima
70.72
74.34
73.66
72.80
72.30
satellite
84.59
81.13
82.48
82.62
86.90
satimage-2
64.63
78.97
99.81
99.76
99.70
SpamBase
56.51
57.05
55.29
56.01
56.30
thyroid
97.69
96.23
90.70
96.94
94.10
Waveform
79.30
81.85
79.57
80.32
84.30
WDBC
87.20
74.90
95.29
97.17
98.40
AVG
72.89
74.70
75,46
76.99
78.93
AUPRC
breastw
92.75
90.20
93.02
97.69
96.90
Cardiotocography
26.90
26.84
28.54
36.30
35.30
fault
42.14
53.49
52.78
45.45
49.10
InternetAds
29.07
30.52
30.36
29.94
32.80
landsat
26.90
24.84
29.80
20.84
28.10
optdigits
6.81
4.57
4.04
3.10
5.00
PageBlocks
57.53
73.25
45.73
43.95
46.20
pendigits
3.34
4.54
4.89
7.85
6.00
Pima
51.02
54.62
54.75
52.42
52.90
satellite
78.03
76.59
81.47
70.82
79.20
satimage-2
7.97
19.50
49.60
96.24
95.70
SpamBase
42.92
44.22
42.26
41.07
42.50
thyroid
55.81
49.82
42.19
37.69
44.30
Waveform
8.40
16.87
14.94
6.96
9.60
WDBC
15.52
39.68
41,25
55.11
57.80
AVG
36.34
40.64
41.04
43.03
45.43
investigate how this influences the performance of UniOD by training UniOD using only the original historical datasets in Table
H.8 T-SNE PLOTS OF LEARNED REPRESENTATIONS Zr, ON MULTIPLE DATASETS.
In Figure we provide t-SNE plots of the learned representations Zr, on multiple datasets to illustrate their structure. We observe that most outliers tend to concentrate into small, dense cluster, while a smaller portion of outliers appear as isolated points.
We also notice that the separation between normal data and outliers is not particularly pronounced in the t-SNE space, which is likely because Zy; are digh-dimensional representations (with dimen- sionality 1000). As such, although simple MLP can effectively separate normal and anomalous samples in this high-dimensional space, t-SNE may not faithfully preserve the underlying geometry of the original embedding space.
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Table 13: Average AUROC (%) and AUPRC (%) UniOD on 15 tabular datasets of ADBench using different numbers M of historical datasets for training.
AUROC
M =
M = 3
M = 5
M = 10
M 15
breastw
84.59
15.39
70.53
98.39
99.10
Cardiotocography
28.37
64.32
57.71
61.71
51.20
fault
51.99
48.67
67.90
56.17
69.60
InternetAds
39.74
61.57
62.53
61.83
63.50
landsat
43.63
55.51
66.89
60.28
69.10
optdigits
43.15
70.63
66.30
62.65
73.80
PageBlocks
20.66
88.03
76.74
89.66
88.20
pendigits
7.19
56.70
79.32
87.98
77.50
Pima
37.73
67.64
72.58
71.18
72.30
satellite
28.42
76.14
84.95
80.18
86.90
satimage-2
7.10
98.12
99.65
99.84
99.70
SpamBase
53.85
56.11
55.42
55.60
56.30
thyroid
14.78
85.55
95.82
96.66
94.10
Waveform
31.75
61.11
77.37
81.22
84.30
WDBC
14.79
95.10
98.60
96.67
98.40
AVG
33.85
66.71
75.49
77.33
78.93
AUPRC
breastw
60.13
33.80
75.76
95.80
96.90
Cardiotocography
14.70
39.23
37.57
38.11
35,30
fault
34.20
31.96
48.42
42.63
49.10
InternetAds
16.35
33.11
30.88
29.74
32.80
landsat
17.39
23.01
27.22
24.05
28.10
optdigits
2.31
5.07
3.82
3.46
5.00
PageBloock
5.57
45.37
24.62
45.44
46.20
pendigits
1.21
4.25
5.05
8.45
6.00
Pima
30.47
49.20
53.20
53.63
52.90
satellite
22.04
74.01
79.25
75.38
79.20
satimage-2
0.65
58.84
92.87
96.69
95.70
SpamBase
48.92
42.50
41.31
41.05
42.50
thyroid
1.37
34.75
35.75
35.44
44.30
Waveform
1.94
3.55
6.22
9.00
9.60
WDBC
1.72
25.55
59.87
33.19
57.80
AVG
17.26
33.61
41.45
42.14
45.43
H.9 ROBUSTNESS EVALUATION OF UNTOD TO THE DOMAIN OF HISTORICAL. DATASETS
In this subsection, we conducted additional experiments where UniOD is evaluated on datasets from the physical, astronautics, and image domains, while systematically removing all historical datasets belonging to the same domain or field during training. As shown in Table 15 we observe that excluding these -mmncff-peccifc datasets does not lead a significant performance drop on the corresponding test domain, suggesting that UniOD is not overly sensitive to the particular composition of the historical training data.
We attribute this robustness to two main factors: (i) Even among tabular datasets within the same domain, the feature spaces and data characteristics can vary substantially. (ii) UniOD does not directly rely on the original raw features. Instead, it leverages similarity matrices to construct uniformly dimensioned representations across datasets. As a result, datasets from different domains may still exhibit similar structural patterns in their similarity matrices, enabling effective cross-domain generalization. Therefore, for a domain without historical data, our model, learned from the historical data of other domains, performs well.
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Published as a conference paper at ICLR 2026
Table 14: Average AUROC (%) and AUPRC (%) of UniOD on 15 tabular datasets of ADBench using only original historical datasets for training.
AUROC
Original
Subsampling
breastw
98.89
99.10
Cardiotocography
69.05
51.20
fault
51.28
69.60
InternetAds
61.62
63.50
landsat
47.11
69.10
optdigits
52.45
73.80
PageBlocks
89.94
88.20
pendigits
88.59
77.50
Pima
68.08
72.30
satellite
69.78
86.90
satimage-2
99.24
99.70
SpamBase
55.63
56.30
thyroid
95.08
94.10
Waveform
64.14
84.30
WDBC
98.54
98.40
AVG
73.96
78.93
AUPRC
breastw
97.73
96.90
Cardiotocography
43.52
35,30
fault
35.17
49.10
InternetAds
30.00
32.80
landsat
20.21
28.10
optdigits
2.73
5.00
PageBlocks
43.68
46.20
pendigits
8.47
6.00
Pima
49.18
52.90
satellite
70.21
79.20
satimage-2
92.35
95.70
SpamBase
40.96
42.50
thyroid
29.17
44.30
Waveform
4.44
9.60
WDBC
52.35
57.80
AVG
41.34
45.43
60
Nomral Outler
Sontal
Nomri Outlee
Outler
40
TSNE-2
-20
20-
-25
-40
-50
-60
-60
-75
50
50
TSNE:
TSME-1
TSNE:1
Cardio
(b) mammog.
(c) shuttle
Figure 5: T-SNE visualization results of learned representations Zy, on several datasets.
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Table 15: Performance (AUROC %) of UniOD on datasets from different domains when removing historical datasets from the corresponding domains.
Physical magic. gamma
Image
Astronautics shuttle
AL.II
celcha
letter
skin
AVG
UniOD
70.10
54.39
81.21
64.05
76.12
99.51
78.52
UniOD without Physical
68.47
54.13
86.48
75.15
87.49
76.42
UniOD without Astronautics
68.67
54.09
83.91
70.10
62.99
98.48
76.02
UniOD without Image
68.44
54.65
80.94
60.89
71.05
96.85
75.32
H.10 EVALUATION OF UNIOD ON LARGE-SCALE DATASETS
In this subsection, we evaluate the performance of UniOD on large-scale datasets. Due to the GPU memory constraint, we randomly partition large-scale datasets into disjoint subsets and run UniOD independently on each partition. Results Table T6 and Table demonstrate its effectiveness.
Table 16: AUROC comparison on large-scale datasets.
Data (samples)
kNN
ECOD
DTE-NP
UniOD
Campaign (41 188)
74.2
70.3
76.9
74.0
75.1
shuttle (49097)
65.8
99.7
99.2
62.5
99.2
Table 17: AUPRC comparison large-scale datasets.
Data (samples)
KNN
IF
ECOD
DTE-NP
UniOD
Campaign (41188)
27.7
30.7
35.4
26.6
28.9
shuttle (49097)
17.4
97.8
90.4
15.6
93.3
H.11 EXPERIMENTAL RESULTS ON THE OTHER 27 DATASETS FROM ADBENCH
To provide a more comprehensive evaluation, we have now conducted additional experiments using Group I for training and testing the remaining 27 datasets. As shown in Table 18 and Table 19 the results consistently demonstrate the effectiveness of UniOD.
29

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Published as a conference paper at ICLR 2026
Table 18: AUROC (%) comparison on the additional 27 datasets of ADBench.
Dataset
DTE-NP
ECOD
KNN
UniOD
annthyroid
81.8
79.1
81.5
79.1
68.8
backdoor
82.5
84.2
76.6
85.4
88.3
census
68.1
67.0
57.2
68.1
67.8
donors
81.6
86.4
76.3
83.5
89.1
fraud
99.5
99.4
99.1
99.6
99.2
ionosphere
92.7
72.8
84.7
92.1
81.5
mnist
82.6
74.1
79.7
85.3
86.1
musk
26.6
95.6
99.9
85.8
100.0
stamps
75.9
87.6
89.1
87.6
93.7
yeast
38.6
44.4
40.5
40.1
38.8
CIFAR10
85.7
84.7
85.3
88.5
89.8
MVTec-AD
99.4
97.9
98.5
99.3
99.0
agnews
62.5
50.5
53.0
61.3
56.0
20news
74.2
60.4
65.0
72.2
55.0
SVHN
61.4
51.2
53.9
59.0
67.0
MNIST-C
37.5
34.6
35.6
41.3
54.0
FashionMNIST
81.5
87.8
87.7
85.9
41.0
amazon
55.2
51.4
48.6
54.5
89.3
yelp
58.5
56.0
51.7
58.0
64.1
imdb
51.4
47.0
49.7
51.3
50.9
glass
86.6
70.5
78.4
86.7
79.4
Hepatitis
68.7
73.9
72.8
75.0
83.8
Lymphography
99.4
99.5
100.0
99.8
98.1
vertebral
36.1
42.0
36.8
35.4
28.6
WBC
98.8
99.4
99.4
98.4
99.2
wine
46.0
73.3
73.7
72.8
99.6
WPBC
49.6
48.1
48.3
52.9
55.1
Average
69.7
71.1
71.2
74.0
74.9
30

---

Published as a conference paper at ICLR 2026
Table 19: AUPRC (%) comparison on the additional 27 datasets of ADBench.
Dataset
DTE-NP
ECOD
KNN
UniOD
annthyroid
23.9
27.8
31.8
23.1
21.7
backdoor
42.7
8.6
5.1
45.5
35.4
census
9.1
8.6
6.6
8.9
8.8
donors
17.3
23.3
11.5
16.9
22.5
fraud
15.5
17.9
14.7
18.6
17.7
ionosphere
92.8
64.6
79.4
91.7
64.5
mnist
38.1
17.5
25.7
40.8
39.5
musk
8.7
49.2
97.9
38.1
100.0
stamps
21.3
31.4
30.8
30.2
45,0
yeast
28.9
33.3
30.4
29.9
29.1
CIFAR10
42.3
31.5
31.6
51.2
46.5
MVTec-AD
97.7
95.3
95.9
97.6
97.4
agnews
7.2
5.0
5.4
7.0
5.8
20news
12.0
6.6
7.2
10.7
5.7
SVHN
6.7
5.2
6.0
6.2
7.8
MNIST-C
3.8
3.5
3.6
4.0
5.5
FashionMNIST
22.7
32.8
34.3
30.5
4.0
amazon
5.6
5.2
4.9
5.4
38.8
yelp
6.2
5.4
5.0
6.1
7.3
imdb
5.0
4.5
4.8
4.9
5.0
glass
16.9
18.6
15.1
16.0
11.3
Hepatitis
23.8
29.2
26.9
31.5
58.2
Lymphography
85.6
89.7
100.0
94.8
71.4
vertebral
9.4
10.7
9.5
9.3
8.5
WBC
84.2
90.3
94.7
76.1
87.1
wine
8.0
19.1
17.4
13.8
94.3
WPBC
22.6
21.8
22.1
23.9
25.6
Average
28.1
28.0
30.3
30.9
35.7
31


Reviews:
[{"review_id": "dCs9aqAEXN", "reviewer": "Reviewer_tKHD", "summary": "This paper introduces UniOD, a novel framework for outlier detection that is generalizable to diverse datasets. The authors address the inefficiency of conventional OD methods, which typically require per-dataset retraining and hyperparameter tuning. UniOD tackles this by leveraging a collection of historical labeled datasets to train a single, universal model. The framework's key innovation is its data unification pipeline, which transforms each dataset into a set of multi-scale similarity matrices to create graph-structured representations. It then employs Singular Value Decomposition (SVD) to generate uniformly dimensioned features. Outlier detection is thus reformulated as a node classification task on these graphs, tackled by a GNN-based model. Once trained, UniOD can be directly applied to new, unseen datasets without any further training, demonstrating superior performance against 17 baseline methods on a benchmark of 30 datasets.", "questions": "1.\tIt will strengthen the paper if providing an analysis of the model's sensitivity to the composition of the historical training data. For example, how does performance on a specific target domain (e.g., finance) change when all finance-related datasets are deliberately excluded from the training pool? This would clarify the practical requirements for curating the training set.\n2.\tThe O(n²) complexity for similarity matrix construction is a potential bottleneck. It will be helpful to explore more scalable graph construction techniques, such as those based on approximate nearest neighbors, to enhance the framework's applicability to datasets with millions of samples.\n3.\tIt will be helpful to provide some qualitative analysis on the structural patterns the GNN model learns to distinguish outliers. For instance, in the graph representation, are outliers typically identified as isolated nodes, or do they belong to small, dense clusters disconnected from the main graph component? This would provide valuable insight into the model's decision-making process.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "•\tA Novel Paradigm for OD: The primary strength is the innovative concept of a universal framework that eliminates the need for per-dataset retraining. This directly addresses a major bottleneck in the practical application of outlier detection.\n•\tElegant Unification of Heterogeneous Data: The use of multi-scale similarity matrices combined with SVD is a powerful and clever technique for creating a unified feature space from datasets with diverse dimensionalities and semantics.\n•\tStrong Empirical and Theoretical Backing: The claims are convincingly supported by comprehensive experiments on a large benchmark, which is further bolstered by a theoretical analysis of the model's generalization ability.\n•\tHigh Practicality and Efficiency: By decoupling training from testing, the framework is highly practical and computationally efficient at inference time, making it well-suited for real-world scenarios requiring rapid analysis of new data.", "weaknesses": "•\tHeavy Reliance on Historical Data Composition: The model's success is fundamentally tied to the quality, scale, and diversity of the historical datasets. The paper lacks an investigation into the sensitivity of the model to the composition of this training pool.\n•\tPotential Scalability Bottlenecks: The methodology relies on constructing an n*n similarity matrix, which has a quadratic complexity (O(n²)) with respect to the number of samples. This could be computationally prohibitive for very large datasets.\n•\tLimited Exploration of Graph Construction: The framework exclusively uses a Gaussian kernel to build the similarity matrices. An investigation into different kernel functions or alternative graph construction techniques would have strengthened the paper's claims of robustness.", "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": "n3XYu8rrxl", "reviewer": "Reviewer_53cw", "summary": "This paper proposed UniOD, a universal pretrained model for outlier detection. UniOD learns from various historical tabular datasets and can directly score the outliers for new datasets in a zero-shot manner, without re-training the model or hyperparameter tuning. The datasets are converted into point-wise kernel matrices at different scales and a GNN is trained on graph-structured datasets.", "questions": "See the weaknesses above.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. Plug-and-play: this paper proposes the UniOD framework by pretraining on various datasets and conduct inference in a zero-shot manner, saving the deployment cost for OD tasks.\n2. Unified dataset representation: this paper utilizes the multi-scale similarity and SVD to produce unified node features, enforcing the generalizability of the model.\n3. The authors provides both comprehensive theoretical justification and extensive empirical analysis of the method. UniOD is well theoretical grounded.", "weaknesses": "1. Dependence on historical datasets. UniOD requires labeled historical datasets, which can be unavailable in real-world applications. The limited historical datasets may impair the performance of UniOD on new datasets, especially when the historical datasets is limited to few domains.\n2. Generality concern: the effect of dataset variability is not fully discussed in the paper, as this will potentially influence the model's generality if the model hasn't encountered datasets from similar distributions.", "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": "WwSAHze8Xj", "reviewer": "Reviewer_efRk", "summary": "This paper proposes UniOD, a universal outlier detection model designed to address the core limitations of conventional methods, including the significant efforts required for hyperparameter tuning, the need for repetitive model training on new datasets, and the inability to leverage knowledge from historical datasets. The key contributions of this work are fourfold:\n\n1. **Problem Formulation**: It is the first to explicitly define and formalize the problem of universal outlier detection, which aims to \"train a single model that can directly generalize to any unseen tabular datasets from diverse domains without any retraining or hyperparameter tuning\".\n\n2. **Technical Framework**: It introduces a novel technical framework based on a \"graph reformulation\" process, which unifies heterogeneous datasets by constructing multi-scale similarity matrices, decomposing them into uniformly dimensioned features via SVD, and subsequently employing graph neural networks for node classification.\n\n3. **Theoretical Analysis**: It provides a theoretical generalization bound, offering mathematical guarantees for the effectiveness of the proposed method.\n\n4. **Experimental Validation**: Extensive experiments demonstrate that UniOD outperforms 17 baseline methods on 30 datasets while achieving faster inference speed.", "questions": "1. **Scalability and Computational Efficiency**  \nThe paper indicates that datasets exceeding 6,000 samples required subsampling due to computational constraints. Have the authors explored more scalable graph construction alternatives, such as k-nearest neighbor sparse graphs or Nyström approximation methods, to avoid full similarity matrix computation? Could experimental results demonstrate whether these approaches maintain performance while handling datasets at larger scales (e.g., tens of thousands of samples), thereby improving practical applicability in big data scenarios?\n2. **Analysis of Performance Boundaries**  \nWhile UniOD shows strong average performance, simpler methods outperform it on specific datasets (e.g., Cardiotocography, Pima). Could the authors provide further analysis identifying dataset characteristics where UniOD may underperform? For instance, are there correlations with meta-features like anomaly ratio, dimensionality, or cluster structure clarity? Defining such boundaries would offer valuable guidance for practical application.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This paper presents several noteworthy strengths:\n\n1. **Paradigm-Shifting Contribution**\n   - First explicit proposal and systematic formalization of \"universal outlier detection\"\n   - Core innovation: single model generalizing across diverse domains without retraining or hyperparameter tuning\n   - Represents fundamental reformulation of conventional outlier detection paradigm\n\n2. **Technical Innovation**\n   - Elegant graph reformulation process transforms heterogeneous tabular data\n   - Creates unified, structurally learnable representations from disparate datasets\n   - Overcomes limitations of existing transfer learning approaches that require:\n     - Extensive hyperparameter evaluation\n     - Strong domain similarity assumptions\n\n3. **Theoretical Rigor**\n   - Provides generalization error analysis beyond empirical demonstrations\n   - Offers mathematical guarantees for method effectiveness\n   - Enhances academic credibility and theoretical foundation", "weaknesses": "While the proposed UniOD framework demonstrates compelling performance, several limitations warrant discussion for future improvement:\n\n1. **Scalability Challenges in Preprocessing**  \nThe O(n²) computational and memory requirements for similarity matrix construction present practical constraints, as evidenced by the needed subsampling for datasets beyond 6,000 samples. Future work could explore approximate nearest neighbor techniques or sparse graph construction to enhance applicability to larger-scale datasets.\n\n2. **Dependence on Euclidean-Based Similarity**  \nThe reliance on Gaussian kernel similarity (and consequently Euclidean distance) may limit performance in scenarios where this metric is suboptimal. Incorporating learnable or adaptive distance metrics could strengthen robustness across diverse data distributions.\n\n3. **Sensitivity to Historical Data Availability**  \nWhile leveraging multiple labeled historical datasets is a strength, the framework's effectiveness in domains with extreme scarcity of labeled anomalies remains unverified. Investigating few-shot or semi-supervised adaptations would valuablely expand its applicability.", "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": "pKjAULr9W9", "reviewer": "Reviewer_v82N", "summary": "The paper proposes UniOD, a universal outlier detection framework that trains a single model on a collection of labeled historical datasets to detect outliers in new, unseen tabular datasets without retraining or hyperparameter tuning. To achieve cross-domain generalization, UniOD constructs multi-scale similarity matrices from each dataset, factorizes them via SVD to obtain uniform-dimensional node features, and then employs a hybrid architecture of GINs and graph transformers to perform node-level binary classification (inlier vs. outlier). The method is evaluated on 15 datasets from ADBench.", "questions": "Could the authors clarify the criteria used to select these 30 datasets?\nCan the authors provide qualitative or quantitative analysis of when and why UniOD fails?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1.\tThe proposed method introduces a novel paradigm shift from dataset-specific to universal outlier detection, which is underexplored in the literature. \n2.\tThe methodology is well-motivated and technically sound. The integration of SVD-based feature unification, graph construction, and GNNs is carefully designed to handle varying feature dimensions and semantics. The theoretical analysis provides a nontrivial generalization bound that aligns with empirical findings.\n3.\tThe paper is generally well-written, with clear figures and a logical flow from problem statement to evaluation.", "weaknesses": "1.\tThe authors state that experiments are conducted on 30 datasets from ADBench, split into two groups of 15 for cross-validation. However, ADBench actually contains 57 datasets, not just 30. The paper does not justify why only a subset was selected, nor does it clarify the criteria for partitioning. This raises concerns about potential cherry-picking. The authors should either (a) use the full ADBench tabular benchmark, or (b) explicitly state the selection rationale and provide results on a broader set to demonstrate robustness.\n2.\tThe paper partitions the 30 ADBench datasets into two fixed groups of 15 for training and testing, and performs a single cross-validation swap. While this demonstrates basic robustness, it does not adequately address how historical datasets should be chosen in practice or how performance varies under different selection strategies.\n3.\tThe claim of universality is compelling but narrowly validated. All experiments are on tabular data; it remains unclear whether UniOD can generalize to other modalities (e.g., images, time series) without significant architectural changes. Clarifying the scope of “universal” (i.e., universal across tabular domains only) would temper overstatement.", "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)