Tabular Anomaly Detection

While deep features have transformed anomaly detection in images and video, their impact on tabular data has been less substantial, partly due to the limited availability of strong deep representations. Recently, prior-data fitted networks (PFNs) have emerged as a promising source of such representations for tabular data. In this work, we investigate how PFN representations can be adapted and leveraged for anomaly detection. The question is harder than it looks. No anomalies are available before deploy- ment, so model parameters cannot be tuned with supervision, and the reference set that defines normal behavior may itself contain the very anomalies it is supposed to reveal. We begin our study using frozen TabPFN features. Scoring each sam- ple by its distance to its nearest neighbors in feature space already gives strong results. We identify which layers to use and a feature-extraction procedure suited to the task. Next, to further improve performance, we use the reference set to fine- tune the model, so that the resulting features better separate normal samples from anomalies. On the ADBench benchmark, our fine-tuning free approach (ZEN) reaches a higher mean AUROC than every baseline, and our fine-tuned method (FOCUS) improves on it further. Our approach also generalizes across PFN models.

Answering questions over imperfect tables requires handling errors that can affect the answer. We investigate two challenges for large language models (LLMs): whether error discovery depends on where errors appear in a table, and whether providing their locations is sufficient for accurate question answering (QA). Using human-reviewed instances from RADAR-T, we conduct controlled studies across three LLMs by varying row order and comparing original, error-marked, and repaired tables. First, reordering rows changes error discovery even when the table contents and gold answer remain unchanged. During direct inspection, LLMs are more likely to discover all rows containing relevant errors when these rows appear later in the table or are grouped more closely together. Second, providing verified error locations alone is insufficient for accurate QA: with code execution, accuracy on repaired tables exceeds that on error-marked tables by 39.0-59.1 percentage points across the three LLMs. As a practical application of these findings, we combine error discovery across shuffled table views with explicit guidance for verifying and handling the reported errors in a simple workflow, Geometry-Balanced Discovery and Intervention (GBDI). On RADAR-T, GBDI improves QA accuracy by 3.8-18.5 percentage points over a code-agent baseline across five LLMs (paired 95% confidence intervals exclude zero for four), at the cost of additional inference. These results highlight the importance of both reliable error discovery and effective error handling in QA over imperfect tables. Code is available at https://github.com/645-t/GBDI-ICLR-2027.

Reconstruction-based anomaly detectors are accurate but opaque: a deep autoencoder flags a sample without telling a practitioner which feature ranges made it anomalous. We propose DIFFINT, an autoencoder whose latent bottleneck is structured as a set of soft, axis-aligned interval memberships learned end-to-end directly from raw numerical data, without any discretization or binarization. Each latent unit corresponds to a human-readable hyper-rectangle in feature space; an instance is encoded by how strongly it falls inside each interval relative to the other units, and its reconstruction error is the anomaly score. This keeps the power of differentiable representation learning while exposing an inspectable internal structure. We make the inductive bias precise: a certified reconstruction-error lower bound for points that fall outside every active coordinate of the learned support (with a Lipschitz-enforced decoder), and a graded, empirically verified suppression mechanism for the usual case in which only a few features are abnormal; and we provide a closed-form, label-free importance that ranks each (unit, feature) pair from quantities the model already maintains, turning trained intervals into auditable candidate constraints without ever seeing an anomaly label. On 48 ADBench benchmarks against 22 baselines under a common [-1, 1]-normalized protocol, DIFFINT attains the best mean rank overall on both metrics (4.10 on ROC-AUC, 4.16 on AUPR); among inlier-only detectors it leads its regime clearly, and it is competitive with the strongest contaminated-data detectors (see the stratified and complete-case analyses). It is the only interpretable detector in the statistically-tied leading cluster of seven methods.

Unsupervised anomaly detection scores each point of an unlabelled, contaminated sample in a single pass, and increasingly must also explain why a point is flagged. Yet the dominant detectors give a score with no account of which features drive it, and explanations are bolted on post-hoc with SHAP or LIME, which re-query the detector thousands of times per point and only approximate it. We introduce WAND, an unsupervised tabular anomaly detector that is explainable by design. WAND organises its computation around directions on the unit sphere, scoring each point by how far its projection escapes a sub-Gaussian extreme-value baseline. The originality of our approach is that the witness directions that flag a point, being vectors in feature space, are its explanation, a per-feature attribution obtained at no cost over scoring and, since the score is differentiable, recoverable by gradients. Scoring is linear in the sample size, and a probe-efficiency bound guarantees every anomaly a witness, hence an explanation. Across 47 ADBench datasets WAND attains the best mean Friedman rank at ROC-AUC parity with 16 unsupervised baselines, so the gain is interpretability at no accuracy cost; its native explanations are more accurate and faithful than post-hoc SHAP/LIME and ECOD at a fraction of the query cost. WAND is thus a practical, interpretable solution for explainable anomaly detection.

Tabular anomaly detection (TAD), which focuses on identifying abnormal samples that deviate from the majority in tabular data, has received growing attention. Recently, there has been an emerging trend towards unified TAD, which seeks to detect anomalies across different datasets using a single generalizable model. In unified TAD, aligning heterogeneous data remains challenging. While existing methods often rely on distance-based unified feature construction, they may obscure the semantics of the original features. Moreover, existing approaches typically formulate anomaly detection as a binary classification task, which may overlook diverse anomaly patterns from various datasets and be misled by unrepresentative synthetic anomalies. To address these challenges, we propose an in-COntext REconstruction approach for unified TAD (CORE for short). It introduces a decorrelated feature alignment module to directly align heterogeneous features into a unified representation space, which retains their semantic information. Meanwhile, CORE formulates unified TAD as an in-context reconstruction problem, eliminating the need for labeled or synthesized anomalies. Specifically, the in-context reconstruction module reconstructs each sample by leveraging contextual normal samples to capture dataset-specific distributions, such that reconstruction errors reflect its deviation from normality, facilitating unified TAD on arbitrary unseen datasets.

Fraud detection systems must scale with rising transaction volume while remaining explainable and reviewable. We study a layered pipeline on the PaySim dataset that combines a gradient-boosted classifier, graph-derived structural features, an autoencoder-based anomaly signal, TreeSHAP explanations, and a bounded LLM investigation agent applied to cases the classifier scores uncertainly. Before any model comparison, we identify and remove a simulator-specific balance shortcut that would otherwise inflate baseline performance. After this correction, neither the graph features nor the anomaly signal improves Average Precision on the full test set. Both, however, rank fraud better within the subset of cases receiving intermediate baseline scores. In a controlled experiment with injected multi-account fraud rings, engineered structural features recover all injected test transactions, while the tabular baseline misses roughly a quarter of them. The investigation agent underperforms direct thresholding of the classifier it relies on, reaching 65.0% accuracy against 71.7% on a balanced 60-case sample, despite having access to model explanations, graph context, and retrieved reference cases. Of the eight decisions the agent changed, six replaced correct classifier outputs with errors, and it produced a coherent written rationale in each case. An exploratory disagreement-based escalation rule flagged two of these agent errors for human review without flagging any correct decision. We conclude that each component of a layered fraud system contributes only under specific conditions, and that a plausible rationale from an investigation agent is not evidence of a better decision.

We introduce FlexTab, a flexible encoder-decoder architecture for in-context learning on tabular data that pairs a single, task-agnostic encoder with a suite of task-specific decoders. Unlike existing tabular in-context learners, which entangle feature representations with a specific prediction target, our design produces target-agnostic row embeddings that can be leveraged across a wide range of downstream tasks within a table-native in-context learning setup. We demonstrate this flexibility on six distinct problems: classification, regression, anomaly detection, clustering, entity matching, and entity classification in relational databases. Both the encoder and the task-specific decoders are trained on a large corpus of real-world, unlabeled tables. FlexTab achieves state-of-the-art performance on classification, regression, anomaly detection and entity matching, while remaining competitive with specialized models on entity classification in a relational setting. These results demonstrate that a single shared encoder, paired with task-specific decoders, can serve as an effective general-purpose backbone for diverse tabular prediction problems. The inference code and checkpoints will be made publicly available at https://github.com/SAP-samples/flextab.

Unsupervised tabular anomaly detection requires methods that are accurate, robust across heterogeneous datasets, and computationally efficient. Classical statistical detectors are often efficient, but they usually rely on a fixed data view and a single notion of abnormality. Deep anomaly detectors can learn more flexible scoring functions, but they are substantially slower and difficult to tune in unsupervised settings due to the lack of a reliable supervisory signal. We propose RGLD, a randomized global-local density estimator for efficient unsupervised tabular anomaly detection. RGLD combines a global random-feature density branch, which identifies samples in broadly low-density regions, with a local neighbor branch, which detects samples that are weakly supported by nearby observations. Both branches operate over feature-bagged randomized views, allowing RGLD to expose anomaly evidence that may be hidden in any single representation. We conduct experiments on 47 tabular datasets against 23 statistical and deep anomaly detection baselines under fully unsupervised setting. RGLD achieves the strongest dataset-level AUROC performance, ranking 1st in dataset wins, and ranks 2nd in AUPRC wins. RGLD is also faster than all evaluated deep detectors, achieving 50x-580x speedups, and remains competitive with statistical methods in runtime, yielding a favorable accuracy-efficiency tradeoff.

Continual anomaly detection in tabular data is challenging and remains largely underexplored, particularly in settings with heterogeneous feature schemas, distribution shifts, and severe class imbalance. In many real-world applications, data arrive sequentially from diverse domains, rendering conventional continual learning methods ineffective due to their reliance on a fixed input space. We propose a continual learning (CL) method, which can overcome these challenges and continually learn from different tasks. Our method consists of three main parts: our AGF model, Taskfusion augmentation, and outlier exposure. The AGF-model maps task-specific features into a shared space, then aligns distributions to reduce representation drift, and learns anomaly decision boundaries in the aligned space. To improve stability, we introduce Taskfusion augmentation, combining boundary-aware interpolation within tasks to refine the model anomaly boundaries and cross-task mixing to transfer anomaly structure across datasets. To handle class imbalance and memory constraints, we employ tabular dataset distillation to store compact synthetic replay samples, which are jointly used with augmented data in an outlier exposure objective for robust anomaly detection. We evaluate the approach on 21 heterogeneous datasets across multiple domains. Results show that our approach substantially improves continual anomaly detection performance over sequential fine-tuning and other CL baselines while reducing catastrophic forgetting and maintaining stable detection across heterogeneous datasets.

Anomaly detection aims to identify samples that deviate from the nominal data distribution and is central to many safety-critical applications. However, developing effective anomaly detection methods for categorical, mixed-type, and discrete sequence data remains challenging and relatively underexplored. Masked diffusion models provide a natural way to model such data by learning to recover masked values from the remaining visible context. In this paper, we propose Masked Diffusion for Anomaly Detection (MaskDiff-AD), a forward-only method based on masked diffusion models trained only on nominal data. Given a test sample, MaskDiff-AD constructs anomaly scores from the difficulty of reconstructing randomly masked coordinates, yielding a content-sensitive score that operates directly on discrete state spaces while avoiding reverse-time sampling. We also develop a non-parametric variant of MaskDiff-AD and provide theoretical guarantees by characterizing Type-I and Type-II errors under a fixed detection threshold. Experiments on fourteen categorical and mixed-type tabular datasets from ADBench and UADAD, as well as four text anomaly detection datasets from NLP-ADBench, show that MaskDiff-AD achieves competitive performance against classical, diffusion-based, and recent tabular/text anomaly detection baselines. Notably, MaskDiff-AD achieves the best overall average rank, outperforming all twelve tabular baseline methods.

Unsupervised anomaly detection is widely used in transaction fraud detection where labels are scarce. Isolation Forest (IF) is among the most popular classical methods due to its scalability and ease of deployment. We propose SilIF, an augmentation of Isolation Forest that adds a silhouette-based scoring layer computed in a representation space induced by the trees of the forest. For each point, we extract a vector of per-tree path lengths, cluster these "fingerprints" into structural groups, and compute a silhouette score that measures how well the point fits its assigned group versus the nearest alternative. The silhouette signal is combined with the base IF score via a single hyperparameter alpha. On the IEEE-CIS Fraud Detection benchmark (~590K transactions, 3.5% fraud), SilIF with alpha=1.0 improves over plain Isolation Forest by +0.0080 AUC-PR on average across five seeds, with SilIF winning on all five seeds (paired t-test p=0.046). We also report results on a synthetic credit-card dataset (Sparkov) where the silhouette augmentation does not improve over plain IF, and we characterize the conditions that distinguish the two outcomes. The paper presents SilIF as a tunable, easy-to-deploy enhancement to Isolation Forest with honest reporting of when it helps and when it does not. Code at https://github.com/venkat15vk/silif-anomaly-detection.

Unsupervised tabular anomaly detection methods typically learn feature patterns from normal samples during training and subsequently identify samples that deviate from these patterns as anomalies during testing. However, in practical scenarios, the limited scale and diversity of training data often lead to an incomplete characterization of normal patterns. While test-time adaptation offers a remedy, its isolated focus on test-time optimization ignores the critical synergy with training-phase learning. Furthermore, indiscriminate adaptation to unlabeled test data inevitably triggers anomaly contamination, preventing the model from fully realizing its discriminative capability between normal and anomalous samples. To address these issues, we propose RTTAD, a Risk-aware Test-time adaptation method for unsupervised Tabular Anomaly Detection. RTTAD holistically tackles normality shifts via a synergistic two-stage mechanism. During training, collaborative dual-task learning captures multi-level representations to establish a robust normal prior. During testing, a Test-Time Contrastive Learning (TTCL) module explicitly accounts for adaptation risk by selectively updating the model using high-confidence pseudo-normal samples while constraining anomalous ones. Additionally, TTCL incorporates a k-nearest neighbor-based contrastive objective to refine embedding distributions, thereby further enhancing the model's discriminative capacity. Extensive experiments on 15 tabular datasets demonstrate that RTTAD achieves state-of-the-art overall detection performance.

Denoising score matching (DSM) provides a way to learn data distributions by training a neural network to recover the score function, defined as the gradient of the log density, from noise-corrupted samples. Once trained, the score magnitude at a test point reflects how consistent that point is with the learned distribution, making it a natural anomaly signal. The key practical challenge is selecting the perturbation scale: too little noise yields unstable score estimates in sparse regions, while too much erases local structure and weakens anomaly sensitivity. This is compounded by the difficulty of hyperparameter tuning when anomalies are unknown and no validation set is available. We introduce kurtosis-based noise scaling (K-DSM), a per-feature scheme that sets noise levels from the shape of each marginal distribution, improving coverage of low-density regions and precision in high-density regions without extra model complexity. Contrary to prior claims that multi-scale or noise-conditioned training is necessary, we find that a carefully trained single-scale model is already a strong anomaly detector. On standard tabular anomaly detection benchmarks, K-DSM achieves state-of-the-art performance in the semi-supervised setting. When combined with a lightweight EMA-teacher filtering rule that removes low-density training points before each gradient step, it also achieves strong performance in the fully unsupervised (contaminated) setting, suggesting that simple, data-adaptive noise scaling enables robust anomaly detection while reducing reliance on hyperparameter tuning.

Ensuring the coherence of regional socio-economic statistics is a central task for national statistical institutes. Traditional validation tools, such as range edits, ratio checks, or univariate outlier detection, are effective for identifying extreme values in individual series but are less suited for detecting unusual combinations of indicators in high-dimensional settings. This paper proposes an unsupervised machine learning framework for identifying structurally atypical regional profiles within Europe using publicly available Eurostat data. We construct a cross-sectional dataset of NUTS2 regions (2022) covering four key indicators: GDP per capita in PPS, unemployment rate, tertiary educational attainment, and population density. We apply and compare five anomaly detection techniques, univariate z-scores, Mahalanobis distance, Isolation Forest, Local Outlier Factor, and One-Class SVM, and classify a region as a structural anomaly if it is flagged by at least three of the five methods. The findings show that machine learning methods identify a consistent set of regions whose multivariate profiles diverge substantially from the EU-wide pattern. These include both highly developed metropolitan economies (Brussels, Vienna, Berlin, Prague) and regions with persistent socio-economic disadvantages (Central and Western Slovakia, Northern Hungary, Castilla-La Mancha, Extremadura), as well as Istanbul, whose profile differs markedly from EU capital regions. Importantly, these anomalies do not necessarily signal data quality issues; rather, they reflect meaningful structural divergence that warrants analytical or policy attention. The proposed framework is fully reproducible, scalable, and compatible with existing validation workflows, offering a flexible tool for early detection of unusual regional configurations within the European Statistical System.

Anomaly detection in tabular data is challenging due to high dimensionality, complex feature dependencies, and heterogeneous noise. Many existing methods rely on proximity-based cues and may miss anomalies caused by violations of complex feature dependencies. Dependency-based anomaly detection provides a principled alternative by identifying anomalies as violations of dependencies among features. However, existing methods often struggle to model such dependencies robustly and to scale to high-dimensional data with complex dependency structures. To address these challenges, we propose uLEAD-TabPFN, a dependency-based anomaly detection framework built on Prior-Data Fitted Networks (PFNs). uLEAD-TabPFN identifies anomalies as violations of conditional dependencies in a learned latent space, leveraging frozen PFNs for dependency estimation. Combined with uncertainty-aware scoring, the proposed framework enables robust and scalable anomaly detection. Experiments on 57 tabular datasets from ADBench show that uLEAD-TabPFN achieves particularly strong performance in medium- and high-dimensional settings, where it attains the top average rank. On high-dimensional datasets, uLEAD-TabPFN improves the average ROC-AUC by nearly 20% over the average baseline and by approximately 2.8% over the best-performing baseline, while maintaining overall superior performance compared to state-of-the-art methods. Further analysis shows that uLEAD-TabPFN provides complementary anomaly detection capability, achieving strong performance on datasets where many existing methods struggle.

Identifying anomalous instances in tabular data is essential for improving data reliability and maintaining system stability. Due to the scarcity of ground-truth anomaly labels, existing methods mainly rely on unsupervised anomaly detection models, or exploit a small number of labeled anomalies to facilitate detection via sample generation or contrastive learning. However, unsupervised methods lack sufficient anomaly awareness, while current generation and contrastive approaches tend to compute anomalies globally, overlooking the localized anomaly patterns of tabular features, resulting in suboptimal detection performance. To address these limitations, we propose PLAG, a pseudo-label-guided anomaly generation method designed to enhance tabular anomaly detection. Specifically, by utilizing pseudo-anomalies as guidance signals and decoupling the overall anomaly quantification of a sample into an accumulation of feature-level abnormalities, PLAG not only effectively obviates the need for scarce ground-truth labels but also provides a novel perspective for the model to comprehend localized anomalous signals at a fine-grained level. Furthermore, a two-stage data selection strategy is proposed, integrating format verification and uncertainty estimation to rigorously filter candidate samples, thereby ensuring the fidelity and diversity of the synthetic anomalies. Ultimately, these filtered synthetic anomalies serve as robust discriminative guidance, empowering the model to better separate normal and anomalous instances. Extensive experiments demonstrate that PLAG achieves state-of-the-art performance against eight representative baselines. Moreover, as a flexible framework, it integrates seamlessly with existing unsupervised detectors, consistently boosting F1-scores by 0.08 to 0.21.

Unsupervised tabular anomaly detection is a critical task with applications spanning offensive language detection, network security, and quality control. Despite extensive research, existing unsupervised anomaly detection methods still face fundamental challenges including conflicting distributional assumptions, computational inefficiency, and difficulty handling different anomaly types. To address these problems, we propose ISER (Isolation-based Spherical Ensemble Representations) that extends existing isolation-based methods by using hypersphere radii as a monotonic transformation of local density characteristics while maintaining linear time and constant space complexity w.r.t. the dataset size. ISER constructs ensemble representations where hypersphere radii encode local sparsity through a monotonic transformation of density: smaller radii correspond to dense regions while larger radii correspond to sparse regions. We introduce a novel similarity-based scoring method that measures pattern consistency by comparing ensemble representations against a theoretical anomaly reference pattern. Additionally, we enhance the performance of Isolation Forest by using ISER and adapting the scoring function to address axis-parallel bias and local anomaly detection limitations. Comprehensive experiments on 20 real-world datasets demonstrate ISER's competitive performance over 12 SOTA methods.