Embedding-Based Anomaly Detection

• Embedding-based anomaly detection is a method that projects data into a high-dimensional latent space, enabling the identification of outliers through deviations from learned geometric and probabilistic patterns.
• It leverages architectures such as autoencoders, contrastive models, and graph-based embeddings to capture manifold structures and support unsupervised, semi-supervised, and few-shot learning scenarios.
• This approach delivers scalable, efficient anomaly detection across applications like industrial inspection, medical imaging, video surveillance, and cybersecurity by aligning embedding geometry with data characteristics.

Embedding-based anomaly detection refers to the class of techniques in which data instances are projected into a latent (typically high-dimensional and continuous) space — an embedding — such that the detection of anomalies (outliers, novelties, or distributional shifts) is recast as identifying points that deviate from the geometric or probabilistic regularities of normal data in that space. This paradigm achieves broad applicability across structured data, time series, graphs, images, video, and text, leveraging advances in deep representation learning, manifold theory, and generative modeling. Embedding-based anomaly detection provides both principled and practical solutions for unsupervised, semi-supervised, and few-shot settings; recent research demonstrates its high effectiveness on structured patterns, complex dynamical systems, industrial inspection, video surveillance, cyber security, and natural language.

1. Theoretical Foundations and Geometry of Embeddings

Embedding-based anomaly detection is grounded in the assumption that normal data populates a compact, low-dimensional manifold or attractor within a higher-dimensional latent space. Theoretical results from dynamical systems underpin this premise. For instance, the Fractal Whitney Embedding Prevalence Theorem states that if the embedding dimension $n > 2d$ (where $d$ is the fractal dimension of the data's attractor), generic smooth mappings $F:\mathbb{R}^k\to \mathbb{R}^n$ are one-to-one and immersions on the dataset, even for non-smooth (fractal) compact sets. This ensures faithful manifold geometry preservation in the embedding space, a property critical for distinguishing regular from anomalous states in time series and dynamical trajectories (Somma et al., 26 Feb 2025).

Similarly, the geometry of the embedding space — Euclidean, hyperbolic, or spherical — can be tailored to reflect the intrinsic structure of the data, amplifying discriminative power and anomaly separability (Hong et al., 2022). Curved embedding spaces can further increase representational capacity by encoding cluster or hierarchical relationships via nonzero curvature.

2. Embedding Architectures and Manifold Learning

A wide repertoire of architectures support the embedding phase:

• Autoencoders and Variational Autoencoders (VAE): Feed-forward or convolutional autoencoders learn mappings $E:\mathbb{R}^k \to \mathbb{R}^m$ compressing the input while preserving information. VAEs add a stochastic latent distribution and penalize prior divergence, making them robust to noise and anomalies. Reconstruction error or the negative ELBO serves as the anomaly score (Deng et al., 2022, Benabderrahmane et al., 13 Feb 2025).
• Contrastive and Discriminative Models: Training objectives such as contrastive loss (in CSE (Thomine et al., 4 Mar 2024)), Deep SVDD, and hypercenter loss (as in one-class neural mapping (Venkatrayappa, 15 Sep 2024)) force normal data to concentrate around a center or cluster, driving anomalies to periphery or low-density regions.
• Graph and Topology-Based Embedding: For graph or behavioral data, embeddings based on explicit edge attributes, node features, or joint graph spectral embeddings (e.g., MASE (Chen et al., 2020), PhoGAD (Yuan et al., 19 Jan 2024)) capture structural and temporal relationships. Persistent homology can further refine cluster boundaries by topologically identifying long-lived cycles in the embedding space.
• Foundation Models and Pretrained Representations: State-of-the-art methods frequently exploit off-the-shelf pretrained networks (DINOv2, CLIP, BERT, OpenAI embeddings) as embedding functions, owing to their extensive semantic coverage and generalization properties for image (Ronecker et al., 12 May 2025, Huang et al., 12 Jun 2025), text (Li et al., 6 Dec 2024, Xiao et al., 16 Jul 2025, Cao et al., 21 Jan 2025), and video (Venkatrayappa, 15 Sep 2024) domains.
• Quantum and Non-Euclidean Embeddings: Quantum autoencoders using data-reuploading, parallel, and alternate embeddings on variational circuits demonstrate substantial gains in distinguishability by extending classical data to higher-dimensional Hilbert spaces (Araz et al., 6 Sep 2024).

3. Anomaly Scoring and Detection Mechanisms

Once embedded, anomaly scoring is formulated via geometric or density-based criteria:

• Distance or Density Methods: k-NN, LOF, ECOD, Isolation Forest, and GNN-based LUNAR construct local outlier scores from embedding distances or densities (Li et al., 6 Dec 2024, Xiao et al., 16 Jul 2025, Cao et al., 21 Jan 2025). Higher distances imply lower density and therefore greater anomaly likelihood.
• Reconstruction Loss: For generative models, the discrepancy between input and reconstruction or predicted features — measured in L2, SSIM, or distributional metrics — flags deviations from the learned normal manifold (Deng et al., 2022, Thomine et al., 4 Mar 2024, Zavrtanik et al., 2021).
• Likelihood-Based and Probabilistic Scoring: In categorical or event data, pairwise compatibility models (APE (Chen et al., 2016)) compute log-likelihoods from learned entity embeddings; anomalies are events with low modeled probability.
• Graph-Based Metrics: For sequences of graphs, anomaly statistics are Frobenius norms or Procrustes-aligned distances between successive embedded adjacency or latent matrices (Chen et al., 2020). For edge- or node-level embeddings, focal loss is adapted to handle heavy imbalances (Yuan et al., 19 Jan 2024).
• Physics-Inspired Consistency Losses: Temporal Differential Consistency (TDC) autoencoders penalize mismatches between learned latent-state derivatives and their finite-difference approximations, exploiting the dynamical invariance violated by anomalous transitions (Somma et al., 26 Feb 2025).
• Hybrid, Multi-Stage Pipelines: Many recent frameworks combine early unsupervised pretraining (autoencoders, contrastive, or pretext tasks) with subsequent clustering, GMM, or SVDD for concentrated anomaly detection, often performing ablations to demonstrate the benefit of pretraining and multi-modal fusion (Venkatrayappa, 15 Sep 2024, Mosayebi et al., 2023, Kang et al., 2022).

4. Domain-Specific Methodologies and Applications

Embedding-based anomaly detection frameworks display substantial domain adaptability:

• Industrial and Surface Defect Detection: Methods such as DRAEM (Zavrtanik et al., 2021) and CSE (Thomine et al., 4 Mar 2024) combine pixel-precise reconstruction, discriminative boundaries, and contrastively selected embeddings to set records on MVTec AD and TTILDA benchmarks.
• Medical Imaging: Joint 2D/3D embedding (ResNet/U-Net) architectures leverage both high-resolution and volumetric cues, trained with self-supervised and joint cosine similarity constraints, outperform 3D-only and other SOTA OOD detectors on benchmarks such as MOOD 2021 (Kang et al., 2022). IQE-CLIP (Huang et al., 12 Jun 2025) demonstrates the extension of prompt-tuned, instance-aware foundation model embeddings for zero/few-shot anomaly detection in medical domains.
• Video Anomaly Detection: Multi-modal fusion (depth, optical flow, appearance) with hybrid autoencoder and hypercenter loss architectures enables robust frame-level anomaly scoring and enables handling of both subtle motion and content deviations (Venkatrayappa, 15 Sep 2024).
• Text and Cybersecurity: Large-scale benchmarks like TAD-Bench (Cao et al., 21 Jan 2025), NLP-ADBench (Li et al., 6 Dec 2024), Text-ADBench (Xiao et al., 16 Jul 2025), and cyber-APT detection frameworks (APT-LLM (Benabderrahmane et al., 13 Feb 2025)) confirm that with LLM-derived embeddings, even simple k-NN or ECOD methods match or surpass deep anomaly detection models, especially under extreme class imbalance.
• Graph and Network Behavior: Embedding and disentanglement of edge representations, persistent topology, and explicit handling of graph heterophily yield robust detection in network intrusion, anonymous traffic, and spam (Yuan et al., 19 Jan 2024, Chen et al., 2020).

5. Empirical Performance, Benchmarks, and Best Practices

Comprehensive benchmarks reveal critical performance patterns:

• Superiority of Strong Embeddings: In text, OpenAI text-embedding-3-large or supervised LLaMA-3 with end-of-sequence pooling consistently provide higher anomaly detection AUCs than classic BERT or GloVe embeddings. For images, DINOv2, CLIP, and their variants lead in segmentation/localization and detection accuracy (Li et al., 6 Dec 2024, Xiao et al., 16 Jul 2025).
• Detector Simplicity is Often Sufficient: On high-quality embeddings, shallow anomaly detectors (kNN, ECOD, Isolation Forest) perform as well as — or better than — deep autoencoders and SVDD, both in text (Xiao et al., 16 Jul 2025, Cao et al., 21 Jan 2025) and video/image (Venkatrayappa, 15 Sep 2024). Low-rank structure in method×embedding performance enables efficient model selection by matrix completion (Xiao et al., 16 Jul 2025).
• Computational Efficiency: State-of-the-art models (e.g., TDC-AE (Somma et al., 26 Feb 2025), CSE (Thomine et al., 4 Mar 2024)) achieve orders-of-magnitude reductions in MAC operations or latency, rendering them suitable for edge devices.
• Adaptive Thresholding and Postprocessing: Thresholds for anomaly scores are typically chosen from quantiles of training/validation losses; false positive suppression (instance-area filtering (Ronecker et al., 12 May 2025), or persistent-homology-based edge selection (Yuan et al., 19 Jan 2024)) can substantially reduce spurious alarms.
• Domain Generalization and Robustness: Embedding-based detectors generalize to distributional shifts, OOD content, rare-events, and severe imbalance, outperforming fully-supervised classifiers where labeled anomalies are scarce or noisy (Mosayebi et al., 2023, Benabderrahmane et al., 13 Feb 2025, Ronecker et al., 12 May 2025).

6. Limitations, Open Questions, and Future Directions

Key challenges and areas for innovation include:

• Embedding Quality Limits: Detection efficacy is fundamentally tied to the expressivity and discriminative fidelity of the embedding; uncommon but nominal scenarios can inflate false positive rates in open-world deployments (Ronecker et al., 12 May 2025).
• Lack of Universally Optimal Detector: No single method achieves SOTA across all domains or anomaly types. Automated model selection, meta-learning, and embedding adaptation remain open directions (Li et al., 6 Dec 2024, Xiao et al., 16 Jul 2025).
• Scalability and Efficiency: Scalability to high-throughput, large-scale graphs or real-time video remains computationally demanding. Topological components (e.g. persistent homology) remain non-differentiable; future work may investigate persistence-weighted losses or approximations (Yuan et al., 19 Jan 2024).
• Interpretability: While anomalies are often points that “leave the learned attractor” in the embedding, there remains a gap in attributing which features or interactions most strongly determine the divergence, especially in complex multi-modal or hierarchical embeddings.
• Extension to Novel Modalities: Extension of these methods to multimodal data, streaming settings, and federated or privacy-preserving scenarios will require embedding strategies that are adaptive, lightweight, and robust to unseen heterogeneity.
• Quantum and Curved Embeddings: The use of enhanced data embedding in quantum circuits or curved manifolds remains at an early stage, but empirical results indicate improved anomaly discrimination through expanded state-space coverage and geometric flexibility (Araz et al., 6 Sep 2024, Hong et al., 2022).

Table: Representative Domains and Embedding Models

Domain	Embedding Model	Detection Method
Industrial image	EfficientNet/ResNet/CLIP/DINOv2	Contrastive, Autoencoder, PI-Forest, Patch/Instance Matching
Video	Multi-modal Conv AE, CentralNet	Hypercenter/One-class loss
Text	BERT, LLaMA, OpenAI embeddings	kNN, ECOD, LOF, DeepSVDD
Graph/Network	Spectral/Edge Embeddings, MASE	Frobenius/Control-statistics
Cybersecurity	LLM (ALBERT, RoBERTa) + AE/VAE/DAE	Recon. Error/ELBO
Dynamical systems	State-derivative embedding	TDC-AE, Consistency Loss

• “Anomaly Detection in Complex Dynamical Systems: A Systematic Framework Using Embedding Theory and Physics-Inspired Consistency” (Somma et al., 26 Feb 2025)
• “Graph Regularized Autoencoder and its Application in Unsupervised Anomaly Detection” (Ahmed et al., 2020)
• “PhoGAD: Graph-based Anomaly Behavior Detection with Persistent Homology Optimization” (Yuan et al., 19 Jan 2024)
• “CSE: Surface Anomaly Detection with Contrastively Selected Embedding” (Thomine et al., 4 Mar 2024)
• “DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection” (Zavrtanik et al., 2021)
• “NLP-ADBench: NLP Anomaly Detection Benchmark” (Li et al., 6 Dec 2024)
• “Text-ADBench: Text Anomaly Detection Benchmark based on LLMs Embedding” (Xiao et al., 16 Jul 2025)
• “APT-LLM: Embedding-Based Anomaly Detection of Cyber Advanced Persistent Threats Using LLMs” (Benabderrahmane et al., 13 Feb 2025)
• “Multiple Network Embedding for Anomaly Detection in Time Series of Graphs” (Chen et al., 2020)
• “Entity Embedding-based Anomaly Detection for Heterogeneous Categorical Events” (Chen et al., 2016)
• “Joint Embedding of 2D and 3D Networks for Medical Image Anomaly Detection” (Kang et al., 2022)
• “Vision Foundation Model Embedding-Based Semantic Anomaly Detection” (Ronecker et al., 12 May 2025)
• “IQE-CLIP: Instance-aware Query Embedding for Zero-/Few-shot Anomaly Detection in Medical Domain” (Huang et al., 12 Jun 2025)
• “A Supervised Embedding and Clustering Anomaly Detection method for classification of Mobile Network Faults” (Mosayebi et al., 2023)
• “Anomaly Detection via Reverse Distillation from One-Class Embedding” (Deng et al., 2022)
• “TAD-Bench: A Comprehensive Benchmark for Embedding-Based Text Anomaly Detection” (Cao et al., 21 Jan 2025)
• “The role of data embedding in quantum autoencoders for improved anomaly detection” (Araz et al., 6 Sep 2024)

In sum, embedding-based anomaly detection has established itself as the standard approach due to its combination of mathematical rigor, universal applicability, and empirical effectiveness, with research converging on leveraging ever-stronger, domain-adaptive embeddings combined with lightweight, interpretable anomaly metrics.