# Anomaly as Non-Conformity via Training-Free Graph Laplacian Energy Minimization

arXiv: https://arxiv.org/abs/2605.28428 · HTML: https://mlsanity.com/paper/2605.28428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 37 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 30 of 30)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [WinCLIP: Zero-/Few-Shot Anomaly Classification and Segmentation](https://mlsanity.com/paper/2303.14814/) (2023)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Real-IAD: A Real-World Multi-View Dataset for Benchmarking Versatile Industrial Anomaly Detection](https://mlsanity.com/paper/2403.12580/) (2024)
- [Registration based Few-Shot Anomaly Detection](https://mlsanity.com/paper/2207.07361/) (2022)
- [PromptAD: Learning Prompts with only Normal Samples for Few-Shot Anomaly Detection](https://mlsanity.com/paper/2404.05231/) (2024)
- [Toward Generalist Anomaly Detection via In-context Residual Learning with Few-shot Sample Prompts](https://mlsanity.com/paper/2403.06495/) (2024)
- [Pushing the Limits of Fewshot Anomaly Detection in Industry Vision: Graphcore](https://mlsanity.com/paper/2301.12082/) (2023)
- [PNI : Industrial Anomaly Detection using Position and Neighborhood Information](https://mlsanity.com/paper/2211.12634/) (2022)
- [Exploring Intrinsic Normal Prototypes within a Single Image for Universal Anomaly Detection](https://mlsanity.com/paper/2503.02424/) (2025)
- [Graph Anomaly Detection with Graph Neural Networks: Current Status and Challenges](https://mlsanity.com/paper/2209.14930/) (2022)
- [Continuous Memory Representation for Anomaly Detection](https://mlsanity.com/paper/2402.18293/) (2024)
- [Kernel-Aware Graph Prompt Learning for Few-Shot Anomaly Detection](https://mlsanity.com/paper/2412.17619/) (2024)
- [Deep Generative Model using Unregularized Score for Anomaly Detection with Heterogeneous Complexity](https://mlsanity.com/paper/1807.05800/) (2018)
- [Graph Laplacian for Image Anomaly Detection](https://mlsanity.com/paper/1802.09843/) (2018)
- [k-NNN: Nearest Neighbors of Neighbors for Anomaly Detection](https://mlsanity.com/paper/2305.17695/) (2023)
- [AD-DINOv3: Enhancing DINOv3 for Zero-Shot Anomaly Detection with Anomaly-Aware Calibration](https://mlsanity.com/paper/2509.14084/) (2025)

## Built on by (most cited first, 1 of 1)

- [Structured Frequency-Domain Evidence for LLM-Based Time-Series Anomaly Detection](https://mlsanity.com/paper/2608.24113/) (2026)

## Abstract (arXiv)

Detecting subtle visual anomalies in images remains challenging, particularly when only normal samples are available a priori. Such unsupervised anomaly detection is typically solved by measuring feature similarity of a query patch to a memory of normal patches. However, similarity alone does not reveal how strongly a query patch violates the structure of the normal feature manifold. We propose a training-free Laplacian graph energy optimization formulation, named ANoCo that scores Anomaly by the cost of Non-Conformity of a query patch to align with a fixed normal manifold. For each query patch, we construct a bipartite query to normal graph weighted by cosine affinity, explicitly removing query-query and normal-normal edges to prevent evidence dilution. We formulate anomaly scoring as a convex Laplacian energy with anchored normal nodes, and solve in closed form. In particular, we do not use the optimized features themselves-the anomaly score is the magnitude of the update required to satisfy normality constraints, reframing the graph Laplacian as a non-conformity operator rather than a smoothing prior. The proposed method introduces no learnable parameters, message passing, or sampling, and has complexity comparable to a single linear solve. Across standard benchmarks, it delivers strong image-level AUROC, stable localization maps, and improved robustness over prior methods, demonstrating the effectiveness of using optimization-induced feature drift as anomaly measure.