# When Rule Violations Are Rare: Chimera Training for Logical Anomaly Detection

arXiv: https://arxiv.org/abs/2605.26171 · HTML: https://mlsanity.com/paper/2605.26171/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 21 of 21)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Inferring and Executing Programs for Visual Reasoning](https://mlsanity.com/paper/1705.03633/) (2017)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Few Shot Part Segmentation Reveals Compositional Logic for Industrial Anomaly Detection](https://mlsanity.com/paper/2312.13783/) (2023)
- [Neural Algebra of Classifiers](https://mlsanity.com/paper/1801.08676/) (2018)
- [LogicAL: Towards logical anomaly synthesis for unsupervised anomaly localization](https://mlsanity.com/paper/2405.06875/) (2024)
- [Compositional Embeddings for Multi-Label One-Shot Learning](https://mlsanity.com/paper/2002.04193/) (2020)

## Abstract (arXiv)

Many practical anomalies are not merely rare inputs, but violations of semantic constraints: objects co-occur in structured ways, actions imply preconditions, and events satisfy temporal or relational regularities. We study anomaly detection in this setting, where constraints are given as logical rules over learned visual concepts, but real rule violations are rare or absent during training. We propose a neural rule evaluator that compiles each constraint into a directed acyclic graph and learns feature-aware subtree MLP gates for its internal logical operators. Each gate maps child features and edge-level negations to a parent representation and a rule-satisfaction probability, with intermediate supervision obtained from exact Boolean propagation over ground-truth concept labels. The key difficulty is that same-image training data often provide insufficient coverage of informative truth configurations and also allow shortcut solutions. To address this, we introduce chimera training: an operand-level counterfactual construction at the feature level. Instead of mixing input images, we concatenate subtree features from different samples; each operand keeps the hard truth label of the sample it came from, and the chimera target is obtained by applying the node's logical operator to those inherited labels. This supplies supervised logical counterexamples without requiring real anomalous images. Across CLEVRER, OpenImages, and VidOR, the resulting evaluator improves rule-level anomaly AUROC over independent-events and same-image semantic-training baselines, especially for compositional and relational rules. The method yields both scalar anomaly scores and rule-level attributions.