# Verification of Size Invariance in DNN Activations using Concept Embeddings

arXiv: https://arxiv.org/abs/2105.06727 · HTML: https://mlsanity.com/paper/2105.06727/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 14 May 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [One weird trick for parallelizing convolutional neural networks](https://mlsanity.com/paper/1404.5997/) (2014)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural Networks](https://mlsanity.com/paper/1801.03454/) (2018)
- [A Disentangling Invertible Interpretation Network for Explaining Latent Representations](https://mlsanity.com/paper/2004.13166/) (2020)
- [Semantics for Global and Local Interpretation of Deep Neural Networks](https://mlsanity.com/paper/1910.09085/) (2019)

## Built on by (most cited first, 9 of 9)

- [Concept Embedding Analysis: A Review](https://mlsanity.com/paper/2203.13909/) (2022)
- [Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?](https://mlsanity.com/paper/2409.13456/) (2024)
- [Evaluating the Stability of Semantic Concept Representations in CNNs for Robust Explainability](https://mlsanity.com/paper/2304.14864/) (2023)
- [Enabling Verification of Deep Neural Networks in Perception Tasks Using Fuzzy Logic and Concept Embeddings](https://mlsanity.com/paper/2201.00572/) (2022)
- [Local Concept Embeddings for Analysis of Concept Distributions in Vision DNN Feature Spaces](https://mlsanity.com/paper/2311.14435/) (2023)
- [Unveiling Ontological Commitment in Multi-Modal Foundation Models](https://mlsanity.com/paper/2409.17109/) (2024)
- [On Background Bias of Post-Hoc Concept Embeddings in Computer Vision DNNs](https://mlsanity.com/paper/2504.08602/) (2025)
- [Attack logics, not outputs: Towards efficient robustification of deep neural networks by falsifying concept-based properties](https://mlsanity.com/paper/2510.03320/) (2025)
- [Explaining, Verifying, and Aligning Semantic Hierarchies in Vision-Language Model Embeddings](https://mlsanity.com/paper/2603.26798/) (2026)

## Abstract (arXiv)

The benefits of deep neural networks (DNNs) have become of interest for safety critical applications like medical ones or automated driving. Here, however, quantitative insights into the DNN inner representations are mandatory. One approach to this is concept analysis, which aims to establish a mapping between the internal representation of a DNN and intuitive semantic concepts. Such can be sub-objects like human body parts that are valuable for validation of pedestrian detection. To our knowledge, concept analysis has not yet been applied to large object detectors, specifically not for sub-parts. Therefore, this work first suggests a substantially improved version of the Net2Vec approach (arXiv:1801.03454) for post-hoc segmentation of sub-objects. Its practical applicability is then demonstrated on a new concept dataset by two exemplary assessments of three standard networks, including the larger Mask R-CNN model (arXiv:1703.06870): (1) the consistency of body part similarity, and (2) the invariance of internal representations of body parts with respect to the size in pixels of the depicted person. The findings show that the representation of body parts is mostly size invariant, which may suggest an early intelligent fusion of information in different size categories.