# Make it SING: Analyzing Semantic Invariants in Classifiers

arXiv: https://arxiv.org/abs/2603.14610 · HTML: https://mlsanity.com/paper/2603.14610/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 52 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [DeiT III: Revenge of the ViT](https://mlsanity.com/paper/2204.07118/) (2022)
- [EVA-02: A Visual Representation for Neon Genesis](https://mlsanity.com/paper/2303.11331/) (2023)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [CLIP-Dissect: Automatic Description of Neuron Representations in Deep Vision Networks](https://mlsanity.com/paper/2204.10965/) (2022)
- [Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models](https://mlsanity.com/paper/2303.11073/) (2023)
- [Diagnosing and Rectifying Vision Models using Language](https://mlsanity.com/paper/2302.04269/) (2023)
- [The Double-Ellipsoid Geometry of CLIP](https://mlsanity.com/paper/2411.14517/) (2024)
- [Mass-Producing Failures of Multimodal Systems with Language Models](https://mlsanity.com/paper/2306.12105/) (2023)
- [Mechanistic understanding and validation of large AI models with SemanticLens](https://mlsanity.com/paper/2501.05398/) (2025)
- [Outlier Detection through Null Space Analysis of Neural Networks](https://mlsanity.com/paper/2007.01263/) (2020)

## Abstract (arXiv)

All classifiers, including state-of-the-art vision models, possess invariants, partially rooted in the geometry of their linear mappings. These invariants, which reside in the null-space of the classifier, induce equivalent sets of inputs that map to identical outputs. The semantic content of these invariants remains vague, as existing approaches struggle to provide human-interpretable information. To address this gap, we present Semantic Interpretation of the Null-space Geometry (SING), a method that constructs equivalent images, with respect to the network, and assigns semantic interpretations to the available variations. We use a mapping from network features to multi-modal vision language models. This allows us to obtain natural language descriptions and visual examples of the induced semantic shifts. SING can be applied to a single image, uncovering local invariants, or to sets of images, allowing a breadth of statistical analysis at the class and model levels. For example, our method reveals that ResNet50 leaks relevant semantic attributes to the null space, whereas DinoViT, a ViT pretrained with self-supervised DINO, is superior in maintaining class semantics across the invariant space.