# Formalizing the Binding Problem

arXiv: https://arxiv.org/abs/2606.03976 · HTML: https://mlsanity.com/paper/2606.03976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 67 references that are in the map.
- First posted on arXiv 2 Jun 2026.

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

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [When and why vision-language models behave like bags-of-words, and what to do about it?](https://mlsanity.com/paper/2210.01936/) (2022)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Bridging the Gap to Real-World Object-Centric Learning](https://mlsanity.com/paper/2209.14860/) (2022)
- [Does CLIP Bind Concepts? Probing Compositionality in Large Image Models](https://mlsanity.com/paper/2212.10537/) (2022)
- [ClevrTex: A Texture-Rich Benchmark for Unsupervised Multi-Object Segmentation](https://mlsanity.com/paper/2111.10265/) (2021)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [Understanding the Limits of Vision Language Models Through the Lens of the Binding Problem](https://mlsanity.com/paper/2411.00238/) (2024)
- [Self-supervised Object-Centric Learning for Videos](https://mlsanity.com/paper/2310.06907/) (2023)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Token Merging for Training-Free Semantic Binding in Text-to-Image Synthesis](https://mlsanity.com/paper/2411.07132/) (2024)
- [CLIP Behaves like a Bag-of-Words Model Cross-modally but not Uni-modally](https://mlsanity.com/paper/2502.03566/) (2025)
- [How Far Are We from Intelligent Visual Deductive Reasoning?](https://mlsanity.com/paper/2403.04732/) (2024)
- [How Do Transformers Learn Variable Binding in Symbolic Programs?](https://mlsanity.com/paper/2505.20896/) (2025)
- [FineCops-Ref: A new Dataset and Task for Fine-Grained Compositional Referring Expression Comprehension](https://mlsanity.com/paper/2409.14750/) (2024)

## Abstract (arXiv)

Representations of the world, arguably, contain information about features (e.g. something is blue, something is a circle) but also information about which features are part of the same object (e.g. the circle is blue), which we call binding information. Any system with the ability to understand scenes with multiple objects must be able to solve the binding problem: it needs to know which features belong together. However, despite work showing that Vision Transformers (ViTs) know which patches belong together, it is not known whether current deep learning models learn to exhibit binding information, i.e., for features. We may believe that there is not much binding information, after all misattributing features to wrong objects is a common failure of ViT-based architectures, especially in scenes with objects sharing features. Here we formalize the binding problem with an information-theoretic approach, and introduce a probing method to measure binding information in model representations. We perform experiments on ViTs, measuring binding from different components of the architecture, such as the image summary token [CLS] or the spatial tokens. We use datasets with different binding challenges, such as feature sharing, occlusion, and natural features, while comparing the performance of several pre-trained ViTs. Overall, our research demonstrates binding as a key ingredient to strong visual recognition and reasoning.