# Unlocking Slot Attention by Changing Optimal Transport Costs

arXiv: https://arxiv.org/abs/2301.13197 · HTML: https://mlsanity.com/paper/2301.13197/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Recurrent Independent Mechanisms](https://mlsanity.com/paper/1909.10893/) (2019)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [SlotFormer: Unsupervised Visual Dynamics Simulation with Object-Centric Models](https://mlsanity.com/paper/2210.05861/) (2022)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [ClevrTex: A Texture-Rich Benchmark for Unsupervised Multi-Object Segmentation](https://mlsanity.com/paper/2111.10265/) (2021)
- [Object Scene Representation Transformer](https://mlsanity.com/paper/2206.06922/) (2022)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Deep Set Prediction Networks](https://mlsanity.com/paper/1906.06565/) (2019)
- [Re-basin via implicit Sinkhorn differentiation](https://mlsanity.com/paper/2212.12042/) (2022)
- [Generative Neurosymbolic Machines](https://mlsanity.com/paper/2010.12152/) (2020)
- [Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning](https://mlsanity.com/paper/2107.00848/) (2021)
- [Unsupervised Layered Image Decomposition into Object Prototypes](https://mlsanity.com/paper/2104.14575/) (2021)
- [Object Files and Schemata: Factorizing Declarative and Procedural Knowledge in Dynamical Systems](https://mlsanity.com/paper/2006.16225/) (2020)
- [Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiation](https://mlsanity.com/paper/2207.00787/) (2022)
- [MarioNette: Self-Supervised Sprite Learning](https://mlsanity.com/paper/2104.14553/) (2021)

## Built on by (most cited first, 16 of 16)

- [Object-centric architectures enable efficient causal representation learning](https://mlsanity.com/paper/2310.19054/) (2023)
- [PEEK: Guiding and Minimal Image Representations for Zero-Shot Generalization of Robot Manipulation Policies](https://mlsanity.com/paper/2509.18282/) (2025)
- [Object-Centric Learning with Slot Mixture Module](https://mlsanity.com/paper/2311.04640/) (2023)
- [Unsupervised Concept Discovery Mitigates Spurious Correlations](https://mlsanity.com/paper/2402.13368/) (2024)
- [On permutation-invariant neural networks](https://mlsanity.com/paper/2403.17410/) (2024)
- [ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Plans](https://mlsanity.com/paper/2502.07962/) (2025)
- [Reusable Slotwise Mechanisms](https://mlsanity.com/paper/2302.10503/) (2023)
- [Attention Normalization Impacts Cardinality Generalization in Slot Attention](https://mlsanity.com/paper/2407.04170/) (2024)
- [Neurosymbolic Object-Centric Learning with Distant Supervision](https://mlsanity.com/paper/2506.16129/) (2025)
- [SMARTe: Slot-based Method for Accountable Relational Triple extraction](https://mlsanity.com/paper/2504.12816/) (2025)
- [Hierarchical Compact Clustering Attention (COCA) for Unsupervised Object-Centric Learning](https://mlsanity.com/paper/2505.02071/) (2025)
- [Mitigating Simplicity Bias in OOD Detection through Object Co-occurrence Analysis](https://mlsanity.com/paper/2605.07821/) (2026)
- [Unsupervised Evolutionary Cell Type Matching via Entropy-Minimized Optimal Transport](https://mlsanity.com/paper/2505.24759/) (2025)
- [Improving Set Function Approximation with Quasi-Arithmetic Neural Networks](https://mlsanity.com/paper/2602.04941/) (2026)
- [When Attention Collapses: Residual Evidence Modeling for Compositional Inference](https://mlsanity.com/paper/2605.02323/) (2026)
- [Spacetime Optimal-Transport Attention for Visuo-Haptic Imitation Learning of Contact-Rich Manipulation](https://mlsanity.com/paper/2605.20433/) (2026)

## Abstract (arXiv)

Slot attention is a powerful method for object-centric modeling in images and videos. However, its set-equivariance limits its ability to handle videos with a dynamic number of objects because it cannot break ties. To overcome this limitation, we first establish a connection between slot attention and optimal transport. Based on this new perspective we propose MESH (Minimize Entropy of Sinkhorn): a cross-attention module that combines the tiebreaking properties of unregularized optimal transport with the speed of regularized optimal transport. We evaluate slot attention using MESH on multiple object-centric learning benchmarks and find significant improvements over slot attention in every setting.