# Contrastive Training of Complex-Valued Autoencoders for Object Discovery

arXiv: https://arxiv.org/abs/2305.15001 · HTML: https://mlsanity.com/paper/2305.15001/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 62 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Kubric: A scalable dataset generator](https://mlsanity.com/paper/2203.03570/) (2022)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [SAVi++: Towards End-to-End Object-Centric Learning from Real-World Videos](https://mlsanity.com/paper/2206.07764/) (2022)
- [SlotFormer: Unsupervised Visual Dynamics Simulation with Object-Centric Models](https://mlsanity.com/paper/2210.05861/) (2022)
- [Sequential Attend, Infer, Repeat: Generative Modelling of Moving Objects](https://mlsanity.com/paper/1806.01794/) (2018)
- [Neural Expectation Maximization](https://mlsanity.com/paper/1708.03498/) (2017)
- [Spatial Broadcast Decoder: A Simple Architecture for Learning Disentangled Representations in VAEs](https://mlsanity.com/paper/1901.07017/) (2019)
- [Unsupervised Learning of Object Keypoints for Perception and Control](https://mlsanity.com/paper/1906.11883/) (2019)
- [Relational Neural Expectation Maximization: Unsupervised Discovery of Objects and their Interactions](https://mlsanity.com/paper/1802.10353/) (2018)
- [Learning Dexterous Grasping with Object-Centric Visual Affordances](https://mlsanity.com/paper/2009.01439/) (2020)
- [Object discovery and representation networks](https://mlsanity.com/paper/2203.08777/) (2022)
- [Tagger: Deep Unsupervised Perceptual Grouping](https://mlsanity.com/paper/1606.06724/) (2016)
- [Attention over learned object embeddings enables complex visual reasoning](https://mlsanity.com/paper/2012.08508/) (2020)
- [An Investigation into Pre-Training Object-Centric Representations for Reinforcement Learning](https://mlsanity.com/paper/2302.04419/) (2023)
- [Complex-Valued Autoencoders for Object Discovery](https://mlsanity.com/paper/2204.02075/) (2022)
- [Efficient Iterative Amortized Inference for Learning Symmetric and Disentangled Multi-Object Representations](https://mlsanity.com/paper/2106.03630/) (2021)
- [Neuronal Synchrony in Complex-Valued Deep Networks](https://mlsanity.com/paper/1312.6115/) (2013)

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

- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Rotating Features for Object Discovery](https://mlsanity.com/paper/2306.00600/) (2023)
- [Slot Abstractors: Toward Scalable Abstract Visual Reasoning](https://mlsanity.com/paper/2403.03458/) (2024)
- [Recurrent Complex-Weighted Autoencoders for Unsupervised Object Discovery](https://mlsanity.com/paper/2405.17283/) (2024)
- [Multi-Scale Fusion for Object Representation](https://mlsanity.com/paper/2410.01539/) (2024)
- [Binding Dynamics in Rotating Features](https://mlsanity.com/paper/2402.05627/) (2024)
- [Latent Noise Segmentation: How Neural Noise Leads to the Emergence of Segmentation and Grouping](https://mlsanity.com/paper/2309.16515/) (2023)
- [unMORE: Unsupervised Multi-Object Segmentation via Center-Boundary Reasoning](https://mlsanity.com/paper/2506.01778/) (2025)
- [Tracking objects that change in appearance with phase synchrony](https://mlsanity.com/paper/2410.02094/) (2024)
- [Enhancing deep neural networks through complex-valued representations and Kuramoto synchronization dynamics](https://mlsanity.com/paper/2502.21077/) (2025)
- [Kuramoto Oscillatory Phase Encoding: Neuro-inspired Synchronization for Improved Learning Efficiency](https://mlsanity.com/paper/2604.07904/) (2026)
- [Parallelized Spatiotemporal Binding](https://mlsanity.com/paper/2402.17077/) (2024)
- [Visual Reasoning in Object-Centric Deep Neural Networks: A Comparative Cognition Approach](https://mlsanity.com/paper/2402.12675/) (2024)
- [Winfree Oscillatory Neural Network](https://mlsanity.com/paper/2605.20922/) (2026)
- [Traveling Waves Integrate Spatial Information Through Time](https://mlsanity.com/paper/2502.06034/) (2025)
- [GASPnet: Global Agreement to Synchronize Phases](https://mlsanity.com/paper/2507.16674/) (2025)

## Abstract (arXiv)

Current state-of-the-art object-centric models use slots and attention-based routing for binding. However, this class of models has several conceptual limitations: the number of slots is hardwired; all slots have equal capacity; training has high computational cost; there are no object-level relational factors within slots. Synchrony-based models in principle can address these limitations by using complex-valued activations which store binding information in their phase components. However, working examples of such synchrony-based models have been developed only very recently, and are still limited to toy grayscale datasets and simultaneous storage of less than three objects in practice. Here we introduce architectural modifications and a novel contrastive learning method that greatly improve the state-of-the-art synchrony-based model. For the first time, we obtain a class of synchrony-based models capable of discovering objects in an unsupervised manner in multi-object color datasets and simultaneously representing more than three objects.