# Complex-Valued Autoencoders for Object Discovery

arXiv: https://arxiv.org/abs/2204.02075 · HTML: https://mlsanity.com/paper/2204.02075/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 66 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [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)
- [Recurrent Independent Mechanisms](https://mlsanity.com/paper/1909.10893/) (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)
- [Illiterate DALL-E Learns to Compose](https://mlsanity.com/paper/2110.11405/) (2021)
- [Neural Expectation Maximization](https://mlsanity.com/paper/1708.03498/) (2017)
- [ClevrTex: A Texture-Rich Benchmark for Unsupervised Multi-Object Segmentation](https://mlsanity.com/paper/2111.10265/) (2021)
- [Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentation](https://mlsanity.com/paper/2104.01148/) (2021)
- [Generalization and Robustness Implications in Object-Centric Learning](https://mlsanity.com/paper/2107.00637/) (2021)
- [Unsupervised Learning of Compositional Energy Concepts](https://mlsanity.com/paper/2111.03042/) (2021)
- [Tagger: Deep Unsupervised Perceptual Grouping](https://mlsanity.com/paper/1606.06724/) (2016)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Conditional Set Generation with Transformers](https://mlsanity.com/paper/2006.16841/) (2020)
- [Neuronal Synchrony in Complex-Valued Deep Networks](https://mlsanity.com/paper/1312.6115/) (2013)
- [Learning Object-Centric Video Models by Contrasting Sets](https://mlsanity.com/paper/2011.10287/) (2020)

## Built on by (most cited first, 30 of 40)

- [Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos](https://mlsanity.com/paper/2205.14065/) (2022)
- [Object-Centric Slot Diffusion](https://mlsanity.com/paper/2303.10834/) (2023)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [SPOT: Self-Training with Patch-Order Permutation for Object-Centric Learning with Autoregressive Transformers](https://mlsanity.com/paper/2312.00648/) (2023)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Neural Systematic Binder](https://mlsanity.com/paper/2211.01177/) (2022)
- [Rotating Features for Object Discovery](https://mlsanity.com/paper/2306.00600/) (2023)
- [Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networks](https://mlsanity.com/paper/2312.08550/) (2023)
- [Promising or Elusive? Unsupervised Object Segmentation from Real-world Single Images](https://mlsanity.com/paper/2210.02324/) (2022)
- [Contrastive Training of Complex-Valued Autoencoders for Object Discovery](https://mlsanity.com/paper/2305.15001/) (2023)
- [Unsupervised Discovery of Object-Centric Neural Fields](https://mlsanity.com/paper/2402.07376/) (2024)
- [MetaSlot: Break Through the Fixed Number of Slots in Object-Centric Learning](https://mlsanity.com/paper/2505.20772/) (2025)
- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [Image segmentation with traveling waves in an exactly solvable recurrent neural network](https://mlsanity.com/paper/2311.16943/) (2023)
- [Recurrent Complex-Weighted Autoencoders for Unsupervised Object Discovery](https://mlsanity.com/paper/2405.17283/) (2024)
- [Differentiable Mathematical Programming for Object-Centric Representation Learning](https://mlsanity.com/paper/2210.02159/) (2022)
- [Binding Dynamics in Rotating Features](https://mlsanity.com/paper/2402.05627/) (2024)
- [Non-contact Sensing for Anomaly Detection in Wind Turbine Blades: A focus-SVDD with Complex-Valued Auto-Encoder Approach](https://mlsanity.com/paper/2306.10808/) (2023)
- [Latent Noise Segmentation: How Neural Noise Leads to the Emergence of Segmentation and Grouping](https://mlsanity.com/paper/2309.16515/) (2023)
- [Benchmarking and Analysis of Unsupervised Object Segmentation from Real-world Single Images](https://mlsanity.com/paper/2312.04947/) (2023)
- [Slot-BERT: Self-supervised Object Discovery in Surgical Video](https://mlsanity.com/paper/2501.12477/) (2025)
- [Dreamweaver: Learning Compositional World Models from Pixels](https://mlsanity.com/paper/2501.14174/) (2025)
- [unMORE: Unsupervised Multi-Object Segmentation via Center-Boundary Reasoning](https://mlsanity.com/paper/2506.01778/) (2025)
- [Dance of SNN and ANN: Solving binding problem by combining spike timing and reconstructive attention](https://mlsanity.com/paper/2211.06027/) (2022)
- [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)
- [A Survey of Deep Learning for Complex Speech Spectrograms](https://mlsanity.com/paper/2505.08694/) (2025)
- [A Circular Argument : Does RoPE need to be Equivariant for Vision?](https://mlsanity.com/paper/2511.08368/) (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)

## Abstract (arXiv)

Object-centric representations form the basis of human perception, and enable us to reason about the world and to systematically generalize to new settings. Currently, most works on unsupervised object discovery focus on slot-based approaches, which explicitly separate the latent representations of individual objects. While the result is easily interpretable, it usually requires the design of involved architectures. In contrast to this, we propose a comparatively simple approach - the Complex AutoEncoder (CAE) - that creates distributed object-centric representations. Following a coding scheme theorized to underlie object representations in biological neurons, its complex-valued activations represent two messages: their magnitudes express the presence of a feature, while the relative phase differences between neurons express which features should be bound together to create joint object representations. In contrast to previous approaches using complex-valued activations for object discovery, we present a fully unsupervised approach that is trained end-to-end - resulting in significant improvements in performance and efficiency. Further, we show that the CAE achieves competitive or better unsupervised object discovery performance on simple multi-object datasets compared to a state-of-the-art slot-based approach while being up to 100 times faster to train.