# Enhancing deep neural networks through complex-valued representations and Kuramoto synchronization dynamics

arXiv: https://arxiv.org/abs/2502.21077 · HTML: https://mlsanity.com/paper/2502.21077/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 70 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Visual Representation Learning Does Not Generalize Strongly Within the Same Domain](https://mlsanity.com/paper/2107.08221/) (2021)
- [Complex-Valued Autoencoders for Object Discovery](https://mlsanity.com/paper/2204.02075/) (2022)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Neuronal Synchrony in Complex-Valued Deep Networks](https://mlsanity.com/paper/1312.6115/) (2013)
- [Contrastive Training of Complex-Valued Autoencoders for Object Discovery](https://mlsanity.com/paper/2305.15001/) (2023)
- [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)
- [KuraNet: Systems of Coupled Oscillators that Learn to Synchronize](https://mlsanity.com/paper/2105.02838/) (2021)
- [Binding Dynamics in Rotating Features](https://mlsanity.com/paper/2402.05627/) (2024)
- [Tracking objects that change in appearance with phase synchrony](https://mlsanity.com/paper/2410.02094/) (2024)
- [Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs](https://mlsanity.com/paper/1903.00385/) (2019)
- [Learning Structured Representations of Visual Scenes](https://mlsanity.com/paper/2207.04200/) (2022)
- [Learning Semantic Structure through First-Order-Logic Translation](https://mlsanity.com/paper/2410.03203/) (2024)
- [On the Generalization of Learned Structured Representations](https://mlsanity.com/paper/2304.13001/) (2023)

## Built on by (most cited first, 3 of 3)

- [Kuramoto Attention: Synchronizing Self-Attention on the Torus](https://mlsanity.com/paper/2606.11585/) (2026)
- [GASPnet: Global Agreement to Synchronize Phases](https://mlsanity.com/paper/2507.16674/) (2025)
- [Diffusion-warm sampling of the XY model enables fast thermalization at scale](https://mlsanity.com/paper/2606.30773/) (2026)

## Abstract (arXiv)

Neural synchrony is hypothesized to play a crucial role in how the brain organizes visual scenes into structured representations, enabling the robust encoding of multiple objects within a scene. However, current deep learning models often struggle with object binding, limiting their ability to represent multiple objects effectively. Inspired by neuroscience, we investigate whether synchrony-based mechanisms can enhance object encoding in artificial models trained for visual categorization. Specifically, we combine complex-valued representations with Kuramoto dynamics to promote phase alignment, facilitating the grouping of features belonging to the same object. We evaluate two architectures employing synchrony: a feedforward model and a recurrent model with feedback connections to refine phase synchronization using top-down information. Both models outperform their real-valued counterparts and complex-valued models without Kuramoto synchronization on tasks involving multi-object images, such as overlapping handwritten digits, noisy inputs, and out-of-distribution transformations. Our findings highlight the potential of synchrony-driven mechanisms to enhance deep learning models, improving their performance, robustness, and generalization in complex visual categorization tasks.