# Neuronal Synchrony in Complex-Valued Deep Networks

arXiv: https://arxiv.org/abs/1312.6115 · HTML: https://mlsanity.com/paper/1312.6115/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2013.

## Built on by (most cited first, 28 of 28)

- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (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)
- [Rotating Features for Object Discovery](https://mlsanity.com/paper/2306.00600/) (2023)
- [Continuous Thought Machines](https://mlsanity.com/paper/2505.05522/) (2025)
- [Capturing the objects of vision with neural networks](https://mlsanity.com/paper/2109.03351/) (2021)
- [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)
- [All-optical graph representation learning using integrated diffractive photonic computing units](https://mlsanity.com/paper/2204.10978/) (2022)
- [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)
- [BCNN: Binary Complex Neural Network](https://mlsanity.com/paper/2104.10044/) (2021)
- [Co-domain Symmetry for Complex-Valued Deep Learning](https://mlsanity.com/paper/2112.01525/) (2021)
- [Adversarial Audio Synthesis with Complex-valued Polynomial Networks](https://mlsanity.com/paper/2206.06811/) (2022)
- [Dance of SNN and ANN: Solving binding problem by combining spike timing and reconstructive attention](https://mlsanity.com/paper/2211.06027/) (2022)
- [CoNO: Complex Neural Operator for Continous Dynamical Physical Systems](https://mlsanity.com/paper/2406.02597/) (2024)
- [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)
- [Complex-valued Neural Networks -- Theory and Analysis](https://mlsanity.com/paper/2312.06087/) (2023)
- [RVFL-X: A Novel Randomized Network Based on Complex Transformed Real-Valued Tabular Datasets](https://mlsanity.com/paper/2510.06278/) (2025)
- [Spectral Complexity-scaled Generalization Bound of Complex-valued Neural Networks](https://mlsanity.com/paper/2112.03467/) (2021)
- [A note on the complex and bicomplex valued neural networks](https://mlsanity.com/paper/2202.02354/) (2022)
- [A photonic chip-based machine learning approach for the prediction of molecular properties](https://mlsanity.com/paper/2203.02285/) (2022)
- [GASPnet: Global Agreement to Synchronize Phases](https://mlsanity.com/paper/2507.16674/) (2025)
- [Do traveling waves make good positional encodings?](https://mlsanity.com/paper/2511.11668/) (2025)

## Abstract (arXiv)

Deep learning has recently led to great successes in tasks such as image recognition (e.g Krizhevsky et al., 2012). However, deep networks are still outmatched by the power and versatility of the brain, perhaps in part due to the richer neuronal computations available to cortical circuits. The challenge is to identify which neuronal mechanisms are relevant, and to find suitable abstractions to model them. Here, we show how aspects of spike timing, long hypothesized to play a crucial role in cortical information processing, could be incorporated into deep networks to build richer, versatile representations. We introduce a neural network formulation based on complex-valued neuronal units that is not only biologically meaningful but also amenable to a variety of deep learning frameworks. Here, units are attributed both a firing rate and a phase, the latter indicating properties of spike timing. We show how this formulation qualitatively captures several aspects thought to be related to neuronal synchrony, including gating of information processing and dynamic binding of distributed object representations. Focusing on the latter, we demonstrate the potential of the approach in several simple experiments. Thus, neuronal synchrony could be a flexible mechanism that fulfills multiple functional roles in deep networks.