# Deep Phasor Networks: Connecting Conventional and Spiking Neural Networks

arXiv: https://arxiv.org/abs/2106.11908 · HTML: https://mlsanity.com/paper/2106.11908/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 15 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [EfficientDet: Scalable and Efficient Object Detection](https://mlsanity.com/paper/1911.09070/) (2019)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [A Survey of Neuromorphic Computing and Neural Networks in Hardware](https://mlsanity.com/paper/1705.06963/) (2017)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [S4NN: temporal backpropagation for spiking neural networks with one spike per neuron](https://mlsanity.com/paper/1910.09495/) (2019)
- [Brain-Inspired Learning on Neuromorphic Substrates](https://mlsanity.com/paper/2010.11931/) (2020)
- [Variable Binding for Sparse Distributed Representations: Theory and Applications](https://mlsanity.com/paper/2009.06734/) (2020)
- [Large-Scale Neuromorphic Spiking Array Processors: A quest to mimic the brain](https://mlsanity.com/paper/1805.08932/) (2018)
- [Robust computation with rhythmic spike patterns](https://mlsanity.com/paper/1901.07718/) (2019)
- [Rapid online learning and robust recall in a neuromorphic olfactory circuit](https://mlsanity.com/paper/1906.07067/) (2019)
- ['Less Than One'-Shot Learning: Learning N Classes From M<N Samples](https://mlsanity.com/paper/2009.08449/) (2020)
- [Biologically inspired sleep algorithm for artificial neural networks](https://mlsanity.com/paper/1908.02240/) (2019)
- [Winner-Take-All Computation in Spiking Neural Networks](https://mlsanity.com/paper/1904.12591/) (2019)
- [Resonator networks for factoring distributed representations of data structures](https://mlsanity.com/paper/2007.03748/) (2020)

## Built on by (most cited first, 4 of 4)

- [Spyx: A Library for Just-In-Time Compiled Optimization of Spiking Neural Networks](https://mlsanity.com/paper/2402.18994/) (2024)
- [Residual and Attentional Architectures for Vector-Symbols](https://mlsanity.com/paper/2207.08953/) (2022)
- [Sparsifying Spiking Networks through Local Rhythms](https://mlsanity.com/paper/2305.10191/) (2023)
- [Lock-in EP: An In-Situ Training Algorithm for Oscillatory Hardware](https://mlsanity.com/paper/2610.07283/) (2026)

## Abstract (arXiv)

In this work, we extend standard neural networks by building upon an assumption that neuronal activations correspond to the angle of a complex number lying on the unit circle, or 'phasor.' Each layer in such a network produces new activations by taking a weighted superposition of the previous layer's phases and calculating the new phase value. This generalized architecture allows models to reach high accuracy and carries the singular advantage that mathematically equivalent versions of the network can be executed with or without regard to a temporal variable. Importantly, the value of a phase angle in the temporal domain can be sparsely represented by a periodically repeating series of delta functions or 'spikes'. We demonstrate the atemporal training of a phasor network on standard deep learning tasks and show that these networks can then be executed in either the traditional atemporal domain or spiking temporal domain with no conversion step needed. This provides a novel basis for constructing deep networkswhich operate via temporal, spike-based calculations suitable for neuromorphic computing hardware.