# Robust computation with rhythmic spike patterns

arXiv: https://arxiv.org/abs/1901.07718 · HTML: https://mlsanity.com/paper/1901.07718/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 21 of 21)

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- [Deep Phasor Networks: Connecting Conventional and Spiking Neural Networks](https://mlsanity.com/paper/2106.11908/) (2021)
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- [Compositional Factorization of Visual Scenes with Convolutional Sparse Coding and Resonator Networks](https://mlsanity.com/paper/2404.19126/) (2024)
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- [Generalized Key-Value Memory to Flexibly Adjust Redundancy in Memory-Augmented Networks](https://mlsanity.com/paper/2203.06223/) (2022)
- [Storing overlapping associative memories on latent manifolds in low-rank spiking networks](https://mlsanity.com/paper/2411.17485/) (2024)
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- [Developing a Foundation of Vector Symbolic Architectures Using Category Theory](https://mlsanity.com/paper/2501.05368/) (2025)
- [A Grid Cell-Inspired Structured Vector Algebra for Cognitive Maps](https://mlsanity.com/paper/2503.08608/) (2025)

## Abstract (arXiv)

Information coding by precise timing of spikes can be faster and more energy-efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing applications. Here, we propose a novel type of attractor neural network in complex state space, and show how it can be leveraged to construct spiking neural networks with robust computational properties through a phase-to-timing mapping. Building on Hebbian neural associative memories, like Hopfield networks, we first propose threshold phasor associative memory (TPAM) networks. Complex phasor patterns whose components can assume continuous-valued phase angles and binary magnitudes can be stored and retrieved as stable fixed points in the network dynamics. TPAM achieves high memory capacity when storing sparse phasor patterns, and we derive the energy function that governs its fixed point attractor dynamics. Second, through simulation experiments we show how the complex algebraic computations in TPAM can be approximated by a biologically plausible network of integrate-and-fire neurons with synaptic delays and recurrently connected inhibitory interneurons. The fixed points of TPAM in the complex domain are commensurate with stable periodic states of precisely timed spiking activity that are robust to perturbation. The link established between rhythmic firing patterns and complex attractor dynamics has implications for the interpretation of spike patterns seen in neuroscience, and can serve as a framework for computation in emerging neuromorphic devices.