# Neuromorphic Computing is Turing-Complete

arXiv: https://arxiv.org/abs/2104.13983 · HTML: https://mlsanity.com/paper/2104.13983/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 57 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [A Survey of Neuromorphic Computing and Neural Networks in Hardware](https://mlsanity.com/paper/1705.06963/) (2017)
- [Benchmarking Keyword Spotting Efficiency on Neuromorphic Hardware](https://mlsanity.com/paper/1812.01739/) (2018)
- [Real-time ultra-low power ECG anomaly detection using an event-driven neuromorphic processor](https://mlsanity.com/paper/1911.05521/) (2019)
- [Neural Population Coding for Effective Temporal Classification](https://mlsanity.com/paper/1909.08018/) (2019)
- [Solving a steady-state PDE using spiking networks and neuromorphic hardware](https://mlsanity.com/paper/2005.10904/) (2020)
- [On the computational power and complexity of Spiking Neural Networks](https://mlsanity.com/paper/2001.08439/) (2020)

## Built on by (most cited first, 6 of 6)

- [Edge-Cloud Collaborative Computing on Distributed Intelligence and Model Optimization: A Survey](https://mlsanity.com/paper/2505.01821/) (2025)
- [On-Sensor Data Filtering using Neuromorphic Computing for High Energy Physics Experiments](https://mlsanity.com/paper/2307.11242/) (2023)
- [NeuroCoreX: An Open-Source FPGA-Based Spiking Neural Network Emulator with On-Chip Learning](https://mlsanity.com/paper/2506.14138/) (2025)
- [General-purpose Dataflow Model with Neuromorphic Primitives](https://mlsanity.com/paper/2408.01090/) (2024)
- [Neuromorphic-based metaheuristics: A new generation of low power, low latency and small footprint optimization algorithms](https://mlsanity.com/paper/2505.16362/) (2025)
- [SuperNeuroMAT: An Efficient Matrix-based Simulator for Spiking Neural Networks](https://mlsanity.com/paper/2608.08479/) (2026)

## Abstract (arXiv)

Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and GPUs. They have the potential to drive critical use cases such as autonomous vehicles, edge computing and internet of things in the future. For this reason, they are sought to be an indispensable part of the future computing landscape. Neuromorphic systems are mainly used for spike-based machine learning applications, although there are some non-machine learning applications in graph theory, differential equations, and spike-based simulations. These applications suggest that neuromorphic computing might be capable of general-purpose computing. However, general-purpose computability of neuromorphic computing has not been established yet. In this work, we prove that neuromorphic computing is Turing-complete and therefore capable of general-purpose computing. Specifically, we present a model of neuromorphic computing, with just two neuron parameters (threshold and leak), and two synaptic parameters (weight and delay). We devise neuromorphic circuits for computing all the μ-recursive functions (i.e., constant, successor and projection functions) and all the μ-recursive operators (i.e., composition, primitive recursion and minimization operators). Given that the μ-recursive functions and operators are precisely the ones that can be computed using a Turing machine, this work establishes the Turing-completeness of neuromorphic computing.