# Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

arXiv: https://arxiv.org/abs/1904.11263 · HTML: https://mlsanity.com/paper/1904.11263/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2019.

## Built on by (most cited first, 10 of 10)

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- [Adaptive Precision Training (AdaPT): A dynamic fixed point quantized training approach for DNNs](https://mlsanity.com/paper/2107.13490/) (2021)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [EnforceSNN: Enabling Resilient and Energy-Efficient Spiking Neural Network Inference considering Approximate DRAMs for Embedded Systems](https://mlsanity.com/paper/2304.04039/) (2023)
- [On the influence of stochastic roundoff errors and their bias on the convergence of the gradient descent method with low-precision floating-point computation](https://mlsanity.com/paper/2202.12276/) (2022)
- [Low-Precision Reinforcement Learning: Running Soft Actor-Critic in Half Precision](https://mlsanity.com/paper/2102.13565/) (2021)
- [tinySNN: Towards Memory- and Energy-Efficient Spiking Neural Networks](https://mlsanity.com/paper/2206.08656/) (2022)
- [FeNN: A RISC-V vector processor for Spiking Neural Network acceleration](https://mlsanity.com/paper/2506.11760/) (2025)
- [Dither computing: a hybrid deterministic-stochastic computing framework](https://mlsanity.com/paper/2102.10732/) (2021)

## Abstract (arXiv)

Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixed-point arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of Ordinary Differential Equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single precision floating-point and fixed-point arithmetic with round-to-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit (LSB) in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by Partial Differential Equations (PDEs).