# Error-free Training for Artificial Neural Network

arXiv: https://arxiv.org/abs/2312.16060 · HTML: https://mlsanity.com/paper/2312.16060/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 16 references that are in the map.
- First posted on arXiv 26 Dec 2023.

## Built on by (most cited first, 2 of 2)

- [Toward Errorless Training ImageNet-1k](https://mlsanity.com/paper/2508.04941/) (2025)
- [Benchmarking PNW Model for MedMNIST to 100% Accuracy](https://mlsanity.com/paper/2604.18916/) (2026)

## Abstract (arXiv)

Conventional training methods for artificial neural network (ANN) models never achieve zero error rate systematically for large data. A new training method consists of three steps: first create an auxiliary data from conventionally trained parameters which correspond exactly to a global minimum for the loss function of the cloned data; second create a one-parameter homotopy (hybrid) of the auxiliary data and the original data; and third train the model for the hybrid data iteratively from the auxiliary data end of the homotopy parameter to the original data end while maintaining the zero-error training rate at every iteration. This continuationmethod is guaranteed to converge numerically by a theorem which converts the ANN training problem into a continuation problem for fixed points of a parameterized transformation in the training parameter space to which the Uniform Contraction Mapping Theorem from dynamical systems applies.