### Abstract

In this paper, we present a homotopy training algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the neural network starting from a simplified version and ending with the fully connected network via adding layers and nodes adaptively. Therefore, the corresponding optimization problem is easy to solve at the beginning and connects to the original model via a continuous path guided by the HTA, which provides a high probability of obtaining a global minimum. By gradually increasing the complexity of the model along the continuous path, the HTA provides a rather good solution to the original loss function. This is confirmed by various numerical results including VGG models on CIFAR-10. For example, on the VGG13 model with batch normalization, HTA reduces the error rate by 11.86% on the test dataset compared with the traditional method. Moreover, the HTA also allows us to find the optimal structure for a fully connected neural network by building the neutral network adaptively.

Original language | English (US) |
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Article number | 20190662 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 475 |

Issue number | 2231 |

DOIs | |

State | Published - Nov 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

### Cite this

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 475, no. 2231, 20190662. https://doi.org/10.1098/rspa.2019.0662

**A homotopy training algorithm for fully connected neural networks.** / Chen, Qipin; Hao, Wenrui.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A homotopy training algorithm for fully connected neural networks

AU - Chen, Qipin

AU - Hao, Wenrui

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this paper, we present a homotopy training algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the neural network starting from a simplified version and ending with the fully connected network via adding layers and nodes adaptively. Therefore, the corresponding optimization problem is easy to solve at the beginning and connects to the original model via a continuous path guided by the HTA, which provides a high probability of obtaining a global minimum. By gradually increasing the complexity of the model along the continuous path, the HTA provides a rather good solution to the original loss function. This is confirmed by various numerical results including VGG models on CIFAR-10. For example, on the VGG13 model with batch normalization, HTA reduces the error rate by 11.86% on the test dataset compared with the traditional method. Moreover, the HTA also allows us to find the optimal structure for a fully connected neural network by building the neutral network adaptively.

AB - In this paper, we present a homotopy training algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the neural network starting from a simplified version and ending with the fully connected network via adding layers and nodes adaptively. Therefore, the corresponding optimization problem is easy to solve at the beginning and connects to the original model via a continuous path guided by the HTA, which provides a high probability of obtaining a global minimum. By gradually increasing the complexity of the model along the continuous path, the HTA provides a rather good solution to the original loss function. This is confirmed by various numerical results including VGG models on CIFAR-10. For example, on the VGG13 model with batch normalization, HTA reduces the error rate by 11.86% on the test dataset compared with the traditional method. Moreover, the HTA also allows us to find the optimal structure for a fully connected neural network by building the neutral network adaptively.

UR - http://www.scopus.com/inward/record.url?scp=85076210360&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076210360&partnerID=8YFLogxK

U2 - 10.1098/rspa.2019.0662

DO - 10.1098/rspa.2019.0662

M3 - Article

C2 - 31824229

AN - SCOPUS:85076210360

VL - 475

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2231

M1 - 20190662

ER -