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Updated: Jun 10, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

A neural network of smooth hinge functions.

Shuning Wang¹, Xiaolin Huang, Yeung Yam

¹Department of Automation, Tsinghua University, Beijing, China. swang@mail.tsinghua.edu.cn

IEEE Transactions on Neural Networks

|August 5, 2010

Summary

Smooth hinging hyperplane (SHH) offers improved function approximation over hinging hyperplane (HH) by resolving nondifferentiability. This advancement enhances neural network performance, particularly when using sigmoidal functions.

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Last Updated: Jun 10, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

Machine Learning
Artificial Intelligence
Neural Networks

Background:

Hinging hyperplane (HH) is a known method in machine learning.
HH has a drawback of nondifferentiability, limiting its application.
Smooth hinging hyperplane (SHH) aims to improve upon HH.

Purpose of the Study:

Introduce a formal characterization of smooth hinge function (SHF).
Develop a method for constructing SHF.
Prove SHH's superiority in functional approximation compared to HH.

Main Methods:

Formal characterization of smooth hinge functions (SHF).
Construction method for SHF.
Theoretical analysis of functional approximation error bounds.

Main Results:

SHH demonstrates superior or equal functional approximation compared to HH.
SHH constructed from 2m SHFs outperforms neural networks with m sigmoidal functions.
An algorithm for SHH identification leveraging differentiability is presented.

Conclusions:

SHH is a more effective approximation tool than HH.
The approximation error bounds for sigmoidal neural networks can be translated to SHH.
SHH offers a promising direction for neural network advancements.