Related Experiment Video
Updated: Jul 31, 2026

End-To-End Deep Neural Network for Salient Object Detection in Complex Environments
Published on: December 15, 2023
Complexity of error hypersurfaces in multilayer perceptrons
1Institute of Computer Science and Technology, Peking University, Beijing 100871, China. liangxun@founder.com
Abstract:
Error hypersurfaces are very valuable to study because of their unique status in multilayer perceptron research. Given the architecture of a multilayer perceptron, if the pattern sets are different, so are the respective error hypersurfaces in the multilayer perceptron. Using the theory of groups and Polya Theorem, this paper constructs classes of congruent pattern sets and classes of congruent error hypersurfaces, and proves that the number of classes of congruent pattern sets is equal to the number of congruent error hypersurfaces. Calculation results lead to much fewer classes of congruent error hypersurfaces than the total error hypersurfaces, and show that as the input dimension N increases, the former number increases at a much lower rate than the latter number, thus simplifying the understanding of the complexity of classes of error hypersurfaces.
Related Concept Videos
Collisions in Multiple Dimensions: Problem Solving
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Propagation of Uncertainty from Random Error
Propagation of Uncertainty from Systematic Error
Anatomy of the Eyeball
Multi-input and Multi-variable systems
In the absence of...
Linear Approximations