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Graph Regularization for High Order Neural Networks: Boundedness, Convergence, and Enhanced Performance With Entropy Error Function [Research Frontier]
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DOI：10.1109/MCI.2026.3655677.png)
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Abstract
En 中文
As a kind of high order neural network, Sigma-Pi-Sigma has strong nonlinear mapping ability, but the complexity of its network structure often leads to low application efficiency and lack of theoretical results. Although traditional regularization methods are more effective in sparsity and preventing overfitting, they do not take into account the topology and connection information between the data. Therefore, in order to sparsely optimize the network structure for improved efficiency and to enable rigorous theoretical analysis of complex inter-node relationships, graph-structured data must be processed more effectively. In this paper, the graph regularization component is integrated into the Sigma-Pi-Sigma neural network (SPSNN) learning framework, and the SPSNN online gradient algorithm based on the Turlaplacian regularization is studied, considering the entropy error measure. Under reasonable conditions, the boundedness of the weights, the monotonicity of the error function, and the convergence of the algorithm are strictly proved. Subsequently, the effectiveness of this method is verified through extensive experimental data. The simulation results are in good agreement with the theoretical results.
Keywords:
Neural networks
Graphical models
Classification algorithms
Biological neural networks
Accuracy
Entropy
Laplace equations
Toxicology
Stability analysis
Overfitting
Artificial intelligence
Training data
Computational complexity
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11.2
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606
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3.1K
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