Poisson Hyperplane Processes with Rectified Linear Units

• URL: http://arxiv.org/abs/2601.05586v1
• Date: Fri, 09 Jan 2026 07:12:50 GMT
• Title: Poisson Hyperplane Processes with Rectified Linear Units
• Authors: Shufei Ge, Shijia Wang, Lloyd Elliott,
• Abstract summary: We establish the connection between the Poisson hyperplane processes (PHP) and two-layer ReLU neural networks.<n>We show that the PHP with a Gaussian prior is an alternative probabilistic representation to a two-layer ReLU neural network.<n>Our numerical experiments demonstrate that our proposed method outperforms the classic two-layer ReLU neural network.
• Score: 2.15746572209356
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Neural networks have shown state-of-the-art performances in various classification and regression tasks. Rectified linear units (ReLU) are often used as activation functions for the hidden layers in a neural network model. In this article, we establish the connection between the Poisson hyperplane processes (PHP) and two-layer ReLU neural networks. We show that the PHP with a Gaussian prior is an alternative probabilistic representation to a two-layer ReLU neural network. In addition, we show that a two-layer neural network constructed by PHP is scalable to large-scale problems via the decomposition propositions. Finally, we propose an annealed sequential Monte Carlo algorithm for Bayesian inference. Our numerical experiments demonstrate that our proposed method outperforms the classic two-layer ReLU neural network. The implementation of our proposed model is available at https://github.com/ShufeiGe/Pois_Relu.git.

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