The optimization phase in deep learning consists in minimizing an objective function w.r.t. the set of

Despite its popularity, self-training is well-believed to be unreliable and often leads to training instability.

Learning feature interactions can be the key for multivariate predictive modeling. ReLU-activated neural networks create piecewise linear prediction models.

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.

Foundation vision, audio, and language models enable zero-shot performance on downstream tasks via their latent representations. Recently, unsupervised learning of data group structure with deep learning methods has gained popularity. TURTLE, a state of the art deep clustering algorithm, uncovers data labeling without supervision by alternating label and hyperplane updates, maximizing the hyperplane margin, in a similar fashion to support vector machines (SVMs). However, TURTLE assumes clusters are balanced; when data is imbalanced, it yields non-ideal hyperplanes that cause higher clustering error. We propose PET-TURTLE, which generalizes the cost function to handle imbalanced data distributions by a power law prior. Additionally, by introducing sparse logits in the labeling process, PET-TURTLE optimizes a simpler search space that in turn improves accuracy for balanced datasets. Experiments on synthetic and real data show that PET-TURTLE improves accuracy for imbalanced sources, prevents over-prediction of minority clusters, and enhances overall clustering.