Existing 3D mask learning methods encounter performance bottlenecks under limited data, and our objective is to overcome this limitation. In this paper, we introduce a triple point masking scheme, named TPM, which serves as a scalable framework for pre-training of masked autoencoders to achieve multi-mask learning for 3D point clouds. Specifically, we augment the baselines with two additional mask choices (i.e., medium mask and low mask) as our core insight is that the recovery process of an object can manifest in diverse ways. Previous high-masking schemes focus on capturing the global representation but lack the fine-grained recovery capability, so that the generated pre-trained weights tend to play a limited role in the fine-tuning process. With the support of the proposed TPM, available methods can exhibit more flexible and accurate completion capabilities, enabling the potential autoencoder in the pre-training stage to consider multiple representations of a single 3D object. In addition, an SVM-guided weight selection module is proposed to fill the encoder parameters for downstream networks with the optimal weight during the fine-tuning stage, maximizing linear accuracy and facilitating the acquisition of intricate representations for new objects. Extensive experiments show that the four baselines equipped with the proposed TPM achieve comprehensive performance improvements on various downstream tasks. Our code and models are available at https://github.com/liujia99/TPM.

Building fair deep neural networks (DNNs) is a crucial step towards achieving trustworthy artificial intelligence. Delving into deeper factors that affect the fairness of DNNs is paramount and serves as the foundation for mitigating model biases. However, current methods are limited in accurately predicting DNN biases, relying solely on the number of training samples and lacking more precise measurement tools. Here, we establish a geometric perspective for analyzing the fairness of DNNs, comprehensively exploring how DNNs internally shape the intrinsic geometric characteristics of datasets-the intrinsic dimensions (IDs) of perceptual manifolds, and the impact of IDs on the fairness of DNNs. Based on multiple findings, we propose Intrinsic Dimension Regularization (IDR), which enhances the fairness and performance of models by promoting the learning of concise and ID-balanced class perceptual manifolds. In various image recognition benchmark tests, IDR significantly mitigates model bias while improving its performance.