Training deep Convolutional Neural Networks (CNNs) presents unique challenges, including the pervasive issue of elimination singularities—consistent deactivation of nodes leading to degenerate manifolds within the loss landscape. These singularities impede efficient learning by disrupting feature propagation. To mitigate this, we introduce Pool Skip, an architectural enhancement that strategically combines a Max Pooling, a Max Unpooling, a 3 × 3 convolution, and a skip connection. This configuration helps stabilize the training process and maintain feature integrity across layers. We also propose the Weight Inertia hypothesis, which underpins the development of Pool Skip, providing theoretical insights into mitigating degradation caused by elimination singularities through dimensional and affine compensation. We evaluate our method on a variety of benchmarks, focusing on both 2D natural and 3D medical imaging applications, including tasks such as classification and segmentation. Our findings highlight Pool Skip's effectiveness in facilitating more robust CNN training and improving model performance.

Generative models can enhance discriminative classifiers by constructing complex feature spaces, thereby improving performance on intricate datasets. Conventional methods typically augment datasets with more detailed feature representations or increase dimensionality to make nonlinear data linearly separable. Utilizing a generative model solely for feature space processing falls short of unlocking its full potential within a classifier and typically lacks a solid theoretical foundation. We base our approach on a novel hypothesis: the probability information (logit) derived from a single model training can be used to generate the equivalent of multiple training sessions. Leveraging the central limit theorem, this synthesized probability information is anticipated to converge toward the true probability more accurately. To achieve this goal, we propose the Bernoulli-Gaussian Decision Block (BGDB), a novel module inspired by the Central Limit Theorem and the concept that the mean of multiple Bernoulli trials approximates the probability of success in a single trial. Specifically, we utilize Improved Denoising Diffusion Probabilistic Models (IDDPM) to model the probability of Bernoulli Trials. Our approach shifts the focus from reconstructing features to reconstructing logits, transforming the logit from a single iteration into logits analogous to those from multiple experiments. We provide the theoretical foundations of our approach through mathematical analysis and validate its effectiveness through experimental evaluation using various datasets for multiple imaging tasks, including both classification and segmentation.

Point cloud analysis is challenging due to the irregularity of the point cloud data structure. Existing works typically employ the ad-hoc sampling-grouping operation of PointNet++, followed by sophisticated local and/or global feature extractors for leveraging the 3D geometry of the point cloud. Unfortunately, the sampling-grouping operations do not address the point cloud's irregularity, whereas the intricate local and/or global feature extractors led to poor computational efficiency. In this paper, we introduce a novel DualNorm module after the sampling-grouping operation to effectively and efficiently address the irregularity issue. The DualNorm module consists of Point Normalization, which normalizes the grouped points to the sampled points, and Reverse Point Normalization, which normalizes the sampled points to the grouped points. The proposed framework, PointNorm, utilizes local mean and global standard deviation to benefit from both local and global features while maintaining a faithful inference speed. Experiments show that we achieved excellent accuracy and efficiency on Model-Net40 classification, ScanObjectNN classification, ShapeNetPart Part Segmentation, and S3DIS Semantic Segmentation. Code is available at https://github.com/ShenZheng2000/PointNorm-for-Point-Cloud-Analysis.