Whole slide image (WSI) refers to a type of high-resolution scanned tissue image, which is extensively employed in computer-assisted diagnosis (CAD). The extremely high resolution and limited availability of region-level annotations make employing deep learning methods for WSI-based digital diagnosis challenging. Recently integrating multiple instance learning (MIL) and Transformer for WSI analysis shows very promising results. However, designing effective Transformers for this weakly-supervised high-resolution image analysis is an underexplored yet important problem. In this paper, we propose a Multi-level MIL (MMIL) scheme by introducing a hierarchical structure to MIL, which enables efficient handling of MIL tasks involving a large number of instances. Based on MMIL, we instantiated MMIL-Transformer, an efficient Transformer model with windowed exact self-attention for large-scale MIL tasks. To validate its effectiveness, we conducted a set of experiments on WSI classification tasks, where MMIL-Transformer demonstrate superior performance compared to existing state-of-the-art methods, i.e., 96.80% test AUC and 97.67% test accuracy on the CAMELYON16 dataset, 99.04% test AUC and 94.37% test accuracy on the TCGA-NSCLC dataset, respectively. All code and pre-trained models are available at: https://github.com/hustvl/MMIL-Transformer

Overparameterization constitutes one of the most significant hallmarks of deep neural networks. Though it can offer the advantage of outstanding generalization performance, it meanwhile imposes substantial storage burden, thus necessitating the study of network pruning. A natural and fundamental question is: How sparse can we prune a deep network (with almost no hurt on the performance)? To address this problem, in this work we take a first principles approach, specifically, by merely enforcing the sparsity constraint on the original loss function, we're able to characterize the sharp phase transition point of pruning ratio, which corresponds to the boundary between the feasible and the infeasible, from the perspective of high-dimensional geometry. It turns out that the phase transition point of pruning ratio equals the squared Gaussian width of some convex body resulting from the $l_1$-regularized loss function, normalized by the original dimension of parameters. As a byproduct, we provide a novel network pruning algorithm which is essentially a global one-shot pruning one. Furthermore, we provide efficient countermeasures to address the challenges in computing the involved Gaussian width, including the spectrum estimation of a large-scale Hessian matrix and dealing with the non-definite positiveness of a Hessian matrix. It is demonstrated that the predicted pruning ratio threshold coincides very well with the actual value obtained from the experiments and our proposed pruning algorithm can achieve competitive or even better performance than the existing pruning algorithms. All codes are available at: https://github.com/QiaozheZhang/Global-One-shot-Pruning