Rényi Sharpness: A Novel Sharpness that Strongly Correlates with Generalization

Sharpness (of the loss minima) is a common measure to investigate the generalization of neural networks. Intuitively speaking, the flatter the landscape near the minima is, the better generalization might be. Unfortunately, the correlation between many existing sharpness measures and the generalization is usually not strong, sometimes even weak. To close the gap between the intuition and the reality, we propose a novel sharpness measure, i.e., \textit{R\'enyi sharpness}, which is defined as the negative R\'enyi entropy (a generalization of the classical Shannon entropy) of the loss Hessian. The main ideas are as follows: 1) we realize that \textit{uniform} (identical) eigenvalues of the loss Hessian is most desirable (while keeping the sum constant) to achieve good generalization; 2) we employ the \textit{R\'enyi entropy} to concisely characterize the extent of the spread of the eigenvalues of loss Hessian. Normally, the larger the spread, the smaller the (R\'enyi) entropy. To rigorously establish the relationship between generalization and (R\'enyi) sharpness, we provide several generalization bounds in terms of R\'enyi sharpness, by taking advantage of the reparametrization invariance property of R\'enyi sharpness, as well as the trick of translating the data discrepancy to the weight perturbation. Furthermore, extensive experiments are conducted to verify the strong correlation (in specific, Kendall rank correlation) between the R\'enyi sharpness and generalization. Moreover, we propose to use a variant of R\'enyi Sharpness as regularizer during training, i.e., R\'enyi Sharpness Aware Minimization (RSAM), which turns out to outperform all existing sharpness-aware minimization methods. It is worthy noting that the test accuracy gain of our proposed RSAM method could be as high as nearly 2.5\%, compared against the classical SAM method.

Analog Self-Interference Cancellation in Full-Duplex Radios: A Fundamental Limit Perspective

Analog self-interference cancellation (A-SIC) plays a crucial role in the implementation of in-band full-duplex (IBFD) radios, due to the fact that the inherent transmit (Tx) noise can only be addressed in the analog domain. It is thus natural to ask what the performance limit of A-SIC is in practical systems, which is still quite underexplored so far. In this paper, we aim to close this gap by characterizing the fundamental performance of A-SIC which employs the common multi-tap delay (MTD) architecture, by accounting for the following practical issues: 1) Nonstationarity of the Tx signal; 2) Nonlinear distortions on the Tx signal; 3) Multipath channel corresponding to the self-interference (SI); 4) Maximum amplitude constraint on the MTD tap weights. Our findings include: 1) The average approximation error for the cyclostationary Tx signals is equal to that for the stationary white Gaussian process, thus greatly simplifying the performance analysis and the optimization procedure. 2) The approximation error for the multipath SI channel can be decomposed as the sum of the approximation error for the single-path scenario. By leveraging these structural results, the optimization framework and algorithms which characterize the fundamental limit of A-SIC, by taking into account all the aforementioned practical factors, are provided.

Multi-user beamforming in RIS-aided communications and experimental validations

Reconfigurable intelligent surface (RIS) is a promising technology for future wireless communications due to its capability of optimizing the propagation environments. Nevertheless, in literature, there are few prototypes serving multiple users. In this paper, we propose a whole flow of channel estimation and beamforming design for RIS, and set up an RIS-aided multi-user system for experimental validations. Specifically, we combine a channel sparsification step with generalized approximate message passing (GAMP) algorithm, and propose to generate the measurement matrix as Rademacher distribution to obtain the channel state information (CSI). To generate the reflection coefficients with the aim of maximizing the spectral efficiency, we propose a quadratic transform-based low-rank multi-user beamforming (QTLM) algorithm. Our proposed algorithms exploit the sparsity and low-rank properties of the channel, which has the advantages of light calculation and fast convergence. Based on the universal software radio peripheral devices, we built a complete testbed working at 5.8GHz and implemented all the proposed algorithms to verify the possibility of RIS assisting multi-user systems. Experimental results show that the system has obtained an average spectral efficiency increase of 13.48bps/Hz, with respective received power gains of 26.6dB and 17.5dB for two users, compared with the case when RIS is powered-off.

How Sparse Can We Prune A Deep Network: A Geometric Viewpoint

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

Multi-level Multiple Instance Learning with Transformer for Whole Slide Image Classification

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 it challenging to employ deep learning methods for WSI-based digital diagnosis. Multiple instance learning (MIL) is a powerful tool to address the weak annotation problem, while Transformer has shown great success in the field of visual tasks. The combination of both should provide new insights for deep learning based image diagnosis. However, due to the limitations of single-level MIL and the attention mechanism's constraints on sequence length, directly applying Transformer to WSI-based MIL tasks is not practical. To tackle this issue, we propose a Multi-level MIL with Transformer (MMIL-Transformer) approach. By introducing a hierarchical structure to MIL, this approach enables efficient handling of MIL tasks that involve a large number of instances. To validate its effectiveness, we conducted a set of experiments on WSIs classification task, where MMIL-Transformer demonstrate superior performance compared to existing state-of-the-art methods. Our proposed approach achieves test AUC 94.74% and test accuracy 93.41% on CAMELYON16 dataset, test AUC 99.04% and test accuracy 94.37% on TCGA-NSCLC dataset, respectively. All code and pre-trained models are available at: https://github.com/hustvl/MMIL-Transformer