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Recently, sharpness-aware minimization (SAM) has attracted much attention because of its surprising effectiveness in improving generalization performance. However, compared to stochastic gradient descent (SGD), it is more prone to getting stuck at the saddle points, which as a result may lead to performance degradation. To address this issue, we propose a simple renormalization strategy, dubbed Stable SAM (SSAM), so that the gradient norm of the descent step maintains the same as that of the ascent step. Our strategy is easy to implement and flexible enough to integrate with SAM and its variants, almost at no computational cost. With elementary tools from convex optimization and learning theory, we also conduct a theoretical analysis of sharpness-aware training, revealing that compared to SGD, the effectiveness of SAM is only assured in a limited regime of learning rate. In contrast, we show how SSAM extends this regime of learning rate and then it can consistently perform better than SAM with the minor modification. Finally, we demonstrate the improved performance of SSAM on several representative data sets and tasks., Comment: 33 pages

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data interpolation. However, they often underperform when the training and test missing patterns do not match. To alleviate this issue, here we propose a novel framework that is built upon the multi-modal adaptable diffusion models. In the training phase, following the common wisdom, we use the denoising diffusion probabilistic model with a cosine noise schedule. This cosine global noise configuration improves the use of seismic data by reducing the involvement of excessive noise stages. In the inference phase, we introduce the denoising diffusion implicit model to reduce the number of sampling steps. Different from the conventional unconditional generation, we incorporate the known trace information into each reverse sampling step for achieving conditional interpolation. To enhance the coherence and continuity between the revealed traces and the missing traces, we further propose two strategies, including successive coherence correction and resampling. Coherence correction penalizes the mismatches in the revealed traces, while resampling conducts cyclic interpolation between adjacent reverse steps. Extensive experiments on synthetic and field seismic data validate our model's superiority and demonstrate its generalization capability to various missing patterns and different noise levels with just one training session. In addition, uncertainty quantification and ablation studies are also investigated., Comment: 14 pages, 13 figures

Guided depth map super-resolution (GDSR), as a hot topic in multi-modal image processing, aims to upsample low-resolution (LR) depth maps with additional information involved in high-resolution (HR) RGB images from the same scene. The critical step of this task is to effectively extract domain-shared and domain-private RGB/depth features. In addition, three detailed issues, namely blurry edges, noisy surfaces, and over-transferred RGB texture, need to be addressed. In this paper, we propose the Spherical Space feature Decomposition Network (SSDNet) to solve the above issues. To better model cross-modality features, Restormer block-based RGB/depth encoders are employed for extracting local-global features. Then, the extracted features are mapped to the spherical space to complete the separation of private features and the alignment of shared features. Shared features of RGB are fused with the depth features to complete the GDSR task. Subsequently, a spherical contrast refinement (SCR) module is proposed to further address the detail issues. Patches that are classified according to imperfect categories are input into the SCR module, where the patch features are pulled closer to the ground truth and pushed away from the corresponding imperfect samples in the spherical feature space via contrastive learning. Extensive experiments demonstrate that our method can achieve state-of-the-art results on four test datasets, as well as successfully generalize to real-world scenes. The code is available at \url{https://github.com/Zhaozixiang1228/GDSR-SSDNet}., Comment: Accepted by ICCV 2023

One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too loose to be informative of the true generalization error or only valid to the compressed nets. In this study, we present a simple yet non-vacuous generalization bound from the optimization perspective. We achieve this goal by leveraging that the hypothesis set accessed by stochastic gradient algorithms is essentially fractal-like and thus can derive a tighter bound over the algorithm-dependent Rademacher complexity. The main argument rests on modeling the discrete-time recursion process via a continuous-time stochastic differential equation driven by fractional Brownian motion. Numerical studies demonstrate that our approach is able to yield plausible generalization guarantees for modern neural networks such as ResNet and Vision Transformer, even when they are trained on a large-scale dataset (e.g. ImageNet-1K)., Comment: 35pages

Stochastic gradient descent (SGD) is of fundamental importance in deep learning. Despite its simplicity, elucidating its efficacy remains challenging. Conventionally, the success of SGD is ascribed to the stochastic gradient noise (SGN) incurred in the training process. Based on this consensus, SGD is frequently treated and analyzed as the Euler-Maruyama discretization of stochastic differential equations (SDEs) driven by either Brownian or Levy stable motion. In this study, we argue that SGN is neither Gaussian nor Levy stable. Instead, inspired by the short-range correlation emerging in the SGN series, we propose that SGD can be viewed as a discretization of an SDE driven by fractional Brownian motion (FBM). Accordingly, the different convergence behavior of SGD dynamics is well-grounded. Moreover, the first passage time of an SDE driven by FBM is approximately derived. The result suggests a lower escaping rate for a larger Hurst parameter, and thus SGD stays longer in flat minima. This happens to coincide with the well-known phenomenon that SGD favors flat minima that generalize well. Extensive experiments are conducted to validate our conjecture, and it is demonstrated that short-range memory effects persist across various model architectures, datasets, and training strategies. Our study opens up a new perspective and may contribute to a better understanding of SGD., Comment: 15pages