Global regularity to the Navier-Stokes equations for a class of large initial data

In [5], Chemin, Gallagher and Paicu proved the global regularity of solutions to the classical Navier-Stokes equations with a class of large initial data on T2 × R. This data varies slowly in vertical variable and has a norm which blows up as the small parameter ( represented by ǫ in the paper) tends to zero. However, to the best of our knowledge, the result is still unclear for the whole spaces R3. In this paper, we consider the generalized Navier-Stokes equations on Rn(n ≥ 3): ∂tu + u · ∇u + Dsu + ∇P = 0, div u = 0. For some suitable number s, we prove that the Cauchy problem with initial data of the form u0ǫ(x) = (v0h(xǫ), ǫ−1v0n(xǫ))T , xǫ = (xh, ǫxn)T , is globally well-posed for all small ǫ > 0, provided that the initial velocity profile v0 is analytic in xn and certain norm of v0 is sufficiently small but independent of ǫ. In particular, our result is true for the n-dimensional classical Navier-Stokes equations with n ≥ 4 and the fractional Navier-Stokes equations with 1 ≤ s < 2 in 3D

Mask-Attention-Free Transformer for 3D Instance Segmentation

Recently, transformer-based methods have dominated 3D instance segmentation, where mask attention is commonly involved. Specifically, object queries are guided by the initial instance masks in the first cross-attention, and then iteratively refine themselves in a similar manner. However, we observe that the mask-attention pipeline usually leads to slow convergence due to low-recall initial instance masks. Therefore, we abandon the mask attention design and resort to an auxiliary center regression task instead. Through center regression, we effectively overcome the low-recall issue and perform cross-attention by imposing positional prior. To reach this goal, we develop a series of position-aware designs. First, we learn a spatial distribution of 3D locations as the initial position queries. They spread over the 3D space densely, and thus can easily capture the objects in a scene with a high recall. Moreover, we present relative position encoding for the cross-attention and iterative refinement for more accurate position queries. Experiments show that our approach converges 4x faster than existing work, sets a new state of the art on ScanNetv2 3D instance segmentation benchmark, and also demonstrates superior performance across various datasets. Code and models are available at https://github.com/dvlab-research/Mask-Attention-Free-Transformer.Comment: Accepted to ICCV 2023. Code and models are available at https://github.com/dvlab-research/Mask-Attention-Free-Transforme

GlyphControl: Glyph Conditional Control for Visual Text Generation

Recently, there has been a growing interest in developing diffusion-based text-to-image generative models capable of generating coherent and well-formed visual text. In this paper, we propose a novel and efficient approach called GlyphControl to address this task. Unlike existing methods that rely on character-aware text encoders like ByT5 and require retraining of text-to-image models, our approach leverages additional glyph conditional information to enhance the performance of the off-the-shelf Stable-Diffusion model in generating accurate visual text. By incorporating glyph instructions, users can customize the content, location, and size of the generated text according to their specific requirements. To facilitate further research in visual text generation, we construct a training benchmark dataset called LAION-Glyph. We evaluate the effectiveness of our approach by measuring OCR-based metrics and CLIP scores of the generated visual text. Our empirical evaluations demonstrate that GlyphControl outperforms the recent DeepFloyd IF approach in terms of OCR accuracy and CLIP scores, highlighting the efficacy of our method.Comment: Technical report. The codes will be released at https://github.com/AIGText/GlyphControl-releas

Data Pruning via Moving-one-Sample-out

In this paper, we propose a novel data-pruning approach called moving-one-sample-out (MoSo), which aims to identify and remove the least informative samples from the training set. The core insight behind MoSo is to determine the importance of each sample by assessing its impact on the optimal empirical risk. This is achieved by measuring the extent to which the empirical risk changes when a particular sample is excluded from the training set. Instead of using the computationally expensive leaving-one-out-retraining procedure, we propose an efficient first-order approximator that only requires gradient information from different training stages. The key idea behind our approximation is that samples with gradients that are consistently aligned with the average gradient of the training set are more informative and should receive higher scores, which could be intuitively understood as follows: if the gradient from a specific sample is consistent with the average gradient vector, it implies that optimizing the network using the sample will yield a similar effect on all remaining samples. Experimental results demonstrate that MoSo effectively mitigates severe performance degradation at high pruning ratios and achieves satisfactory performance across various settings.Comment: Accepted by the Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS 2023