Since being proposed, Neural Radiance Fields (NeRF) have achieved great success in related tasks, mainly adopting the hierarchical volume sampling (HVS) strategy for volume rendering. However, the HVS of NeRF approximates distributions using piecewise constant functions, which provides a relatively rough estimation. Based on the observation that a well-trained weight function $w(t)$ and the $L_0$ distance between points and the surface have very high similarity, we propose $L_0$-Sampler by incorporating the $L_0$ model into $w(t)$ to guide the sampling process. Specifically, we propose to use piecewise exponential functions rather than piecewise constant functions for interpolation, which can not only approximate quasi-$L_0$ weight distributions along rays quite well but also can be easily implemented with few lines of code without additional computational burden. Stable performance improvements can be achieved by applying $L_0$-Sampler to NeRF and its related tasks like 3D reconstruction. Code is available at //ustc3dv.github.io/L0-Sampler/ .
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In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension $d$ and the total sensitivity $\mathfrak S$ in remarkably general settings. However, guarantees going beyond this general bound of $\mathfrak S d$ are known in perhaps only one setting, for $\ell_2$ subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for $\ell_p$ subspace embeddings for $p > 2$ that improve over the general $\mathfrak S d$ bound, achieving a bound of roughly $\mathfrak S^{2-2/p}$ for $2<p<\infty$. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly $d$ for $1\leq p<2$, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly $d^{2/p}\mathfrak S^{2-4/p}$ for $2<p<\infty$. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small $\ell_p$ sensitivity.
Diffusion Magnetic Resonance Imaging (dMRI) plays a crucial role in the noninvasive investigation of tissue microstructural properties and structural connectivity in the \textit{in vivo} human brain. However, to effectively capture the intricate characteristics of water diffusion at various directions and scales, it is important to employ comprehensive q-space sampling. Unfortunately, this requirement leads to long scan times, limiting the clinical applicability of dMRI. To address this challenge, we propose SSOR, a Simultaneous q-Space sampling Optimization and Reconstruction framework. We jointly optimize a subset of q-space samples using a continuous representation of spherical harmonic functions and a reconstruction network. Additionally, we integrate the unique properties of diffusion magnetic resonance imaging (dMRI) in both the q-space and image domains by applying $l1$-norm and total-variation regularization. The experiments conducted on HCP data demonstrate that SSOR has promising strengths both quantitatively and qualitatively and exhibits robustness to noise.
Pulmonary embolism (PE) is a prevalent lung disease that can lead to right ventricular hypertrophy and failure in severe cases, ranking second in severity only to myocardial infarction and sudden death. Pulmonary artery CT angiography (CTPA) is a widely used diagnostic method for PE. However, PE detection presents challenges in clinical practice due to limitations in imaging technology. CTPA can produce noises similar to PE, making confirmation of its presence time-consuming and prone to overdiagnosis. Nevertheless, the traditional segmentation method of PE can not fully consider the hierarchical structure of features, local and global spatial features of PE CT images. In this paper, we propose an automatic PE segmentation method called SCUNet++ (Swin Conv UNet++). This method incorporates multiple fusion dense skip connections between the encoder and decoder, utilizing the Swin Transformer as the encoder. And fuses features of different scales in the decoder subnetwork to compensate for spatial information loss caused by the inevitable downsampling in Swin-UNet or other state-of-the-art methods, effectively solving the above problem. We provide a theoretical analysis of this method in detail and validate it on publicly available PE CT image datasets FUMPE and CAD-PE. The experimental results indicate that our proposed method achieved a Dice similarity coefficient (DSC) of 83.47% and a Hausdorff distance 95th percentile (HD95) of 3.83 on the FUMPE dataset, as well as a DSC of 83.42% and an HD95 of 5.10 on the CAD-PE dataset. These findings demonstrate that our method exhibits strong performance in PE segmentation tasks, potentially enhancing the accuracy of automatic segmentation of PE and providing a powerful diagnostic tool for clinical physicians. Our source code and new FUMPE dataset are available at //github.com/JustlfC03/SCUNet-plusplus.
Diffusion models have emerged as powerful generative tools, rivaling GANs in sample quality and mirroring the likelihood scores of autoregressive models. A subset of these models, exemplified by DDIMs, exhibit an inherent asymmetry: they are trained over $T$ steps but only sample from a subset of $T$ during generation. This selective sampling approach, though optimized for speed, inadvertently misses out on vital information from the unsampled steps, leading to potential compromises in sample quality. To address this issue, we present the S$^{2}$-DMs, which is a new training method by using an innovative $L_{skip}$, meticulously designed to reintegrate the information omitted during the selective sampling phase. The benefits of this approach are manifold: it notably enhances sample quality, is exceptionally simple to implement, requires minimal code modifications, and is flexible enough to be compatible with various sampling algorithms. On the CIFAR10 dataset, models trained using our algorithm showed an improvement of 3.27% to 14.06% over models trained with traditional methods across various sampling algorithms (DDIMs, PNDMs, DEIS) and different numbers of sampling steps (10, 20, ..., 1000). On the CELEBA dataset, the improvement ranged from 8.97% to 27.08%. Access to the code and additional resources is provided in the github.
In deep learning, classification tasks are formalized as optimization problems solved via the minimization of the cross-entropy. However, recent advancements in the design of objective functions allow the $f$-divergence measure to generalize the formulation of the optimization problem for classification. With this goal in mind, we adopt a Bayesian perspective and formulate the classification task as a maximum a posteriori probability problem. We propose a class of objective functions based on the variational representation of the $f$-divergence, from which we extract a list of five posterior probability estimators leveraging well-known $f$-divergences. In addition, driven by the challenge of improving the state-of-the-art approach, we propose a bottom-up method that leads us to the formulation of a new objective function (and posterior probability estimator) corresponding to a novel $f$-divergence referred to as shifted log (SL). First, we theoretically prove the convergence property of the posterior probability estimators. Then, we numerically test the set of proposed objective functions in three application scenarios: toy examples, image data sets, and signal detection/decoding problems. The analyzed tasks demonstrate the effectiveness of the proposed estimators and that the SL divergence achieves the highest classification accuracy in almost all the scenarios.
Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an $\ell^1$-prior. Moreover, we develop parameter selection strategies. Finally, we quantitatively and qualitatively evaluate the proposed algorithmic scheme on the 3D Open MPI data set with different levels of preprocessing.
The most advanced text-to-image (T2I) models require significant training costs (e.g., millions of GPU hours), seriously hindering the fundamental innovation for the AIGC community while increasing CO2 emissions. This paper introduces PIXART-$\alpha$, a Transformer-based T2I diffusion model whose image generation quality is competitive with state-of-the-art image generators (e.g., Imagen, SDXL, and even Midjourney), reaching near-commercial application standards. Additionally, it supports high-resolution image synthesis up to 1024px resolution with low training cost, as shown in Figure 1 and 2. To achieve this goal, three core designs are proposed: (1) Training strategy decomposition: We devise three distinct training steps that separately optimize pixel dependency, text-image alignment, and image aesthetic quality; (2) Efficient T2I Transformer: We incorporate cross-attention modules into Diffusion Transformer (DiT) to inject text conditions and streamline the computation-intensive class-condition branch; (3) High-informative data: We emphasize the significance of concept density in text-image pairs and leverage a large Vision-Language model to auto-label dense pseudo-captions to assist text-image alignment learning. As a result, PIXART-$\alpha$'s training speed markedly surpasses existing large-scale T2I models, e.g., PIXART-$\alpha$ only takes 10.8% of Stable Diffusion v1.5's training time (675 vs. 6,250 A100 GPU days), saving nearly \$300,000 (\$26,000 vs. \$320,000) and reducing 90% CO2 emissions. Moreover, compared with a larger SOTA model, RAPHAEL, our training cost is merely 1%. Extensive experiments demonstrate that PIXART-$\alpha$ excels in image quality, artistry, and semantic control. We hope PIXART-$\alpha$ will provide new insights to the AIGC community and startups to accelerate building their own high-quality yet low-cost generative models from scratch.
Traffic accidents, being a significant contributor to both human casualties and property damage, have long been a focal point of research for many scholars in the field of traffic safety. However, previous studies, whether focusing on static environmental assessments or dynamic driving analyses, as well as pre-accident predictions or post-accident rule analyses, have typically been conducted in isolation. There has been a lack of an effective framework for developing a comprehensive understanding and application of traffic safety. To address this gap, this paper introduces AccidentGPT, a comprehensive accident analysis and prevention multi-modal large model. AccidentGPT establishes a multi-modal information interaction framework grounded in multi-sensor perception, thereby enabling a holistic approach to accident analysis and prevention in the field of traffic safety. Specifically, our capabilities can be categorized as follows: for autonomous driving vehicles, we provide comprehensive environmental perception and understanding to control the vehicle and avoid collisions. For human-driven vehicles, we offer proactive long-range safety warnings and blind-spot alerts while also providing safety driving recommendations and behavioral norms through human-machine dialogue and interaction. Additionally, for traffic police and management agencies, our framework supports intelligent and real-time analysis of traffic safety, encompassing pedestrian, vehicles, roads, and the environment through collaborative perception from multiple vehicles and road testing devices. The system is also capable of providing a thorough analysis of accident causes and liability after vehicle collisions. Our framework stands as the first large model to integrate comprehensive scene understanding into traffic safety studies. Project page: //accidentgpt.github.io
We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed to handle digraphs with weights of arbitrary sign). In addition to its generality, our Quaternionic Laplacian is the only Laplacian to completely preserve the topology of a digraph, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weights without reducing them to a single (directed or undirected) edge as done with other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.
Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.
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