Statistical Optimality of Deep Wide Neural Networks

In this paper, we consider the generalization ability of deep wide feedforward ReLU neural networks defined on a bounded domain $\mathcal X \subset \mathbb R^{d}$. We first demonstrate that the generalization ability of the neural network can be fully characterized by that of the corresponding deep neural tangent kernel (NTK) regression. We then investigate on the spectral properties of the deep NTK and show that the deep NTK is positive definite on $\mathcal{X}$ and its eigenvalue decay rate is $(d+1)/d$. Thanks to the well established theories in kernel regression, we then conclude that multilayer wide neural networks trained by gradient descent with proper early stopping achieve the minimax rate, provided that the regression function lies in the reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK. Finally, we illustrate that the overfitted multilayer wide neural networks can not generalize well on $\mathbb S^{d}$. We believe our technical contributions in determining the eigenvalue decay rate of NTK on $\mathbb R^{d}$ might be of independent interests

Functional Slicing-free Inverse Regression via Martingale Difference Divergence Operator

Functional sliced inverse regression (FSIR) is one of the most popular algorithms for functional sufficient dimension reduction (FSDR). However, the choice of slice scheme in FSIR is critical but challenging. In this paper, we propose a new method called functional slicing-free inverse regression (FSFIR) to estimate the central subspace in FSDR. FSFIR is based on the martingale difference divergence operator, which is a novel metric introduced to characterize the conditional mean independence of a functional predictor on a multivariate response. We also provide a specific convergence rate for the FSFIR estimator. Compared with existing functional sliced inverse regression methods, FSFIR does not require the selection of a slice number. Simulations demonstrate the efficiency and convenience of FSFIR

Likelihood-Based Text-to-Image Evaluation with Patch-Level Perceptual and Semantic Credit Assignment

Text-to-image synthesis has made encouraging progress and attracted lots of public attention recently. However, popular evaluation metrics in this area, like the Inception Score and Fr'echet Inception Distance, incur several issues. First of all, they cannot explicitly assess the perceptual quality of generated images and poorly reflect the semantic alignment of each text-image pair. Also, they are inefficient and need to sample thousands of images to stabilise their evaluation results. In this paper, we propose to evaluate text-to-image generation performance by directly estimating the likelihood of the generated images using a pre-trained likelihood-based text-to-image generative model, i.e., a higher likelihood indicates better perceptual quality and better text-image alignment. To prevent the likelihood of being dominated by the non-crucial part of the generated image, we propose several new designs to develop a credit assignment strategy based on the semantic and perceptual significance of the image patches. In the experiments, we evaluate the proposed metric on multiple popular text-to-image generation models and datasets in accessing both the perceptual quality and the text-image alignment. Moreover, it can successfully assess the generation ability of these models with as few as a hundred samples, making it very efficient in practice

Mesh-MLP: An all-MLP Architecture for Mesh Classification and Semantic Segmentation

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions are helpful, a simple architecture based exclusively on multi-layer perceptrons (MLPs) is competent enough to deal with mesh classification and semantic segmentation. Our new network architecture, named Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles as the input, replaces the convolution module of a ResNet with Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform the normalization of the layers. The all-MLP architecture operates in an end-to-end fashion and does not include a pooling module. Extensive experimental results on the mesh classification/segmentation tasks validate the effectiveness of the all-MLP architecture.Comment: 8 pages, 6 figure

Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods

Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction

Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns the noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised fashion. We use the IMLS to regularize the distance values reported by the MLP while using the MLP to regularize the normals of the data points for running the IMLS. We also prove that at the convergence, our neural network, benefiting from the mutual learning mechanism between the MLP and the IMLS, produces a faithful SDF whose zero-level set approximates the underlying surface. We conducted extensive experiments on various benchmarks, including synthetic scans and real scans. The experimental results show that {\em Neural-IMLS} can reconstruct faithful shapes on various benchmarks with noise and missing parts. The source code can be found at~\url{https://github.com/bearprin/Neural-IMLS}

Outcomes of two types of iodine-125 seed delivery with metal stents in treating malignant biliary obstruction: a systematic review and meta-analysis

PURPOSETo conduct a meta-analysis comparing the efficacy and safety of two types of iodine-125 (I-125) seed delivery with metal stents (the study group) versus conventional metal stents (the control group) in patients with malignant biliary obstruction (MBO).METHODSOur team systematically searched the PubMed, Embase, and Cochrane Library databases for relevant studies published from January 2012 up to July 2021. Survival time and stent dysfunction were the primary measured outcomes. Subgroup analyses were conducted according to the type of I-125 seed delivery.RESULTSEleven studies, including 1057 patients in total, were pooled for stent dysfunction. The study group showed a lower risk of stent dysfunction than the control group [odds ratio (OR): 0.61, 95% confidence interval (CI) 0.46–0.81, P = 0.001]. The pooled results of six studies reporting overall survival (OS) showed that the study group had a better survival outcome than the control group [hazard ratio (HR): 0.34, 95% CI: 0.28–0.42, P 0.05). The study group was significantly superior to the control group, with better survival and decreased stent dysfunction. Meanwhile, the delivery of I-125 seeds did not increase adverse events.CONCLUSIONThe delivery of I-125 with metal stents may be considered a preferable technique for MBO

Process of Extraction Protein from Selenium-enriched Lyophyllum decastes Mycelia and Analysis of Its Amino Acid

The process of extracting seleno-protein from the selenium enriched Lyophyllum decastes mycelia cultured in a 20 L fermentor was optimized, and the effects of selenium enrichment on both types and contents of amino acids in Lyophyllum decastes mycelia were analyzed. Single factor tests and Box-Benhnken central combined response surface test were used to optimize process of extracting seleno-protein from Lyophyllum decastes mycelia. The content of protein was determined by 3,3'-diaminobenzidine spectrophotometry. The types and contents of amino acids in mycelia protein before and after selenium enrichment were compared by means of amino acid analyzer. The results showed that the optimal conditions of extracting seleno-protein from mycelia of Lyophyllum decastes were extraction temperature of 64 ℃, extraction time of 60 min, liquid-solid ratio of 200:1 g/mL, and extraction times of 2. The protein extraction rate was 75.13%, and the content of selenium in mycelia was 63.87 μg/g. The amino acid composition were analyzed by means amino acid score (AAS) and chemical score (CS), and the nutritional value of the protein in the selenium-enriched Lyophyllum decastes mycelia was evaluated. The varieties of amino acids in the selenium-enriched Lyophyllum decastes mycelia were abundant and the content of essential amino acids for human body was 17.20 g/100 g, 19.75% higher than that in the non-selenium-ecriched Lyophyllum decastes mycelia. The ratio of EAA/NEAA was 0.51, close to the recommended value proposed by WHO, and the values of both AAS and CS were close to the those in the model protein. In summary, the protein extraction rate could be improved by optimizing the extraction process, and there was selenium in the protein from selenium-enriched mycelia, which promoted the increase of amino acid content. The nutritional value of protein in selenium-enriched mycelia was higher than that in non-selenium-riched mycelia, and selenium-enrichec mycelia had potential edible and application value

Rare Copy Number Variants Identify Novel Genes in Sporadic Total Anomalous Pulmonary Vein Connection

Total anomalous pulmonary venous connection (TAPVC) is a rare congenital heart anomaly. Several genes have been associated TAPVC but the mechanisms remain elusive. To search novel CNVs and candidate genes, we screened a cohort of 78 TAPVC cases and 100 healthy controls for rare copy number variants (CNVs) using whole exome sequencing (WES). Then we identified pathogenic CNVs by statistical comparisons between case and control groups. After that, we identified altogether eight pathogenic CNVs of seven candidate genes (PCSK7, RRP7A, SERHL, TARP, TTN, SERHL2, and NBPF3). All these seven genes have not been described previously to be related to TAPVC. After network analysis of these candidate genes and 27 known pathogenic genes derived from the literature and publicly database, PCSK7 and TTN were the most important genes for TAPVC than other genes. Our study provides novel candidate genes potentially related to this rare congenital birth defect (CHD) which should be further fundamentally researched and discloses the possible molecular pathogenesis of TAPVC