Is Solving Graph Neural Tangent Kernel Equivalent to Training Graph Neural Network?

A rising trend in theoretical deep learning is to understand why deep learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method that is equivalent to using gradient descent to train a multi-layer infinitely-wide neural network. NTK is a major step forward in the theoretical deep learning because it allows researchers to use traditional mathematical tools to analyze properties of deep neural networks and to explain various neural network techniques from a theoretical view. A natural extension of NTK on graph learning is \textit{Graph Neural Tangent Kernel (GNTK)}, and researchers have already provide GNTK formulation for graph-level regression and show empirically that this kernel method can achieve similar accuracy as GNNs on various bioinformatics datasets [dhs+19]. The remaining question now is whether solving GNTK regression is equivalent to training an infinite-wide multi-layer GNN using gradient descent. In this paper, we provide three new theoretical results. First, we formally prove this equivalence for graph-level regression. Second, we present the first GNTK formulation for node-level regression. Finally, we prove the equivalence for node-level regression

Query Complexity of Active Learning for Function Family With Nearly Orthogonal Basis

Many machine learning algorithms require large numbers of labeled data to deliver state-of-the-art results. In applications such as medical diagnosis and fraud detection, though there is an abundance of unlabeled data, it is costly to label the data by experts, experiments, or simulations. Active learning algorithms aim to reduce the number of required labeled data points while preserving performance. For many convex optimization problems such as linear regression and $p$-norm regression, there are theoretical bounds on the number of required labels to achieve a certain accuracy. We call this the query complexity of active learning. However, today's active learning algorithms require the underlying learned function to have an orthogonal basis. For example, when applying active learning to linear regression, the requirement is the target function is a linear composition of a set of orthogonal linear functions, and active learning can find the coefficients of these linear functions. We present a theoretical result to show that active learning does not need an orthogonal basis but rather only requires a nearly orthogonal basis. We provide the corresponding theoretical proofs for the function family of nearly orthogonal basis, and its applications associated with the algorithmically efficient active learning framework

Improved Reconstruction for Fourier-Sparse Signals

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq k$), from minimum \emph{noisy} samples of $x(t)$ in the time domain. We present a unified framework for this problem by developing a theory of sparse Fourier transforms (SFT) for frequencies lying on a \emph{lattice}, which can be viewed as a ``semi-continuous'' version of SFT in between discrete and continuous domains. Using this framework, we obtain the following results: $\bullet$ **Dimension-free Fourier sparse recovery** We present a sample-optimal discrete Fourier Set-Query algorithm with $O(k^{\omega+1})$ reconstruction time in one dimension, \emph{independent} of the signal's length ($n$) and $\ell_\infty$-norm. This complements the state-of-art algorithm of [Kapralov, STOC 2017], whose reconstruction time is $\tilde{O}(k \log^2 n \log R^*)$, where $R^* \approx \|\hat{x}\|_\infty$ is a signal-dependent parameter, and the algorithm is limited to low dimensions. By contrast, our algorithm works for arbitrary $d$ dimensions, mitigating the $\exp(d)$ blowup in decoding time to merely linear in $d$. A key component in our algorithm is fast spectral sparsification of the Fourier basis. $\bullet$ **High-accuracy Fourier interpolation** In one dimension, we design a poly-time $(3+ \sqrt{2} +\epsilon)$-approximation algorithm for continuous Fourier interpolation. This bypasses a barrier of all previous algorithms [Price and Song, FOCS 2015, Chen, Kane, Price and Song, FOCS 2016], which only achieve $c>100$ approximation for this basic problem. Our main contribution is a new analytic tool for hierarchical frequency decomposition based on \emph{noise cancellation}

A novel high-strength large vibrating screen with duplex statically indeterminate mesh beam structure

Screening is an indispensable unit process for separation of materials. Large vibrating screen is extensively used in coal processing because of its large production capacity. In this study, a novel large vibrating screen with duplex statically indeterminate mesh beam structure (VSDSIMBS) was presented. The dynamic model of VSDSIMBS was proposed, and characteristic parameters were obtained by theoretical calculations. In order to obtain more reliable and believable research results, model of a traditional vibrating screen (TVS) with the same mass was also established for comparisons with VSDSIMBS. The finite element (FE) method was applied to study the performance of VSDSIMBS and FE analysis of VSDSIMBS and TVS was completed by using characteristic parameters. Modal analysis results indicated that VSDSIMBS could avoid the resonance and run more smoothly than TVS. Furthermore, harmonic response analysis results showed that VSDSIMBS could improve the entire stress distribution, reduce high stress areas, and increase the strength of vibrating screen. With DSIMBS, the maximum stress of vibrating screen decreased from 130.53 to 64.54 MPa. The full-scale experimental tests were performed to validate the credibility and accuracy of FE analysis results. The stress and displacements of VSDSIMBS were measured under working conditions. The test results obtained are in good agreement with simulation results, and accord with conclusions made from FE analysis

The complete chloroplast genome of Heteromorpha arborescens (Apiaceae)

Heteromorpha arborescens has long been recognized and cultivated as an important medicinal plant. We reported its complete plastid genome for the first time and reconstructed its phylogenetic position. The complete plastid genome was 157,172 bp in length with a typical quadripartite organization: a large single-copy (LSC) region of 86,436 bp, a small single-copy (SSC) region of 18,222 bp, and two inverted repeat regions (IRa and IRb), each of 26,257 bp. A total of 130 functional genes were recovered, consisting of 85 protein-coding genes, 37 tRNA genes, and 8 rRNA genes. The phylogenetic analysis suggested that H. arborescens is sister to other species except Cetella arborescens in Apiaceae with strong ultrafast support

Automatic Railway Traffic Object Detection System Using Feature Fusion Refine Neural Network under Shunting Mode

Many accidents happen under shunting mode when the speed of a train is below 45 km/h. In this mode, train attendants observe the railway condition ahead using the traditional manual method and tell the observation results to the driver in order to avoid danger. To address this problem, an automatic object detection system based on convolutional neural network (CNN) is proposed to detect objects ahead in shunting mode, which is called Feature Fusion Refine neural network (FR-Net). It consists of three connected modules, i.e., the depthwise-pointwise convolution, the coarse detection module, and the object detection module. Depth-wise-pointwise convolutions are used to improve the detection in real time. The coarse detection module coarsely refine the locations and sizes of prior anchors to provide better initialization for the subsequent module and also reduces search space for the classification, whereas the object detection module aims to regress accurate object locations and predict the class labels for the prior anchors. The experimental results on the railway traffic dataset show that FR-Net achieves 0.8953 mAP with 72.3 FPS performance on a machine with a GeForce GTX1080Ti with the input size of 320 × 320 pixels. The results imply that FR-Net takes a good tradeoff both on effectiveness and real time performance. The proposed method can meet the needs of practical application in shunting mode

Structure of active human telomerase with telomere shelterin protein TPP1.

Human telomerase is a RNA-protein complex that extends the 3' end of linear chromosomes by synthesizing multiple copies of the telomeric repeat TTAGGG1. Its activity is a determinant of cancer progression, stem cell renewal and cellular aging2-5. Telomerase is recruited to telomeres and activated for telomere repeat synthesis by the telomere shelterin protein TPP16,7. Human telomerase has a bilobal structure with a catalytic core ribonuclear protein and a H and ACA box ribonuclear protein8,9. Here we report cryo-electron microscopy structures of human telomerase catalytic core of telomerase reverse transcriptase (TERT) and telomerase RNA (TER (also known as hTR)), and of telomerase with the shelterin protein TPP1. TPP1 forms a structured interface with the TERT-unique telomerase essential N-terminal domain (TEN) and the telomerase RAP motif (TRAP) that are unique to TERT, and conformational dynamics of TEN-TRAP are damped upon TPP1 binding, defining the requirements for recruitment and activation. The structures further reveal that the elements of TERT and TER that are involved in template and telomeric DNA handling-including the TEN domain and the TRAP-thumb helix channel-are largely structurally homologous to those in Tetrahymena telomerase10, and provide unique insights into the mechanism of telomerase activity. The binding site of the telomerase inhibitor BIBR153211,12 overlaps a critical interaction between the TER pseudoknot and the TERT thumb domain. Numerous mutations leading to telomeropathies13,14 are located at the TERT-TER and TEN-TRAP-TPP1 interfaces, highlighting the importance of TER-TERT and TPP1 interactions for telomerase activity, recruitment and as drug targets