Uniform Convergence of Deep Neural Networks With Lipschitz Continuous Activation Functions and Variable Widths

We consider deep neural networks (DNNs) with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias vectors together with the Lipschitz constant are provided to ensure uniform convergence of DNNs to a meaningful function as the number of their layers tends to infinity. In the framework, special results on uniform convergence of DNNs with a fixed width, bounded widths and unbounded widths are presented. In particular, as convolutional neural networks are special DNNs with weight matrices of increasing widths, we put forward conditions on the mask sequence which lead to uniform convergence of the resulting convolutional neural networks. The Lipschitz continuity assumption on the activation functions allows us to include in our theory most of commonly used activation functions in applications

Refinement of Operator-valued Reproducing Kernels

This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occurs. Numerical simulations confirm that the established refinement kernel method is able to meet this need. Various characterizations are provided based on feature maps and vector-valued integral representations of operator-valued reproducing kernels. Concrete examples of refining translation invariant and finite Hilbert-Schmidt operator-valued reproducing kernels are provided. Other examples include refinement of Hessian of scalar-valued translation-invariant kernels and transformation kernels. Existence and properties of operator-valued reproducing kernels preserved during the refinement process are also investigated

Universal Kernels

In this paper we investigate conditions on the features of a continuous kernel so that it may approximate an arbitrary continuous target function uniformly on any compact subset of the input space. A number of concrete examples are given of kernels with this universal approximating property

Microstructure and Magnetic Properties of NdFeB Films through Nd Surface Diffusion Process

Ta/Nd/NdFeB/Nd/Ta films were deposited by magnetron sputtering on Si (100) substrates and subsequently annealed for 30 min at 923 K in vacuum. It was found that the microstructure and magnetic properties of Ta/Nd/NdFeB/Nd/Ta films strongly depend on the NdFeB layer thickness. With NdFeB layer thickness increasing, both the grain size and the strain firstly reduce and then increase. When NdFeB layer thickness is 750 nm, the strain reaches the minimum value. Meanwhile, both the in-plane and perpendicular coercivities firstly drastically increase and then slowly decrease with NdFeB layer thickness increasing. The highest in-plane and perpendicular coercivities can be obtained at NdFeB layer thickness of 750 nm, which are 21.2 kOe and 19.5 kOe, respectively. In addition, the high remanence ratio (remanent magnetization/saturation magnetization) of 0.87 can also be achieved in Ta/Nd/NdFeB (750 nm)/Nd/Ta film

Exploring the Complexity of Location Choices of the Creative Class in Europe: Evidence from the EU Labor Force Survey 1995-2010

This paper proposes a new idea for the current argument over Florida's cultural policies, as location choices of the creative class is a complex process involving some basic aspects of socio-economic progress. Based on the European Labor Force Survey (EU LFE) dataset, tolerance and openness indicators which represent the quality of a "people climate" are found to be positively correlated with the creative class’s location in large regions and less so in smaller ones, where business climate-related parameters, i.e., the quality of local governments and the location of universities, have stronger positive effects on locational choices of the creative class. Moreover, graduates with non-creative jobs and creative professionals (i.e., workers who provide creative solutions during the work process such as high-tech technicians or legal and healthcare workers) are concerned more about the people climate, while creative workers with a degree and a creative core (e.g., workers who provide original ideas such as scientists, engineers and artists) are more likely to prioritize a business climate. Therefore, we argue that the promotion of a "tolerant" climate, as Florida advocates, is not a one-size-fits-all solution. Instead, policy makers should appropriately relate different preferences of creative workers to their unique strengths. This provides more insights into defining the concept of creativity beyond prioritized individual success, as well as understanding the preferences and actual needs of highly skilled workers in Europe

Crystalline Electric Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO4_4

We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb$^{3+}$ crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO$_4$. Three CEF excitations from the ground-state Kramers doublet are centered at the energies $\hbar \omega$ = 39, 61, and 97\,meV in agreement with the effective \mbox{spin-1/2} $g$-factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg$^{2+}$ and Ga$^{3+}$ giving rise to a distribution of Yb--O distances and orientations and, thus, of CEF parameters that account for the peculiar energy profile of the CEF excitations. The CEF randomness gives rise to a distribution of the effective spin-1/2 $g$-factors and explains the unprecedented broadening of low-energy magnetic excitations in the fully polarized ferromagnetic phase of YbMgGaO$_4$, although a distribution of magnetic couplings due to the Mg/Ga disorder may be important as well.Comment: Accepted in Phys. Rev. Let

Nearest-neighbor resonating valence bonds in YbMgGaO4

Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids (QSL). Here, we show that excitations related to singlet breaking on nearest-neighbor bonds describe the high-energy part of the excitation spectrum in YbMgGaO4, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering (INS) study, we demonstrate that nearest-neighbor RVB excitations account for the bulk of the spectral weight above 0.5 meV. This renders YbMgGaO4 the first experimental system where putative RVB correlations restricted to nearest neighbors are observed, and poses a fundamental question of how complex interactions on the triangular lattice conspire to form this unique many-body state.Comment: To be published in Nature Communication

A Segmentation Foundation Model for Diverse-type Tumors

Large pre-trained models with their numerous model parameters and extensive training datasets have shown excellent performance in various tasks. Many publicly available medical image datasets do not have a sufficient amount of data so there are few large-scale models in medical imaging. We propose a large-scale Tumor Segmentation Foundation Model (TSFM) with 1.6 billion parameters using Resblock-backbone and Transformer-bottleneck,which has good transfer ability for downstream tasks. To make TSFM exhibit good performance in tumor segmentation, we make full use of the strong spatial correlation between tumors and organs in the medical image, innovatively fuse 7 tumor datasets and 3 multi-organ datasets to build a 3D medical dataset pool, including 2779 cases with totally 300k medical images, whose size currently exceeds many other single publicly available datasets. TSFM is the pre-trained model for medical image segmentation, which also can be transferred to multiple downstream tasks for fine-tuning learning. The average performance of our pre-trained model is 2% higher than that of nnU-Net across various tumor types. In the transfer learning task, TSFM only needs 5% training epochs of nnU-Net to achieve similar performance and can surpass nnU-Net by 2% on average with 10% training epoch. Pre-trained TSFM and its code will be released soon.Comment: 10 pages, 2 figures.About Medical image segmentation and Foundation Mode