Search

We constrain the halo profiles outside the halo boundaries by solving for the matching profiles required by the halo model. In the halo model framework, the matter distribution in the universe can be decomposed into the spatial distribution of halos convolved with their internal structures. This leads to a set of linear equations in Fourier space which uniquely determines the optimal halo profiles for any given halo catalog. In this work, we construct three halo catalogs with different boundary definitions, and solve for the optimal profiles in each case using measurements of halo-matter and halo-halo power spectra. Our results show that for a given halo field, there is always a set of matching profiles to accurately reconstruct the input statistics of the matter field, even though it might be complex to model the profiles analytically. Comparing the solutions from different halo catalogs, we find their mass distributions inside the inner depletion radii are nearly identical, while they deviate from each other on larger scales, with a larger boundary resulting in a more extended profile. For the depletion radius based catalog, the numerical solution agrees well with the Einasto profile. Coupling the Einasto profile with the depletion catalog, the resulting halo model can simultaneously predict the halo-matter power spectra to $10\%$ and matter-matter power spectrum to $5\%$, improving over conventional models in both the interpretability and versatility., Comment: 15 pages, 10 figures

Instance-incremental learning (IIL) focuses on learning continually with data of the same classes. Compared to class-incremental learning (CIL), the IIL is seldom explored because IIL suffers less from catastrophic forgetting (CF). However, besides retaining knowledge, in real-world deployment scenarios where the class space is always predefined, continual and cost-effective model promotion with the potential unavailability of previous data is a more essential demand. Therefore, we first define a new and more practical IIL setting as promoting the model's performance besides resisting CF with only new observations. Two issues have to be tackled in the new IIL setting: 1) the notorious catastrophic forgetting because of no access to old data, and 2) broadening the existing decision boundary to new observations because of concept drift. To tackle these problems, our key insight is to moderately broaden the decision boundary to fail cases while retain old boundary. Hence, we propose a novel decision boundary-aware distillation method with consolidating knowledge to teacher to ease the student learning new knowledge. We also establish the benchmarks on existing datasets Cifar-100 and ImageNet. Notably, extensive experiments demonstrate that the teacher model can be a better incremental learner than the student model, which overturns previous knowledge distillation-based methods treating student as the main role., Comment: 14 pages

We develop a self-consistent and accurate halo model by partitioning matter according to the depletion radii of haloes. Unlike conventional models that define haloes with the virial radius while relying on a separate exclusion radius or ad-hoc fixes to account for halo exclusion, our model distributes mass across all scales self-consistently and accounts for both the virialized and non-virialized matter distribution around each halo. Using a cosmological simulation, we show that our halo definition leads to very simple and intuitive model components, with the one-halo term given by the Einasto profile with no truncation needed, and the halo-halo correlation function following a universal power-law form down to the halo boundary. The universal halo-halo correlation also allows us to easily model the distribution of unresolved haloes as well as diffuse matter. Convolving the halo profile with the halo-halo correlation function, we obtain a complete description of the halo-matter correlation across all scales, which self-consistently accounts for halo exclusion at the transition scale. Mass conservation is explicitly maintained in our model, and the scale dependence of the classical halo bias is easily reproduced. Our model can successfully reconstruct the halo-matter correlation function within an accuracy of $9\%$ for halo virial masses in the range of $10^{11.5}h^{-1}{\rm M}_{\odot}

To achieve promising results on blind image super-resolution (SR), some attempts leveraged the low resolution (LR) images to predict the kernel and improve the SR performance. However, these Supervised Kernel Prediction (SKP) methods are impractical due to the unavailable real-world blur kernels. Although some Unsupervised Degradation Prediction (UDP) methods are proposed to bypass this problem, the \textit{inconsistency} between degradation embedding and SR feature is still challenging. By exploring the correlations between degradation embedding and SR feature, we observe that jointly learning the content and degradation aware feature is optimal. Based on this observation, a Content and Degradation aware SR Network dubbed CDSR is proposed. Specifically, CDSR contains three newly-established modules: (1) a Lightweight Patch-based Encoder (LPE) is applied to jointly extract content and degradation features; (2) a Domain Query Attention based module (DQA) is employed to adaptively reduce the inconsistency; (3) a Codebook-based Space Compress module (CSC) that can suppress the redundant information. Extensive experiments on several benchmarks demonstrate that the proposed CDSR outperforms the existing UDP models and achieves competitive performance on PSNR and SSIM even compared with the state-of-the-art SKP methods.

To achieve promising results on removing noise from real-world images, most of existing denoising networks are formulated with complex network structure, making them impractical for deployment. Some attempts focused on reducing the number of filters and feature channels but suffered from large performance loss, and a more practical and lightweight denoising network with fast inference speed is of high demand. To this end, a \textbf{Thu}mb\textbf{n}ail based \textbf{D}\textbf{e}noising Netwo\textbf{r}k dubbed Thunder, is proposed and implemented as a lightweight structure for fast restoration without comprising the denoising capabilities. Specifically, the Thunder model contains two newly-established modules: (1) a wavelet-based Thumbnail Subspace Encoder (TSE) which can leverage sub-bands correlation to provide an approximate thumbnail based on the low-frequent feature; (2) a Subspace Projection based Refine Module (SPR) which can restore the details for thumbnail progressively based on the subspace projection approach. Extensive experiments have been carried out on two real-world denoising benchmarks, demonstrating that the proposed Thunder outperforms the existing lightweight models and achieves competitive performance on PSNR and SSIM when compared with the complex designs.

Image denoising is one of the most critical problems in mobile photo processing. While many solutions have been proposed for this task, they are usually working with synthetic data and are too computationally expensive to run on mobile devices. To address this problem, we introduce the first Mobile AI challenge, where the target is to develop an end-to-end deep learning-based image denoising solution that can demonstrate high efficiency on smartphone GPUs. For this, the participants were provided with a novel large-scale dataset consisting of noisy-clean image pairs captured in the wild. The runtime of all models was evaluated on the Samsung Exynos 2100 chipset with a powerful Mali GPU capable of accelerating floating-point and quantized neural networks. The proposed solutions are fully compatible with any mobile GPU and are capable of processing 480p resolution images under 40-80 ms while achieving high fidelity results. A detailed description of all models developed in the challenge is provided in this paper., Comment: Mobile AI 2021 Workshop and Challenges: https://ai-benchmark.com/workshops/mai/2021/. arXiv admin note: substantial text overlap with arXiv:2105.07809, arXiv:2105.07825

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1} \mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance matrix $\mathbf{\Sigma}$. We study the minimax estimation of the functional in the high-dimensional setting where $\mathbf{\Sigma}^{-1} \mathbf{\mu}$ is sparse. Akin to past works on functional estimation, we show that the optimal rate for estimating the functional undergoes a phase transition between regular parametric rate and some form of high-dimensional estimation rate. We further show that the optimal rate is attained by a carefully designed plug-in estimator based on de-biasing, while a family of naive plug-in estimators are proved to fall short. We further generalize the estimation problem and techniques that allow robust inputs of mean and covariance matrix estimators. Extensive numerical experiments lend further supports to our theoretical results.

As2S3 film doped with erbium is prepared using multi-layer magnetron sputtering. The optical properties were measured by reflectance spectroscopy, and its chemical composition is examined by x-ray photoelectron, Rutherford backscattering, and Raman spectroscopy. The results show that the refractive index and absorption coefficient follow closely to a sputtered As2S3 film, and there are no detectable Er-S clusters and photo-induced As2O3 in the film. Rutherford backscattering spectroscopy shows that the film is homogeneous, and revealed the concentration level of erbium, and the stoichiometry of the film. The deposition method was used to fabricate an integrated Erdoped As2S3 Mach-Zehnder Interferometer and the presence of active erbium ions in the waveguide is evident from the green luminescence it emitted when it was pumped by 1488 nm diode laser. This method is attractive because the doping process can produce an Er:As2S3 film that is close to the ideal stoichiometry of As2S3 with lower risk of photo-decomposed As2O3 crystals developing on the surface when the as-deposited film is exposed to the environment., Comment: 18 pages and 7 figures