Miracle-dz/UniFAR-FTUs huggingface dataset:
Do Inpainting Yourself: Generative Facial Inpainting Guided by Exemplars

We present EXE-GAN, a novel exemplar-guided facial inpainting framework using generative adversarial networks. Our approach can not only preserve the quality of the input facial image but also complete the image with exemplar-like facial attributes. We achieve this by simultaneously leveraging the global style of the input image, the stochastic style generated from the random latent code, and the exemplar style of exemplar image. We introduce a novel attribute similarity metric to encourage networks to learn the style of facial attributes from the exemplar in a self-supervised way. To guarantee the natural transition across the boundaries of inpainted regions, we introduce a novel spatial variant gradient backpropagation technique to adjust the loss gradients based on the spatial location. Extensive evaluations and practical applications on public CelebA-HQ and FFHQ datasets validate the superiority of EXE-GAN in terms of the visual quality in facial inpainting.
Detection of Ubiquitous Weak and Impulsive Nonthermal Emissions from the Solar Corona

A ubiquitous presence of weak energy releases is one of the most promising hypotheses to explain coronal heating, referred to as the nanoflare hypothesis. The accelerated electrons associated with such weak heating events are also expected to give rise to coherent impulsive emission via plasma instabilities in the meterwave radio band, making this a promising spectral window to look for their presence. Recently Mondal et al. reported the presence of weak and impulsive emissions from quiet Sun regions which seem to meet the requirements of being radio counterparts of the hypothesized nanoflares. Detection of such low-contrast weak emission from the quiet Sun is challenging and, given their implications, it is important to confirm their presence. In this work, using data from the Murchison Widefield Array, we explore the use of an independent robust approach for their detection by separating the dominant, slowly varying component of emission from the weak impulsive one in the visibility domain. We detect milli-Solar Flux Unit-level bursts taking place all over the Sun and characterize their brightness temperatures, distributions, morphologies, durations, and associations with features seen in extreme-UV images. We also attempt to constrain the energies of the nonthermal particles using inputs from the FORWARD coronal model along with some reasonable assumptions, and find them to lie in the subpico flare (∼1019–1021 erg) range. In the process, we also discover perhaps the weakest type III radio burst and another that shows clear signatures of the weakest quasi-periodic pulsations.
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class

In this paper, we construct neural networks with ReLU, sine and $2^x$ as activation functions. For general continuous $f$ defined on $[0,1]^d$ with continuity modulus $\omega_f(\cdot)$, we construct ReLU-sine-$2^x$ networks that enjoy an approximation rate $\mathcal{O}(\omega_f(\sqrt{d})\cdot2^{-M}+\omega_{f}\left(\frac{\sqrt{d}}{N}\right))$, where $M,N\in \mathbb{N}^{+}$ denote the hyperparameters related to widths of the networks. As a consequence, we can construct ReLU-sine-$2^x$ network with the depth $5$ and width $\max\left\{\left\lceil2d^{3/2}\left(\frac{3\mu}{\epsilon}\right)^{1/{\alpha}}\right\rceil,2\left\lceil\log_2\frac{3\mu d^{\alpha/2}}{2\epsilon}\right\rceil+2\right\}$ that approximates $f\in \mathcal{H}_{\mu}^{\alpha}([0,1]^d)$ within a given tolerance $\epsilon>0$ measured in $L^p$ norm $p\in[1,\infty)$, where $\mathcal{H}_{\mu}^{\alpha}([0,1]^d)$ denotes the H\"older continuous function class defined on $[0,1]^d$ with order $\alpha \in (0,1]$ and constant $\mu>0$. Therefore, the ReLU-sine-$2^x$ networks overcome the curse of dimensionality on $\mathcal{H}_{\mu}^{\alpha}([0,1]^d)$. In addition to its supper expressive power, functions implemented by ReLU-sine-$2^x$ networks are (generalized) differentiable, enabling us to apply SGD to train.
Equivariant Finite Normalizing Flows

Generative modelling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through in-variances and equivariances to certain transformation laws. However, current approaches to representing these symmetries are couched in the formalism of continuous normalizing ﬂows that require the construction of equivariant vector ﬁelds—inhibiting their simple application to conventional higher dimensional generative modelling domains like natural images. In this paper, we focus on building equivariant normalizing ﬂows using discrete layers. We ﬁrst theoretically prove the existence of an equivariant map for compact groups whose actions are on compact spaces. We further introduce three new equivariant ﬂows: G -Residual Flows, G -Coupling Flows, and G -Inverse Autoregressive Flows that elevate classical Residual, Coupling, and Inverse Autoregressive Flows with equivariant maps to a prescribed group G . Our construction of G -Residual Flows are also universal, in the sense that we prove an G -equivariant diﬀeomorphism can be exactly mapped by a G -residual ﬂow. Finally, we complement our theoretical insights with demonstrative experiments—for the ﬁrst time— on image datasets like CIFAR-10 and show G -Equivariant Finite Normalizing ﬂows lead to increased data eﬃciency, faster convergence, and improved likelihood estimates.
Families of homomorphic mappings in the polydisk

We study classes of locally biholomorphic mappings defined in the $\P$ that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes.
The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$

A subspace $H$ of a rearrangement invariant space $X$ on $[0,1]$ is strongly embedded in $X$ if, in $H$, convergence in $X$-norm is equivalent to convergence in measure. We obtain necessary and sufficient conditions on an Orlicz function $M$, under which the unit ball of an arbitrary strongly embedded subspace in the Orlicz space $L_M$ has equi-absolutely continuous norms in $L_M$.
Metallicities of Five z > 5 Emission-line Galaxies in SMACS 0723 Revealed by JWST

JWST’s Early Release Observations of the lensing cluster SMACS J0723.3–7327 have given an unprecedented spectroscopic look into the high-redshift universe. These observations reveal five galaxies at z > 5. All five have detectable [O iii]λ4363 line emission, indicating that these galaxies have high temperatures and low metallicities and that they are highly star-forming. In recent work, the metallicities of these five galaxies have been studied using various techniques. Here we summarize and compare these previous results, as well as perform our own measurements of the metallicities using improved methodologies that optimize the extraction of the emission lines. In particular, we use simultaneous line fitting and a fixed Balmer decrement correction, as well as a novel footprint measurement of the emission lines in the 2D spectra, to produce higher-fidelity line ratios that are less sensitive to calibration and systematic effects. We then compare our metallicities to those of z ≲ 1 galaxies with high rest-frame equivalent widths of Hβ, finding that they may be good analogs. Finally, we estimate that the JWST galaxies out to z ∼ 8 are young compared to the age of the universe.
Deep Reinforcement Learning Approach for Trading Automation in the Stock Market

Deep Reinforcement Learning (DRL) algorithms can scale to previously intractable problems. The automation of profit generation in the stock market is possible using DRL, by combining the financial assets price “prediction” step and the “allocation” step of the portfolio in one unified process to produce fully autonomous systems capable of interacting with their environment to make optimal decisions through trial and error. This work represents a DRL model to generate profitable trades in the stock market, effectively overcoming the limitations of supervised learning approaches. We formulate the trading problem as a Partially Observed Markov Decision Process (POMDP) model, considering the constraints imposed by the stock market, such as liquidity and transaction costs. We then solve the formulated POMDP problem using the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm reporting a 2.68 Sharpe Ratio on unseen data set (test data). From the point of view of stock market forecasting and the intelligent decision-making mechanism, this paper demonstrates the superiority of DRL in financial markets over other types of machine learning and proves its credibility and advantages in strategic decision-making.
On a Mechanism Framework of Autoencoders

This paper proposes a theoretical framework on the mechanism of autoencoders. To the encoder part, under the main use of dimensionality reduction, we investigate its two fundamental properties: bijective maps and data disentangling. The general construction methods of an encoder that satisﬁes either or both of the above two properties are given. To the decoder part, as a consequence of the encoder constructions, we present a new basic principle of the solution, without using afﬁne transforms. The generalization mechanism of autoencoders is modeled. The results of ReLU autoencoders are generalized to some non-ReLU cases, particularly for the sigmoid-unit autoencoder. Based on the theoretical framework above, we explain some experimental results of variational autoencoders, denoising autoencoders, and linear-unit autoencoders, with emphasis on the interpretation of the lower-dimensional representation of data via encoders; and the mechanism of image restoration through autoencoders is natural to be understood by those explanations. Compared to PCA and decision trees, the advantages of (gener-alized) autoencoders on dimensionality reduction and classiﬁcation are demonstrated, respectively. Convolutional neural networks and randomly weighted neural networks are also interpreted by this framework.
Modeling Biological Face Recognition with Deep Convolutional Neural Networks

Abstract Deep convolutional neural networks (DCNNs) have become the state-of-the-art computational models of biological object recognition. Their remarkable success has helped vision science break new ground, and recent efforts have started to transfer this achievement to research on biological face recognition. In this regard, face detection can be investigated by comparing face-selective biological neurons and brain areas to artificial neurons and model layers. Similarly, face identification can be examined by comparing in vivo and in silico multidimensional “face spaces. ” In this review, we summarize the first studies that use DCNNs to model biological face recognition. On the basis of a broad spectrum of behavioral and computational evidence, we conclude that DCNNs are useful models that closely resemble the general hierarchical organization of face recognition in the ventral visual pathway and the core face network. In two exemplary spotlights, we emphasize the unique scientific contributions of these models. First, studies on face detection in DCNNs indicate that elementary face selectivity emerges automatically through feedforward processing even in the absence of visual experience. Second, studies on face identification in DCNNs suggest that identity-specific experience and generative mechanisms facilitate this particular challenge. Taken together, as this novel modeling approach enables close control of predisposition (i.e., architecture) and experience (i.e., training data), it may be suited to inform long-standing debates on the substrates of biological face recognition.
Noise Stability on the Boolean Hypercube via a Renormalized Brownian Motion

We consider a variant of the classical notion of noise on the Boolean hypercube which gives rise to a new approach to inequalities regarding noise stability. We use this approach to give a new proof of the Majority is Stablest theorem by Mossel, O'Donnell, and Oleszkiewicz, improving the dependence of the bound on the maximal influence of the function from logarithmic to polynomial. We also show that a variant of the conjecture by Courtade and Kumar regarding the most informative Boolean function, where the classical noise is replaced by our notion, holds true. Our approach is based on a stochastic construction that we call the renormalized Brownian motion, which facilitates the use of inequalities in Gaussian space in the analysis of Boolean functions.
Petascale Brownian dynamics simulations of highly resolved polymer chains with hydrodynamic interactions using modern GPUs

Brownian dynamics simulations of fairly long, highly detailed polymer chains, at the resolution of a single Kuhn step, remains computationally prohibitive even on the modern processors. This is especially true when the beads on the chain experience hydrodynamic interactions (HI), which requires the usage of methods like Cholesky decomposition of large matrices at every timestep. In this study, we perform Petascale BD simulations, with HI, of fairly long and highly resolved polymer chains on modern GPUs. Our results clearly highlight the inadequacies of the typical models that use beads connected by springs. In this manuscript, firstly, we present the details of a highly scalable, parallel hybrid code implemented on a GPU for BD simulations of chains resolved to a single Kuhn step. In this hybrid code using CUDA and MPI, we have incorporated HI using the Cholesky decomposition method. Next, we validate the GPU implementation extensively with theoretical expectations for polymer chains at equilibrium and in flow with results in the absence of HI. Further, our results in flow with HI show significantly different temporal variations of stretch, in both startup extensional and shear flows, relative to the conventional bead-spring models. In all cases investigated, the ensemble averaged chain stretch is much lower than bead-spring predictions. Also, quite remarkably, our GPU implementation shows a scaling of $\sim$$N^{1.2}$ and $\sim$$N^{2.2}$ of the computational times for shorter and longer chains in the most modern available GPU, respectively, which is significantly lower than the theoretically expected $\sim$$N^{3}$. We expect our methods and results to pave the way for further analysis of polymer physics in flow fields, with long and highly detailed chain models.
The SVD of Convolutional Weights: A CNN Interpretability Framework

Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to convolutional filters to explain a model's reasoning process and confirm its use of relevant information from the input domain. Fully connected layers can be studied by decomposing their weight matrices using a singular value decomposition, in effect studying the correlations between the rows in each matrix to discover the dynamics of the map. In this work we define a singular value decomposition for the weight tensor of a convolutional layer, which provides an analogous understanding of the correlations between filters, exposing the dynamics of the convolutional map. We validate our definition using recent results in random matrix theory. By applying the decomposition across the linear layers of an image classification network we suggest a framework against which interpretability methods might be applied using hypergraphs to model class separation. Rather than looking to the activations to explain the network, we use the singular vectors with the greatest corresponding singular values for each linear layer to identify those features most important to the network. We illustrate our approach with examples and introduce the DeepDataProfiler library, the analysis tool used for this study.
Limit analysis of strut nets

Truss structures composed of members that work exclusively in tension or in compression appear in several problems of science and engineering, e.g., in the study of the resisting mechanisms of masonry structures, as well as in the design of spider web-inspired web structures. This work generalizes previous results on the existence of cable webs that are able to support assigned sets of nodal forces under tension. We extend such a problem to the limit analysis of compression-only “strut nets” subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces (“underlying masonry structures”). It is assumed that fixed nodal forces are combined with variable forces growing proportionally to a scalar multiplier (load multiplier), and that the supporting strut net is subjected to kinematic constraints at given nodal positions.
Partial Differential Equations of Mixed Type: Analysis and Applications

Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of mixed type is still in its infancy. The aim of this expository paper is to show, through several longstanding fundamental problems in fluid mechanics, differential geometry, and other areas, that many nonlinear PDEs arising in these areas are no longer of standard types, but lie at the boundaries of the classification of PDEs or, indeed, go beyond the classification to be of mixed type. Some interrelated connections, historical perspectives, recent developments, and current trends in the analysis of nonlinear PDEs of mixed type are also presented.
Magnetic field properties in star formation: A review of their analysis methods and interpretation

Linearly polarized emission from dust grains and molecular spectroscopy is an effective probe of the magnetic field topology in the interstellar medium and molecular clouds. The longstanding Davis-Chandrasekhar-Fermi (DCF) method and the recently developed Histogram of Relative Orientations (HRO) analysis and the polarization-intensity gradient (KTH) method are widely used to assess the dynamic role of magnetic fields in star formation based on the plane-of-sky component of field orientations inferred from the observations. We review the advances and limitations of these methods and summarize their applications to observations. Numerical tests of the DCF method, including its various variants, indicate that its largest uncertainty may come from the assumption of energy equipartition, which should be further calibrated with simulations and observations. We suggest that the ordered and turbulent magnetic fields of particular observations are local properties of the considered region. An analysis of the polarization observations using DCF estimations suggests that magnetically trans-to-super-critical and averagely trans-to-super-Alfvénic clumps/cores form in sub-critical clouds. High-mass star-forming regions may be more gravity-dominant than their low-mass counterparts due to higher column density. The observational HRO studies clearly reveal that the preferential relative orientation between the magnetic field and density structures changes from parallel to perpendicular with increasing column densities, which, in conjunction with simulations, suggests that star formation is ongoing in trans-to-sub-Alfvénic clouds. There is a possible transition back from perpendicular to random alignment at higher column densities. Results from observational studies using the KTH method broadly agree with those of the HRO and DCF studies.
MaskBlock: Transferable Adversarial Examples with Bayes Approach

The transferability of adversarial examples (AEs) across diverse models is of critical importance for black-box adversarial attacks, where attackers cannot access the information about black-box models. However, crafted AEs always present poor transferability. In this paper, by regarding the transferability of AEs as generalization ability of the model, we reveal that vanilla black-box attacks craft AEs via solving a maximum likelihood estimation (MLE) problem. For MLE, the results probably are model-specific local optimum when available data is small, i.e., limiting the transferability of AEs. By contrast, we re-formulate crafting transferable AEs as the maximizing a posteriori probability estimation problem, which is an effective approach to boost the generalization of results with limited available data. Because Bayes posterior inference is commonly intractable, a simple yet effective method called MaskBlock is developed to approximately estimate. Moreover, we show that the formulated framework is a generalization version for various attack methods. Extensive experiments illustrate MaskBlock can significantly improve the transferability of crafted adversarial examples by up to about 20%.
Pyramidal Predictive Network: A Model for Visual-frame Prediction Based on Predictive Coding Theory

Visual-frame prediction is a pixel-dense prediction task that infers future frames from past frames. A lack of appearance details, low prediction accuracy and a high computational overhead are still major problems associated with current models or methods. In this paper, we propose a novel neural network model inspired by the well-known predictive coding theory to deal with these problems. Predictive coding provides an interesting and reliable computational framework. We combined this approach with other theories, such as the theory that the cerebral cortex oscillates at different frequencies at different levels, to design an efficient and reliable predictive network model for visual-frame prediction. Specifically, the model is composed of a series of recurrent and convolutional units forming the top-down and bottom-up streams, respectively. The update frequency of neural units on each of the layers decreases with the increase in the network level, which means that neurons of a higher level can capture information in longer time dimensions. According to the experimental results, this model showed better compactness and comparable predictive performance with those of existing works, implying lower computational cost and higher prediction accuracy.