Qi Tang

Alec J. Linot, Joshua W. Burby, Qi Tang et al.

In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or chaotic dynamics. We present a data-driven modeling method that accurately captures shocks and chaotic dynamics by proposing a novel architecture, stabilized neural ordinary differential equation (ODE). In our proposed architecture, we learn the right-hand-side (RHS) of an ODE by adding the outputs of two NN together where one learns a linear term and the other a nonlinear term. Specifically, we implement this by training a sparse linear convolutional NN to learn the linear term and a dense fully-connected nonlinear NN to learn the nonlinear term. This is in contrast with the standard neural ODE which involves training only a single NN for learning the RHS. We apply this setup to the viscous Burgers equation, which exhibits shocked behavior, and show better short-time tracking and prediction of the energy spectrum at high wavenumbers than a standard neural ODE. We also find that the stabilized neural ODE models are much more robust to noisy initial conditions than the standard neural ODE approach. We also apply this method to chaotic trajectories of the Kuramoto-Sivashinsky equation. In this case, stabilized neural ODEs keep long-time trajectories on the attractor, and are highly robust to noisy initial conditions, while standard neural ODEs fail at achieving either of these results. We conclude by demonstrating how stabilizing neural ODEs provide a natural extension for use in reduced-order modeling by projecting the dynamics onto the eigenvectors of the learned linear term.

Andrew J. Christlieb, Yuan Liu, Qi Tang et al.

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under the constrained transport (CT) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously. Numerical examples in 1D, 2D and 3D are provided to demonstrate the performance of the proposed method.

J. W. Banks, W. D. Henshaw, D. W. Schwendeman et al.

This paper describes a novel partitioned algorithm for fluid-structure interaction (FSI) problems that couples the motion of rigid bodies and incompressible flow. This is the first partitioned algorithm that remains stable and second-order accurate, without sub-time-step iterations, for very light, and even zero-mass, bodies in three dimensions. This new added-mass partitioned (AMP) algorithm extends the previous developments in [1, 2] by generalizing the added-damping tensors to account for arbitrary three-dimensional rotations, and by employing a general quadrature for the surface integral over a rigid body to derive the discrete AMP interface condition for the fluid pressure. Stability analyses for two three-dimensional model problems show that the algorithm remains stable for bodies of any mass when applied to the relevant model problems. The resulting AMP algorithm is implemented in parallel using a moving composite grid framework to treat one or more rigid bodies in complex three-dimensional configurations. The new three-dimensional algorithm is verified and validated though several benchmark problems, including the motion of a sphere in a viscous incompressible fluid and the interaction of a bi-leaflet mechanical heart valve and a pulsating fluid. Numerical simulations confirm the predictions of the stability analysis even for complex problems, and show that the AMP algorithm remains stable, without sub-iterations, for light and even zero-mass three-dimensional rigid bodies of general shape. These benchmark problems are further used to examine the parallel performance of the algorithm and to investigate the conditioning of the linear system for the pressure including the newly derived AMP interface conditions.

J. W. Banks, W. D. Henshaw, D. W. Schwendeman et al.

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added-mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this first part of a two-part series, the properties of the AMP scheme are motivated and evaluated through the development and analysis of some model problems. The analysis shows when and why the traditional partitioned scheme becomes unstable due to either added-mass or added-damping effects. The analysis also identifies the proper form of the added-damping which depends on the discrete time-step and the grid-spacing normal to the rigid body. The results of the analysis are confirmed with numerical simulations that also demonstrate a second-order accurate implementation of the AMP scheme.

Andrew J. Christlieb, Xiao Feng, David C. Seal et al.

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage, single-step, maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in [SINUM, 53 (2015), pp. 1833--1856], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic and magnetic potential equations, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these curls to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. Positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. This positivity limiter lacks energy conservation. However, this limiter can be dropped for problems where the pressure does not become negative. We present two and three dimensional numerical results for several standard test problems. These results assert the robustness and verify the high-order of accuracy of the proposed scheme.

J. W. Banks, W. D. Henshaw, D. W. Schwendeman et al.

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. The numerical scheme is verified on a number of difficult benchmark problems.

Andrew J. Christlieb, Xiao Feng, Yan Jiang et al.

A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-oscillatory (WENO) scheme. It computes a high-order numerical flux by a Taylor expansion in space, with the lowest-order term solved from a Riemann solver and the higher-order terms constructed from physical fluxes by limited central differences. The scheme coupled with several Riemann solvers, including a Lax-Friedrichs solver and HLL-type solvers, is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems. In particular, a HLLD solver on Cartesian meshes is extended to curvilinear meshes with proper modifications. A numerical boundary condition for the perfect electrical conductor (PEC) boundary is derived for general geometry and verified through a bow shock flow. Numerical results also confirm the advantages of using low dissipative Riemann solvers in the current framework.

David C. Seal, Qi Tang, Zhengfu Xu et al.

In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory (WENO) method. Time is discretized through a Lax-Wendroff procedure that is constructed from the Picard integral formulation (PIF) of the partial differential equation. The method can be viewed as a modified flux approach, where a linear combination of a low- and high-order flux defines the numerical flux used for a single-step update. The coefficients of the linear combination are constructed by solving a simple optimization problem at each time step. The high-order flux itself is constructed through the use of Taylor series and the Cauchy-Kowalewski procedure that incorporates higher-order terms. Numerical results in one- and two-dimensions are presented.

Roger Trullo, Quoc-Anh Bui, Qi Tang et al.

Numerous deep learning based methods have been developed for nuclei segmentation for H&E images and have achieved close to human performance. However, direct application of such methods to another modality of images, such as Immunohistochemistry (IHC) images, may not achieve satisfactory performance. Thus, we developed a Generative Adversarial Network (GAN) based approach to translate an IHC image to an H&E image while preserving nuclei location and morphology and then apply pre-trained nuclei segmentation models to the virtual H&E image. We demonstrated that the proposed methods work better than several baseline methods including direct application of state of the art nuclei segmentation methods such as Cellpose and HoVer-Net, trained on H&E and a generative method, DeepLIIF, using two public IHC image datasets.

Valentin Duruisseaux, Joshua W. Burby, Qi Tang

A continuous-time dynamical system with parameter $\varepsilon$ is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as $\varepsilon$ approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal $U(1)$ symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal $U(1)$ symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.

Xin Li, Kun Yuan, Bingchen Li et al.

This paper presents a review for the NTIRE 2025 Challenge on Short-form UGC Video Quality Assessment and Enhancement. The challenge comprises two tracks: (i) Efficient Video Quality Assessment (KVQ), and (ii) Diffusion-based Image Super-Resolution (KwaiSR). Track 1 aims to advance the development of lightweight and efficient video quality assessment (VQA) models, with an emphasis on eliminating reliance on model ensembles, redundant weights, and other computationally expensive components in the previous IQA/VQA competitions. Track 2 introduces a new short-form UGC dataset tailored for single image super-resolution, i.e., the KwaiSR dataset. It consists of 1,800 synthetically generated S-UGC image pairs and 1,900 real-world S-UGC images, which are split into training, validation, and test sets using a ratio of 8:1:1. The primary objective of the challenge is to drive research that benefits the user experience of short-form UGC platforms such as Kwai and TikTok. This challenge attracted 266 participants and received 18 valid final submissions with corresponding fact sheets, significantly contributing to the progress of short-form UGC VQA and image superresolution. The project is publicly available at https://github.com/lixinustc/KVQE- ChallengeCVPR-NTIRE2025.

Henry Tischler, Wenting Li, Qi Tang et al.

Accurate knowledge of the atomistic transition pathways in materials and material surfaces is crucial for many material science problems. However, conventional simulation techniques used to find these transitions are extremely computationally intensive. Even with large-scale, accelerated material simulations, the computational cost constrains the applicable domain in practice. Machine learning models, with the potential to learn the complex emergent behaviors governing atomistic transitions as a fast surrogate model, have great promise to predict transitions with a vastly reduced computational cost. Here, we demonstrate how transformers can be trained to predict atomistic transitions in nano-clusters. We show how we evaluate physical validity of the predictions and how a multitude of additional, different microstates can be generated by slightly varying the data provided to the model.

Mandela B. Quashie, J. W. Burby, Andrew J. Christlieb et al.

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

Xinxi Chen, Li Wang, Wei Wu et al.

Hallucination is a key roadblock for applications of Large Language Models (LLMs), particularly for enterprise applications that are sensitive to information accuracy. To address this issue, two general approaches have been explored: Retrieval-Augmented Generation (RAG) to supply LLMs with updated information as context, and fine-tuning the LLMs with new information and desired output styles. In this paper, we propose Honest AI: a novel strategy to fine-tune "small" language models to say "I don't know" to reduce hallucination, along with several alternative RAG approaches. The solution ranked 1st in Task 2 for the false premise question. The alternative approaches include using RAG with search engine and knowledge graph results, fine-tuning base LLMs with new information and combinations of both approaches. Although all approaches improve the performance of the LLMs, RAG alone does not significantly improve the performance and fine-tuning is needed for better results. Finally, the hybrid approach achieved the highest score in the CRAG benchmark. In addition, our approach emphasizes the use of relatively small models with fewer than 10 billion parameters, promoting resource efficiency.

Qi Tang, Yao Zhao, Meiqin Liu et al.

As a critical clue of video super-resolution (VSR), inter-frame alignment significantly impacts overall performance. However, accurate pixel-level alignment is a challenging task due to the intricate motion interweaving in the video. In response to this issue, we introduce a novel paradigm for VSR named Semantic Lens, predicated on semantic priors drawn from degraded videos. Specifically, video is modeled as instances, events, and scenes via a Semantic Extractor. Those semantics assist the Pixel Enhancer in understanding the recovered contents and generating more realistic visual results. The distilled global semantics embody the scene information of each frame, while the instance-specific semantics assemble the spatial-temporal contexts related to each instance. Furthermore, we devise a Semantics-Powered Attention Cross-Embedding (SPACE) block to bridge the pixel-level features with semantic knowledge, composed of a Global Perspective Shifter (GPS) and an Instance-Specific Semantic Embedding Encoder (ISEE). Concretely, the GPS module generates pairs of affine transformation parameters for pixel-level feature modulation conditioned on global semantics. After that, the ISEE module harnesses the attention mechanism to align the adjacent frames in the instance-centric semantic space. In addition, we incorporate a simple yet effective pre-alignment module to alleviate the difficulty of model training. Extensive experiments demonstrate the superiority of our model over existing state-of-the-art VSR methods.

Shuli Wang, Xue Wei, Senjie Kou et al.

Reranking plays a crucial role in modern multi-stage recommender systems by rearranging the initial ranking list. Due to the inherent challenges of combinatorial search spaces, some current research adopts an evaluator-generator paradigm, with a generator generating feasible sequences and an evaluator selecting the best sequence based on the estimated list utility. However, these methods still face two issues. Firstly, due to the goal inconsistency problem between the evaluator and generator, the generator tends to fit the local optimal solution of exposure distribution rather than combinatorial space optimization. Secondly, the strategy of generating target items one by one is difficult to achieve optimality because it ignores the information of subsequent items. To address these issues, we propose a utilizing Neighbor Lists model for Generative Reranking (NLGR), which aims to improve the performance of the generator in the combinatorial space. NLGR follows the evaluator-generator paradigm and improves the generator's training and generating methods. Specifically, we use neighbor lists in combination space to enhance the training process, making the generator perceive the relative scores and find the optimization direction. Furthermore, we propose a novel sampling-based non-autoregressive generation method, which allows the generator to jump flexibly from the current list to any neighbor list. Extensive experiments on public and industrial datasets validate NLGR's effectiveness and we have successfully deployed NLGR on the Meituan food delivery platform.

Yubin Lu, Xiaofan Li, Chun Liu et al.

Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct regression of governing equations or velocity fields, which can be sensitive to noise and external perturbations and may fail when observations are incomplete. In this work, we propose a structure-aware, energy-based learning framework for inferring unknown potential functions in generalized diffusion processes, grounded in the energetic variational approach. Starting from the energy-dissipation law associated with the Fokker-Planck equation, we construct loss functions based on the De Giorgi dissipation functional, which consistently couple the free energy and the dissipation mechanism of the system. This formulation avoids explicit enforcement of the governing partial differential equation and preserves the underlying variational structure of the dynamics. Through numerical experiments in one, two, and three dimensions, we demonstrate that the proposed energy-based loss exhibits enhanced robustness with respect to observation time, noise level, and the diversity and amount of available training data. These results highlight the effectiveness of energy-dissipation principles as a reliable foundation for learning stochastic diffusion dynamics from data.

Yongsheng Chen, Wei Guo, Qi Tang et al.

We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces. Latent dynamics are advanced by a symplectic flow map implemented as a HenonNet. This unified neural architecture ensures exact preservation of the underlying symplectic structure at the reduced-order level, significantly enhancing the fidelity and long-term stability of the resulting ROM. We validate our method through comprehensive numerical experiments on canonical Hamiltonian systems. The results demonstrate the method's capability for accurate trajectory reconstruction, robust predictive performance beyond the training horizon, and accurate Hamiltonian preservation. These promising outcomes underscore the effectiveness and potential applicability of our symplectic ROM framework for complex dynamical systems across a broad range of scientific and engineering disciplines.

Linfeng He, Meiqin Liu, Qi Tang et al.

Video super-resolution (VSR) faces critical challenges in effectively modeling non-local dependencies across misaligned frames while preserving computational efficiency. Existing VSR methods typically rely on optical flow strategies or transformer architectures, which struggle with large motion displacements and long video sequences. To address this, we propose MambaVSR, the first state-space model framework for VSR that incorporates an innovative content-aware scanning mechanism. Unlike rigid 1D sequential processing in conventional vision Mamba methods, our MambaVSR enables dynamic spatiotemporal interactions through the Shared Compass Construction (SCC) and the Content-Aware Sequentialization (CAS). Specifically, the SCC module constructs intra-frame semantic connectivity graphs via efficient sparse attention and generates adaptive spatial scanning sequences through spectral clustering. Building upon SCC, the CAS module effectively aligns and aggregates non-local similar content across multiple frames by interleaving temporal features along the learned spatial order. To bridge global dependencies with local details, the Global-Local State Space Block (GLSSB) synergistically integrates window self-attention operations with SSM-based feature propagation, enabling high-frequency detail recovery under global dependency guidance. Extensive experiments validate MambaVSR's superiority, outperforming the Transformer-based method by 0.58 dB PSNR on the REDS dataset with 55% fewer parameters.

Jing Sun, Qi Tang

Artificial neural networks learn various rules and algorithms to form different ways of processing information, and have been widely used in various chemical processes. Among them, with the development of rectification technology, its production scale continues to expand, and its calculation requirements are also more stringent, because the artificial neural network has the advantages of self-learning, associative storage and high-speed search for optimized solutions, it can make high-precision simulation predictions for rectification operations, so it is widely used in the chemical field of rectification. This article gives a basic overview of artificial neural networks, and introduces the application research of artificial neural networks in distillation at home and abroad.

Qi Tang, Runmin Cong, Ronghui Sheng et al.

Depth map super-resolution is a task with high practical application requirements in the industry. Existing color-guided depth map super-resolution methods usually necessitate an extra branch to extract high-frequency detail information from RGB image to guide the low-resolution depth map reconstruction. However, because there are still some differences between the two modalities, direct information transmission in the feature dimension or edge map dimension cannot achieve satisfactory result, and may even trigger texture copying in areas where the structures of the RGB-D pair are inconsistent. Inspired by the multi-task learning, we propose a joint learning network of depth map super-resolution (DSR) and monocular depth estimation (MDE) without introducing additional supervision labels. For the interaction of two subnetworks, we adopt a differentiated guidance strategy and design two bridges correspondingly. One is the high-frequency attention bridge (HABdg) designed for the feature encoding process, which learns the high-frequency information of the MDE task to guide the DSR task. The other is the content guidance bridge (CGBdg) designed for the depth map reconstruction process, which provides the content guidance learned from DSR task for MDE task. The entire network architecture is highly portable and can provide a paradigm for associating the DSR and MDE tasks. Extensive experiments on benchmark datasets demonstrate that our method achieves competitive performance. Our code and models are available at https://rmcong.github.io/proj_BridgeNet.html.

Qi Tang, Tongmei Fan, Ruchen Shi et al.

In order to further overcome the difficulties of the existing models in dealing with the non-stationary and nonlinear characteristics of high-frequency financial time series data, especially its weak generalization ability, this paper proposes an ensemble method based on data denoising methods, including the wavelet transform (WT) and singular spectrum analysis (SSA), and long-term short-term memory neural network (LSTM) to build a data prediction model, The financial time series is decomposed and reconstructed by WT and SSA to denoise. Under the condition of denoising, the smooth sequence with effective information is reconstructed. The smoothing sequence is introduced into LSTM and the predicted value is obtained. With the Dow Jones industrial average index (DJIA) as the research object, the closing price of the DJIA every five minutes is divided into short-term (1 hour), medium-term (3 hours) and long-term (6 hours) respectively. . Based on root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and absolute percentage error standard deviation (SDAPE), the experimental results show that in the short-term, medium-term and long-term, data denoising can greatly improve the accuracy and stability of the prediction, and can effectively improve the generalization ability of LSTM prediction model. As WT and SSA can extract useful information from the original sequence and avoid overfitting, the hybrid model can better grasp the sequence pattern of the closing price of the DJIA. And the WT-LSTM model is better than the benchmark LSTM model and SSA-LSTM model.

Qi Tang, Vardaan Kishore Kumar

Failures in Phase 3 clinical trials contribute to expensive cost of drug development in oncology. To drastically reduce such cost, responders to an oncology treatment need to be identified early on in the drug development process with limited amount of patient data before the planning of Phase 3 clinical trials. Despite the challenge of small sample size, we pioneered the use of deep-learning derived digital pathology scores to identify responders based on the immunohistochemistry images of the target antigen expressed in tumor biopsy samples from a Phase 1 Non-small Cell Lung Cancer clinical trial. Based on repeated 10-fold cross validations, the deep-learning derived score on average achieved 4% higher AUC of ROC curve and 6% higher AUC of Precision-Recall curve comparing to the tumor proportion score (TPS) based clinical benchmark. In a small independent testing set of patients, we also demonstrated that the deep-learning derived score achieved numerically at least 25% higher responder rate in the enriched population than the TPS clinical benchmark.

Di Wu, Qi Tang, Yongle Zhao et al.

The 8 bits quantization has been widely applied to accelerate network inference in various deep learning applications. There are two kinds of quantization methods, training-based quantization and post-training quantization. Training-based approach suffers from a cumbersome training process, while post-training quantization may lead to unacceptable accuracy drop. In this paper, we present an efficient and simple post-training method via scale optimization, named EasyQuant (EQ),that could obtain comparable accuracy with the training-based method.Specifically, we first alternately optimize scales of weights and activations for all layers target at convolutional outputs to further obtain the high quantization precision. Then, we lower down bit width to INT7 both for weights and activations, and adopt INT16 intermediate storage and integer Winograd convolution implementation to accelerate inference.Experimental results on various computer vision tasks show that EQ outperforms the TensorRT method and can achieve near INT8 accuracy in 7 bits width post-training.

Zixuan Wang, Qi Tang, Wei Guo et al.

This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many applications due to their distinctive features. However, they are often deemed too costly because of the large number of degrees of freedom of the approximation space, which are the main bottleneck for simulations in high dimensions. In this paper, we develop sparse grid DG methods for elliptic equations with the aim of breaking the \emph{curse of dimensionality}. Using a hierarchical basis representation, we construct a sparse finite element approximation space, reducing the degrees of freedom from the standard {$O(h^{-d})$ to $O(h^{-1}|\log_2 h|^{d-1})$} for $d$-dimensional problems, where $h$ is the uniform mesh size in each dimension. Our method, based on the interior penalty (IP) DG framework, can achieve accuracy of $O(h^{k}|\log_2 h|^{d-1})$ in the energy norm, where $k$ is the degree of polynomials used. Error estimates are provided and confirmed by numerical tests in multi-dimensions.