Miracle-dz/UniFAR-FTUs huggingface dataset:
Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems

In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulted from the Legendre dual-Petrov-Galerkin (LDPG) method for the $m$th-order initial value problem (IVP): $u^{(m)}(t)=\sigma u(t),\, t\in (-1,1)$ with constant $\sigma\not=0$ and usual initial conditions at $t=-1,$ are associated with the generalised Bessel polynomials (GBPs). The essential idea of the analysis is to properly construct the basis functions for the solution and its dual spaces so that the matrix of the $m$th derivative is an identity matrix, and the mass matrix is then identical or approximately equals to the Jacobi matrix of the three-term recurrence of GBPs with specific integer parameters. This allows us to characterise the eigenvalue distributions and identify the eigenvectors. As a by-product, we are able to answer some open questions related to the very limited known results on the collocation method at Legendre points (studied in 1980s) for the first-order IVP, by reformulating it into a Petrov-Galerkin formulation. Moreover, we present two stable algorithms for computing zeros of the GBPs, and develop a general space-time spectral method for evolutionary PDEs using either the matrix diagonalisation, which is restricted to a small number of unknowns in time due to the ill-conditioning but is fully parallel, or the QZ decomposition which is numerically stable for a large number of unknowns in time but involves sequential computations. We provide ample numerical results to demonstrate the high accuracy and robustness of the space-time spectral methods for some interesting examples of linear and nonlinear wave problems.
LidarGait: Benchmarking 3D Gait Recognition with Point Clouds

Video-based gait recognition has achieved impressive results in constrained scenarios. However, visual cameras neglect human 3D structure information, which limits the feasibility of gait recognition in the 3D wild world. Instead of extracting gait features from images, this work explores precise 3D gait features from point clouds and proposes a simple yet efficient 3D gait recognition framework, termed LidarGait. Our proposed approach projects sparse point clouds into depth maps to learn the representations with 3D geometry information, which outperforms existing point-wise and camera-based methods by a significant margin. Due to the lack of point cloud datasets, we build the first large-scale LiDAR-based gait recognition dataset, SUSTech1K, collected by a LiDAR sensor and an RGB camera. The dataset contains 25,239 sequences from 1,050 subjects and covers many variations, including visibility, views, occlusions, clothing, carrying, and scenes. Extensive experiments show that (1) 3D structure information serves as a significant feature for gait recognition. (2) LidarGait outperforms existing point-based and silhouette-based methods by a significant margin, while it also offers stable cross-view results. (3) The LiDAR sensor is superior to the RGB camera for gait recognition in the outdoor environment. The source code and dataset have been made available at https://lidargait.github. io.
On Multi-head Ensemble of Smoothed Classifiers for Certified Robustness

Randomized Smoothing (RS) is a promising technique for certiﬁed robustness, and recently in RS the ensemble of multiple deep neural networks (DNNs) has shown state-of-the-art performances. However, such an ensemble brings heavy computation burdens in both training and certiﬁcation, and yet under-exploits individual DNNs and their mutual effects, as the communication between these classiﬁers is commonly ignored in optimization. In this work, starting from a single DNN, we augment the network with multiple heads, each of which pertains a classiﬁer for the ensemble. A novel training strategy, namely Self-PAced Circular-TEaching (SPACTE), is proposed accordingly. SPACTE enables a circular communication ﬂow among those augmented heads, i.e., each head teaches its neighbor with the self-paced learning using smoothed losses, which are speciﬁcally designed in relation to certiﬁed robustness. The deployed multi-head structure and the circular-teaching scheme of SPACTE jointly contribute to diversify and enhance the classiﬁers in augmented heads for ensemble, leading to even stronger certiﬁed robustness than ensembling multiple DNNs (effectiveness) at the cost of much less computational expenses (efﬁciency), veriﬁed by extensive experiments and discussions. pioneering work trained on Gaussian corruptions of samples, Consistency [16]: the SOTA regularization-based method by adding a Kullback-Leibler (KL) divergence loss to regularize the prediction consistency within N ( x , σ 2 I ) , and SmoothMix [18]: the SOTA data-augmentation-based method by mixing the adversarial examples. The current SOTA ensemble methods are also compared, i.e., , Horváth et al. [19]: the ensemble method via averaging the logits of multiple separately-trained DNNs. Other popular RS-based methods are also included into comparisons, including MACER [15] and SmoothAdv [17].
FakeSV: A Multimodal Benchmark with Rich Social Context for Fake News Detection on Short Video Platforms

Short video platforms have become an important channel for news sharing, but also a new breeding ground for fake news. To mitigate this problem, research of fake news video detection has recently received a lot of attention. Existing works face two roadblocks: the scarcity of comprehensive and largescale datasets and insufficient utilization of multimodal information. Therefore, in this paper, we construct the largest Chinese short video dataset about fake news named FakeSV, which includes news content, user comments, and publisher profiles simultaneously. To understand the characteristics of fake news videos, we conduct exploratory analysis of FakeSV from different perspectives. Moreover, we provide a new multimodal detection model named SV-FEND, which exploits the cross-modal correlations to select the most informative features and utilizes the social context information for detection. Extensive experiments evaluate the superiority of the proposed method and provide detailed comparisons of different methods and modalities for future works. Our dataset and codes are available in https://github.com/ICTMCG/FakeSV.
Measure transfer and $S$-adic developments for subshifts

Based on previous work of the authors, to any $S$-adic development of a subshift $X$ a"directive sequence"of commutative diagrams is associated, which consists at every level $n \geq 0$ of the measure cone and the letter frequency cone of the level subshift $X_n$ associated canonically to the given $S$-adic development. The issuing rich picture enables one to deduce results about $X$ with unexpected directness. For instance, we exhibit a large class of minimal subshifts with entropy zero that all have infinitely many ergodic probability measures. As a side result we also exhibit, for any integer $d \geq 2$, an $S$-adic development of a minimal, aperiodic, uniquely ergodic subshift $X$, where all level alphabets ${\cal A}_n$ have cardinality $d\,$, while none of the $d-2$ bottom level morphisms is recognizable in its level subshift $X_n \subset {\cal A}_n^\mathbb Z$.
Linear Stability Hypothesis and Rank Stratification for Nonlinear Models

Models with nonlinear architectures/parameterizations such as deep neural networks (DNNs) are well known for their mysteriously good generalization performance at overparameterization. In this work, we tackle this mystery from a novel perspective focusing on the transition of the target recovery/fitting accuracy as a function of the training data size. We propose a rank stratification for general nonlinear models to uncover a model rank as an"effective size of parameters"for each function in the function space of the corresponding model. Moreover, we establish a linear stability theory proving that a target function almost surely becomes linearly stable when the training data size equals its model rank. Supported by our experiments, we propose a linear stability hypothesis that linearly stable functions are preferred by nonlinear training. By these results, model rank of a target function predicts a minimal training data size for its successful recovery. Specifically for the matrix factorization model and DNNs of fully-connected or convolutional architectures, our rank stratification shows that the model rank for specific target functions can be much lower than the size of model parameters. This result predicts the target recovery capability even at heavy overparameterization for these nonlinear models as demonstrated quantitatively by our experiments. Overall, our work provides a unified framework with quantitative prediction power to understand the mysterious target recovery behavior at overparameterization for general nonlinear models.
Efficient Second-Order Plane Adjustment

Planes are generally used in 3D reconstruction for depth sensors, such as RGB-D cameras and LiDARs. This paper focuses on the problem of estimating the optimal planes and sensor poses to minimize the point-to-plane distance. The resulting least-squares problem is referred to as plane adjustment (PA) in the literature, which is the counterpart of bundle adjustment (BA) in visual reconstruction. Iterative methods are adopted to solve these least-squares problems. Typically, Newton's method is rarely used for a large-scale least-squares problem, due to the high computational complexity of the Hessian matrix. Instead, methods using an approximation of the Hessian matrix, such as the Levenberg-Marquardt (LM) method, are generally adopted. This paper adopts the Newton's method to efficiently solve the PA problem. Specifically, given poses, the optimal plane have a close-form solution. Thus we can eliminate planes from the cost function, which significantly reduces the number of variables. Furthermore, as the optimal planes are functions of poses, this method actually ensures that the optimal planes for the current estimated poses can be obtained at each iteration, which benefits the convergence. The difficulty lies in how to efficiently compute the Hessian matrix and the gradient of the resulting cost. This paper provides an efficient solution. Empirical evaluation shows that our algorithm outperforms the state-of-the-art algorithms.
A Generalized EigenGame with Extensions to Multiview Representation Learning

Generalized Eigenvalue Problems (GEPs) encompass a range of interesting dimensionality reduction methods. Development of efficient stochastic approaches to these problems would allow them to scale to larger datasets. Canonical Correlation Analysis (CCA) is one example of a GEP for dimensionality reduction which has found extensive use in problems with two or more views of the data. Deep learning extensions of CCA require large mini-batch sizes, and therefore large memory consumption, in the stochastic setting to achieve good performance and this has limited its application in practice. Inspired by the Generalized Hebbian Algorithm, we develop an approach to solving stochastic GEPs in which all constraints are softly enforced by Lagrange multipliers. Then by considering the integral of this Lagrangian function, its pseudo-utility, and inspired by recent formulations of Principal Components Analysis and GEPs as games with differentiable utilities, we develop a game-theory inspired approach to solving GEPs. We show that our approaches share much of the theoretical grounding of the previous Hebbian and game theoretic approaches for the linear case but our method permits extension to general function approximators like neural networks for certain GEPs for dimensionality reduction including CCA which means our method can be used for deep multiview representation learning. We demonstrate the effectiveness of our method for solving GEPs in the stochastic setting using canonical multiview datasets and demonstrate state-of-the-art performance for optimizing Deep CCA.
Unifying Tracking and Image-Video Object Detection

Objection detection (OD) has been one of the most fundamental tasks in computer vision. Recent developments in deep learning have pushed the performance of image OD to new heights by learning-based, data-driven approaches. On the other hand, video OD remains less explored, mostly due to much more expensive data annotation needs. At the same time, multi-object tracking (MOT) which requires reasoning about track identities and spatio-temporal trajectories, shares similar spirits with video OD. However, most MOT datasets are class-specific (e.g., person-annotated only), which constrains a model's flexibility to perform tracking on other objects. We propose TrIVD (Tracking and Image-Video Detection), the first framework that unifies image OD, video OD, and MOT within one end-to-end model. To handle the discrepancies and semantic overlaps of category labels across datasets, TrIVD formulates detection/tracking as grounding and reasons about object categories via visual-text alignments. The unified formulation enables cross-dataset, multi-task training, and thus equips TrIVD with the ability to leverage frame-level features, video-level spatio-temporal relations, as well as track identity associations. With such joint training, we can now extend the knowledge from OD data, that comes with much richer object category annotations, to MOT and achieve zero-shot tracking capability. Experiments demonstrate that multi-task co-trained TrIVD outperforms single-task baselines across all image/video OD and MOT tasks. We further set the first baseline on the new task of zero-shot tracking.
Manifolds of Lie-Group-Valued Cocycles and Discrete Cohomology

Consider a compact group $G$ acting on a real or complex Banach Lie group $U$, by automorphisms in the relevant category, and leaving a central subgroup $K\le U$ invariant. We define the spaces ${}_KZ^n(G,U)$ of $K$-relative continuous cocycles as those maps ${G^n\to U}$ whose coboundary is a $K$-valued $(n+1)$-cocycle; this applies to possibly non-abelian $U$, in which case $n=1$. We show that the ${}_KZ^n(G,U)$ are analytic submanifolds of the spaces $C(G^n,U)$ of continuous maps $G^n\to U$ and that they decompose as disjoint unions of fiber bundles over manifolds of $K$-valued cocycles. Applications include: (a) the fact that ${Z^n(G,U)\subset C(G^n,U)}$ is an analytic submanifold and its orbits under the adjoint of the group of $U$-valued $(n-1)$-cochains are open; (b) hence the cohomology spaces $H^n(G,U)$ are discrete; (c) for unital $C^*$-algebras $A$ and $B$ with $A$ finite-dimensional the space of morphisms $A\to B$ is an analytic manifold and nearby morphisms are conjugate under the unitary group $U(B)$; (d) the same goes for $A$ and $B$ Banach, with $A$ finite-dimensional and semisimple; (e) and for spaces of projective representations of compact groups in arbitrary $C^*$ algebras (the last recovering a result of Martin's).
Provably Uncertainty-Guided Universal Domain Adaptation

Universal domain adaptation (UniDA) aims to transfer the knowledge from a labeled source domain to an unlabeled target domain without any assumptions of the label sets, which requires distinguishing the unknown samples from the known ones in the target domain. A main challenge of UniDA is that the nonidentical label sets cause the misalignment between the two domains. Moreover, the domain discrepancy and the supervised objectives in the source domain easily lead the whole model to be biased towards the common classes and produce overconfident predictions for unknown samples. To address the above challenging problems, we propose a new uncertainty-guided UniDA framework. Firstly, we introduce an empirical estimation of the probability of a target sample belonging to the unknown class which fully exploits the distribution of the target samples in the latent space. Then, based on the estimation, we propose a novel neighbors searching scheme in a linear subspace with a $\delta$-filter to estimate the uncertainty score of a target sample and discover unknown samples. It fully utilizes the relationship between a target sample and its neighbors in the source domain to avoid the influence of domain misalignment. Secondly, this paper well balances the confidences of predictions for both known and unknown samples through an uncertainty-guided margin loss based on the confidences of discovered unknown samples, which can reduce the gap between the intra-class variances of known classes with respect to the unknown class. Finally, experiments on three public datasets demonstrate that our method significantly outperforms existing state-of-the-art methods.
Spatio-temporal point processes with deep non-stationary kernels

Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may not successfully capture sophisticated non-stationary dependencies in the data due to their recurrent structures. Another popular type of deep model for point process data is based on representing the influence kernel (rather than the intensity function) by neural networks. We take the latter approach and develop a new deep non-stationary influence kernel that can model non-stationary spatio-temporal point processes. The main idea is to approximate the influence kernel with a novel and general low-rank decomposition, enabling efficient representation through deep neural networks and computational efficiency and better performance. We also take a new approach to maintain the non-negativity constraint of the conditional intensity by introducing a log-barrier penalty. We demonstrate our proposed method's good performance and computational efficiency compared with the state-of-the-art on simulated and real data.
Accuracy Boosters: Epoch-Driven Mixed-Mantissa Block Floating-Point for DNN Training

The unprecedented growth in DNN model complexity, size, and amount of training data has led to a commensurate increase in demand for computing and a search for minimal encoding. Recent research advocates Hybrid Block Floating Point (HBFP) to minimize silicon provisioning in accelerators by converting the majority of arithmetic operations in training to 8-bit fixed point. In this paper, we perform a full-scale exploration of the HBFP design space using mathematical tools to study the interplay among various parameters and identify opportunities for even smaller encodings across layers and epochs. Based on our findings, we propose Accuracy Boosters, an epoch-driven mixed-mantissa HBFP technique that uses 6-bit mantissas only in the last epoch and first/last layers, and 4-bit mantissas for $99.7\%$ of all other arithmetic operations in training. Using analytic models, we show Accuracy Boosters enable increasing arithmetic density for an HBFP training accelerator by up to $21.3\times$ compared to FP32 and up to $4.4\times$ compared to another SOTA format Bfloat16, while preserving or outperforming FP32 accuracy.
Approximate Uncertainty Propagation for Continuous Gaussian Process Dynamical Systems

When learning continuous dynamical systems with Gaussian Processes, computing trajectories requires repeatedly mapping the distributions of uncertain states through the distribution of learned nonlinear functions, which is generally intractable. Since sampling-based approaches are computationally expensive, we consider approximations of the output and trajectory distributions. We show that existing methods make an incorrect implicit independence assumption and underestimate the model-induced uncertainty. We propose a piecewise linear approximation of the GP model yielding a class of numerical solvers for eﬃcient uncertainty estimates matching sampling-based methods.
Learning Low-Rank Representations for Model Compression

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied, optimizations via the reduction of subvector dimensionality are not carefully considered. This paper reports our recent progress on model compression with the combination of dimensionality reduction and vector quantization, proposing Low-Rank Representation Vector Quantization (LR2VQ). LR2VQ joins low-rank representation with subvector clustering to construct a new kind of building block that is optimized by end-to-end training. In our method, the compression ratio could be directly controlled by the dimensionality of subvectors, and the final accuracy is solely determined by clustering dimensionality $\tilde{d}$. We recognize $\tilde{d}$ as a trade-off between low-rank approximation error and clustering error and carry out both theoretical analysis and experimental observations that empower the estimation of the proper $\tilde{d}$ before fine-tuning. With a proper $\tilde{d}$, we evaluate LR2VQ with ResNet-18/ResNet-50 on ImageNet classification datasets, achieving 2.8%/1.0% top-1 accuracy improvements over the current state-of-the-art model compression algorithms with 43×/31× compression factor.
Uniform convergence of optimal order under a balanced norm of a local discontinuous Galerkin method on a Shishkin mesh

For singularly perturbed reaction-diﬀusion problems in 1D and 2D, we study a local discontinuous Galerkin (LDG) method on a Shishkin mesh. In these cases, the standard energy norm is too weak to capture adequately the behavior of the boundary layers that appear in the solutions. To deal with this deﬁciency, we introduce a balanced norm stronger than the energy norm. In order to achieve optimal convergence under the balanced norm in one-dimensional case, we design novel numerical ﬂuxes and propose a special interpolation that consists of a Gauss-Radau projection and a local L 2 projection. Moreover, we generalize the numerical ﬂuxes and interpolation, and extend convergence analysis of optimal order from 1D to 2D. Finally, numerical experiments are presented to conﬁrm the theoretical results.
Semi-supervised Local Cluster Extraction by Compressive Sensing

Local clustering problem aims at extracting a small local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a compressive sensing problem where the indices of target cluster can be thought as a sparse solution to a linear system. In this paper, we propose a new semi-supervised local cluster extraction approach by applying the idea of compressive sensing based on two pioneering works under the same framework. Our approves improves the existing works by making the initial cut to be the entire graph and hence overcomes a major limitation of existing works, which is the low quality of initial cut. Extensive experimental results on multiple benchmark datasets demonstrate the effectiveness of our approach.