Miracle-dz/UniFAR-FTUs huggingface dataset:
The Circular Matern Covariance Function and its Link to Markov Random Fields on the Circle

Abstract: The link between Gaussian random fields and Markov random fields is well established based on a stochastic partial differential equation in Euclidean spaces, where the Matérn covariance functions are essential. However, the Matérn covariance functions are not always positive definite on circles and spheres. In this manuscript, we focus on the extension of this link to circles, and show that the link between Gaussian random fields and Markov random fields on circles is valid based on the circular Matérn covariance function instead. First, we show that this circular Matérn function is the covariance of the stationary solution to the stochastic differential equation on the circle with a formally defined white noise space measure. Then, for the corresponding conditional autoregressive model, we derive a closed form formula for its covariance function. Together with a closed form formula for the circular Matérn covariance function, the link between these two random fields can be established explicitly. Additionally, it is known that the estimator of the mean is not consistent on circles, we provide an equivalent Gaussian measure explanation for this non-ergodicity issue.
Semantic-assisted image compression

Conventional image compression methods typically aim at pixel-level consistency while ignoring the performance of downstream AI tasks.To solve this problem, this paper proposes a Semantic-Assisted Image Compression method (SAIC), which can maintain semantic-level consistency to enable high performance of downstream AI tasks.To this end, we train the compression network using semantic-level loss function. In particular, semantic-level loss is measured using gradient-based semantic weights mechanism (GSW). GSW directly consider downstream AI tasks' perceptual results. Then, this paper proposes a semantic-level distortion evaluation metric to quantify the amount of semantic information retained during the compression process. Experimental results show that the proposed SAIC method can retain more semantic-level information and achieve better performance of downstream AI tasks compared to the traditional deep learning-based method and the advanced perceptual method at the same compression ratio.
GSN: A Universal Graph Neural Network Inspired by Spring Network

The design of universal Graph Neural Networks (GNNs) that operate on both homophilous and heterophilous graphs has received increased research attention in recent years. Existing heterophilous GNNs, particularly those designed in the spatial domain, lack a convincing theoretical or physical motivation. In this paper, we propose the Graph Spring Network (GSN), a universal GNN model that works for both homophilous and heterophilous graphs, inspired by spring networks and metric learning. We show that the GSN framework interprets many existing GNN models from the perspective of spring potential energy minimization with various metrics, which gives these models strong physical motivations. We also conduct extensive experiments to demonstrate our GSN framework’s superior performance on real-world homophilous and heterophilous datasets.
Facets of Symmetric Edge Polytopes for Graphs with Few Edges

Symmetric edge polytopes, also called adjacency polytopes, are lattice polytopes determined by simple undirected graphs. We introduce the integer array \(\mathrm{maxf}(n,m)\) giving the maximum number of facets of a symmetric edge polytope for a connected graph having \(n\) vertices and \(m\) edges, and the corresponding sequence \(\mathrm{minf}(n,m)\) of minimal values. We establish formulas for the number of facets obtained in several classes of sparse graphs and provide partial progress toward conjectures that identify facet-maximizing graphs in these classes. These formulas are combinatorial in nature and lead to independently interesting observations and conjectures regarding integer sequences defined by sums of products of binomial coefficients.
DoubleU-Net++: Architecture with Exploit Multiscale Features for Vertebrae Segmentation

Accurate segmentation of the vertebra is an important prerequisite in various medical applications (E.g. tele surgery) to assist surgeons. Following the successful development of deep neural networks, recent studies have focused on the essential rule of vertebral segmentation. Prior works contain a large number of parameters, and their segmentation is restricted to only one view. Inspired by DoubleU-Net, we propose a novel model named DoubleU-Net++ in which DensNet as feature extractor, special attention module from Convolutional Block Attention on Module (CBAM) and, Pyramid Squeeze Attention (PSA) module are employed to improve extracted features. We evaluate our proposed model on three different views (sagittal, coronal, and axial) of VerSe2020 and xVertSeg datasets. Compared with state-of-the-art studies, our architecture is trained faster and achieves higher precision, recall, and F1-score as evaluation (imporoved by 4-6%) and the result of above 94% for sagittal view and above 94% for both coronal view and above 93% axial view were gained for VerSe2020 dataset, respectively. Also, for xVertSeg dataset, we achieved precision, recall,and F1-score of above 97% for sagittal view, above 93% for coronal view ,and above 96% for axial view.
Current induced switching in Mn2Au from first principles

It is well established that it is possible to switch certain antiferromagnets electrically, yet the interplay of N\'{e}el-spin-orbit torques and thermal activation is only poorly understood. Combining ab initio calculations and atomistic spin dynamics simulations we develop a multiscale model to study the current induced switching in Mn2Au. We compute from first principles the strength and direction of the electrically induced magnetic moments, caused by the Rashba--Edelstein effect, and take these into account in atomistic spin dynamics simulations. Our simulations reveal the switching paths as well as the time scales for switching. The size of the induced moments, however, turns out to be insufficient to lead to fully deterministic switching. Instead, we find that a certain degree of thermal activation is required to help overcoming the relevant energy barrier.
Asynchronous Opinion Dynamics in Social Networks

Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not influence each other. We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of O(n |E |2 (ε/δ)2) on the expected number of opinion updates until convergence, where |E | is the number of edges of the social network. For the complete social network we show a bound of O(n3 (n2 + (ε/δ)2)) that represents a major improvement over the previously best upper bound of O(n9 (ε/δ)2). Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.
Out-of-distribution Detection Using Kernel Density Polytopes

Any reasonable machine learning (ML) model should not only interpolate efﬁciently in between the training samples provided (in-distribution region), but also approach the extrapolative or out-of-distribution (OOD) region without being overconﬁdent. Our experiment on human subjects justiﬁes the aforementioned properties for human intelligence as well. Many state-of-the-art algorithms have tried to ﬁx the overconﬁdence problem of ML models in the OOD region. However, in doing so, they have often impaired the in-distribution performance of the model. Our key insight is that ML models partition the feature space into polytopes and learn constant (random forests) or afﬁne (ReLU networks) functions over those polytopes. This leads to the OOD overconﬁdence problem for the polytopes which lie in the training data boundary and extend to inﬁnity. To resolve this issue, we propose kernel density meth-ods that ﬁt Gaussian kernel over the polytopes, which are learned using ML models. Speciﬁcally, we introduce two variants of kernel density polytopes: Kernel Density Forest (KDF) and Kernel Density Network (KDN) based on random forests and deep networks, respectively. Studies on various simulation settings show that both KDF and KDN achieve uniform conﬁdence over the classes in the OOD region while maintaining good in-distribution accuracy compared to that of their respective parent models.
A Complete Helmholtz Decomposition on Multiply Connected Subdivision Surfaces and Its Application to Integral Equations

The analysis of electromagnetic (EM) scattering in the isogeometric analysis (IGA) framework based on the Loop subdivision has long been restricted to simply connected geometries. The inability to analyze multiply connected objects is a glaring omission. In this article, we address this challenge. IGA provides seamless integration between the geometry and analysis using the same basis set to represent both. In particular, IGA methods using subdivision basis sets exploit the fact that the basis functions used for surface description are smooth (with continuous second derivatives) almost everywhere. On simply connected surfaces, this permits the definition of basis sets that are divergence-free and curl-free. What is missing from this suite is a basis set that is both divergence-free and curl-free, a necessary ingredient for a complete Helmholtz decomposition of currents on multiply connected structures. In this article, we achieve this missing ingredient numerically using random polynomial vector fields. We show that this basis set is analytically divergence-free and curl-free. Furthermore, we show that these bases recover curl-free, divergence-free, and both curl-free and divergence-free fields. Finally, we use this basis set to discretize a well-conditioned integral equation for analyzing perfectly conducting objects and demonstrate excellent agreement with other methods.
LBCF: A Large-Scale Budget-Constrained Causal Forest Algorithm

Offering incentives (e.g., coupons at Amazon, discounts at Uber and video bonuses at Tiktok) to user is a common strategy used by online platforms to increase user engagement and platform revenue. Despite its proven effectiveness, these marketing incentives incur an inevitable cost and might result in a low ROI (Return on Investment) if not used properly. On the other hand, different users respond differently to these incentives, for instance, some users never buy certain products without coupons, while others do anyway. Thus, how to select the right amount of incentives (i.e. treatment) to each user under budget constraints is an important research problem with great practical implications. In this paper, we call such problem as a budget-constrained treatment selection (BTS) problem. The challenge is how to efficiently solve BTS problem on a Large-Scale dataset and achieve improved results over the existing techniques. We propose a novel tree-based treatment selection technique under budget constraints, called Large-Scale Budget-Constrained Causal Forest (LBCF) algorithm, which is also an efficient treatment selection algorithm suitable for modern distributed computing systems. A novel offline evaluation method is also proposed to overcome an intrinsic challenge in assessing solutions’ performance for BTS problem in randomized control trials (RCT) data. We deploy our approach in a real-world scenario on a large-scale video platform, where the platform gives away bonuses in order to increase users’ campaign engagement duration. The simulation analysis, offline and online experiments all show that our method outperforms various tree-based state-of-the-art baselines 1. The proposed approach is currently serving over hundreds of millions of users on the platform and achieves one of the most tremendous improvements over these months.
ProtoRes: Proto-Residual Network for Pose Authoring via Learned Inverse Kinematics

Our work focuses on the development of a learnable neural representation of human pose for advanced AI assisted animation tooling. Specifically, we tackle the problem of constructing a full static human pose based on sparse and variable user inputs (e.g. locations and/or orientations of a subset of body joints). To solve this problem, we propose a novel neural architecture that combines residual connections with prototype encoding of a partially specified pose to create a new complete pose from the learned latent space. We show that our architecture outperforms a baseline based on Transformer, both in terms of accuracy and computational efficiency. Additionally, we develop a user interface to integrate our neural model in Unity, a real-time 3D development platform. Furthermore, we introduce two new datasets representing the static human pose modeling problem, based on high-quality human motion capture data, which will be released publicly along with model code.
Monitoring a Bolted Vibrating Structure Using Multiple Acoustic Emission Sensors: A Benchmark

The dataset presented in this work, called ORION-AE, is made of raw AE data streams collected by three different AE sensors and a laser vibrometer during five campaigns of measurements by varying the tightening conditions of two bolted plates submitted to harmonic vibration tests. With seven different operating conditions, this dataset was designed to challenge supervised and unsupervised machine/deep learning as well as signal processing methods which are developed for material characterization or structural health monitoring (SHM). One motivation of this work was to create a common benchmark for comparing data-driven methods dedicated to AE data interpretation. The dataset is made of time series collected during an experiment designed to reproduce the loosening phenomenon observed in aeronautics, automotive, or civil engineering structures where parts are assembled together by means of bolted joints. Monitoring loosening in jointed structures during operation remains challenging because contact and friction in bolted joints induce a nonlinear stochastic behavior.
JEDAI: A System for Skill-Aligned Explainable Robot Planning

This paper presents JEDAI, an AI system designed for outreach and educational efforts aimed at non-AI experts. JEDAI features a novel synthesis of research ideas from integrated task and motion planning and explainable AI. JEDAI helps users create high-level, intuitive plans while ensuring that they will be executable by the robot. It also provides users customized explanations about errors and helps improve their understanding of AI planning as well as the limits and capabilities of the underlying robot system.
Joint Dynamic Models and Statistical Inference for Recurrent Competing Risks, Longitudinal Marker, and Health Status

Consider a subject or unit in a longitudinal biomedical, public health, engineering, economic or social science study which is being monitored over a possibly random duration. Over time this unit experiences recurrent events of several types and a longitudinal marker transitions over a discrete state-space. In addition, its “health” status also transitions over a discrete state-space with at least one absorbing state. A vector of covariates will also be associated with this unit. Of major interest for this unit is the time-to-absorption of its health status process, which could be viewed as the unit’s lifetime. Aside from being affected by its covariate vector, there could be associations among the recurrent competing risks processes, the longitudinal marker process, and the health status process in the sense that the time-evolution of each process is associated with the other processes. To obtain more realistic models and enhance inferential performance, a joint dynamic stochastic model for these components is proposed and statistical inference methods are developed. This joint model, formulated via counting processes and continuous-time Markov chains, has the potential of facilitating ‘personalized’ interventions. This could enhance, for example, the implementation and adoption of precision medicine in medical settings. Semi-parametric and likelihood-based inferential methods for the model parameters are developed when a sample of these units is available. Finite-sample and asymptotic properties of estimators of model parameters, both finiteand infinite-dimensional, are obtained analytically or through simulation studies. The developed procedures are illustrated using a real data set.
Kronecker-factored Quasi-Newton Methods for Deep Learning

Second-order methods have the capability of accelerating optimization by using much richer curvature information than first-order methods. However, most are impractical for deep learning, where the number of training parameters is huge. In Goldfarb et al. (2020), practical quasi-Newton methods were proposed that approximate the Hessian of a multilayer perceptron (MLP) model by a layer-wise block diagonal matrix where each layer's block is further approximated by a Kronecker product corresponding to the structure of the Hessian restricted to that layer. Here, we extend these methods to enable them to be applied to convolutional neural networks (CNNs), by analyzing the Kronecker-factored structure of the Hessian matrix of convolutional layers. Several improvements to the methods in Goldfarb et al. (2020) are also proposed that can be applied to both MLPs and CNNs. These new methods have memory requirements comparable to first-order methods and much less per-iteration time complexity than those in Goldfarb et al. (2020). Moreover, convergence results are proved for a variant under relatively mild conditions. Finally, we compared the performance of our new methods against several state-of-the-art (SOTA) methods on MLP autoencoder and CNN problems, and found that they outperformed the first-order SOTA methods and performed comparably to the second-order SOTA methods.
Nys-Newton: Nystr\"om-Approximated Curvature for Stochastic Optimization

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely used second-order optimization methods such as quasi-Newton methods generally provide curvature information by approximating the Hessian using the secant equation. However, the secant equation becomes insipid in approximating the Newton step owing to its use of the first-order derivatives. In this study, we propose an approximate Newton sketch-based stochastic optimization algorithm for large-scale empirical risk minimization. Specifically, we compute a partial column Hessian of size ($d\times m$) with $m\ll d$ randomly selected variables, then use the \emph{Nystr\"om method} to better approximate the full Hessian matrix. To further reduce the computational complexity per iteration, we directly compute the update step ($\Delta\boldsymbol{w}$) without computing and storing the full Hessian or its inverse. We then integrate our approximated Hessian with stochastic gradient descent and stochastic variance-reduced gradient methods. The results of numerical experiments on both convex and non-convex functions show that the proposed approach was able to obtain a better approximation of Newton\textquotesingle s method, exhibiting performance competitive with that of state-of-the-art first-order and stochastic quasi-Newton methods. Furthermore, we provide a theoretical convergence analysis for convex functions.
Deep Visual Constraints: Neural Implicit Models for Manipulation Planning From Visual Input

Manipulation planning is the problem of finding a sequence of robot configurations that involves interactions with objects in the scene, e.g., grasping and placing an object, or more general tool-use. To achieve such interactions, traditional approaches require hand-engineering of object representations and interaction constraints, which easily becomes tedious when complex objects/interactions are considered. Inspired by recent advances in 3D modeling, e.g. NeRF, we propose a method to represent objects as continuous functions upon which constraint features are defined and jointly trained. In particular, the proposed pixel-aligned representation is directly inferred from images with known camera geometry and naturally acts as a perception component in the whole manipulation pipeline, thereby enabling long-horizon planning only from visual input.
Evaluating Disentanglement of Structured Representations

We introduce the first metric for evaluating disentanglement at individual hierarchy levels of a structured latent representation. Applied to object-centric generative models, this offers a systematic, unified approach to evaluating (i) object separation between latent slots (ii) disentanglement of object properties inside individual slots (iii) disentanglement of intrinsic and extrinsic object properties. We theoretically show that for structured representations, our framework gives stronger guarantees of selecting a good model than previous disentanglement metrics. Experimentally, we demonstrate that viewing object compositionality as a disentanglement problem addresses several issues with prior visual metrics of object separation. As a core technical component, we present the first representation probing algorithm handling slot permutation invariance.
Power-Law Escape Rate of SGD

Stochastic gradient descent (SGD) undergoes complicated multiplicative noise for the mean-square loss. We use this property of SGD noise to derive a stochastic differential equation (SDE) with simpler additive noise by performing a random time change. Using this formalism, we show that the log loss barrier $\Delta\log L=\log[L(\theta^s)/L(\theta^*)]$ between a local minimum $\theta^*$ and a saddle $\theta^s$ determines the escape rate of SGD from the local minimum, contrary to the previous results borrowing from physics that the linear loss barrier $\Delta L=L(\theta^s)-L(\theta^*)$ decides the escape rate. Our escape-rate formula strongly depends on the typical magnitude $h^*$ and the number $n$ of the outlier eigenvalues of the Hessian. This result explains an empirical fact that SGD prefers flat minima with low effective dimensions, giving an insight into implicit biases of SGD.