Miracle-dz/UniFAR-FTUs huggingface dataset:
Gravitational-wave imprints of compact and galactic-scale environments in extreme-mass-ratio binaries

Circumambient and galactic-scale environments are intermittently present around black holes that reside in active galactic nuclei. As supermassive black holes impart energy on their host galaxy, so the galactic environment affects the dynamics of solar-mass objects around black holes and the gravitational waves emitted from non-vacuum asymmetric binaries. Only recently an exact general-relativistic solution has been found that describes a Schwarzschild black hole immersed in a dark matter halo of the Hernquist type. We perform an extensive analysis of generic geodesics delving in such non-vacuum spacetimes and compare our results with those obtained in Schwarzschild, as well as calculate their gravitational-wave emission. Our findings indicate that the radial and polar oscillation frequency ratios descend deeper into the strong gravity region as the compactness of the halo increases. This translates to a redshift of non-vacuum geodesics and their resulting waveforms with respect to the vacuum ones. We calculate the overlap between waveforms resulting from Schwarzschild and non-vacuum geometries and find that it decreases as the halo compactness grows, meaning that dark matter environments should be distinguishable by space-borne detectors. For compact environments, we find that the apsidal precession is strongly affected due to the gravitational pull of dark matter; the orbit's axis can rotate in the opposite direction as that of the orbital motion, leading to a retrograde precession drift that depends on the halo mass, as opposed to the typical prograde precession transpiring in galactic-scale environments. Gravitational waves in retrograde-to-prograde alterations demonstrate transient frequency phenomena around critical non-precessing turning points, thus they may serve as `smoking guns' for the presence of compact dark matter environments around supermassive black holes.
Multiple Instance Learning via Iterative Self-Paced Supervised Contrastive Learning

Learning representations for individual instances when only bag-level labels are available is a fundamental challenge in multiple instance learning (MIL). Recent works have shown promising results using contrastive self-supervised learning (CSSL), which learns to push apart representations corresponding to two different randomly-selected instances. Unfortunately, in real-world applications such as medical image classification, there is often class imbalance, so randomly-selected instances mostly belong to the same majority class, which precludes CSSL from learning inter-class differences. To address this issue, we propose a novel framework, Iterative Self-paced Supervised Contrastive Learning for MIL Representations (ItS2CLR), which improves the learned representation by exploiting instance-level pseudo labels derived from the bag-level labels. The framework employs a novel self-paced sampling strategy to ensure the accuracy of pseudo labels. We evaluate ItS2CLR on three medical datasets, showing that it improves the quality of instance-level pseudo labels and representations, and outperforms existing MIL methods in terms of both bag and instance level accuracy.11Code is available at https://github.com/Kangningthu/ItS2CLR
Understanding COVID-19 Vaccine Campaign on Facebook using Minimal Supervision

In the age of social media, where billions of internet users share information and opinions, the negative impact of pandemics is not limited to the physical world. It provokes a surge of incomplete, biased, and incorrect information, also known as an infodemic. This global infodemic jeopardizes measures to control the pandemic by creating panic, vaccine hesitancy, and fragmented social response. Platforms like Facebook allow advertisers to adapt their messaging to target different demographics and help alleviate or exacerbate the infodemic problem depending on their content. In this paper, we propose a minimally supervised multi-task learning framework for understanding messaging on Facebook related to the COVID vaccine by identifying ad themes and moral foundations. Furthermore, we perform a more nuanced thematic analysis of messaging tactics of vaccine campaigns on social media so that policymakers can make better decisions on pandemic control.
Towards Task-Specific Modular Gripper Fingers: Automatic Production of Fingertip Mechanics

The adaption of robotic assembly lines to new products is generally slow and costly, binding the economical usage of a single line to a few products manufactured in masses. An important time factor is the adaption of the assembly robot's gripper fingers to the new product components - since finger design, production, and mounting is done manually. In this letter, we introduce an approach for automatic task-specific fingertip production and application. Our system is potentially able to reduce the assembly line customization time mentioned above by automatically printing customized fingertips onto a pre-produced finger-base and storing them in a dedicated finger library before the product assembly process begins. The assembly robot can then autonomously load and use these produced and stored fingers for the designated manipulation task by utilizing a specially developed quick finger exchange system. The setup is experimentally validated by conducting automatic production of three different fingertips and executing grasp-stability tests as well as multiple pick- and insertion tasks, with and without position offsets - using these fingertips. The proposed approach, indeed, goes beyond fingertip production and serves as a foundation for a fully automatic fingertip design, production, and application pipeline.
On certain Lagrangian submanifolds of S2 ×S2 and ℂPn

We consider various constructions of monotone Lagrangian submanifolds of $C P^n, S^2\times S^2$, and quadric hypersurfaces of $C P^n$. In $S^2\times S^2$ and $C P^2$ we show that several different known constructions of exotic monotone tori yield results that are Hamiltonian isotopic to each other, in particular answering a question of Wu by showing that the monotone fiber of a toric degeneration model of $C P^2$ is Hamiltonian isotopic to the Chekanov torus. Generalizing our constructions to higher dimensions leads us to consider monotone Lagrangian submanifolds (typically not tori) of quadrics and of $C P^n$ which can be understood either in terms of the geodesic flow on $T^*S^n$ or in terms of the Biran circle bundle construction. Unlike previously-known monotone Lagrangian submanifolds of closed simply connected symplectic manifolds, many of our higher-dimensional Lagrangian submanifolds are provably displaceable.
Representation Power of Graph Convolutions : Neural Tangent Kernel Analysis

The fundamental principle of Graph Neural Networks (GNNs) is to exploit the structural information of the data by aggregating the neighboring nodes using a ‘graph convolution’. Therefore, understanding its inﬂuence on the network performance is crucial. Convolutions based on graph Laplacian have emerged as the dominant choice with the symmetric normalization of the adjacency matrix A , de-ﬁned as D − 12 AD − 12 , being the most widely adopted one, where D is the degree matrix. However, some empirical studies show that row normalization D − 1 A outperforms it in node classiﬁcation. Despite the widespread use of GNNs, there is no rigorous theoretical study on the representation power of these convolution operators, that could explain this behavior. In this work, we analyze the inﬂuence of the graph convolutions theoretically using Graph Neural Tangent Kernel in a semi-supervised node classiﬁcation setting. Under a Degree Corrected Stochastic Block Model , we prove that: (i) row normalization preserves the underlying class structure better than other convolutions; (ii) performance degrades with network depth due to over-smoothing, but the loss in class information is the slowest in row normalization; (iii) skip connections retain the class information even at inﬁ-nite depth, thereby eliminating over-smoothing. We ﬁnally validate our theoretical ﬁndings on real datasets.
Differentiable Physics Simulation of Dynamics-Augmented Neural Objects

We present a differentiable pipeline for simulating the motion of objects that represent their geometry as a continuous density field parameterized as a deep network. This includes Neural Radiance Fields (NeRFs), and other related models. From the density field, we estimate the dynamical properties of the object, including its mass, center of mass, and inertia matrix. We then introduce a differentiable contact model based on the density field for computing normal and friction forces resulting from collisions. This allows a robot to autonomously build object models that are visually and dynamically accurate from still images and videos of objects in motion. The resulting Dynamics-Augmented Neural Objects (DANOs) are simulated with an existing differentiable simulation engine, Dojo, interacting with other standard simulation objects, such as spheres, planes, and robots specified as URDFs. A robot can use this simulation to optimize grasps and manipulation trajectories of neural objects, or to improve the neural object models through gradient-based real-to-simulation transfer. We demonstrate the pipeline to learn the coefficient of friction of a bar of soap from a real video of the soap sliding on a table. We also learn the coefficient of friction and mass of a Stanford bunny through interactions with a Panda robot arm from synthetic data, and we optimize trajectories in simulation for the Panda arm to push the bunny to a goal location.
Approximate Stochastic Optimal Control for Linear Time Invariant Systems with Heavy-tailed Disturbances

We propose an open loop control scheme for linear time invariant systems perturbed by multivariate $t$ disturbances through the use of quantile reformulations. The multivariate $t$ disturbance is motivated by heavy tailed phenomena that arise in multi-vehicle planning planning problems through unmodeled perturbation forces, linearization effects, or faulty actuators. Our approach relies on convex quantile reformulations of the polytopic target sets and norm based collision avoidance constraints to enable fast computation. We embed quantile approximations of the Student's $t$ distribution and the beta prime distribution in a difference-of-convex function framework to compute provably safe but likely suboptimal controllers. We demonstrate our method with three satellite rendezvous examples and provide a comparison with particle control.
Obstruction-free gluing for the Einstein equations

In this paper we develop a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to the previous constructions, the new perspective actively utilizes the nonlinearity of the constraint equations. As a result, we are able to remove the $10$-dimensional spaces of obstructions to the null and spacelike (asymptotically flat) gluing problems, previously known in the literature. In particular, we show that any asymptotically flat spacelike initial data can be glued to the Schwarzschild initial data of mass $M$ for any $M>0$ sufficiently large. More generally, compared to the celebrated result of Corvino-Schoen, our methods allow us to choose ourselves the Kerr spacelike initial data that is being glued onto. As in our earlier work, our primary focus is the analysis of the null problem, where we develop a new technique of combining low-frequency linear analysis with high-frequency nonlinear control. The corresponding spacelike results are derived a posteriori by solving a characteristic initial value problem.
Discovery of One Neutron Star Candidate from Radial-velocity Monitoring

We report the discovery of one possible neutron star binary (P orb = 0.8666 days) by using LAMOST low-resolution spectroscopic data. The visible companion is a late A-type dwarf (T eff = 7900 ± 200 K; logg = 4.3 ± 0.2; M = 1.7 ± 0.1 M ⊙; R = 1.7 ± 0.2 R ⊙) at a distance of 1.11 ± 0.03 kpc. No double-lined feature can be seen from the Gran Telescopio Canarias/HORuS high-resolution spectra; thus the radial-velocity variation indicates an invisible object hiding in the binary. The system’s optical light curves show clear ellipsoidal variability, suggesting that the visible companion is tidal distorted. By fitting the multiband light curves with the eclipsing light-curve (ELC) code and the Wilson–Devinney (WD) code, we constrain the mass of the invisible star to be 1.1–1.3 M ⊙. Spectral disentangling shows no additional component with optical absorption spectra, supporting the idea that the system contains one compact object. No X-ray or UV emission is detected in the ROSAT archive observations. Therefore, we suspect the invisible object is more likely a neutron star rather than a white dwarf. Our finding suggests the ability of LAMOST spectroscopic survey to discover X-ray-quiescent compact objects.
Wiener-Hopf analysis of the vector diffraction problem for a cylindrical waveguide cavity

The analysis of electromagnetic wave scattering by open-ended metallic waveguide cavities has received much attention in connection with the prediction and reduction of the radar cross section (RCS) of a target. This problem serves as a simple model of duct structures such as jet engine intakes of an aircraft and cracks occurring on surfaces of general complicated bodies. We consider the vector diffraction by a cavity formed by a semi-infinite circular waveguide with an interior planar termination as a generalization of our previous scalar problems, and analyze the non-symmetric electromagnetic wave diffraction by means of the Wiener-Hopf technique.
Learning Less Generalizable Patterns with an Asymmetrically Trained Double Classifier for Better Test-Time Adaptation

Deep neural networks often fail to generalize outside of their training distribution, in particular when only a single data domain is available during training. While test-time adaptation has yielded encouraging results in this setting, we argue that, to reach further improvements, these ap-proaches should be combined with training procedure mod-ifications aiming to learn a more diverse set of patterns. Indeed, test-time adaptation methods usually have to rely on a limited representation because of the shortcut learning phenomenon: only a subset of the available predictive patterns is learned with standard training. In this paper, we first show that the combined use of existing training-time strategies, and test-time batch normalization, a simple adaptation method, does not always improve upon the test-time adaptation alone on the PACS benchmark. Furthermore, experiments on Office-Home show that very few training-time methods improve upon standard training, with or without test-time batch normalization. We therefore propose a novel approach using a pair of classifiers and a shortcut patterns avoidance loss that mitigates the shortcut learning behavior by reducing the generalization ability of the secondary classifier, using the additional shortcut patterns avoidance loss that encourages the learning of samples specific patterns. The primary classifier is trained normally, resulting in the learning of both the natural and the more complex, less generalizable, features. Our experiments show that our method improves upon the state-of-the-art results on both benchmarks and
Addressing the Extreme Cold-Start Problem in Group Recommendation

The task of recommending items to a group of users, a.k. a. group recommendation, is receiving increasing attention. However, the cold-start problem inherent in recommender systems is amplified in group recommendation because interaction data between groups and items are extremely scarce in practice. Most existing work exploits associations between groups and items to mitigate the data scarcity problem. However, existing approaches inevitably fail in extreme cold-start scenarios where associations between groups and items are lacking. For this reason, we design a group recommendation model for EXreme cold-starT in group REcommendation (EXTRE) suitable for the extreme cold start scenario. The basic idea behind EXTRE is to use the limit theory of graph convolutional neural networks to establish implicit associations between groups and items, and the derivation of these associations does not require explicit interaction data, making it suitable for cold start scenarios. The training process of EXTRE depends on the newly defined and interpretable concepts of consistency and discrepancy, other than commonly used negative sampling with pairwise ranking, which can improve the performance of the group recommendation. Extensive experiments validate the efficacy of the proposed model EXTRE.
A Mixing Time Lower Bound for a Simplified Version of BART

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression algorithm. The posterior is a distribution over sums of decision trees, and predictions are made by averaging approximate samples from the posterior. The combination of strong predictive performance and the ability to provide uncertainty measures has led BART to be commonly used in the social sciences, biostatistics, and causal inference. BART uses Markov Chain Monte Carlo (MCMC) to obtain approximate posterior samples over a parameterized space of sums of trees, but it has often been observed that the chains are slow to mix. In this paper, we provide the first lower bound on the mixing time for a simplified version of BART in which we reduce the sum to a single tree and use a subset of the possible moves for the MCMC proposal distribution. Our lower bound for the mixing time grows exponentially with the number of data points. Inspired by this new connection between the mixing time and the number of data points, we perform rigorous simulations on BART. We show qualitatively that BART's mixing time increases with the number of data points. The slow mixing time of the simplified BART suggests a large variation between different runs of the simplified BART algorithm and a similar large variation is known for BART in the literature. This large variation could result in a lack of stability in the models, predictions, and posterior intervals obtained from the BART MCMC samples. Our lower bound and simulations suggest increasing the number of chains with the number of data points.
Measure-valued processes for energy markets

We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how the Heath-Jarrow-Morton approach can be translated to this framework, thus guaranteeing arbitrage free modeling in infinite dimensions. We derive an analog to the HJM-drift condition and then treat in a Markovian setting existence of non-negative measure-valued diffusions that satisfy this condition. To analyze mathematically convenient classes we build on Cuchiero et al. (2021) and consider measure-valued polynomial and affine diffusions, where we can precisely specify the diffusion part in terms of continuous functions satisfying certain admissibility conditions. For calibration purposes these functions can then be parameterized by neural networks yielding measure-valued analogs of neural SPDEs. By combining Fourier approaches or the moment formula with stochastic gradient descent methods, this then allows for tractable calibration procedures which we also test by way of example on market data. We also sketch how measure-valued processes can be applied in the context of renewable energy production modeling.
Predicting Winning Regions in Parity Games via Graph Neural Networks (Extended Abstract)

Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We present a incomplete polynomial-time approach to determining the winning regions of parity games via graph neural networks. Our evaluation on 900 randomly generated parity games shows that this approach is effective and efficient in practice. It correctly determines the winning regions of $\sim$60\% of the games in our data set and only incurs minor errors in the remaining ones. We believe that this approach can be extended to efficiently solve parity games as well.
Bag All You Need: Learning a Generalizable Bagging Strategy for Heterogeneous Objects

We introduce a practical robotics solution for the task of heterogeneous bagging, requiring the placement of multiple rigid and deformable objects into a deformable bag. This is a difficult task as it features complex interactions between multiple highly deformable objects under limited observability. To tackle these challenges, we propose a robotic system consisting of two learned policies: a rearrangement policy that learns to place multiple rigid objects and fold deformable objects in order to achieve desirable pre-bagging conditions, and a lifting policy to infer suitable grasp points for bi-manual bag lifting. We evaluate these learned policies on a real-world three-arm robot platform that achieves a 70% heterogeneous bagging success rate with novel objects. To facilitate future research and comparison, we also develop a novel heterogeneous bagging simulation benchmark that will be made publicly available.
Finite-time analysis of single-timescale actor-critic

Actor-critic methods have achieved significant success in many challenging applications. However, its finite-time convergence is still poorly understood in the most practical single-timescale form. Existing works on analyzing single-timescale actor-critic have been limited to i.i. d. sampling or tabular setting for simplicity. We investigate the more practical online single-timescale actor-critic algorithm on continuous state space, where the critic assumes linear function approximation and updates with a single Markovian sample per actor step. Previous analysis has been unable to establish the convergence for such a challenging scenario. We demonstrate that the online single-timescale actor-critic method provably finds an $\epsilon$-approximate stationary point with $\widetilde{\mathcal{O}}(\epsilon^{-2})$ sample complexity under standard assumptions, which can be further improved to $\mathcal{O}(\epsilon^{-2})$ under the i.i. d. sampling. Our novel framework systematically evaluates and controls the error propagation between the actor and critic. It offers a promising approach for analyzing other single-timescale reinforcement learning algorithms as well.