Miracle-dz/UniFAR-FTUs huggingface dataset:
Generalization and Stability of Interpolating Neural Networks with Minimal Width

We investigate the generalization and optimization properties of shallow neural-network classifiers trained by gradient descent in the interpolating regime. Specifically, in a realizable scenario where model weights can achieve arbitrarily small training error $\epsilon$ and their distance from initialization is $g(\epsilon)$, we demonstrate that gradient descent with $n$ training data achieves training error $O(g(1/T)^2 /T)$ and generalization error $O(g(1/T)^2 /n)$ at iteration $T$, provided there are at least $m=\Omega(g(1/T)^4)$ hidden neurons. We then show that our realizable setting encompasses a special case where data are separable by the model's neural tangent kernel. For this and logistic-loss minimization, we prove the training loss decays at a rate of $\tilde O(1/ T)$ given polylogarithmic number of neurons $m=\Omega(\log^4 (T))$. Moreover, with $m=\Omega(\log^{4} (n))$ neurons and $T\approx n$ iterations, we bound the test loss by $\tilde{O}(1/n)$. Our results differ from existing generalization outcomes using the algorithmic-stability framework, which necessitate polynomial width and yield suboptimal generalization rates. Central to our analysis is the use of a new self-bounded weak-convexity property, which leads to a generalized local quasi-convexity property for sufficiently parameterized neural-network classifiers. Eventually, despite the objective's non-convexity, this leads to convergence and generalization-gap bounds that resemble those found in the convex setting of linear logistic regression.
Distributional Offline Policy Evaluation with Predictive Error Guarantees

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.
Mental Health Coping Stories on Social Media: A Causal-Inference Study of Papageno Effect

The Papageno effect concerns how media can play a positive role in preventing and mitigating suicidal ideation and behaviors. With the increasing ubiquity and widespread use of social media, individuals often express and share lived experiences and struggles with mental health. However, there is a gap in our understanding about the existence and effectiveness of the Papageno effect in social media, which we study in this paper. In particular, we adopt a causal-inference framework to examine the impact of exposure to mental health coping stories on individuals on Twitter. We obtain a Twitter dataset with ∼ 2M posts by ∼ 10K individuals. We consider engaging with coping stories as the Treatment intervention, and adopt a stratified propensity score approach to find matched cohorts of Treatment and Control individuals. We measure the psychosocial shifts in affective, behavioral, and cognitive outcomes in longitudinal Twitter data before and after engaging with the coping stories. Our findings reveal that, engaging with coping stories leads to decreased stress and depression, and improved expressive writing, diversity, and interactivity. Our work discusses the practical and platform design implications in supporting mental wellbeing.
Coordinating Multiple Intelligent Reflecting Surfaces Without Channel Information

Conventional beamforming methods for intelligent reflecting surfaces (IRSs) or reconfigurable intelligent surfaces (RISs) typically entail the full channel state information (CSI). However, the computational cost of channel acquisition soars exponentially with the number of IRSs. To bypass this difficulty, we propose a novel strategy called blind beamforming that coordinates multiple IRSs by means of statistics without knowing CSI. Blind beamforming only requires measuring the received signal power at the user terminal for a sequence of randomly generated phase shifts across all IRSs. The main idea is to extract the key statistical quantity for beamforming by exploring only a small portion of the whole solution space of phase shifts. We show that blind beamforming guarantees a signal-to-noise ratio (SNR) boost of <inline-formula><tex-math notation="LaTeX">$\Theta(N^{2L})$</tex-math></inline-formula> under certain conditions, where <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula> is the number of IRSs and <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of reflecting elements per IRS. The proposed conditions for achieving the optimal SNR boost of <inline-formula><tex-math notation="LaTeX">$\Theta(N^{4})$</tex-math></inline-formula> in a double-IRS system are much easier to satisfy than the existing ones in the literature. Most importantly, the proposed conditions can be extended to a fully general <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula>-IRS system. The above result significantly improves upon the state of the art in the area of multi-IRS-assisted communication. Moreover, blind beamforming is justified via field tests and simulations. In particular, as shown in our field tests at 2.6 GHz, our method yields up to 17 dB SNR boost; to the best of our knowledge, this is the first time that the use of multiple IRSs gets verified in the real world.
On the fractional Musielak-Sobolev spaces in R^d: Embedding results&applications

This paper deals with new continuous and compact embedding theorems for the fractional Musielak-Sobolev spaces in $\mathbb{R}^d$. As an application, using the variational methods, we obtain the existence of nontrivial weak solution for the following Schr\"odinger equation $$ (-\Delta)_{g_{x,y}}^s u+V(x)g(x,x,u)=b(x)\vert u\vert^{p(x)-2}u,\ \text{for all}\ x\in \mathbb{R}^d,$$ where $(-\Delta)_{g_{x,y}}^s$ is the fractional Museilak $g_{x,y}$-Laplacian, $V$ is a potential function, $b\in L^{\delta^{'}(x)}(\mathbb{R}^d)$, and $p,\delta\in C\left(\mathbb{R}^d,(1,+\infty)\right)\cap L^{\infty}(\mathbb{R}^d)$. We would like to mention that the theory of the fractional Musielak-Sobolev spaces is in a developing state and there are few papers in this topic, see \cite{M1,M8,M9}. Note that, all these latter works dealt with bounded case and there are no results devoted for the fractional Musielak-Sobolev spaces in $\mathbb{R}^d$. Since the embedding results are crucial in applying variational methods, this work will provide a bridge between the fractional Mueislak-Sobolev theory and PDE's.
Supersingular reduction of Kummer surfaces in residue characteristic $2$

Given an abelian surface $A$, defined over a discrete valuation field and having good reduction, does the attached Kummer surface $\mathrm{Km}(A)$ also have good reduction? In this paper we give an affirmative answer in the extreme case, that is, when the abelian surface has supersingular reduction in characteristic $2$.
Hiding Dust around ϵ Eridani

With a Jupiter-like exoplanet and a debris disk with both asteroid and Kuiper Belt analogs, ϵ Eridani has a fascinating resemblance to our expectations for a young solar system. We present a deep Hubble Space Telescope/Space Telescope Imaging Spectrograph coronographic data set using eight orbit visits and the point-spread function calibrator δ Eridani. While we were unable to detect the debris disk, we place stringent constraints on the scattered light surface brightness of ∼4μJyarcsec−2. We combine this scattered light detection limit with a reanalysis of archival near- and mid-infrared observations and a dynamical model of the full planetary system to refine our model of the ϵ Eridani debris disk components. Radiative transfer modeling suggests an asteroid belt analog inside of 3 au, an intermediate disk component in the 6–37 au region, and a Kuiper Belt analog colocated with the narrow belt observed in the millimeter (69 au). Modeling also suggests a large minimum grain size requiring either very porous grains or a suppression of small grain production, and a radially stratified particle size distribution. The inner disk regions require a steep power-law slope (s −3.8 where s is the grain size) weighted toward smaller grains and the outer disk prefers a shallower slope (s −3.4) with a minimum particle size of >2 μm. These conclusions will be enhanced by upcoming coronagraphic observations of the system with the James Webb Space Telescope, which will pinpoint the radial location of the dust belts and further diagnose the dust particle properties.
Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernels

Surrogate kernel-based methods offer a flexible solution to structured output prediction by leveraging the kernel trick in both input and output spaces. In contrast to energy-based models, they avoid to pay the cost of inference during training, while enjoying statistical guarantees. However, without approximation, these approaches are condemned to be used only on a limited amount of training data. In this paper, we propose to equip surrogate kernel methods with approximations based on sketching, seen as low rank projections of feature maps both on input and output feature maps. We showcase the approach on Input Output Kernel ridge Regression (or Kernel Dependency Estimation) and provide excess risk bounds that can be in turn directly plugged on the final predictive model. An analysis of the complexity in time and memory show that sketching the input kernel mostly reduces training time while sketching the output kernel allows to reduce the inference time. Furthermore, we show that Gaussian and sub-Gaussian sketches are admissible sketches in the sense that they induce projection operators ensuring a small excess risk. Experiments on different tasks consolidate our findings.
Comparison of two efficient ML algorithms for high resolution sources tracking-time recursive implementation

A comparison is made of two fast Newton-Gauss algorithms for implementation of the exact maximum-likelihood (ML) and an approximate ML (AML) previously introduced by the authors (1989). The AML is impeded by the need of an eigenvalue decomposition of the covariance matrix, but it exhibits better robustness and a lower signal-to-noise ratio (SNR) threshold. The availability of efficient ML algorithms opens the way to interesting recursive or adaptive tracking methods. If an a priori Gaussian probability is assumed for bearing parameters, the algorithm can be easily modified, and it provides the updated estimates and their posteriori covariance. A dynamic model may be also introduced, and then all the requirements for building a Kalman-like recursive estimation scheme for fast moving sources tracking are presented. The update may be made with a small number of snapshots, even a single one, when the a priori covariance has converged to a small enough value. This one snapshot case is very interesting, since the ML algorithm then takes a much simplified form. <<ETX>>
Codes Over Absorption Channels

In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from invivo nano-machines, emerging medical applications, and brain-machine interfaces that communicate over the nervous system.For any given finite alphabet, we give codes that can correct absorption errors. For the binary alphabet, the known binary (multiple-)deletion correcting codes already provide a good solution. For single-absorption error, we prove that the Varshamov-Tenengolts codes can provide a near-optimal code in our setting. When the alphabet size q is at least 3, we first construct a single-absorption correcting code whose redundancy is at most 3 logq (n)+O(1). Then, based on this code and ideas introduced in [1], we give a second construction of single-absorption correcting codes with redundancy logq(n) + 12 logq logq(n) + O(1), which is optimal up to an O(logq logq(n)). Finally, we apply the syndrome compression technique with pre-coding to obtain a subcode of the single-absorption correcting code. This subcode can combat multiple-absorption errors and has low redundancy.
VARIATIONS OF SOLAR ROTATION AND SUNSPOT ACTIVITY

The continuous wavelet transformation is used to study the temporal variations of the rotational cycle length of daily sunspot numbers from 1849 January 1 to 2010 February 28, from a global point of view. The rotational cycle length of the Sun is found to have a secular trend, which statistically shows a linear decrease by about 0.47 days during the time interval considered. The empirical mode decomposition analysis of the temporal variations of the rotational cycle length shows an acceleration trend for the surface rotation rate from cycles 11 to 19, but a deceleration trend from the beginning of cycle 20 onward. We cannot determine whether the rotation rate around the maximum times of the Schwable cycles should be faster or slower than that around the minimum times, implying no Schwable cycle in the long-term variations of rotation. The results obtained are compared to those from the literature. It is inferred that the variation of the rotational cycle length may be related to the variation of sunspot activity in the long run.
X-Adv: Physical Adversarial Object Attacks against X-ray Prohibited Item Detection

Adversarial attacks are valuable for evaluating the robustness of deep learning models. Existing attacks are primarily conducted on the visible light spectrum (e.g., pixel-wise texture perturbation). However, attacks targeting texture-free X-ray images remain underexplored, despite the widespread application of X-ray imaging in safety-critical scenarios such as the X-ray detection of prohibited items. In this paper, we take the first step toward the study of adversarial attacks targeted at X-ray prohibited item detection, and reveal the serious threats posed by such attacks in this safety-critical scenario. Specifically, we posit that successful physical adversarial attacks in this scenario should be specially designed to circumvent the challenges posed by color/texture fading and complex overlapping. To this end, we propose X-adv to generate physically printable metals that act as an adversarial agent capable of deceiving X-ray detectors when placed in luggage. To resolve the issues associated with color/texture fading, we develop a differentiable converter that facilitates the generation of 3D-printable objects with adversarial shapes, using the gradients of a surrogate model rather than directly generating adversarial textures. To place the printed 3D adversarial objects in luggage with complex overlapped instances, we design a policy-based reinforcement learning strategy to find locations eliciting strong attack performance in worst-case scenarios whereby the prohibited items are heavily occluded by other items. To verify the effectiveness of the proposed X-Adv, we conduct extensive experiments in both the digital and the physical world (employing a commercial X-ray security inspection system for the latter case). Furthermore, we present the physical-world X-ray adversarial attack dataset XAD.
The Communication Complexity of Efficient Allocation Problems

We analyze the communication burden of surplus-maximizing allocations. We study both the continuous and discrete models of communication, measuring its burden with the dimensionality of the message space and the number of transmitted bits, respectively. In both cases, we offer a lower bound on the amount of communication. This bound is applied to the problem of allocating L heterogeneous objects among N agents, whose valuations are (i) unrestricted, (ii) submodular, or (iii) homogeneous in objects. In cases (i) and (ii), efficiency requires exponential communication in L. Furthermore, in case (i), polynomial communication in L cannot ensure a higher surplus than selling all objects as a bundle. On the other hand, in case (iii), exact efficiency requires the transmission of L numbers, but can be approximated arbitrarily closely using only O(logL) bits. When a Walrasian equilibrium with per-item prices exists, efficiency is achieved with deterministic communication that is polynomial in L.
Self-supervised Cloth Reconstruction via Action-conditioned Cloth Tracking

State estimation is one of the greatest challenges for cloth manipulation due to cloth's high dimensionality and self-occlusion. Prior works propose to identify the full state of crumpled clothes by training a mesh reconstruction model in simulation. However, such models are prone to suffer from a sim-to-real gap due to differences between cloth simulation and the real world. In this work, we propose a self-supervised method to finetune a mesh reconstruction model in the real world. Since the full mesh of crumpled cloth is difficult to obtain in the real world, we design a special data collection scheme and an action-conditioned model-based cloth tracking method to generate pseudo-labels for self-supervised learning. By finetuning the pretrained mesh reconstruction model on this pseudo-labeled dataset, we show that we can improve the quality of the reconstructed mesh without requiring human annotations, and improve the performance of downstream manipulation task. More visualizations and results can be found on our project website.
Generalized Weyl's theorem and hyponormal operators

Abstract Let T be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of T is the set σBW(T) of all λ ∈ Сsuch that T − λI is not a B-Fredholm operator of index 0. Let E(T) be the set of all isolated eigenvalues of T. The aim of this paper is to show that if T is a hyponormal operator, then T satisfies generalized Weyl's theorem σBW(T) = σ(T)/E(T), and the B-Weyl spectrum σBW(T) of T satisfies the spectral mapping theorem. We also consider commuting finite rank perturbations of operators satisfying generalized Weyl's theorem.
Simulating supermassive black hole mass measurements for a sample of ultramassive galaxies using ELT/HARMONI high-spatial-resolution integral-field stellar kinematics

As the earliest relics of star formation episodes of the Universe, the most massive galaxies are the key to our understanding of the stellar population, cosmic structure, and supermassive black hole (SMBH) evolution. However, the details of their formation histories remain uncertain. We address these problems by planning a large survey sample of 101 ultramassive galaxies (z ≤ 0.3, |δ + 24°| < 45°, |b| > 8°), including 76 per cent ellipticals, 17 per cent lenticulars, and 7 per cent spirals brighter than MK ≤ −27 mag (stellar mass 2 × 1012 ≲ M⋆ ≲ 5 × 1012 M⊙) with ELT/HARMONI. Our sample comprises diverse galaxy environments ranging from isolated to dense-cluster galaxies. The primary goals of the project are to (1) explore the stellar dynamics inside galaxy nuclei and weigh SMBHs, (2) constrain the black hole scaling relations at the highest mass, and (3) probe the late-time assembly of these most massive galaxies through the stellar population and kinematical gradients. We describe the survey, discuss the distinct demographics and environmental properties of the sample, and simulate their HARMONI Iz-, Iz + J-, and H + K-band observations by combining the inferred stellar-mass models from Pan-STARRS observations, an assumed synthetic spectrum of stars, and SMBHs with masses estimated based on different black hole scaling relations. Our simulations produce excellent state-of-the-art integral field spectrography and stellar kinematics (ΔVrms ≲ 1.5 per cent) in a relatively short exposure time. We use these stellar kinematics in combination with the Jeans anisotropic model to reconstruct the SMBH mass and its error using a Markov chain Monte Carlo simulation. Thus, these simulations and modellings can be benchmarks to evaluate the instrument models and pipelines dedicated to HARMONI to exploit the unprecedented capabilities of ELT.
Because Every Sensor Is Unique, so Is Every Pair: Handling Dynamicity in Traffic Forecasting

Traffic forecasting is a critical task to extract values from cyber-physical infrastructures, which is the backbone of smart transportation. However owing to external contexts, the dynamics at each sensor are unique. For example, the afternoon peaks at sensors near schools are more likely to occur earlier than those near residential areas. In this paper, we first analyze real-world traffic data to show that each sensor has a unique dynamic. Further analysis also shows that each pair of sensors also has a unique dynamic. Then, we explore how node embedding learns the unique dynamics at every sensor location. Next, we propose a novel module called Spatial Graph Transformers (SGT) where we use node embedding to leverage the self-attention mechanism to ensure that the information flow between two sensors is adaptive with respect to the unique dynamic of each pair. Finally, we present Graph Self-attention WaveNet (G-SWaN) to address the complex, non-linear spatiotemporal traffic dynamics. Through empirical experiments on four real-world, open datasets, we show that the proposed method achieves superior performance on both traffic speed and flow forecasting. Code is available at: https://github.com/aprbw/G-SWaN
Free-Form Variational Inference for Gaussian Process State-Space Models

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.