Miracle-dz/UniFAR-FTUs huggingface dataset:
Distribution free optimality intervals for clustering

Summary . We address the problem of validating the ouput of clustering algorithms. Given data D and a partition C of these data into K clusters, when can we say that the clusters obtained are correct or meaningful for the data? This paper introduces a paradigm in which a clustering C is considered meaningful if it is good with respect to a loss function such as the K-means distortion, and stable , i.e. the only good clustering up to small perturbations. Furthermore, we present a generic method to obtain post-inference guarantees of near-optimality and stability for a clustering C . The method can be instantiated for a variety of clustering criteria (also called loss functions) for which convex relaxations exist. Obtaining the guarantees amounts to solving a convex optimization problem. We demonstrate the practical relevance of this method by obtaining guarantees for the K-means and the Normalized Cut clustering criteria on realistic data sets. We also prove that asymptotic instability implies ﬁnite sample instability w.h. p., allowing inferences about the population clusterability from a sample. The guarantees do not depend on any distributional assumptions, but they depend on the data set D admitting a stable clustering.
Strategically Efficient Exploration in Competitive Multi-agent Reinforcement Learning

High sample complexity remains a barrier to the application of reinforcement learning (RL), particularly in multi-agent systems. A large body of work has demonstrated that exploration mechanisms based on the principle of optimism under uncertainty can significantly improve the sample efficiency of RL in single agent tasks. This work seeks to understand the role of optimistic exploration in non-cooperative multi-agent settings. We will show that, in zero-sum games, optimistic exploration can cause the learner to waste time sampling parts of the state space that are irrelevant to strategic play, as they can only be reached through cooperation between both players. To address this issue, we introduce a formal notion of strategically efficient exploration in Markov games, and use this to develop two strategically efficient learning algorithms for finite Markov games. We demonstrate that these methods can be significantly more sample efficient than their optimistic counterparts.
A scalable and robust preconditioner for high-order FEM based on the fast diagonalization method

Pavarino proved that the additive Schwarz method with vertex patches and a low-order coarse space gives a p -robust solver for symmetric and coercive problems [32]. However, for very high polynomial degree it is not feasible to assemble or factorize the matrices for each patch. In this work we introduce a direct solver for separable patch problems that scales to very high polynomial degree on tensor product cells. The solver constructs a tensor product basis that diagonalizes the blocks in the stiﬀness matrix for the internal degrees of freedom of each individual cell. As a result, the non-zero structure of the cell matrices is that of the graph connecting internal degrees of freedom to their projection onto the facets. In the new basis, the patch problem is as sparse as a low-order ﬁnite diﬀerence discretization, while having a sparser Cholesky factorization. We can thus aﬀord to assemble and factorize the matrices for the vertex-patch problems, even for very high polynomial degree. In the non-separable case, the method can be applied as a preconditioner by approximating the problem with a separable surrogate.
Optimal unique continuation for periodic elliptic equations on large scales

We prove a quantitative, large-scale doubling inequality and large-scale three-ellipsoid inequality for solutions of uniformly elliptic equations with periodic coefficients. These estimates are optimal in terms of the minimal length scale on which they are valid, and are at least"almost"optimal in the prefactor constants--up to, at most, an iterated logarithm of the initial doubling ratio.
Manipulating Identical Filter Redundancy for Efficient Pruning on Deep and Complicated CNN

The existence of redundancy in convolutional neural networks (CNNs) enables us to remove some filters/channels with acceptable performance drops. However, the training objective of CNNs usually tends to minimize an accuracy-related loss function without any attention paid to the redundancy, making the redundancy distribute randomly on all the filters, such that removing any of them may trigger information loss and accuracy drop, necessitating a fine-tuning step for recovery. In this article, we propose to manipulate the redundancy during training to facilitate network pruning. To this end, we propose a novel centripetal SGD (C-SGD) to make some filters identical, resulting in ideal redundancy patterns, as such filters become purely redundant due to their duplicates, hence removing them does not harm the network. As shown on CIFAR and ImageNet, C-SGD delivers better performance because the redundancy is better organized, compared to the existing methods. The efficiency also characterizes C-SGD because it is as fast as regular SGD, requires no fine-tuning, and can be conducted simultaneously on all the layers even in very deep CNNs. Besides, C-SGD can improve the accuracy of CNNs by first training a model with the same architecture but wider layers and then squeezing it into the original width.
Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems

Motivated by the phenomenon of duality for interacting particle systems we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the `bulk' and at the `edge'. Using the probabilistic method due to Mark Kac, we prove two Szeg\H{o}-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredholm Pfaffian through expectations with respect to the random walk, and analyse the expectations using general results on random walks. We demonstrate the utility of the theorems by calculating asymptotics for the empty interval and non-crossing probabilities for a number of examples of Pfaffian point processes: coalescing/annihilating Brownian motions, massive coalescing Brownian motions, real zeros of Gaussian power series and Kac polynomials, and real eigenvalues for the real Ginibre ensemble.
Perceiver IO: A General Architecture for Structured Inputs & Outputs

A central goal of machine learning is the development of systems that can solve many problems in as many data domains as possible. Current architectures, however, cannot be applied beyond a small set of stereotyped settings, as they bake in domain&task assumptions or scale poorly to large inputs or outputs. In this work, we propose Perceiver IO, a general-purpose architecture that handles data from arbitrary settings while scaling linearly with the size of inputs and outputs. Our model augments the Perceiver with a flexible querying mechanism that enables outputs of various sizes and semantics, doing away with the need for task-specific architecture engineering. The same architecture achieves strong results on tasks spanning natural language and visual understanding, multi-task and multi-modal reasoning, and StarCraft II. As highlights, Perceiver IO outperforms a Transformer-based BERT baseline on the GLUE language benchmark despite removing input tokenization and achieves state-of-the-art performance on Sintel optical flow estimation with no explicit mechanisms for multiscale correspondence.
Layered Double Hydroxides: New Technology in Phosphate Fertilizers Based on Nanostructured Materials

Layered Double Hydroxide (LDH) intercalated with phosphate ions (LDH-phosphate) was synthesized by ion-exchange method from a precursor containing nitrate ions between the layers. The materials were characterized by X-ray diffraction (XRD), attenuated total reflectance–Fourier transform infrared spectroscopy (ATR-FTIR), thermogravimetric analysis coupled to differential scanning calorimetry and mass spectrometry (TGA-DSC-MS), specific surface area (BET), scanning electron microscopy (SEM), and elemental analysis. We hypothesized that LDH-phosphate can be used as a slow release fertilizer and help increase phosphate fertilization efficiency in tropical weathered soils. This new fertilizer technology was tested in a kinetic study of P release and a bioassay with controlled conditions of light, humidity, and temperature using maize (Zea mays) as our indicator plant. The bioassay was performed using an adaptation of the Neubauer method, wherein the LDH-phosphate was compared to the commercial triple superphos.
A Second Planet Transiting LTT 1445A and a Determination of the Masses of Both Worlds

LTT 1445 is a hierarchical triple M-dwarf star system located at a distance of 6.86 pc. The primary star LTT 1445A (0.257 M ⊙) is known to host the transiting planet LTT 1445Ab with an orbital period of 5.36 days, making it the second-closest known transiting exoplanet system, and the closest one for which the host is an M dwarf. Using Transiting Exoplanet Survey Satellite data, we present the discovery of a second planet in the LTT 1445 system, with an orbital period of 3.12 days. We combine radial-velocity measurements obtained from the five spectrographs, Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations, High Accuracy Radial Velocity Planet Searcher, High-Resolution Echelle Spectrometer, MAROON-X, and Planet Finder Spectrograph to establish that the new world also orbits LTT 1445A. We determine the mass and radius of LTT 1445Ab to be 2.87 ± 0.25 M ⊕ and 1.304−0.060+0.067 R ⊕, consistent with an Earth-like composition. For the newly discovered LTT 1445Ac, we measure a mass of 1.54−0.19+0.20 M ⊕ and a minimum radius of 1.15 R ⊕, but we cannot determine the radius directly as the signal-to-noise ratio of our light curve permits both grazing and nongrazing configurations. Using MEarth photometry and ground-based spectroscopy, we establish that star C (0.161 M ⊙) is likely the source of the 1.4 day rotation period, and star B (0.215 M ⊙) has a likely rotation period of 6.7 days. We estimate a probable rotation period of 85 days for LTT 1445A. Thus, this triple M-dwarf system appears to be in a special evolutionary stage where the most massive M dwarf has spun down, the intermediate mass M dwarf is in the process of spinning down, while the least massive stellar component has not yet begun to spin down.
The fast radio burst FRB 20201124A in a star-forming region: Constraints to the progenitor and multiwavelength counterparts

We present the results of a multiwavelength campaign of FRB 20201124A, the third closest repeating fast radio burst recently localized in a nearby (z=0.0978) galaxy. Deep VLA observations led to the detection of quiescent radio emission, also marginally visible in X-rays with Chandra. Imaging at 22 GHz allowed us to resolve the source on a scale of $\gtrsim$ 1 arcsec and locate it at the position of the FRB, within an error of 0.2 arcsec. EVN and e-MERLIN observations sampled small angular scales, from 2 to 100 mas, providing tight upper limits on the presence of a compact source and evidence for diffuse radio emission. We argue that this emission is associated with enhanced star formation activity in the proximity of the FRB, corresponding to a star formation rate of $\approx 10\ {\rm M}_\odot {\rm yr}^{-1}$. The surface star formation rate at the location of FRB 20201124A is two orders of magnitude larger than typically observed in other precisely localized FRBs. Such a high SFR is indicative of this FRB source being a new-born magnetar produced from a SN explosion of a massive star progenitor. Upper limits to the X-ray counterparts of 49 radio bursts observed in our simultaneous FAST, SRT and Chandra campaign are consistent with a magnetar scenario.
The Universal Elliptic KZB Connection in Higher Level

The level $N$ elliptic KZB connection is a flat connection over the universal elliptic curve in level $N$ with its $N$-torsion sections removed. Its fiber over the point $(E,x)$ is the unipotent completion of $\pi_1(E - E[N],x)$. It was constructed by Calaque and Gonzalez. In this paper, we show that the connection underlies an admissible variation of mixed Hodge structure and that it degenerates to the cyclotomic KZ connection over the singular fibers of the compactified universal elliptic curve. These are the first steps in a larger project to compute the action of the Galois group of mixed Tate motives unramified over $\mathbb{Z}[\mathbf{\mu}_N,1/N]$ on the unipotent fundamental group of $\mathbb{P}^1 - \{0,\mathbf{\mu}_N,\infty\}$ and to better understand Goncharov's higher cyclotomy.
Integrated Photometry of Multiple Stellar Populations in Globular Clusters

Evidence that multiple populations (MPs) are common properties of globular clusters (GCs) has accumulated over the past decades from clusters in the Milky Way and in its satellites. This finding has revived research into GCs, and suggested that their formation at high redshift must have been a much more complex phenomenon than imagined before. However, most information on MPs is limited to nearby GCs. The main limitation is that most studies of MPs rely on resolved stars, posing a major challenge to the investigation of the MP phenomenon in distant galaxies. Here we search for integrated colors of old GCs that are sensitive to the MP phenomenon. To do this, we exploit integrated magnitudes of simulated GCs with MPs, and multiband Hubble Space Telescope photometry of 56 Galactic GCs, where MPs are widely studied, and characterized as part of the UV Legacy Survey of Galactic GCs. We find that both integrated C F275W,F336W,F438W and m F275W − m F814W colors strongly correlate with the iron abundance of the host GC. To second order, the pseudo two-color diagram built with these integrated colors is sensitive to the MP phenomenon. In particular, once the dependence on cluster metallicity is removed, the color residuals depend on the maximum internal helium variation within GCs and on the fraction of second-generation stars. This diagram, which we define here for Galactic GCs, has the potential to detect and characterize MPs from integrated photometry of old GCs, thus providing the possibility to extend their investigation outside the Local Group.
Time-Slicing Path-integral in Curved Space

Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them covariant with respect to nonlinear transform of variables (NTV). In this work, we construct a rigorous and covariant formulation of time-slicing path integrals for dynamics in curved space. We first establish a rigorous criterion for equivalence of time-slice Green's function (TSGF) in the continuum limit (Lemma 1). This implies the existence of infinitely many equivalent representations for time-slicing path integral. We then show that, for any dynamics with second order generator, all time-slice actions are equivalent to a Gaussian (Lemma 2). We further construct a continuous family of equivalent path-integral actions parameterized by an interpolation parameter α∈[0,1] (Lemma 3). The action generically contains term linear in Δx, whose concrete form depends on α. Finally we also establish the covariance of our path-integral formalism, by demonstrating how the action transforms under NTV. The α=0 representation of time-slice action is particularly convenient because it is Gaussian and transforms as a scalar, as long as Δx transforms according to Ito's formula.
Inference for Dependent Data with Learned Clusters

This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized by a known, observed dissimilarity measure over spatial indices. Observations are partitioned into clusters with the use of an unsupervised clustering algorithm applied to the dissimilarity measure. Once the partition into clusters is learned, a cluster-based inference procedure is applied to a statistical hypothesis testing procedure. The procedure proposed in the paper allows the number of clusters to depend on the data, which gives researchers a principled method for choosing an appropriate clustering level. The paper gives conditions under which the proposed procedure asymptotically attains correct size. A simulation study shows that the proposed procedure attains near nominal size in finite samples in a variety of statistical testing problems with dependent data.
A Novel Approach towards the Search for Gamma-ray Emission from the Northern Fermi Bubble with HAWC

The Fermi bubbles are structures observed in gamma rays at GeV energies, emanating from the central region of our galaxy and extending up to 8.5 kpc above and below the galactic plane. While initial studies showed a flat brightness across the entire structure, more recent work found a brightening at the base. We perform a template-based search for TeV signals from the northern Fermi bubble and just from the base of it in data from the High AltitudeWater Cherenkov (HAWC) gamma-ray observatory. We employ a profile likelihood approach to calculate the significance and flux from the search regions. With no significant signal from the northern Fermi bubble and its base, we report new upper limits on the integral flux at 95% confidence level. Our integral flux upper limits for the northern Fermi bubble are more constraining than the previous limits reported by HAWC. Moreover, we present, for the first time, TeV limits pertaining to the base of the bubble which constitutes a more fair comparison to Fermi Large Area Telescope data points close to this particular region.
DPT: Deformable Patch-based Transformer for Visual Recognition

Transformer has achieved great success in computer vision, while how to split patches in an image remains a problem. Existing methods usually use a fixed-size patch embedding which might destroy the semantics of objects. To address this problem, we propose a new Deformable Patch (DePatch) module which learns to adaptively split the images into patches with different positions and scales in a data-driven way rather than using predefined fixed patches. In this way, our method can well preserve the semantics in patches. The DePatch module can work as a plug-and-play module, which can easily be incorporated into different transformers to achieve an end-to-end training. We term this DePatch-embedded transformer as Deformable Patch-based Transformer (DPT) and conduct extensive evaluations of DPT on image classification and object detection. Results show DPT can achieve 81.8% top-1 accuracy on ImageNet classification, and 43.7% box AP with RetinaNet, 44.3% with Mask R-CNN on MSCOCO object detection. Code has been made available at: https://github.com/CASIA-IVA-Lab/DPT.
Tiny Machine Learning for Concept Drift

Tiny machine learning (TML) is a new research area whose goal is to design machine and deep learning (DL) techniques able to operate in embedded systems and the Internet-of-Things (IoT) units, hence satisfying the severe technological constraints on memory, computation, and energy characterizing these pervasive devices. Interestingly, the related literature mainly focused on reducing the computational and memory demand of the inference phase of machine and deep learning models. At the same time, the training is typically assumed to be carried out in cloud or edge computing systems (due to the larger memory and computational requirements). This assumption results in TML solutions that might become obsolete when the process generating the data is affected by concept drift (e.g., due to periodicity or seasonality effect, faults or malfunctioning affecting sensors or actuators, or changes in the users' behavior), a common situation in real-world application scenarios. For the first time in the literature, this article introduces a TML for concept drift (TML-CD) solution based on deep learning feature extractors and a k -nearest neighbors ( k -NNs) classifier integrating a hybrid adaptation module able to deal with concept drift affecting the data-generating process. This adaptation module continuously updates (in a passive way) the knowledge base of TML-CD and, at the same time, employs a change detection test (CDT) to inspect for changes (in an active way) to quickly adapt to concept drift by removing obsolete knowledge. Experimental results on both image and audio benchmarks show the effectiveness of the proposed solution, whilst the porting of TML-CD on three off-the-shelf micro-controller units (MCUs) shows the feasibility of what is proposed in real-world pervasive systems.
Binary evolution pathways of blue large-amplitude pulsators

Blue large-amplitude pulsators (BLAPs) are a recently discovered class of pulsating star, believed to be proto-white dwarfs, produced by mass stripping of a red giant when it has a small helium core. An outstanding question is why the stars in this class of pulsator seem to form two distinct groups by surface gravity, despite predictions that stars in the gap between them should also pulsate. We use a binary population synthesis model to identify potential evolutionary pathways that a star can take to become a BLAP. We find that BLAPs can be produced either through common envelope evolution or through Roche lobe overflow, with a main-sequence star or an evolved compact object being responsible for the envelope stripping. The mass distribution of the inferred population indicates that fewer stars would be expected in the range of masses intermediate to the two known groups of pulsators, suggesting that the lack of observational discoveries in this region may be a result of the underlying population of pre-white dwarf stars. We also consider metallicity variation and find evidence that BLAPs at Z = 0.010 (half-solar) would be pulsationally unstable and may also be more common. Based on this analysis, we expect the Milky Way to host around 12 000 BLAPs and we predict the number density of sources expected in future observations such as the Legacy Survey of Space and Time at the Vera Rubin Observatory.