Miracle-dz/UniFAR-FTUs huggingface dataset:
A Simple Approximation Method for the Fisher–Rao Distance between Multivariate Normal Distributions

We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby normal distributions on the curves by the square roots of their Jeffreys divergences. We consider experimentally the linear interpolation curves in the ordinary, natural, and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller’s isometric embedding of the Fisher–Rao d-variate normal manifold into the cone of (d+1)×(d+1) symmetric positive–definite matrices. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information–geometric properties of Calvo and Oller’s isometric embedding.
Evaluating and Improving the Coreference Capabilities of Machine Translation Models

Machine translation (MT) requires a wide range of linguistic capabilities, which current end-to-end models are expected to learn implicitly by observing aligned sentences in bilingual corpora.In this work, we ask: {emph{How well MT models learn coreference resolution via implicit signal? } To answer this question, we develop an evaluation methodology that derives coreference clusters from MT output and evaluates them without requiring annotations in the target language.Following, we evaluate several prominent open-source and commercial MT systems, translating from English to six target languages, and compare them to state-of-the-art coreference resolvers on three challenging benchmarks.Our results show that the monolingual resolvers greatly outperform MT models. Motivated by this result, we experiment with different methods for incorporating the output of coreference resolution models in MT, showing improvement over strong baselines.
Temporal Graph Neural Networks for Irregular Data

This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is achieved by introducing a time-continuous latent state in each node, following a linear Ordinary Differential Equation (ODE) defined by the output of a Gated Recurrent Unit (GRU). The ODE has an explicit solution as a combination of exponential decay and periodic dynamics. Observations in the graph neighborhood are taken into account by integrating graph neural network layers in both the GRU state update and predictive model. The time-continuous dynamics additionally enable the model to make predictions at arbitrary time steps. We propose a loss function that leverages this and allows for training the model for forecasting over different time horizons. Experiments on simulated data and real-world data from traffic and climate modeling validate the usefulness of both the graph structure and time-continuous dynamics in settings with irregular observations.
Measuring magnetic fields of early-type stars with $\vec{FORS{\it 1}}$ at the $\vec{VLT}$

This paper describes an experiment aimed at evaluating the capability of the FORS1 instrument at the VLT for measuring weak ('0.1%) Zeeman circular polarization signatures in stellar H Balmer lines. We have obtained low-resolution polarized spectra at 3500{5800 A of two bright A-type stars, HD 94660, and HD 96441. The former is a well known magnetic star, the latter an apparently non-magnetic, unpolarized star that was observed for comparison purposes. In order to test the possibility of performing multi-object spectropolarimetric measurements (e.g., for cluster studies), observations were taken both on-axis (i.e., at the CCD eld center) and o-axis (i.e., at the edges of the CCD). In HD 94660 (the magnetic star), we detected a clear signal of circular polarization in all observed hydrogen Balmer lines (i.e., from H to the Balmer limit), with a typical peak-to-peak amplitude of about 0.8%. From the analysis of Stokes V under the weak-eld approximation, we have estimated a mean longitudinal eld of 2085 85 G, a value fully consistent with previous studies of this star. Notably, we found that at wavelengths shorter than about 4100 A, the polarization signal detected o-axis is about 20{30% smaller than that detected on-axis. No polarization due to the Zeeman eect was detected in the comparison star HD 96441, and we estimate that the contribution due to instrumental circular polarization is limited to the order of 0:01%. This experiment demonstrates the eectiveness of FORS1 at the VLT as a tool for high-sensitivity diagnosis of the magnetic eld in upper main sequence stars, providing the potential for measuring elds in fainter and more rapidly rotating stars than has previously been possible.
Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations

We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via infinite-dimensional banded matrix factorizations and may be used to compute the modified Jacobi matrices all in linear complexity with respect to the truncation degree. A family of orthogonal polynomials with modified classical weights is constructed that support banded differentiation matrices, enabling sparse spectral methods with modified classical orthogonal polynomials.
Formality of hypercommutative algebras of K\"ahler and Calabi-Yau manifolds

Any Batalin-Vilkovisky algebra with a homotopy trivialization of the BV-operator gives rise to a hypercommutative algebra structure at the cochain level which, in general, contains more homotopical information than the hypercommutative algebra introduced by Barannikov and Kontsevich on cohomology. In this paper, we use the purity of mixed Hodge structures to show that the canonical hypercommutative algebra defined on any compact Calabi-Yau manifold is formal. We also study related hypercommutative algebras associated to compact K\"ahler and Hermitian manifolds.
Learning to Initialize: Can Meta Learning Improve Cross-task Generalization in Prompt Tuning?

Prompt tuning (PT) which only tunes the embeddings of an additional sequence of tokens per task, keeping the pre-trained language model (PLM) frozen, has shown remarkable performance in few-shot learning. Despite this, PT has been shown to rely heavily on good initialization of the prompt embeddings. In this work, we study meta prompt tuning (MPT) to systematically explore how meta-learning can help improve (if it can) cross-task generalization in PT through learning to initialize the prompt embeddings from other relevant tasks. We empirically analyze a representative set of meta learning algorithms in a wide range of adaptation settings with different source/target task configurations on a large set of few-shot tasks. With extensive experiments and analysis, we demonstrate the effectiveness of MPT. We find the improvement to be significant particularly on classification tasks. For other kinds of tasks such as question answering, we observe that while MPT can outperform PT in most cases, it does not always outperform multi-task learning. We further provide an in-depth analysis from the perspective of task similarity.
Masking and Mixing Adversarial Training

While convolutional neural networks (CNNs) have achieved excellent performances in various computer vision tasks, they often misclassify with malicious samples, a.k. a. adversarial examples. Adversarial training is a popular and straightforward technique to defend against the threat of adversarial examples. Unfortunately, CNNs must sacrifice the accuracy of standard samples to improve robustness against adversarial examples when adversarial training is used. In this work, we propose Masking and Mixing Adversarial Training (M2AT) to mitigate the trade-off between accuracy and robustness. We focus on creating diverse adversarial examples during training. Specifically, our approach consists of two processes: 1) masking a perturbation with a binary mask and 2) mixing two partially perturbed images. Experimental results on CIFAR-10 dataset demonstrate that our method achieves better robustness against several adversarial attacks than previous methods.
Predicting Gender and Political Affiliation Using Mobile Payment Data

We explore the understudied area of social payments to evaluate whether or not we can predict the gender and political affiliation of Venmo users based on the content of their Venmo transactions. Latent attribute detection has been successfully applied in the domain of studying social media. However, there remains a dearth of previous work using data other than Twitter. There is also a continued need for studies which explore mobile payments spaces like Venmo, which remain understudied due to the lack of data access. We hypothesize that using methods similar to latent attribute analysis with Twitter data, machine learning algorithms will be able to predict gender and political affiliation of Venmo users with a moderate degree of accuracy. We collected crowdsourced training data that correlates participants' political views with their public Venmo transaction history through the paid Prolific service. Additionally, we collected 21 million public Venmo transactions from recently active users to use for gender classification. We then ran the collected data through a TF-IDF vectorizer and used that to train a support vector machine (SVM). After hyperparameter training and additional feature engineering, we were able to predict user's gender with a high level of accuracy (.91) and had modest success predicting user's political orientation (.63).
Product Question Answering in E-Commerce: A Survey

Product question answering (PQA), aiming to automatically provide instant responses to customer’s questions in E-Commerce platforms, has drawn increasing attention in recent years. Compared with typical QA problems, PQA exhibits unique challenges such as the subjectivity and reliability of user-generated contents in E-commerce platforms. Therefore, various problem settings and novel methods have been proposed to capture these special characteristics. In this paper, we aim to systematically review existing research efforts on PQA. Specifically, we categorize PQA studies into four problem settings in terms of the form of provided answers. We analyze the pros and cons, as well as present existing datasets and evaluation protocols for each setting. We further summarize the most significant challenges that characterize PQA from general QA applications and discuss their corresponding solutions. Finally, we conclude this paper by providing the prospect on several future directions.
3D-aware Conditional Image Synthesis

We propose pix2pix3D, a 3D-aware conditional generative model for controllable photorealistic image synthesis. Given a 2D label map, such as a segmentation or edge map, our model learns to synthesize a corresponding image from different viewpoints. To enable explicit 3D user control, we extend conditional generative models with neural radiance fields. Given widely-available posed monocular image and label map pairs, our model learns to assign a label to every 3D point in addition to color and density, which enables it to render the image and pixel-aligned label map simultaneously. Finally, we build an interactive system that allows users to edit the label map from different viewpoints and generate outputs accordingly.
Adaptive Selective Sampling for Online Prediction with Experts

We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard procedures, while still retaining optimal worst-case regret guarantees. These algorithms are based on exponentially weighted forecasters, suitable for settings with and without a perfect expert. For a scenario where one expert is strictly better than the others in expectation, we show that the label complexity of the label-efficient forecaster scales roughly as the square root of the number of rounds. Finally, we present numerical experiments empirically showing that the normalized regret of the label-efficient forecaster can asymptotically match known minimax rates for pool-based active learning, suggesting it can optimally adapt to benign settings.
A Composite Perspective of the Extratropical Flow Response to Recurving Western North Pacific Tropical Cyclones

AbstractThis study investigates the composite extratropical flow response to recurving western North Pacific tropical cyclones (WNP TCs), and the dependence of this response on the strength of the TC–extratropical flow interaction as defined by the negative potential vorticity advection (PV) by the irrotational wind associated with the TC. The 2.5° NCEP–NCAR reanalysis is used to construct composite analyses of all 1979–2009 recurving WNP TCs and of subsets that undergo strong and weak TC–extratropical flow interactions.Findings indicate that recurving WNP TCs are associated with the amplification of a preexisting Rossby wave train (RWT) that disperses downstream and modifies the large-scale flow pattern over North America. This RWT affects approximately 240° of longitude and persists for approximately 10 days. Recurving TCs associated with strong TC–extratropical flow interactions are associated with a stronger extratropical flow response than those associated with weak TC–extratropical flow interactions.
MC-finiteness of restricted set partition functions

A sequence $s(n)$ of integers is MC-finite if for every $m \in \mathbb{N}^+$ the sequence $s^m(n) = s(n) \bmod{m}$ is ultimately periodic. We discuss various ways of proving and disproving MC-finiteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.
Super-Efficient Prediction Based on High-Quality Marker Information

Abstract Nielsen (1999) showed the surprising fact that a nonparametric one-dimensional hazard as a function of time can be estimated -consistently if a high quality marker is observed. In this paper we show that the hazard relevant for predicting remaining duration time, given the current status of a high quality marker, can be estimated -consistently if a Markov type property holds for the high quality marker.
Text-driven Visual Synthesis with Latent Diffusion Prior

There has been tremendous progress in large-scale text-to-image synthesis driven by diffusion models enabling versatile downstream applications such as 3D object synthesis from texts, image editing, and customized generation. We present a generic approach using latent diffusion models as powerful image priors for various visual synthesis tasks. Existing methods that utilize such priors fail to use these models' full capabilities. To improve this, our core ideas are 1) a feature matching loss between features from different layers of the decoder to provide detailed guidance and 2) a KL divergence loss to regularize the predicted latent features and stabilize the training. We demonstrate the efficacy of our approach on three different applications, text-to-3D, StyleGAN adaptation, and layered image editing. Extensive results show our method compares favorably against baselines.
A weighted subspace exponential kernel for support tensor machines

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been proposed. However, what decisive features of the tensors are exploited by these kernels is often unclear. In this paper we propose a novel kernel that is based on the Tucker decomposition. For this kernel the Tucker factors are computed based on re-weighting of the Tucker matrices with tuneable powers of singular values from the HOSVD decomposition. This provides a mechanism to balance the contribution of the Tucker core and factors of the data. We benchmark support tensor machines with this new kernel on several datasets. First we generate synthetic data where two classes differ in either Tucker factors or core, and compare our novel and previously existing kernels. We show robustness of the new kernel with respect to both classification scenarios. We further test the new method on real-world datasets. The proposed kernel has demonstrated a higher test accuracy than the state-of-the-art tensor train multi-way multi-level kernel, and a significantly lower computational time.
Prompt Tuning of Deep Neural Networks for Speaker-adaptive Visual Speech Recognition

Visual Speech Recognition (VSR) aims to infer speech into text depending on lip movements alone. As it focuses on visual information to model the speech, its performance is inherently sensitive to personal lip appearances and movements, and this makes the VSR models show degraded performance when they are applied to unseen speakers. In this paper, to remedy the performance degradation of the VSR model on unseen speakers, we propose prompt tuning methods of Deep Neural Networks (DNNs) for speaker-adaptive VSR. Specifically, motivated by recent advances in Natural Language Processing (NLP), we finetune prompts on adaptation data of target speakers instead of modifying the pre-trained model parameters. Different from the previous prompt tuning methods mainly limited to Transformer variant architecture, we explore different types of prompts, the addition, the padding, and the concatenation form prompts that can be applied to the VSR model which is composed of CNN and Transformer in general. With the proposed prompt tuning, we show that the performance of the pre-trained VSR model on unseen speakers can be largely improved by using a small amount of adaptation data (e.g., less than 5 minutes), even if the pre-trained model is already developed with large speaker variations. Moreover, by analyzing the performance and parameters of different types of prompts, we investigate when the prompt tuning is preferred over the finetuning methods. The effectiveness of the proposed method is evaluated on both word- and sentence-level VSR databases, LRW-ID and GRID.
Revisiting the Slichter mode of Mercury in the context of differentiated models

We revisit the Slichter mode of a set of differentiated Mercury models that were considered previously. We apply a different and independent formalism, based on variational principles of mechanics, to analytically model the internal translations of a body with a global internal perfect fluid layer limited by two differentiated rigid solid constituents that have a spherical symmetric mass distribution. The Slichter mode is specified by providing the time evolution of the barycenters of the solid constituents, the amplitude ratio of the mantle to the inner core, and the period of the oscillatory motion. All these parameters only depend on the mass of the body, the mass of the inner core, the density of the fluid, and the mean density of the inner core. For previously developed Mercury models we find, in contrast to other results, that there are no discontinuities in the Slichter period when passing from undifferentiated to differentiated inner cores. Hence, in a general situation, a potential detection of the Slichter mode cannot determine the differentiation of the inner core. We also find that the BepiColombo mission may be able to detect the Slichter mode caused by an impactor meteroid with a mass of about 1012 kg in the most favorable of circumstances. This shows that a measurable excitation of the mode by this mechanism is even more unlikely than was previously established, where a mass about 1010 kg was found.
Comparing Information Content of Upwelling Far-Infrared and Midinfrared Radiance Spectra for Clear Atmosphere Profiling

AbstractThe information content of high-spectral-resolution midinfrared (MIR; 650–2300 cm−1) and far-infrared (FIR; 200–685 cm−1) upwelling radiance spectra is calculated for clear-sky temperature and water vapor profiles. The wavenumber ranges of the two spectral bands overlap at the central absorption line in the CO2 ν2 absorption band, and each contains one side of the full absorption band. Each spectral band also includes a water vapor absorption band; the MIR contains the first vibrational–rotational absorption band, while the FIR contains the rotational absorption band. The upwelling spectral radiances are simulated with the line-by-line radiative transfer model (LBLRTM), and the retrievals and information content analysis are computed using standard optimal estimation techniques. Perturbations in the surface temperature and in the trace gases methane, ozone, and nitrous oxide (CH4, O3, and N2O) are introduced to represent forward-model errors. Each spectrum is observed by a simulated infrared spect.
Optimal adaptive control of uncertain stochastic linear systems

The problem of optimal control of stochastic linear time-invariant uncertain systems on finite time interval is formulated and solved. This optimal solution shows that previously published adaptive optimal control schemes and indirect adaptive control schemes do not need heuristics for their rationalization. It is shown that these schemes are suboptimal causal approximations of the optimal solution. The solution is achieved by the introduction of the state and parameters observability form (SPOF). This new canonical representation of linear time-invariant systems enables direct application of the existing LQR-LQG theory of control and estimation of discrete linear time-varying systems. The optimal solution is exact and non causal. It is composed of the a linear time varying optimal estimator of the augmented state composed of the state of the system and the parameters, and of the optimal LQR controller. The estimator is causal. The controller is non-causal. As causal approximation control schemes based on the SPOF and the certainty equivalence principle and separation theorems are presented.
Characterizations of right Nakayama rings

We have studied relationships between almost relative projectivity and Nakayamaings [8]. In this paper we shall further investigate certain characterizations of right Nakayama rings in terms of almost relative projectives (or injectives). We shall consider three conditions (A), (B) and (C) (see Section 1), which are always satisfied for the relative projective modules, but not for almost relative projectives in general. As an application of [9, Theorem] and [10, Theorem 2], we shall show that a right artinian ring is right Nakayama if and only if one of the above three conditions holds true for almost relative projectives (Corollary to Theorem 1). Moreover we shall give a characterization of two-sided Nakayama rings related to (C) and the dual (C#) (Theorem 2). Finally we shall investigate the transitivity of almost relative projectives, which is the converse of (B), and give some characterizations of right Nakayama rings related to the transitivity.