Miracle-dz/UniFAR-FTUs huggingface dataset:
General order adjusted Edgeworth expansions for generalized $t$-tests

We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted Edgeworth expansions that allow polynomials in the terms to depend on a sample size in a specific way and prove their validity. Provided results up to 5th order include one and two-sample ordinary $t$-statistics with biased and unbiased variance estimators, Welch $t$-test, and moderated $t$-statistics based on empirical Bayes method, as well as general results for any statistic with available moments of the sampling distribution. These results are included in a software package that aims to reach a broad community of researchers and serve to improve inference in a wide variety of analytical procedures; practical considerations of using such expansions are discussed.
Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene

A two-dimensional electron system placed in a magnetic field develops Landau levels, where strong Coulomb interactions lead to the appearance of many-body correlated ground states. Quantum numbers similar to the electron spin enable the understanding and control of complex ground state order and collective excitations. Owing to its spin, valley and orbital degrees of freedom, Bernal-stacked bilayer graphene offers a rich platform to pursue correlated phenomena in two dimensions. In this work, we fabricate dual-gated Bernal-stacked bilayer graphene devices and demonstrate unprecedented fine control over its valley isospin degrees of freedom using a perpendicular electric field. Higher sample quality enables us to probe regimes obscured by disorder in previous studies. We present evidence for a new even-denominator fractional quantum Hall state at filling factor {\nu} = 5/2. The 5/2 state is found to be spontaneously valley polarized in the limit of vanishing valley Zeeman splitting, consistent with a theoretical prediction made regarding the spin polarization of the Moore-Read state. In the vicinity of the even-denominator fractional quantum Hall states, we observe the appearance of the predicted Levin-Halperin daughter states of the Moore-Read Pfaffian wave function at {\nu}= 3/2, 7/2, and -1/2 and of the anti-Pfaffian at {\nu}= 5/2. These observations suggest the breaking of particle-hole symmetry in bilayer graphene. We construct a comprehensive valley polarization phase diagram for the Jain sequence fractional states surrounding filling factor 3/2. These results are well explained by a two-component composite fermion model, further demonstrating the SU(2) nature of the valley isospin in bilayer graphene. Our experiment paves the path for future efforts of manipulating the valley isospin in bilayer graphene to engineer exotic topological orders and quantum information processes.
Are Convolutional Neural Networks or Transformers more like human vision?

Modern machine learning models for computer vision exceed humans in accuracy on specific visual recognition tasks, notably on datasets like ImageNet. However, high accuracy can be achieved in many ways. The particular decision function found by a machine learning system is determined not only by the data to which the system is exposed, but also the inductive biases of the model, which are typically harder to characterize. In this work, we follow a recent trend of in-depth behavioral analyses of neural network models that go beyond accuracy as an evaluation metric by looking at patterns of errors. Our focus is on comparing a suite of standard Convolutional Neural Networks (CNNs) and a recently-proposed attention-based network, the Vision Transformer (ViT), which relaxes the translation-invariance constraint of CNNs and therefore represents a model with a weaker set of inductive biases. Attention-based networks have previously been shown to achieve higher accuracy than CNNs on vision tasks, and we demonstrate, using new metrics for examining error consistency with more granularity, that their errors are also more consistent with those of humans. These results have implications both for building more human-like vision models, as well as for understanding visual object recognition in humans.
Rethinking the Design Principles of Robust Vision Transformer

Recent advances on Vision Transformers (ViT) have shown that self-attention-based networks, which take advantage of long-range dependencies modeling ability, sur-passed traditional convolution neural networks (CNNs) in most vision tasks. To further expand the applicability for computer vision, many improved variants are proposed to re-design the Transformer architecture by considering the superiority of CNNs, i.e., locality, translation invariance, for better performance. However, these methods only consider the standard accuracy or computation cost of the model. In this paper, we rethink the design principles of ViTs based on the robustness. We found some design components greatly harm the robustness and generalization ability of ViTs while some others are beneﬁcial. By combining the robust design components, we propose Robust Vision Transformer (RVT) . RVT is a new vision transformer, which has superior performance and strong robustness. We further propose two new plug-and-play techniques called position-aware attention rescaling and patch-wise augmentation to train our RVT. The experimental results on Ima-geNet and six robustness benchmarks show the advanced robustness and generalization ability of RVT compared with previous Transformers and state-of-the-art CNNs. Our RVT-S ∗ also achieves Top-1 rank on multiple robustness leaderboards including ImageNet-C and ImageNet-Sketch. The code will be available at https://github.com/ vtddggg/Robust-Vision-Transformer .
In Congestion Games, Taxes Achieve Optimal Approximation

We consider the problem of minimizing social cost in atomic congestion games and show, perhaps surprisingly, that efficiently computed taxation mechanisms yield the same performance achievable by the best polynomial time algorithm, even when the latter has full control over the players' actions. It follows that no other tractable approach geared at incentivizing desirable system behavior can improve upon this result, regardless of whether it is based on taxations, coordination mechanisms, information provision, or any other principle. Three technical contributions underpin this conclusion. First, we show that computing the minimum social cost is NP-hard to approximate within a given factor depending solely on the admissible resource costs. Second, we design a tractable taxation mechanism whose efficiency (price of anarchy) matches this hardness factor, and thus is optimal. As these results extend to coarse correlated equilibria, any no-regret algorithm inherits the same performances, allowing us to devise polynomial time algorithms with optimal approximation.
Pairwise interactions of ring dark solitons with vortices and other rings: Stationary states, stability features, and nonlinear dynamics

Wenlong Wang,1, ∗ Theodore Kolokolnikov,2 D. J. Frantzeskakis,3 R. Carretero-González,4 and P. G. Kevrekidis5, † College of Physics, Sichuan University, Chengdu 610065, China Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 15784 Athens, Greece Nonlinear Dynamical Systems Group,‡ Computational Sciences Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515 USA
Decimations for two-dimensional Ising and rotator models

We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range as well as vector-spin interactions. Our main tools consist in a two-dimensional use of “equivalence of boundary conditions” in the long-range case and an extension of global specifications for two-dimensional vector spins.
The Main Asteroid Belt: The Primary Source of Debris on Comet-like Orbits

Jupiter-family comets (JFCs) contribute a significant amount of debris to near-Earth space. However, telescopic observations of these objects seem to suggest that they have short physical lifetimes. If this is true, the material generated will also be short-lived, but fireball observation networks still detect material on cometary orbits. This study examines centimeter-to-meter-scale sporadic meteoroids detected by the Desert Fireball Network from 2014 to 2020 originating from JFC-like orbits. Analyzing each event’s dynamic history and physical characteristics, we confidently determined whether they originated from the main asteroid belt or the trans-Neptunian region. Our results indicate that <4% of sporadic meteoroids on JFC-like orbits are genetically cometary. This observation is statistically significant and shows that cometary material is too friable to survive in near-Earth space. Even when considering shower contributions, meteoroids on JFC-like orbits are primarily from the main belt. Thus, the presence of genuine cometary meteorites in terrestrial collections is highly unlikely.
Explicit Superlinear Convergence Rates of The SR1 Algorithm

We study the convergence rate of the famous Symmetric Rank-1 (SR1) algorithm which has wide applications in different scenarios. Although it has been extensively investigated, SR1 still lacks a non-asymptotic superlinear rate compared with other quasi-Newton methods such as DFP and BFGS. In this paper we address this problem. Inspired by the recent work on explicit convergence analysis of quasi-Newton methods, we obtain the first explicit non-asymptotic rates of superlinear convergence for the vanilla SR1 methods with correction strategy to achieve the numerical stability. Specifically, the vanilla SR1 with the correction strategy achieves the rates of the form $\left(\frac{4n\ln(e\kappa) }{k}\right)^{k/2}$ for general smooth strongly-convex functions where $k$ is the iteration counter, $\kappa$ is the condition number of the objective function and $n$ is the dimension of the problem. For the quadratic function, the vanilla SR1 algorithm can find the optima of the objective function at most $n$ steps.
Large-Scale Unsupervised Person Re-Identification with Contrastive Learning

Existing public person Re-Identification~(ReID) datasets are small in modern terms because of labeling difficulty. Although unlabeled surveillance video is abundant and relatively easy to obtain, it is unclear how to leverage these footage to learn meaningful ReID representations. In particular, most existing unsupervised and domain adaptation ReID methods utilize only the public datasets in their experiments, with labels removed. In addition, due to small data sizes, these methods usually rely on fine tuning by the unlabeled training data in the testing domain to achieve good performance. Inspired by the recent progress of large-scale self-supervised image classification using contrastive learning, we propose to learn ReID representation from large-scale unlabeled surveillance video alone. Assisted by off-the-shelf pedestrian detection tools, we apply the contrastive loss at both the image and the tracklet levels. Together with a principal component analysis step using camera labels freely available, our evaluation using a large-scale unlabeled dataset shows far superior performance among unsupervised methods that do not use any training data in the testing domain. Furthermore, the accuracy improves with the data size and therefore our method has great potential with even larger and more diversified datasets.
Can self-training identify suspicious ugly duckling lesions?

One commonly used clinical approach towards detecting melanomas recognises the existence of Ugly Duckling nevi, or skin lesions which look different to the other lesions on the same patient. An automatic method of detecting and analysing these lesions would help to standardize studies, compared with manual screening methods. However, it is difficult to obtain expertly-labelled images for ugly duckling lesions. We therefore propose to use self-supervised machine learning to automatically detect outlier lesions. We first automatically detect and extract all the lesions from a wide-field skin image, and calculate an embedding for each detected lesion in a patient image, based on automatically identified features. These embeddings are then used to calculate the L2 distances as a way to measure dissimilarity. Using this deep learning method, Ugly Ducklings are identified as outliers which should deserve more attention from the examining physician. We evaluate through comparison with dermatologists, and achieve a sensitivity rate of 72.1% and diagnostic accuracy of 94.2% on the held-out test set.
Data-Driven Reachability Analysis From Noisy Data

We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and, under the assumption of Lipschitz continuity, to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and comparisons are made between algorithms.
On Achievable Rates of Line Networks with Generalized Batched Network Coding

To better understand the wireless network design with a large number of hops, we investigate a line network formed by general discrete memoryless channels (DMCs), which may not be identical. Our focus lies on Generalized Batched Network Coding (GBNC) that encompasses most existing schemes as special cases and achieves the min-cut upper bounds as the parameters batch size and inner block length tend to infinity. The inner blocklength of GBNC provides upper bounds on the required latency and buffer size at intermediate network nodes. By employing a bottleneck status technique, we derive new upper bounds on the achievable rates of GBNCs These bounds surpass the min-cut bound for large network lengths when the inner blocklength and batch size are small. For line networks of canonical channels, certain upper bounds hold even with relaxed inner blocklength constraints. Additionally, we employ a channel reduction technique to generalize the existing achievability results for line networks with identical DMCs to networks with non-identical DMCs. For line networks with packet erasure channels, we make refinement in both the upper bound and the coding scheme, and showcase their proximity through numerical evaluations.
Vision Transformers are Robust Learners

Transformers, composed of multiple self-attention layers, hold strong promises toward a generic learning primitive applicable to different data modalities, including the recent breakthroughs in computer vision achieving state-of-the-art (SOTA) standard accuracy. What remains largely unexplored is their robustness evaluation and attribution. In this work, we study the robustness of the Vision Transformer (ViT) (Dosovitskiy et al. 2021) against common corruptions and perturbations, distribution shifts, and natural adversarial examples. We use six different diverse ImageNet datasets concerning robust classification to conduct a comprehensive performance comparison of ViT(Dosovitskiy et al. 2021) models and SOTA convolutional neural networks (CNNs), Big-Transfer (Kolesnikov et al. 2020). Through a series of six systematically designed experiments, we then present analyses that provide both quantitative andqualitative indications to explain why ViTs are indeed more robust learners. For example, with fewer parameters and similar dataset and pre-training combinations, ViT gives a top-1accuracy of 28.10% on ImageNet-A which is 4.3x higher than a comparable variant of BiT. Our analyses on image masking, Fourier spectrum sensitivity, and spread on discrete cosine energy spectrum reveal intriguing properties of ViT attributing to improved robustness. Code for reproducing our experiments is available at https://git.io/J3VO0.
Stationary Discounted and Ergodic Mean Field Games of Singular Control

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove existence and uniqueness of the mean field equilibria, which are completely characterized through nonlinear equations. Furthermore, we relate the mean field equilibria for the discounted and the ergodic games by showing the validity of an Abelian limit. The latter allows also to approximate Nash equilibria of - so far unexplored - symmetric N-player ergodic singular control games through the mean field equilibrium of the discounted game. Numerical examples finally illustrate in a case study the dependency of the mean field equilibria with respect to the parameters of the games.
LocalNewton: Reducing Communication Bottleneck for Distributed Learning

To address the communication bottleneck problem in distributed optimization within a master-worker framework, we propose LocalNewton, a distributed second-order algorithm with local averaging. In LocalNewton, the worker machines update their model in every iteration by finding a suitable second-order descent direction using only the data and model stored in their own local memory. We let the workers run multiple such iterations locally and communicate the models to the master node only once every few (say L) iterations. LocalNewton is highly practical since it requires only one hyperparameter, the number L of local iterations. We use novel matrix concentration-based techniques to obtain theoretical guarantees for LocalNewton, and we validate them with detailed empirical evaluation. To enhance practicability, we devise an adaptive scheme to choose L, and we show that this reduces the number of local iterations in worker machines between two model synchronizations as the training proceeds, successively refining the model quality at the master. Via extensive experiments using several real-world datasets with AWS Lambda workers and an AWS EC2 master, we show that LocalNewton requires fewer than 60% of the communication rounds (between master and workers) and less than 40% of the end-to-end running time, compared to state-of-the-art algorithms, to reach the same training~loss.
Measuring the User Satisfaction in a Recommendation Interface with Multiple Carousels

It is common for video-on-demand and music streaming services to adopt a user interface composed of several recommendation lists, i.e., widgets or swipeable carousels, each generated according to a specific criterion or algorithm (e.g., most recent, top popular, recommended for you, editors’ choice, etc.). Selecting the appropriate combination of carousel has significant impact on user satisfaction. A crucial aspect of this user interface is that to measure the relevance a new carousel for the user it is not sufficient to account solely for its individual quality. Instead, it should be considered that other carousels will already be present in the interface. This is not considered by traditional evaluation protocols for recommenders systems, in which each carousel is evaluated in isolation, regardless of (i) which other carousels are displayed to the user and (ii) the relative position of the carousel with respect to other carousels. Hence, we propose a two-dimensional evaluation protocol for a carousel setting that will measure the quality of a recommendation carousel based on how much it improves upon the quality of an already available set of carousels. Our evaluation protocol takes into account also the position bias, i.e., users do not explore the carousels sequentially, but rather concentrate on the top-left corner of the screen. We report experiments on the movie domain and notice that under a carousel setting the definition of which criteria has to be preferred to generate a list of recommended items changes with respect to what is commonly understood.
Nonparametric regression for locally stationary functional time series

In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a semi-metric space. Then, we propose a nonparametric model for LSFTS with a regression function that changes smoothly over time. We establish the uniform convergence rates of a class of kernel estimators, the Nadaraya-Watson (NW) estimator of the regression function, and a central limit theorem of the NW estimator.
On the Waldschmidt constant of square-free principal Borel ideals

Fix a square-free monomial m ∈ S = K[x1, . , xn]. The square-free principal Borel ideal generated by m, denoted sfBorel(m), is the ideal generated by all the square-free monomials that can be obtained via Borel moves from the monomial m. We give upper and lower bounds for the Waldschmidt constant of sfBorel(m) in terms of the support of m, and in some cases, exact values. For any rational a b ≥ 1, we show that there exists a square-free principal Borel ideal with Waldschmidt constant equal to a b .
Visual analogy: Deep learning versus compositional models

Is analogical reasoning a task that must be learned to solve from scratch by applying deep learning models to massive numbers of reasoning problems? Or are analogies solved by computing similarities between structured representations of analogs? We address this question by comparing human performance on visual analogies created using images of familiar three-dimensional objects (cars and their subregions) with the performance of alternative computational models. Human reasoners achieved above-chance accuracy for all problem types, but made more errors in several conditions (e.g., when relevant subregions were occluded). We compared human performance to that of two recent deep learning models (Siamese Network and Relation Network) directly trained to solve these analogy problems, as well as to that of a compositional model that assesses relational similarity between part-based representations. The compositional model based on part representations, but not the deep learning models, generated qualitative performance similar to that of human reasoners.