Miracle-dz/UniFAR-FTUs huggingface dataset:
A Classification of G-invariant Shallow Neural Networks

When trying to fit a deep neural network (DNN) to a $G$-invariant target function with $G$ a group, it only makes sense to constrain the DNN to be $G$-invariant as well. However, there can be many different ways to do this, thus raising the problem of ``$G$-invariant neural architecture design'': What is the optimal $G$-invariant architecture for a given problem? Before we can consider the optimization problem itself, we must understand the search space, the architectures in it, and how they relate to one another. In this paper, we take a first step towards this goal; we prove a theorem that gives a classification of all $G$-invariant single-hidden-layer or ``shallow'' neural network ($G$-SNN) architectures with ReLU activation for any finite orthogonal group $G$, and we prove a second theorem that characterizes the inclusion maps or ``network morphisms'' between the architectures that can be leveraged during neural architecture search (NAS). The proof is based on a correspondence of every $G$-SNN to a signed permutation representation of $G$ acting on the hidden neurons; the classification is equivalently given in terms of the first cohomology classes of $G$, thus admitting a topological interpretation. The $G$-SNN architectures corresponding to nontrivial cohomology classes have, to our knowledge, never been explicitly identified in the literature previously. Using a code implementation, we enumerate the $G$-SNN architectures for some example groups $G$ and visualize their structure. Finally, we prove that architectures corresponding to inequivalent cohomology classes coincide in function space only when their weight matrices are zero, and we discuss the implications of this for NAS.
Designing Policies to Make Cars Greener: A Review of the Literature

We review what is known about the economic efficiency of fuel taxes relative to efficiency standards aimed at mitigating environmental externalities from automobiles. We present a simplified model of car choice that allows us to emphasize the relationships between fuel economy, other car attributes, and miles traveled. We focus on greenhouse gas emissions, although we note how other environmental externalities affect our conclusions. Our main conclusion—that standards are substantially less efficient than a fuel tax—is already familiar. Less familiar are points we make about the relative importance of the rebound effect, on the effects of attribute-based policies, and the implications of behavioral biases. We point to areas where we believe future research can have the greatest contribution, including work on uncertainty, heterogeneity, and empirical work in low and middle-income countries.
Magnetic warping in topological insulators

We analyze the electronic structure of topological surface states in the family of magnetic topological insulators MnBi$_{2n}$Te$_{3n+1}$. We show that, at natural-cleavage surfaces, the Dirac cone warping changes its symmetry from hexagonal to trigonal at the magnetic ordering temperature. In particular, an energy splitting develops between the surface states of same band index but opposite surface momenta upon formation of the long-range magnetic order. As a consequence, measurements of such energy splittings constitute a simple protocol to detect the magnetic ordering via the surface electronic structure, alternative to the detection of the surface magnetic gap. Interestingly, while the latter signals a nonzero surface magnetic flux, the trigonal warping predicted here is, in addition, sensitive to the direction of the surface magnetic flux.
Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators

Significance Intrinsic magnetic topological insulators (MTIs) MnBi2Te4 have recently emerged as a new frontier of topological quantum materials. Theoretical predicted exotic quantum phases of its thin-film form, such as Chern and axion insulator states, both have Dirac mass gaps in their surface states. However, direct observation of the Dirac mass gap has proved challenging. Here, we report the direct observation of the Dirac mass gap. We further reveal microscopically the essential role of native magnetic antisite defects in controlling the formation of the Dirac mass gap. Our work provides unambiguous evidence of a Dirac mass gap in MnBi2Te4 thin film and identifies magnetic defects as an important parameter in designing the topological quantum material.
RankGen: Improving Text Generation with Large Ranking Models

Given an input sequence (or prefix), modern language models often assign high probabilities to output sequences that are repetitive, incoherent, or irrelevant to the prefix; as such, model-generated text also contains such artifacts. To address these issues we present RankGen, a 1.2B parameter encoder model for English that scores model generations given a prefix. RankGen can be flexibly incorporated as a scoring function in beam search and used to decode from any pretrained language model. We train RankGen using large-scale contrastive learning to map a prefix close to the ground-truth sequence that follows it and far away from two types of negatives: (1) random sequences from the same document as the prefix, and (2) sequences generated from a large language model conditioned on the prefix. Experiments across four different language models (345M-11B parameters) and two domains show that RankGen significantly outperforms decoding algorithms like nucleus, top-k, and typical sampling on both automatic metrics (85.0 vs 77.3 MAUVE) as well as human evaluations with English writers (74.5% human preference over nucleus sampling). Analysis reveals that RankGen outputs are more relevant to the prefix and improve continuity and coherence compared to baselines. We release our model checkpoints, code, and human preference data with explanations to facilitate future research.
Exact mobility edges in Aubry-Andr\'{e}-Harper models with relative phases

Mobility edge (ME), a critical energy separating localized and extended states in spectrum, is a central concept in understanding the localization physics. However, there are few models with exact MEs. In the paper, we generalize the Aubry-Andr´e-Harper model proposed in [Phys. Rev. Lett. 114 , 146601 (2015)] and recently realized in [Phys. Rev. Lett. 126 , 040603 (2021)], by introducing a relative phase in the quasiperiodic potential. Applying Avila’s global theory we analytically compute localization lengths of all single-particle states and determine the exact expression of ME, which both signiﬁcantly depend on the relative phase. They are veriﬁed by numerical simulations, and a physical perception of the exact expression is also provided. We further demonstrate that the exact expression of ME works for an even broad class of generalized Aubry-Andr´e-Harper models. Moreover, we show that the exact ME is related to the one in the dual model which has long-range hoppings.
Provably Precise, Succinct and Efficient Explanations for Decision Trees

Decision trees (DTs) embody interpretable classifiers. DTs have been advocated for deployment in high-risk applications, but also for explaining other complex classifiers. Nevertheless, recent work has demonstrated that predictions in DTs ought to be explained with rigorous approaches. Although rigorous explanations can be computed in polynomial time for DTs, their size may be beyond the cognitive limits of human decision makers. This paper investigates the computation of {\delta}-relevant sets for DTs. {\delta}-relevant sets denote explanations that are succinct and provably precise. These sets represent generalizations of rigorous explanations, which are precise with probability one, and so they enable trading off explanation size for precision. The paper proposes two logic encodings for computing smallest {\delta}-relevant sets for DTs. The paper further devises a polynomial-time algorithm for computing {\delta}-relevant sets which are not guaranteed to be subset-minimal, but for which the experiments show to be most often subset-minimal in practice. The experimental results also demonstrate the practical efficiency of computing smallest {\delta}-relevant sets.
Twist Decoding: Diverse Generators Guide Each Other

Many language generation models are now available for a wide range of generation tasks, including machine translation and summarization. Combining such diverse models may lead to further progress, but ensembling generation models is challenging during inference: conventional ensembling methods (e.g., shallow fusion) require that the models share vocabulary/tokenization schemes. We introduce Twist decoding, a simple and general text generation algorithm that benefits from diverse models at inference time. Our method does not assume the vocabulary, tokenization or even generation order is shared. Our extensive evaluations on machine translation and scientific paper summarization demonstrate that Twist decoding substantially outperforms each model decoded in isolation over various scenarios, including cases where domain-specific and general-purpose models are both available. Twist decoding also consistently outperforms the popular reranking heuristic where output candidates from one model are rescored by another. We hope that our work will encourage researchers and practitioners to examine generation models collectively, not just independently, and to seek out models with complementary strengths to the currently available models.
H\"older and Kurokawa meet Borwein--Dykshoorn and Adamchik

Following our discovery of a nice identity in a recent preprint of Hu and Kim, we show a link between the Kurokawa multiple trigonometric functions and two functions introduced respectively by Borwein-Dykshoorn and by Adamchik. In particular several identities involving ζ (3), π and the Catalan constant G that are proved in these three papers are related.
Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties

Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other and the age structure of individuals matters. In the first part of our series papers, we study the principal spectral theory of age-structured models with nonlocal diffusion of Dirichlet type. First, we provide two criteria on the existence of principal eigenvalues by using the theory of resolvent positive operators with their perturbations. Then we define the generalized principal eigenvalue and use it to investigate the influence of diffusion rate on the principal eigenvalue. In addition, we establish the strong maximum principle for age-structured nonlocal diffusion operators. In the second part \cite{Ducrot2022Age-structuredII} we will investigate the effects of principal eigenvalues on the global dynamics of the model with monotone nonlinearity in the birth rate and show that the principal eigenvalue being zero is critical.
Hybrid Machine Learning Modeling of Engineering Systems - A Probabilistic Perspective Tested on a Multiphase Flow Modeling Case Study

To operate process engineering systems in a safe and reliable manner, predictive models are often used in decision making. In many cases, these are mechanistic ﬁrst principles models which aim to accurately describe the process. In practice, the parameters of these models need to be tuned to the process conditions at hand. If the conditions change, which is common in practice, the model becomes inaccurate and needs to be re-tuned. In this paper, we propose a hybrid modeling machine learning framework which allows to tune ﬁrst principles models to process conditions using two different types of Bayesian Neural Networks. Our approach not only estimates the expected values of the ﬁrst principles model parameters but also quantiﬁes the uncertainty of these estimates. Such an approach of hybrid machine learning modeling is not yet well described in the literature, so we believe this paper will provide an additional angle at which hybrid machine learning modeling of physical systems can be considered. As an example, we choose a multiphase pipe ﬂow process for which we constructed a three-phase steady state model based on the drift-ﬂux approach which can be used for modeling of pipe and well ﬂow behavior in oil and gas production systems with or without the neural network tuning. In the simulation results, we show how uncertainty estimates of the resulting hybrid models can be used to make better operation decisions.
Computing the Ensemble Spread From Deterministic Weather Predictions Using Conditional Generative Adversarial Networks

Ensemble prediction systems are an invaluable tool for weather forecasting. Practically, ensemble predictions are obtained by running several perturbations of the deterministic control forecast. However, ensemble prediction is associated with a high computational cost and often involves statistical post‐processing steps to improve its quality. Here we propose to use deep‐learning‐based algorithms to learn the statistical properties of an ensemble prediction system, the ensemble spread, given only the deterministic control forecast. Thus, once trained, the costly ensemble prediction system will not be needed anymore to obtain future ensemble forecasts, and the statistical properties of the ensemble can be derived from a single deterministic forecast. We adapt the classical pix2pix architecture to a three‐dimensional model and train them against several years of operational (ensemble) weather forecasts for the 500 hPa geopotential height. The results demonstrate that the trained models indeed allow obtaining a highly accurate ensemble spread from the control forecast only.
On the large-Weissenberg-number scaling laws in viscoelastic pipe flows

Abstract This work explains a scaling law of the first Landau coefficient of the derived Ginzburg–Landau equation in the weakly nonlinear analysis of axisymmetric viscoelastic pipe flows in the large-Weissenberg-number ($Wi$) limit, recently reported in Wan et al. (J. Fluid Mech., vol. 929, 2021, A16). Using an asymptotic method, we derive a reduced system, which captures the characteristics of the linear centre-mode instability near the critical condition in the large-$Wi$ limit. Based on the reduced system we then conduct a weakly nonlinear analysis using a multiple-scale expansion method, which readily explains the aforementioned scaling law of the Landau coefficient and some other scaling laws. Particularly, the equilibrium amplitude of disturbance near linear critical conditions is found to scale as $Wi^{-1/2}$, which may be of interest to experimentalists. The current analysis reduces the numbers of parameters and unknowns and exemplifies an approach to studying the viscoelastic flow at large $Wi$, which could shed new light on the understanding of its nonlinear dynamics.
Metrics of calibration for probabilistic predictions

Predictions are often probabilities; e.g., a prediction could be for precipitation tomorrow, but with only a 30% chance. Given such probabilistic predictions together with the actual outcomes,"reliability diagrams"help detect and diagnose statistically significant discrepancies -- so-called"miscalibration"-- between the predictions and the outcomes. The canonical reliability diagrams histogram the observed and expected values of the predictions; replacing the hard histogram binning with soft kernel density estimation is another common practice. But, which widths of bins or kernels are best? Plots of the cumulative differences between the observed and expected values largely avoid this question, by displaying miscalibration directly as the slopes of secant lines for the graphs. Slope is easy to perceive with quantitative precision, even when the constant offsets of the secant lines are irrelevant; there is no need to bin or perform kernel density estimation. The existing standard metrics of miscalibration each summarize a reliability diagram as a single scalar statistic. The cumulative plots naturally lead to scalar metrics for the deviation of the graph of cumulative differences away from zero; good calibration corresponds to a horizontal, flat graph which deviates little from zero. The cumulative approach is currently unconventional, yet offers many favorable statistical properties, guaranteed via mathematical theory backed by rigorous proofs and illustrative numerical examples. In particular, metrics based on binning or kernel density estimation unavoidably must trade-off statistical confidence for the ability to resolve variations as a function of the predicted probability or vice versa. Widening the bins or kernels averages away random noise while giving up some resolving power. Narrowing the bins or kernels enhances resolving power while not averaging away as much noise.
SRGA J181414.6-225604: A New Galactic Symbiotic X-Ray Binary Outburst Triggered by an Intense Mass-loss Episode of a Heavily Obscured Mira Variable

We present the discovery and multiwavelength characterization of SRGA J181414.6-225604, a Galactic hard X-ray transient discovered during the ongoing SRG/ART-XC sky survey. Using data from the Palomar Gattini-IR survey, we identify a spatially and temporally coincident variable infrared (IR) source, IRAS 18111-2257, and classify it as a very-late-type (M7–M8), long-period (1502 ± 24 days), and luminous (M K ≈ −9.9 ± 0.2) O-rich Mira donor star located at a distance of ≈14.6+2.9 −2.3 kpc. Combining multicolor photometric data over the last ≈25 yr, we show that the IR counterpart underwent a recent (starting ≈800 days before the X-ray flare) enhanced mass-loss (reaching ≈2.1 × 10−5 M ⊙ yr−1) episode, resulting in an expanding dust shell obscuring the underlying star. Multi-epoch follow-up observations from Swift, NICER, and NuSTAR reveal a ≈200 day long X-ray outburst reaching a peak luminosity of L X ≈ 2.5 × 1036 erg s−1, characterized by a heavily absorbed (N H ≈ 6 × 1022 cm−2) X-ray spectrum consistent with an optically thick Comptonized plasma. The X-ray spectral and timing behavior suggest the presence of clumpy wind accretion, together with a dense ionized nebula overabundant in silicate material surrounding the compact object. Together, we show that SRGA J181414.6-225604 is a new symbiotic X-ray binary in outburst, triggered by an intense dust-formation episode of a highly evolved donor. Our results offer the first direct confirmation for the speculated connection between enhanced late-stage donor mass loss and the active lifetimes of symbiotic X-ray binaries.
Modeling Exemplification in Long-form Question Answering via Retrieval

Exemplification is a process by which writers explain or clarify a concept by providing an example. While common in all forms of writing, exemplification is particularly useful in the task of long-form question answering (LFQA), where a complicated answer can be made more understandable through simple examples. In this paper, we provide the first computational study of exemplification in QA, performing a fine-grained annotation of different types of examples (e.g., hypotheticals, anecdotes) in three corpora. We show that not only do state-of-the-art LFQA models struggle to generate relevant examples, but also that standard evaluation metrics such as ROUGE are insufficient to judge exemplification quality. We propose to treat exemplification as a retrieval problem in which a partially-written answer is used to query a large set of human-written examples extracted from a corpus. Our approach allows a reliable ranking-type automatic metrics that correlates well with human evaluation. A human evaluation shows that our model’s retrieved examples are more relevant than examples generated from a state-of-the-art LFQA model.
Optimal Dividends for a Two-Dimensional Risk Model with Simultaneous Ruin of Both Branches

We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions.
Sign Switching Dark Energy from a Running Barrow Entropy

Barrow proposed that the area law of the entropy associated with a horizon might receive a “fractal correction” due to quantum gravitational effects—in place of S∝A, we have instead S∝A1+δ/2, where 0⩽δ⩽1 measures the deviation from the standard area law (δ=0). Based on black hole thermodynamics, we argue that the Barrow entropy should run (i.e., energy scale dependent), which is reasonable given that quantum gravitational corrections are expected to be important only in the high-energy regime. When applied to the Friedmann equation, we demonstrate the possibility that such a running Barrow entropy index could give rise to a dynamical effective dark energy, which is asymptotically positive and vanishing, but negative at the Big Bang. Such a sign switching dark energy could help to alleviate the Hubble tension. Other cosmological implications are discussed.
Learning from Bootstrapping and Stepwise Reinforcement Reward: A Semi-Supervised Framework for Text Style Transfer

Text style transfer is an important task in controllable language generation. Supervised approaches have pushed performance improvement on style-oriented rewriting such as formality conversion. However, challenges remain due to the scarcity of large-scale parallel data in many domains. While unsupervised approaches do not rely on annotated sentence pairs for each style, they are often plagued with instability issues such as mode collapse or quality degradation. To take advantage of both supervised and unsupervised paradigms and tackle the challenges, in this work, we propose a semi-supervised framework for text style transfer. First, the learning process is bootstrapped with supervision guided by automatically constructed pseudo-parallel pairs using lexical and semantic-based methods. Then the model learns from unlabeled data via reinforcement rewards. Specifically, we propose to improve the sequence-to-sequence policy gradient via stepwise reward optimization, providing fine-grained learning signals and stabilizing the reinforced learning process. Experimental results show that the proposed approach achieves state-of-the-art performance on multiple datasets, and produces effective generation with as minimal as 10\% of training data.