Search

The broad physics reach of the LUX-ZEPLIN (LZ) experiment covers rare phenomena beyond the direct detection of dark matter. We report precise measurements of the extremely rare decay of $^{124}$Xe through the process of two-neutrino double electron capture (2$\nu$2EC), utilizing a $1.39\,\mathrm{kg} \times \mathrm{yr}$ isotopic exposure from the first LZ science run. A half-life of $T_{1/2}^{2\nu2\mathrm{EC}} = (1.09 \pm 0.14_{\text{stat}} \pm 0.05_{\text{sys}}) \times 10^{22}\,\mathrm{yr}$ is observed with a statistical significance of $8.3\,\sigma$, in agreement with literature. First empirical measurements of the KK capture fraction relative to other K-shell modes were conducted, and demonstrate consistency with respect to recent signal models at the $1.4\,\sigma$ level., Comment: 15 pages, 3 figures

The Baade-Wesselink method allows us to estimate distances to individual pulsating stars. Accurate geometric parallaxes obtained by the Gaia mission serve us in the calibration of the method and in the determination of its precision. The method also provides a way of determining mean radii of pulsating stars. The main aim of this work is to determine the scatter and possible dependence of p- factors of RR Lyrae stars on their pulsation periods. The secondary objective is to determine mean radius - period relations for these stars. Our calibrations for RR Lyrae stars are based on photometric data gathered at the Cerro Murphy Observatory. We obtained spectroscopic data specifically for this project using high resolution spectrographs. We use the Infrared Surface Brightness (IRSB) version of the method that relies on a surface brightness - color relation dependent on the (V-K) color. We obtain the spread of p- factors of around 0.07-0.08 for our sample of 9 RR Lyrae stars from the solar neighborhood. However, we also find relations between the p-factor and the pulsation period for RRab stars with the rms scatter around the relation of around 0.05, but with relatively large uncertainty of relations' parameters. We present relations between the mean radius and period for RR Lyrae pulsating in the fundamental mode with the rms scatter around the relation of $0.012R_{\odot}$. We observe a clear offset between p- factors obtained using the IRSB technique (with mean p between 1.39 and 1.45) and values inferred by Bras et al. (2024) using the SPIPS tool (M\'erand et al. 2015). On the other hand, we obtain a similar scatter of p of as observed by Bras et al. (2024). Our period-radius relations are in a good agreement with both the inference of Bras et al. (2024) based on SPIPS and theoretical predictions of Marconi et al. (2005, 2015), Comment: accepted for publication in A&A

While hallucinations of large language models (LLMs) prevail as a major challenge, existing evaluation benchmarks on factuality do not cover the diverse domains of knowledge that the real-world users of LLMs seek information about. To bridge this gap, we introduce WildHallucinations, a benchmark that evaluates factuality. It does so by prompting LLMs to generate information about entities mined from user-chatbot conversations in the wild. These generations are then automatically fact-checked against a systematically curated knowledge source collected from web search. Notably, half of these real-world entities do not have associated Wikipedia pages. We evaluate 118,785 generations from 15 LLMs on 7,919 entities. We find that LLMs consistently hallucinate more on entities without Wikipedia pages and exhibit varying hallucination rates across different domains. Finally, given the same base models, adding a retrieval component only slightly reduces hallucinations but does not eliminate hallucinations.

The 30 year orbit of the Cepheid Polaris has been followed with observations by the CHARA Array (Center for High Angular Resolution Astronomy) from 2016 through 2021. An additional measurement has been made with speckle interferometry at the Apache Point Observatory. Detection of the companion is complicated by its comparative faintness--an extreme flux ratio. Angular diameter measurements appear to show some variation with pulsation phase. Astrometric positions of the companion were measured with a custom grid-based model-fitting procedure and confirmed with the CANDID software. These positions were combined with the extensive radial velocities discussed by Torres (2023) to fit an orbit. Because of the imbalance of the sizes of the astrometry and radial velocity datasets, several methods of weighting are discussed. The resulting mass of the Cepheid is 5.13$\pm$ 0.28 $M_\odot$. Because of the comparatively large eccentricity of the orbit (0.63), the mass derived is sensitive to the value found for the eccentricity. The mass combined with the distance shows that the Cepheid is more luminous than predicted for this mass from evolutionary tracks. The identification of surface spots is discussed. This would give credence to the identification of photometric variation with a period of approximately 120 days as a rotation period. Polaris has some unusual properties (rapid period change, a phase jump, variable amplitude, unusual polarization). However, a pulsation scenario involving pulsation mode, orbital periastron passage (Torres 2023), and low pulsation amplitude can explain these characteristics within the framework of pulsation seen in Cepheids., Comment: ApJ in press

Type II Cepheids are old pulsating stars that can be used to trace the distribution of an old stellar population and to measure distances to globular clusters and galaxies within several megaparsecs. One method that can be used to measure the distances of Type II Cepheids relies on period-luminosity relations, which are quite widely explored in the literature. The semi-geometrical Baade-Wesselink technique is another method that allows distances of radially pulsating stars, such as Type II Cepheids, to be measured if the so-called projection factor is known. Using the surface brightness-colour relation version of the Baade-Wesselink technique, we determined the projection factors and radii of eight nearby BL Her type stars. We adopted accurate distances of target stars from Gaia Data Release 3. Time series photometry in the V and K bands have been collected with two telescopes located at the Rolf Chini Cerro Murphy Observatory, while spectroscopic data have been obtained with instruments hosted by the European Southern Observatory. The measured projection factors for the stars with good quality data are in the range between 1.21 and 1.36. The typical uncertainty of projection factors is 0.1. The mean value is 1.330$\pm$0.058, which gives the uncertainty of $\sim$4%. The main sources of uncertainty on the p-factors are statistical errors of the Baade-Wesselink fit and parallax. In the case of radii, the biggest contribution to the error budget comes from the K band photometry systematic uncertainty and parallax. The determined radii allowed us to construct the period-radius relation for BL Her stars. Our period-radius relation is in good agreement with the previous empirical calibration, while two theoretical calibrations found in the literature agree with our relation within 2$\sigma$. We also confirm that BL Her and RR Lyr stars obey an apparent common period-radius relation., Comment: 17 pages, 15 figures, 6 tables, Accepted for publication in A&A

A flag $C_0 \subsetneq C_1 \cdots \subsetneq C_s \subsetneq {\mathbb F}_q^n $ of linear codes is said to be self-orthogonal if the duals of the codes in the flag satisfy $C_{i}^\perp=C_{s-i}$, and it is said to satisfy the isometry-dual property with respect to an isometry vector ${\bf x}$ if $C_i^\perp={\bf x} C_{s-i}$ for $i=1, \dots, s$. We characterize complete (i.e. $s=n$) flags with the isometry-dual property by means of the existence of a word with non-zero coordinates in a certain linear subspace of ${\mathbb F}_q^n$. For flags of algebraic geometry (AG) codes we prove a so-called translation property of isometry-dual flags and give a construction of complete self-orthogonal flags, providing examples of self-orthogonal flags over some maximal function fields. At the end we characterize the divisors giving the isometry-dual property and the related isometry vectors showing that for each function field there is only a finite number of isometry vectors and that they are related by cyclic repetitions.

We introduce WildBench, an automated evaluation framework designed to benchmark large language models (LLMs) using challenging, real-world user queries. WildBench consists of 1,024 tasks carefully selected from over one million human-chatbot conversation logs. For automated evaluation with WildBench, we have developed two metrics, WB-Reward and WB-Score, which are computable using advanced LLMs such as GPT-4-turbo. WildBench evaluation uses task-specific checklists to evaluate model outputs systematically and provides structured explanations that justify the scores and comparisons, resulting in more reliable and interpretable automatic judgments. WB-Reward employs fine-grained pairwise comparisons between model responses, generating five potential outcomes: much better, slightly better, slightly worse, much worse, or a tie. Unlike previous evaluations that employed a single baseline model, we selected three baseline models at varying performance levels to ensure a comprehensive pairwise evaluation. Additionally, we propose a simple method to mitigate length bias, by converting outcomes of ``slightly better/worse'' to ``tie'' if the winner response exceeds the loser one by more than $K$ characters. WB-Score evaluates the quality of model outputs individually, making it a fast and cost-efficient evaluation metric. WildBench results demonstrate a strong correlation with the human-voted Elo ratings from Chatbot Arena on hard tasks. Specifically, WB-Reward achieves a Pearson correlation of 0.98 with top-ranking models. Additionally, WB-Score reaches 0.95, surpassing both ArenaHard's 0.91 and AlpacaEval2.0's 0.89 for length-controlled win rates, as well as the 0.87 for regular win rates., Comment: Link: https://hf.co/spaces/allenai/WildBench

Weakly interacting massive particles (WIMPs) may interact with a virtual pion that is exchanged between nucleons. This interaction channel is important to consider in models where the spin-independent isoscalar channel is suppressed. Using data from the first science run of the LUX-ZEPLIN dark matter experiment, containing 60 live days of data in a 5.5~tonne fiducial mass of liquid xenon, we report the results on a search for WIMP-pion interactions. We observe no significant excess and set an upper limit of $1.5\times10^{-46}$~cm$^2$ at a 90\% confidence level for a WIMP mass of 33~GeV/c$^2$ for this interaction.

The Data Acquisition System (DAQ) for the LUX-ZEPLIN (LZ) dark matter detector is described. The signals from 745 PMTs, distributed across three subsystems, are sampled with 100-MHz 32-channel digitizers (DDC-32s). A basic waveform analysis is carried out on the on-board Field Programmable Gate Arrays (FPGAs) to extract information about the observed scintillation and electroluminescence signals. This information is used to determine if the digitized waveforms should be preserved for offline analysis. The system is designed around the Kintex-7 FPGA. In addition to digitizing the PMT signals and providing basic event selection in real time, the flexibility provided by the use of FPGAs allows us to monitor the performance of the detector and the DAQ in parallel to normal data acquisition. The hardware and software/firmware of this FPGA-based Architecture for Data acquisition and Realtime monitoring (FADR) are discussed and performance measurements are described., Comment: 18 pages, 24 figures

LUX-ZEPLIN (LZ) is a tonne-scale experiment searching for direct dark matter interactions and other rare events. It is located at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, USA. The core of the LZ detector is a dual-phase xenon time projection chamber (TPC), designed with the primary goal of detecting Weakly Interacting Massive Particles (WIMPs) via their induced low energy nuclear recoils. Surrounding the TPC, two veto detectors immersed in an ultra-pure water tank enable reducing background events to enhance the discovery potential. Intricate calibration systems are purposely designed to precisely understand the responses of these three detector volumes to various types of particle interactions and to demonstrate LZ's ability to discriminate between signals and backgrounds. In this paper, we present a comprehensive discussion of the key features, requirements, and performance of the LZ calibration systems, which play a crucial role in enabling LZ's WIMP-search and its broad science program. The thorough description of these calibration systems, with an emphasis on their novel aspects, is valuable for future calibration efforts in direct dark matter and other rare-event search experiments.

The first science run of the LUX-ZEPLIN (LZ) experiment, a dual-phase xenon time project chamber operating in the Sanford Underground Research Facility in South Dakota, USA, has reported leading limits on spin-independent WIMP-nucleon interactions and interactions described from a non-relativistic effective field theory (NREFT). Using the same 5.5~t fiducial mass and 60 live days of exposure we report on the results of a relativistic extension to the NREFT. We present constraints on couplings from covariant interactions arising from the coupling of vector, axial currents, and electric dipole moments of the nucleon to the magnetic and electric dipole moments of the WIMP which cannot be described by recasting previous results described by an NREFT. Using a profile-likelihood ratio analysis, in an energy region between 0~keV$_\text{nr}$ to 270~keV$_\text{nr}$, we report 90% confidence level exclusion limits on the coupling strength of five interactions in both the isoscalar and isovector bases., Comment: 7 pages, 4 figures

An inner companion has recently been discovered orbiting the prototype of classical Cepheids, delta Cep, whose orbital parameters are still not fully constrained. We collected new precise radial velocity measurements of delta Cep in 2019 using the HARPS-N spectrograph mounted at the Telescopio Nazionale Galileo. Using these radial velocity measurements, we aimed to improve the orbital parameters of the system. We considered a template available in the literature as a reference for the radial velocity curve of the pulsation of the star. We then calculated the residuals between our global dataset (composed of the new 2019 observations plus data from the literature) and the template as a function of the pulsation phase and the barycentric Julian date. This provides the orbital velocity of the Cepheid component. Using a Bayesian tool, we derived the orbital parameters of the system. Considering priors based on already published Gaia constraints, we find for the orbital period a maximum a posteriori probability of Porb=9.32+/-0.03 years (uncertainties correspond to the 95% highest density probability interval), and we obtain an eccentricity e=0.71+/-0.02, a semimajor axis a=0.029 +/-0.003 arcsecond, and a center-of-mass velocity V0=-17.28+/-0.08 km/s, among other parameters. In this short analysis we derive the orbital parameters of the delta Cep inner binary system and provide a cleaned radial velocity curve of the pulsation of the star, which will be used to study its Baade-Wesselink projection factor in a future publication., Comment: accepted for publication in A&A Letters

The surface figure of an x-ray mirror was improved by differential deposition of WSi$_2$ layers. DC magnetron sputtering through beam-defining apertures was applied on moving substrates to generate thin films with arbitrary longitudinal thickness variations. The required velocity profiles were calculated using a deconvolution algorithm. Height errors were evaluated after each correction iteration using offline visible light surface metrology. WSi$_2$ was selected as a promising material since it conserves the initial substrate surface roughness and limits the film stress to acceptable levels. On a 300 mm long flat Si mirror the shape error was reduced to less than 0.2 nm RMS.

Searches for dark matter with liquid xenon time projection chamber experiments have traditionally focused on the region of the parameter space that is characteristic of weakly interacting massive particles, ranging from a few GeV/$c^2$ to a few TeV/$c^2$. Models of dark matter with a mass much heavier than this are well motivated by early production mechanisms different from the standard thermal freeze-out, but they have generally been less explored experimentally. In this work, we present a re-analysis of the first science run (SR1) of the LZ experiment, with an exposure of $0.9$ tonne$\times$year, to search for ultraheavy particle dark matter. The signal topology consists of multiple energy deposits in the active region of the detector forming a straight line, from which the velocity of the incoming particle can be reconstructed on an event-by-event basis. Zero events with this topology were observed after applying the data selection calibrated on a simulated sample of signal-like events. New experimental constraints are derived, which rule out previously unexplored regions of the dark matter parameter space of spin-independent interactions beyond a mass of 10$^{17}$ GeV/$c^2$., Comment: 9 pages, 7 figures

We prove that, for each fixed genus, the portion of semigroups of that genus belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinite. This means that most numerical semigroups have a finite number of descendants in the semigroup tree. This problem has been open since 2009.

A promising approach to attain long-distance coherent spin propagation is accessing quantum Hall topological spin-polarized edge states in graphene. Achieving this without large external magnetic fields necessitates engineering graphene band structure, obtainable through proximity to 2D magnetic materials. In this work, we detect spin-polarized helical edge transport in graphene at zero external magnetic field, allowed by the out-of-plane magnetic proximity of CrPS$_4$ that spin-splits the zeroth Landau level. This zero-field detection of the quantum anomalous spin Hall state is enabled by large induced spin-orbit and exchange couplings in the graphene that also lead to the detection of an enhanced Berry curvature, shifting the Landau levels, and result in an unconventional sequence of quantum Hall plateaus. Remarkably, we observe that the quantum anomalous Hall transport in the magnetized graphene persists up to room temperature. The detection of spin-polarized helical edge states at zero magnetic field and the robustness of the quantum anomalous Hall transport up to room temperature open the route for practical applications of magnetic graphene in quantum information processing and spintronic circuitries.

We present NovaCOMET, an open commonsense knowledge model, that combines the best aspects of knowledge and general task models. Compared to previous knowledge models, NovaCOMET allows open-format relations enabling direct application to reasoning tasks; compared to general task models like Flan-T5, it explicitly centers knowledge, enabling superior performance for commonsense reasoning. NovaCOMET leverages the knowledge of opaque proprietary models to create an open knowledge pipeline. First, knowledge is symbolically distilled into NovATOMIC, a publicly-released discrete knowledge graph which can be audited, critiqued, and filtered. Next, we train NovaCOMET on NovATOMIC by fine-tuning an open-source pretrained model. NovaCOMET uses an open-format training objective, replacing the fixed relation sets of past knowledge models, enabling arbitrary structures within the data to serve as inputs or outputs. The resulting generation model, optionally augmented with human annotation, matches or exceeds comparable open task models like Flan-T5 on a range of commonsense generation tasks. NovaCOMET serves as a counterexample to the contemporary focus on instruction tuning only, demonstrating a distinct advantage to explicitly modeling commonsense knowledge as well.

For any rigid space over a perfectoid extension of $\mathbb Q_p$ that admits a liftable smooth formal model, we construct an isomorphism between the moduli stacks of Hitchin-small Higgs bundles and Hitchin-small v-vector bundles. This constitutes a moduli-theoretic improvement of the small $p$-adic Simpson correspondence of Faltings, Abbes-Gros, Tsuji and Wang. Our construction is based on the Hodge-Tate stack of Bhatt-Lurie. We also prove an analogous correspondence in the arithmetic setting of rigid spaces of good reduction over $p$-adic fields., Comment: revised version of what used to be the second part of arXiv:2302.12747

Following the first science results of the LUX-ZEPLIN (LZ) experiment, a dual-phase xenon time projection chamber operating from the Sanford Underground Research Facility in Lead, South Dakota, USA, we report the initial limits on a model-independent non-relativistic effective field theory describing the complete set of possible interactions of a weakly interacting massive particle (WIMP) with a nucleon. These results utilize the same 5.5 t fiducial mass and 60 live days of exposure collected for the LZ spin-independent and spin-dependent analyses while extending the upper limit of the energy region of interest by a factor of 7.5 to 270 keVnr. No significant excess in this high energy region is observed. Using a profile-likelihood ratio analysis, we report 90% confidence level exclusion limits on the coupling of each individual non-relativistic WIMP-nucleon operator for both elastic and inelastic interactions in the isoscalar and isovector bases., Comment: 17 pages 11 figures

The process of differential deposition is currently applied at the ESRF in order to correct figure errors of x-ray optics substrates, prior to multilayer deposition. The substrate is moved at a controlled speed in front of a sputtering source to precisely control the deposition profile. This work will describe the concept of differential deposition at the ESRF as well as recent results of its implementation to correct a real mirror substrate surface. Finally, initial studies using a synchrotron beamline characterization technique based on x-ray total reflection are presented., Comment: 6 pages, 7 figures, SPIE Optics + Optoelectronics 2023, Prague

Plasma physics simulations create complex datasets for which researchers need state-of-the-art visualization tools to gain insights. These datasets are 3D in nature but are commonly depicted and analyzed using 2D idioms displayed on 2D screens. These offer limited understandability in a domain where spatial awareness is key. Virtual reality (VR) can be used as an alternative to conventional means for analyzing such datasets. VR has been known to improve depth and spatial relationship perception, which are fundamental for obtaining insights into 3D plasma morphology. Likewise, VR can potentially increase user engagement by offering more immersive and enjoyable experiences. Methods This study presents PlasmaVR, a proof-of-concept VR tool for visualizing datasets resulting from plasma physics simulations. It enables immersive multidimensional data visualization of particles, scalar, and vector fields and uses a more natural interface. The study includes user evaluation with domain experts where PlasmaVR was employed to assess the possible benefits of immersive environments in plasma physics visualization. The experimental group comprised five plasma physics researchers who were asked to perform tasks designed to represent their typical analysis workflow. To assess the suitability of the prototype for the different types of tasks, a set of objective metrics, such as completion time and number of errors, were measured. The prototype's usability was also evaluated using a standard System Usability Survey questionnaire.

We explore the creative problem-solving capabilities of modern LLMs in a novel constrained setting. To this end, we create MACGYVER, an automatically generated dataset consisting of over 1,600 real-world problems deliberately designed to trigger innovative usage of objects and necessitate out-of-the-box thinking. We then present our collection to both LLMs and humans to compare and contrast their problem-solving abilities. MACGYVER is challenging for both groups, but in unique and complementary ways. For instance, humans excel in tasks they are familiar with but struggle with domain-specific knowledge, leading to a higher variance. In contrast, LLMs, exposed to a variety of specialized knowledge, attempt broader problems but fail by proposing physically-infeasible actions. Finally, we provide a detailed error analysis of LLMs, and demonstrate the potential of enhancing their problem-solving ability with novel prompting techniques such as iterative step-wise reflection and divergent-convergent thinking. This work (1) introduces a fresh arena for intelligent agents focusing on intricate aspects of physical reasoning, planning, and unconventional thinking, which supplements the existing spectrum of machine intelligence; and (2) provides insight into the constrained problem-solving capabilities of both humans and AI., Comment: NAACL 2024

Theory of mind (ToM) evaluations currently focus on testing models using passive narratives that inherently lack interactivity. We introduce FANToM, a new benchmark designed to stress-test ToM within information-asymmetric conversational contexts via question answering. Our benchmark draws upon important theoretical requisites from psychology and necessary empirical considerations when evaluating large language models (LLMs). In particular, we formulate multiple types of questions that demand the same underlying reasoning to identify illusory or false sense of ToM capabilities in LLMs. We show that FANToM is challenging for state-of-the-art LLMs, which perform significantly worse than humans even with chain-of-thought reasoning or fine-tuning., Comment: EMNLP 2023. Code and dataset can be found here: https://hyunw.kim/fantom

One major problem in the study of numerical semigroups is determining the growth of the semigroup tree. In the present work, infinite chains of numerical semigroups in the semigroup tree, firstly introduced in Bras-Amor\'os and Nulygin (2009), are studied. Computational results show that these chains are rare, but without them the tree would not be infinite. It is proved that for each genus $g\geq 5$ there are more semigroups of that genus not belonging to infinite chains than semigroups belonging. The reference Bras-Amor\'os and Bulygin (2009) presented a characterization of the semigroups that belong to infinite chains in terms of the coprimality of the left elements of the semigroup as well as a result on the cardinality of the set of infinite chains to which a numerical semigroup belongs in terms of the primality of the greatest common divisor of these left elements. We revisit these results and fix an imprecision on the cardinality of the set of infinite chains to which a semigroup belongs in the case when the greatest common divisor of the left elements is a prime number. We then look at infinite chains in subtrees with fixed multiplicity. When the multiplicity is a prime number there is only one infinite chain in the tree of semigroups with such multiplicity. When the multpliplicity is $4$ or $6$ we prove a self-replication behavior in the subtree and prove a formula for the number of semigroups in infinite chains of a given genus and multiplicity $4$ and $6$, respectively.

We introduce a new class of numerical semigroups, which we call the class of {\it acute} semigroups and we prove that they generalize symmetric and pseudo-symmetric numerical semigroups, Arf numerical semigroups and the semigroups generated by an interval. For a numerical semigroup $\Lambda=\{\lambda_0<\lambda_1<\dots\}$ denote $\nu_i=\#\{j\mid\lambda_i-\lambda_j\in\Lambda\}$. Given an acute numerical semigroup $\Lambda$ we find the smallest non-negative integer $m$ for which the order bound on the minimum distance of one-point Goppa codes with associated semigroup $\Lambda$ satisfies $d_{ORD}(C_i)(:=\min\{\nu_j\mid j>i\})=\nu_{i+1}$ for all $i\geq m$. We prove that the only numerical semigroups for which the sequence $(\nu_i)$ is always non-decreasing are ordinary numerical semigroups. Furthermore we show that a semigroup can be uniquely determined by its sequence $(\nu_i)$., Comment: Published in IEEE Trans. Inf. Theory, 2004. MR2094884. arXiv admin note: substantial text overlap with arXiv:1706.09765

The LUX-ZEPLIN (LZ) experiment is a dark matter detector centered on a dual-phase xenon time projection chamber. We report searches for new physics appearing through few-keV-scale electron recoils, using the experiment's first exposure of 60 live days and a fiducial mass of 5.5t. The data are found to be consistent with a background-only hypothesis, and limits are set on models for new physics including solar axion electron coupling, solar neutrino magnetic moment and millicharge, and electron couplings to galactic axion-like particles and hidden photons. Similar limits are set on weakly interacting massive particle (WIMP) dark matter producing signals through ionized atomic states from the Migdal effect., Comment: 13 pages, 10 figures. See https://tinyurl.com/LZDataReleaseRun1ER for a data release related to this paper

We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some stochastic differential equation and $f$ is a test function. The new estimator is $(f(X^1_T) + f(X^2_T))/2$, where $X^1$ and $X^2$ have same marginal law as $X$ but are pathwise correlated so that to reduce the variance. The optimal correlation function $\rho$ is approximated by a deep neural network and is calibrated along the trajectories of $(X^1, X^2)$ by policy gradient and reinforcement learning techniques. Finding an optimal coupling given marginal laws has links with maximum optimal transport., Comment: 7 pages

We give a graphical reinterpretation of the seeds algorithm to explore the tree of numerical semigroups. We then exploit the seeds algorithm to find all the Eliahou semigroups of genus up to 65. Since all these semigroups satisfy the Wilf conjecture, this shows that the Wilf conjecture holds up to genus 65.

We present a revisit of the seeds algorithm to explore the semigroup tree. First, an equivalent definition of seed is presented, which seems easier to manage. Second, we determine the seeds of semigroups with at most three left elements. And third, we find the great-grandchildren of any numerical semigroup in terms of its seeds. The RGD algorithm is the fastest known algorithm at the moment. But if one compares the originary seeds algorithm with the RGD algorithm, one observes that the seeds algorithm uses more elaborated mathematical tools while the RGD algorithm uses data structures that are better adapted to the final C implementations. For genera up to around one half of the maximum size of native integers, the newly defined seeds algorithm performs significantly better than the RGD algorithm. For future compilators allowing larger native sized integers this may constitute a powerful tool to explore the semigroup tree up to genera never explored before. The new seeds algorithm uses bitwise integer operations, the knowledge of the seeds of semigroups with at most three left elements and of the great-grandchildren of any numerical semigroup, apart from techniques such as parallelization and depth first search as wisely introduced in this context by Fromentin and Hivert. The algorithm has been used to prove that there are no Eliahou semigroups of genus $66$, hence proving the Wilf conjecture for genus up to $66$. We also found three Eliahou semigroups of genus $67$. One of these semigroups is neither of Eliahou-Fromentin type, nor of Delgado's type. However, it is a member of a new family suggested by Shalom Eliahou., Comment: Accepted for publication at Mathematics of Computation

Despite serving as the foundation models for a wide range of NLP benchmarks, pre-trained language models have shown limited capabilities of acquiring implicit commonsense knowledge from self-supervision alone, compared to learning linguistic and factual knowledge that appear more explicitly in the surface patterns in text. In this work, we introduce commonsense knowledge transfer, a framework to transfer the commonsense knowledge stored in a neural commonsense knowledge model to a general-purpose pre-trained language model. It first exploits general texts to form queries for extracting commonsense knowledge from the neural commonsense knowledge model and then refines the language model with two self-supervised objectives: commonsense mask infilling and commonsense relation prediction, which align human language with the underlying commonsense knowledge. Empirical results show that our approach consistently improves the model's performance on downstream tasks that require commonsense reasoning. Moreover, we find that the improvement is more significant in the few-shot setting. This suggests that our approach helps language models better transfer to downstream tasks without extensive supervision by injecting commonsense knowledge into their parameters., Comment: ACL 2023 Findings

Pre-trained Transformer models like T5 and BART have advanced the state of the art on a wide range of text generation tasks. Compressing these models into smaller ones has become critically important for practical use. Common neural network compression techniques such as knowledge distillation or quantization are limited to static compression where the compression ratio is fixed. In this paper, we introduce Modular Transformers, a modularized encoder-decoder framework for flexible sequence-to-sequence model compression. Modular Transformers train modularized layers that have the same function of two or more consecutive layers in the original model via module replacing and knowledge distillation. After training, the modularized layers can be flexibly assembled into sequence-to-sequence models that meet different performance-efficiency trade-offs. Experimental results show that after a single training phase, by simply varying the assembling strategy, Modular Transformers can achieve flexible compression ratios from 1.1x to 6x with little to moderate relative performance drop., Comment: ACL 2023 Findings

Design biases in NLP systems, such as performance differences for different populations, often stem from their creator's positionality, i.e., views and lived experiences shaped by identity and background. Despite the prevalence and risks of design biases, they are hard to quantify because researcher, system, and dataset positionality is often unobserved. We introduce NLPositionality, a framework for characterizing design biases and quantifying the positionality of NLP datasets and models. Our framework continuously collects annotations from a diverse pool of volunteer participants on LabintheWild, and statistically quantifies alignment with dataset labels and model predictions. We apply NLPositionality to existing datasets and models for two tasks -- social acceptability and hate speech detection. To date, we have collected 16,299 annotations in over a year for 600 instances from 1,096 annotators across 87 countries. We find that datasets and models align predominantly with Western, White, college-educated, and younger populations. Additionally, certain groups, such as non-binary people and non-native English speakers, are further marginalized by datasets and models as they rank least in alignment across all tasks. Finally, we draw from prior literature to discuss how researchers can examine their own positionality and that of their datasets and models, opening the door for more inclusive NLP systems., Comment: ACL 2023

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify transformer LLMs, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that transformer LLMs solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how autoregressive generations' performance can rapidly decay with\,increased\,task\,complexity., Comment: 10 pages + appendix (40 pages)

Dogwhistles are coded expressions that simultaneously convey one meaning to a broad audience and a second one, often hateful or provocative, to a narrow in-group; they are deployed to evade both political repercussions and algorithmic content moderation. For example, in the sentence 'we need to end the cosmopolitan experiment,' the word 'cosmopolitan' likely means 'worldly' to many, but secretly means 'Jewish' to a select few. We present the first large-scale computational investigation of dogwhistles. We develop a typology of dogwhistles, curate the largest-to-date glossary of over 300 dogwhistles with rich contextual information and examples, and analyze their usage in historical U.S. politicians' speeches. We then assess whether a large language model (GPT-3) can identify dogwhistles and their meanings, and find that GPT-3's performance varies widely across types of dogwhistles and targeted groups. Finally, we show that harmful content containing dogwhistles avoids toxicity detection, highlighting online risks of such coded language. This work sheds light on the theoretical and applied importance of dogwhistles in both NLP and computational social science, and provides resources for future research in modeling dogwhistles and mitigating their online harms., Comment: ACL 2023, see https://dogwhistles.allen.ai/ for the glossary and other materials

Reinforcement Learning with Human Feedback (RLHF) is the most prominent method for Language Model (LM) alignment. However, RLHF is an unstable and data-hungry process that continually requires new high-quality LM-generated data for finetuning. We introduce Advantage-Leftover Lunch RL (A-LoL), a new class of offline policy gradient algorithms that enable RL training on any pre-existing data. By assuming the entire LM output sequence as a single action, A-LoL allows incorporating sequence-level classifiers or human-designed scoring functions as rewards. Subsequently, by using LM's value estimate, A-LoL only trains on positive advantage (leftover) data points, making it resilient to noise. Overall, A-LoL is an easy-to-implement, sample-efficient, and stable LM training recipe. We demonstrate the effectiveness of A-LoL and its variants with a set of four different language generation tasks. We compare against both online RL (PPO) and recent preference-based (DPO, PRO) and reward-based (GOLD) offline RL baselines. On the commonly-used RLHF benchmark, Helpful and Harmless Assistant (HHA), LMs trained with A-LoL methods achieve the highest diversity while also being rated more safe and helpful than the baselines according to humans. Additionally, in the remaining three tasks, A-LoL could optimize multiple distinct reward functions even when using noisy or suboptimal training data. We also release our experimental code. https://github.com/abaheti95/LoL-RL, Comment: published at ICLR 2024

Molecular contamination is a well-known problem in space flight. Water is the most common contaminant and alters numerous properties of a cryogenic optical system. Too much ice means that Euclid's calibration requirements and science goals cannot be met. Euclid must then be thermally decontaminated, a long and risky process. We need to understand how iced optics affect the data and when a decontamination is required. This is essential to build adequate calibration and survey plans, yet a comprehensive analysis in the context of an astrophysical space survey has not been done before. In this paper we look at other spacecraft with well-documented outgassing records, and we review the formation of thin ice films. A mix of amorphous and crystalline ices is expected for Euclid. Their surface topography depends on the competing energetic needs of the substrate-water and the water-water interfaces, and is hard to predict with current theories. We illustrate that with scanning-tunnelling and atomic-force microscope images. Industrial tools exist to estimate contamination, and we must understand their uncertainties. We find considerable knowledge errors on the diffusion and sublimation coefficients, limiting the accuracy of these tools. We developed a water transport model to compute contamination rates in Euclid, and find general agreement with industry estimates. Tests of the Euclid flight hardware in space simulators did not pick up contamination signals; our in-flight calibrations observations will be much more sensitive. We must understand the link between the amount of ice on the optics and its effect on Euclid's data. Little research is available about this link, possibly because other spacecraft can decontaminate easily, quenching the need for a deeper understanding. In our second paper we quantify the various effects of iced optics on spectrophotometric data., Comment: 35 pages, 22 figures, A&A in press. Changes to previous version: language edits, added Z. Bolag as author in the arxiv PDF (was listed in the ASCII author list and in the journal PDF, but not in the arxiv PDF). This version is identical to the journal version

We present a novel method, based on the Saunderson corrections, to predict the reflectance between a liquid interface and a dielectric diffuser. In this method, the diffuse properties of the dielectric are characterized using a single parameter, the multiple-scattering albedo, which is the same irrespective of being in contact with air or liquid. We tested this method using an apparatus based on a total integrating sphere capable of measuring reflectance in both liquid and gas interfaces across various wavelengths of light. We observed that the difference in the value of the multiple-scattering albedo between the sphere full of liquid and empty was less than 0.9$\times 10^{-3}$, with the average difference normalized to the respective uncertainty of only 0.7. These results confirm the reliability of our method and its potential for use in a wide range of practical applications., Comment: 15 pages, 7 figures