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Nanoelectrical and photonic integration of quantum optical components is crucial for scalable solid-state quantum technologies. Silicon carbide stands out as a material with mature quantum defects and a wide variety of applications in semiconductor industry. Here, we study the behaviour of single silicon vacancy (V2) colour centres in a metal-semiconductor (Au/Ti/4H-SiC) epitaxial wafer device, operating in a Schottky diode configuration. We explore the depletion of free carriers in the vicinity of the defect, as well as electrical tuning of the defect optical transition lines. By detecting single charge traps, we investigate their impact on V2 optical line width. Additionally, we investigate the charge-photon-dynamics of the V2 centre and find its dominating photon-ionisation processes characteristic rate and wavelength dependence. Finally, we probe the spin coherence properties of the V2 system in the junction and demonstrate several key protocols for quantum network applications. Our work shows the first demonstration of low temperature integration of a Schottky device with optical microstructures for quantum applications and paves the way towards fundamentally scalable and reproducible optical spin defect centres in solids.

Given the prompt "Rome is in", can we steer a language model to flip its prediction of an incorrect token "France" to a correct token "Italy" by only multiplying a few relevant activation vectors with scalars? We argue that successfully intervening on a model is a prerequisite for interpreting its internal workings. Concretely, we establish a three-term objective: a successful intervention should flip the correct with the wrong token and vice versa (effectiveness), and leave other tokens unaffected (faithfulness), all while being sparse (minimality). Using gradient-based optimization, this objective lets us learn (and later evaluate) a specific kind of efficient and interpretable intervention: activation scaling only modifies the signed magnitude of activation vectors to strengthen, weaken, or reverse the steering directions already encoded in the model. On synthetic tasks, this intervention performs comparably with steering vectors in terms of effectiveness and faithfulness, but is much more minimal allowing us to pinpoint interpretable model components. We evaluate activation scaling from different angles, compare performance on different datasets, and make activation scalars a learnable function of the activation vectors themselves to generalize to varying-length prompts., Comment: Findings of the Association for Computational Linguistics: EMNLP 2024

High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates the observed data to a latent low-dimensional multivariate Gaussian variable via a Poisson distribution. Variational inference methods have become a golden standard solution to infer such a model. While computationally efficient, they usually lack theoretical statistical properties with respect to the model. To address this issue we propose a projected stochastic gradient scheme that directly maximizes the log-likelihood. We prove the convergence of the proposed method when using importance sampling for estimating the gradient. Specifically, we obtain a rate of convergence of $O(T^{-1/2} + N^{-1})$ with $T$ the number of iterations and $N$ the number of Monte Carlo draws. The latter follows from a novel descent lemma for non convex $L$-smooth objective functions, and random biased gradient estimate. We also demonstrate numerically the efficiency of our solution compared to its variational competitor. Our method not only scales with respect to the number of observed samples but also provides access to the desirable properties of the maximum likelihood estimator.

Nanoscale magnetic resonance imaging (nanoMRI) aims at obtaining structure at the single molecule level. Most of the techniques for effecting a nanoMRI gradient use small permanent magnets. Here, we present a switchable magnetic field gradient on a tip, which is designed to provide a local and controllable magnetic field with a high gradient on the nanometer scale. We incorporate the gradient field with a nanoscale magnetic resonance sensor, a single nitrogen-vacancy (NV) center in diamond, to provide high-resolution magnetic resonance imaging. The device is a metal microwire deposited along a quartz tip, with the current flowing along the tip inducing a magnetic field around its apex. This field can be manipulated throughout a measurement by controlling the current along the wire. We achieved gradients as high as 1 $\mathrm{\mu}\text{T/nm}$ at fields weaker than 200 $\mathrm{\mu}\text{T}$. Such a gradient can facilitate electron spin mapping with 1 nm resolution using single NV sensors, allowing for nanoscale imaging of electrons. The ability to switch the current on and off and to position the device with high precision overcomes limitations such as limited emitter contrast and the flexibility in sample preparation. Moreover, we show that proximity of the metallic tip to the sensor modifies the Rabi power in a spatially dependent manner, providing regions with enhanced ($\times$3.5) and decreased Rabi power. This spatial gradient, induced by the tip, offers the opportunity for selective pulses on nearby spin species where the same microwave power will result in different spin manipulation characteristics.

We give a complete classification, up to birational equivalence, of all fibrations by plane projective rational quartic curves in characteristic two., Comment: 31 pages. Comments welcome at any time!

The National Technical Assistance Center on Transition: the Collaborative (NTACT:C) Collaborative Assessment Guide for Transition Planning (CAG) is intended to help students, family members, educators, vocational rehabilitation counselors, human services and health agency staff, and other partners develop a coordinated assessment approach for transition planning and service delivery. The set of resources which make up the CAG includes sections designed for students and families. It also includes a supplement to highlight the assessment requirements of the Individuals with Disabilities Education Act (IDEA, 2004) and the Rehabilitation Act of 1973 (Rehab Act), as amended by title IV of the Workforce Innovation and Opportunity Act (WIOA) as well as a supplement of Definitions referenced throughout. Finally, it includes a supplement of sample assessment tools. The assessment process for identifying post-school goals and relevant transition services for students and youth consists of six separate but interconnected processes: (1) Determining What to Assess; (2) Determining Stakeholders; (3) Selecting Appropriate Assessments; (4) Conducting Assessments; (5) Reviewing Assessment Results; and (6) Using Assessment Data.

Magnetic auto-oscillations are damping-compensated magnetization precessions. They can be generated in spin Hall nano-oscillators (SHNO) among others. Current research on these devices is dedicated to create next generation energy-efficient hardware for communication technologies. However, the underlying physics governing the formation of auto-oscillation modes, their output power and line width in a single SHNO device have remained elusive so far. We image the sources of magnetic auto-oscillations in a metallic SHNO using a single spin quantum sensor. We directly measure the microwave field generated by an auto-oscillation spot at the nanoscale by driving the electron spin resonance transition of the sensor spin, enabling faster acquisition speed (100 ms/pixel). Instead of being defined by the points of the largest antidamping only, we experimentally demonstrate for the first time with quantitative magnetometry that the auto-oscillation spots are determined by the positions of the magnetic field minima. The latter act as local potential wells for confining spin-waves, thus supporting large amplitude auto-oscillations. By comparing the magnitude of the magnetic stray field at these spots, we decipher the different frequencies of the auto-oscillation modes. The insights gained regarding the interaction between auto-oscillation modes and spin-wave potential wells enable advanced engineering of real devices.

To answer a question, language models often need to integrate prior knowledge learned during pretraining and new information presented in context. We hypothesize that models perform this integration in a predictable way across different questions and contexts: models will rely more on prior knowledge for questions about entities (e.g., persons, places, etc.) that they are more familiar with due to higher exposure in the training corpus, and be more easily persuaded by some contexts than others. To formalize this problem, we propose two mutual information-based metrics to measure a model's dependency on a context and on its prior about an entity: first, the persuasion score of a given context represents how much a model depends on the context in its decision, and second, the susceptibility score of a given entity represents how much the model can be swayed away from its original answer distribution about an entity. We empirically test our metrics for their validity and reliability. Finally, we explore and find a relationship between the scores and the model's expected familiarity with an entity, and provide two use cases to illustrate their benefits., Comment: Long paper accepted at ACL 2024

Can we localize the weights and mechanisms used by a language model to memorize and recite entire paragraphs of its training data? In this paper, we show that while memorization is spread across multiple layers and model components, gradients of memorized paragraphs have a distinguishable spatial pattern, being larger in lower model layers than gradients of non-memorized examples. Moreover, the memorized examples can be unlearned by fine-tuning only the high-gradient weights. We localize a low-layer attention head that appears to be especially involved in paragraph memorization. This head is predominantly focusing its attention on distinctive, rare tokens that are least frequent in a corpus-level unigram distribution. Next, we study how localized memorization is across the tokens in the prefix by perturbing tokens and measuring the caused change in the decoding. A few distinctive tokens early in a prefix can often corrupt the entire continuation. Overall, memorized continuations are not only harder to unlearn, but also to corrupt than non-memorized ones.

Inferring parameters of a latent variable model can be a daunting task when the conditional distribution of the latent variables given the observed ones is intractable. Variational approaches prove to be computationally efficient but, possibly, lack theoretical guarantees on the estimates, while sampling based solutions are quite the opposite. Starting from already available variational approximations, we define a first Monte Carlo EM algorithm to obtain maximum likelihood estimators, focusing on the Poisson log-normal model which provides a generic framework for the analysis of multivariate count data. We then extend this algorithm to the case of a composite likelihood in order to be able to handle higher dimensional count data.

Simulating mixtures of distributions with signed weights proves a challenge as standard simulation algorithms are inefficient in handling the negative weights. In particular, the natural representation of mixture variates as associated with latent component indicators is no longer available. We propose here an exact accept-reject algorithm in the general case of finite signed mixtures that relies on optimaly pairing positive and negative components and designing a stratified sampling scheme on pairs. We analyze the performances of our approach, relative to the inverse cdf approach, since the cdf of the distribution remains available for standard signed mixtures.

Emitters in high refractive index materials like 4H-SiC suffer from reduced detection of photons because of losses caused by total internal reflection. Thus, integration into efficient nanophotonic structures which couple the emission of photons to a well defined waveguide mode can significantly enhance the photon detection efficiency. In addition, interfacing this waveguide to a classical fiber network is of similar importance to detect the photons and perform experiments. Here, we show a waveguide fiber interface in SiC. By careful measurements we determine efficiencies exceeding 93 % for the transfer of photons from SiC nanobeams to fibers. We use this interface to create a bright single photon source based on waveguide integrated V2 defects in 4H-SiC and achieve an overall photon count rate of 181 kilo-counts per second. We observe and quantify the strain induced shift of the ground state spin states and demonstrate coherent control of the electron spin with a coherence time of T2=42.5 $\rm\mu$s.

Investigating spin and charge noise in strongly correlated electron systems is a valuable way to analyze their physical properties and unlock new phases of matter. In this context, nitrogen-vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use longitudinal relaxation time $T_1$ of single NV centers to investigate the spin dynamics of nanometers-thin flakes of $\alpha$-RuCl$_3$ at room temperature. We observe a significant reduction in the $T_1$ in the presence of $\alpha$-RuCl$_3$ in proximity to our NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal plane. Furthermore, the $T_1$ time exhibits an almost linear increase with an applied external magnetic field. We associate this trend with the alteration of spin and charge noise in $\alpha$-RuCl$_3$ under an external magnetic field. These findings suggest that the influence of the room-temperature spin dynamics of $\alpha$-RuCl$_3$ on the longitudinal relaxation time of the NV center can be used to gain information on the material itself and the technique to be used on other 2D materials.

An ESO internal ALMA development study, BRAIN, is addressing the ill-posed inverse problem of synthesis image analysis employing astrostatistics and astroinformatics. These emerging fields of research offer interdisciplinary approaches at the intersection of observational astronomy, statistics, algorithm development, and data science. In this study, we provide evidence of the benefits of employing these approaches to ALMA imaging for operational and scientific purposes. We show the potential of two techniques, RESOLVE and DeepFocus, applied to ALMA calibrated science data. Significant advantages are provided with the prospect to improve the quality and completeness of the data products stored in the science archive and overall processing time for operations. Both approaches evidence the logical pathway to address the incoming revolution in data rates dictated by the planned electronic upgrades. Moreover, we bring to the community additional products through a new package, ALMASim, to promote advancements in these fields, providing a refined ALMA simulator usable by a large community for training and/or testing new algorithms., Comment: 9 pages, 5 figures, MaxEnt2023 conference

The astronomical community is grappling with the increasing volume and complexity of data produced by modern telescopes, due to difficulties in reducing, accessing, analyzing, and combining archives of data. To address this challenge, we propose the establishment of a coordinating body, an "entity," with the specific mission of enhancing the interoperability, archiving, distribution, and production of both astronomical data and software. This report is the culmination of a workshop held in February 2023 on the Future of Astronomical Data Infrastructure. Attended by 70 scientists and software professionals from ground-based and space-based missions and archives spanning the entire spectrum of astronomical research, the group deliberated on the prevailing state of software and data infrastructure in astronomy, identified pressing issues, and explored potential solutions. In this report, we describe the ecosystem of astronomical data, its existing flaws, and the many gaps, duplication, inconsistencies, barriers to access, drags on productivity, missed opportunities, and risks to the long-term integrity of essential data sets. We also highlight the successes and failures in a set of deep dives into several different illustrative components of the ecosystem, included as an appendix., Comment: 59 pages; please send comments and/or questions to foadi@googlegroups.com

Colour centres in silicon carbide emerge as a promising semiconductor quantum technology platform with excellent spin-optical coherences.However, recent efforts towards maximising the photonic efficiency via integration into nanophotonic structures proved to be challenging due to reduced spectral stabilities. Here, we provide a large-scale systematic investigation on silicon vacancy centres in thin silicon carbide membranes with thicknesses down to $0.25\,\rm\mu m$. Our membrane fabrication process involves a combination of chemical mechanical polishing, reactive ion etching, and subsequent annealing. This leads to highly reproducible membranes with roughness values of $3-4\,\rm\r{A}$, as well as negligible surface fluorescence. We find that silicon vacancy centres show close-to lifetime limited optical linewidths with almost no signs of spectral wandering down to membrane thicknesses of $0.7 \,\rm\mu m$. For silicon vacancy centres in thinner membranes down to $0.25\,\rm\mu m$, we observe spectral wandering, however, optical linewidths remain below $200\,\rm MHz$, which is compatible with spin-selective excitation schemes. Our work clearly shows that silicon vacancy centres can be integrated into sub-micron silicon carbide membranes, which opens the avenue towards obtaining the necessary improvements in photon extraction efficiency based on nanophotonic structuring., Comment: 10 pages, 4 figures, plus supplementary information

Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank product reviews by sentiment. We compare pairwise, pointwise and listwise prompting techniques to elicit a language model's ranking knowledge. However, we find that even with careful calibration and constrained decoding, prompting-based techniques may not always be self-consistent in the rankings they produce. This motivates us to explore an alternative approach that is inspired by an unsupervised probing method called Contrast-Consistent Search (CCS). The idea is to train a probe guided by a logical constraint: a language model's representation of a statement and its negation must be mapped to contrastive true-false poles consistently across multiple statements. We hypothesize that similar constraints apply to ranking tasks where all items are related via consistent, pairwise or listwise comparisons. To this end, we extend the binary CCS method to Contrast-Consistent Ranking (CCR) by adapting existing ranking methods such as the Max-Margin Loss, Triplet Loss and an Ordinal Regression objective. Across different models and datasets, our results confirm that CCR probing performs better or, at least, on a par with prompting., Comment: Long Paper at EACL 2024

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned optical injection. We show that in the limit of large delay, square wave solutions of the time-delayed system can be treated as relative homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of square wave solutions. In particular, we unveil the mechanisms behind the collapsed snaking scenario of square waves and explain the formation of complex-shaped multistable square wave solutions through a Bykov T-point. Finally we relate the position of the T-point to the position of the Maxwell point in the original time-delayed system.

Many-body dispersion (MBD) is a powerful framework to treat van der Waals (vdW) dispersion interactions in density-functional theory and related atomistic modeling methods. Several independent implementations of MBD with varying degree of functionality exist across a number of electronic structure codes, which both limits the current users of those codes and complicates dissemination of new variants of MBD. Here, we develop and document libMBD, a library implementation of MBD that is functionally complete, efficient, easy to integrate with any electronic structure code, and already integrated in FHI-aims, DFTB+, VASP, Q-Chem, CASTEP, and Quantum ESPRESSO. libMBD is written in modern Fortran with bindings to C and Python, uses MPI/ScaLAPACK for parallelization, and implements MBD for both finite and periodic systems, with analytical gradients with respect to all input parameters. The computational cost has asymptotic cubic scaling with system size, and evaluation of gradients only changes the prefactor of the scaling law, with libMBD exhibiting strong scaling up to 256 processor cores. Other MBD properties beyond energy and gradients can be calculated with libMBD, such as the charge-density polarization, first-order Coulomb correction, the dielectric function, or the order-by-order expansion of the energy in the dipole interaction. Calculations on supramolecular complexes with MBD-corrected electronic structure methods and a meta-review of previous applications of MBD demonstrate the broad applicability of the libMBD package to treat vdW interactions., Comment: 14 pages, 6 figures, submitted to JCP

Conspiracy Theory Identication task is a new shared task proposed for the first time at the Evalita 2023. The ACTI challenge, based exclusively on comments published on conspiratorial channels of telegram, is divided into two subtasks: (i) Conspiratorial Content Classification: identifying conspiratorial content and (ii) Conspiratorial Category Classification about specific conspiracy theory classification. A total of fifteen teams participated in the task for a total of 81 submissions. We illustrate the best performing approaches were based on the utilization of large language models. We finally draw conclusions about the utilization of these models for counteracting the spreading of misinformation in online platforms., Comment: Accepted at the Evalita Workshop 2023

Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model's output with respect to its inputs. While these methods can indicate which input features may be important for the model's prediction, they reveal little about the inner workings of the model itself. In this paper, we observe that the gradient computation of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics about the gradient graph of a neural network, such as the highest-weighted path and entropy. We implement this generalized algorithm, evaluate it on synthetic datasets to better understand the statistics it computes, and apply it to study BERT's behavior on the subject-verb number agreement task (SVA). With this method, we (a) validate that the amount of gradient flow through a component of a model reflects its importance to a prediction and (b) for SVA, identify which pathways of the self-attention mechanism are most important., Comment: Long paper accepted at ACL 2023

We classify fibrations by integral plane projective rational quartic curves whose generic fibre is regular but admits a non-smooth point that is a canonical divisor. These fibrations can only exist in characteristic two. The geometric generic fibre, which determines the generic behaviour of the special fibres, is an integral plane projective rational quartic curve over the algebraic closure of the function field of the base. It has the remarkable property that the tangent lines at the non-singular points are either all bitangents or all non-ordinary inflection tangents; moreover it is strange, that is, all the tangent lines meet in a common point. We construct two fibrations that are universal in the sense that any other fibration with the aforementioned properties can be obtained from one of them by a base extension. Furthermore, among these fibrations we choose a pencil of plane quartic curves and study in detail its geometry. We determine the corresponding minimal regular model and we describe it as a purely inseparable double covering of a quasi-elliptic fibration., Comment: 24 pages. Slightly expanded version

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space., Comment: ACL Findings 2023

Charge state instabilities have been a bottleneck for the implementation of solid-state spin systems and pose a major challenge to the development of spin-based quantum technologies. Here we investigate the stabilization of negatively charged nitrogen-vacancy (NV$^-$) centers in phosphorus-doped diamond at liquid helium temperatures. Photoionization of phosphorous donors in conjunction with charge diffusion at the nanoscale enhances NV$^0$ to NV$^-$ conversion and stabilizes the NV$^-$ charge state without the need for an additional repump laser. The phosphorus-assisted stabilization is explored and confirmed both with experiments and our theoretical model. Stable photoluminescence-excitation spectra are obtained for NV$^-$ centers created during the growth. The fluorescence is continuously recorded under resonant excitation to real-time monitor the charge state and the ionization and recombination rates are extracted from time traces. We find a linear laser power dependence of the recombination rate as opposed to the conventional quadratic dependence, which is attributed to the photo-ionization of phosphorus atoms., Comment: 8 pages, 4 figures

The Atacama Large Millimetre/submillimetre Array (ALMA) is the world's most advanced radio interferometric facility, producing science data with an average rate of about 1 TB per day. After a process of calibration, imaging and quality assurance, the scientific data are stored in the ALMA Science Archive (ASA), along with the corresponding raw data, making the ASA an invaluable resource for original astronomical research. Due to their complexity, each ALMA data set has the potential for scientific results that go well beyond the ideas behind the original proposal that led to each observation. For this reason, the European ALMA Regional Centre initiated the High-Level Data Products initiative to develop science-oriented data products derived from data sets publicly available in the ASA, that go beyond the formal ALMA deliverables. The first instance of this initiative is the creation of a catalogue of submillimetre (submm) detections of Sloan Digital Sky Survey (SDSS) quasars from the SDSS Data Release 14 that lie in the aggregate ALMA footprint observed since ALMA Cycle 0. The ALMA fluxes are extracted in an automatic fashion, using the ALMA Data Mining Toolkit. All extractions above a signal-to-noise cut of 3.5 are considered, they have been visually inspected and the reliable detections are presented in a catalogue of 376 entries, corresponding to 275 unique quasars. Interesting targets found in the process, i.e. lensed or jetted quasars as well as quasars with nearby submm counterparts are highlighted, to facilitate further studies or potential follow up observations.

We present a long-term overview of the atmospheric phase stability at the Atacama Large Millimeter/submillimeter Array (ALMA) site, using >5 years of data, that acts as the successor to the studies summarized two decades ago by Evans et al 2003. Importantly, we explore the atmospheric variations, the `phase RMS', and associated metadata of over 17000 accrued ALMA observations taken since Cycle 3 (2015) by using the Bandpass calibrator source scans. We indicate the temporal phase RMS trends for average baseline lengths of 500, 1000, 5000, and 10000m, in contrast to the old stability studies that used a single 300m baseline phase monitor system. At the ALMA site, on the Chajnantor plateau, we report the diurnal variations and monthly changes in the phase RMS on ALMA relevant baselines lengths, measured directly from data, and we reaffirm such trends in atmospheric transmission (via Precipitable Water Vapour - PWV). We confirm that day observations have respectively higher phase RMS and PWV in contrast to night, while the monthly variations show Chilean winter (June - August) providing the best, high-frequency and long-baseline observing conditions - low (stable) phase RMS and low PWV. Yet, not all good phase stability condition occur when the PWV is low. Measurements of the phase RMS as a function of short timescales, 30 to 240s, that tie with typical target source scan times, and as a function of baseline length indicate that phase variations are smaller for short timescales and baselines and larger for longer timescales and baselines. We illustrate that fast-switching phase-referencing techniques, that allow short target scan times, could work well in reducing the phase RMS to suitable levels specifically for high-frequencies (Band 8, 9 and 10), long-baselines, and the two combined., Comment: 34 pages, 19 Figures, 10 Tables ALMA Memo 624: https://library.nrao.edu/public/memos/alma/main/memo624.pdf

Decision-makers in the humanitarian sector rely on timely and exact information during crisis events. Knowing how many civilians were injured during an earthquake is vital to allocate aids properly. Information about such victim counts is often only available within full-text event descriptions from newspapers and other reports. Extracting numbers from text is challenging: numbers have different formats and may require numeric reasoning. This renders purely string matching-based approaches insufficient. As a consequence, fine-grained counts of injured, displaced, or abused victims beyond fatalities are often not extracted and remain unseen. We cast victim count extraction as a question answering (QA) task with a regression or classification objective. We compare regex, dependency parsing, semantic role labeling-based approaches, and advanced text-to-text models. Beyond model accuracy, we analyze extraction reliability and robustness which are key for this sensitive task. In particular, we discuss model calibration and investigate few-shot and out-of-distribution performance. Ultimately, we make a comprehensive recommendation on which model to select for different desiderata and data domains. Our work is among the first to apply numeracy-focused large language models in a real-world use case with a positive impact., Comment: Long paper accepted at EACL 2023 main conference

Many dynamical systems in the real world are naturally described by latent states with intrinsic orderings, such as "ally", "neutral", and "enemy" relationships in international relations. These latent states manifest through countries' cooperative versus conflictual interactions over time. State-space models (SSMs) explicitly relate the dynamics of observed measurements to transitions in latent states. For discrete data, SSMs commonly do so through a state-to-action emission matrix and a state-to-state transition matrix. This paper introduces the Ordered Matrix Dirichlet (OMD) as a prior distribution over ordered stochastic matrices wherein the discrete distribution in the kth row stochastically dominates the (k+1)th, such that probability mass is shifted to the right when moving down rows. We illustrate the OMD prior within two SSMs: a hidden Markov model, and a novel dynamic Poisson Tucker decomposition model tailored to international relations data. We find that models built on the OMD recover interpretable ordered latent structure without forfeiting predictive performance. We suggest future applications to other domains where models with stochastic matrices are popular (e.g., topic modeling), and publish user-friendly code., Comment: Presented at the 26th International Conference on Artificial Intelligence and Statistics (AISTATS) 2023