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The XLZD collaboration is developing a two-phase xenon time projection chamber with an active mass of 60 to 80 t capable of probing the remaining WIMP-nucleon interaction parameter space down to the so-called neutrino fog. In this work we show that, based on the performance of currently operating detectors using the same technology and a realistic reduction of radioactivity in detector materials, such an experiment will also be able to competitively search for neutrinoless double beta decay in $^{136}$Xe using a natural-abundance xenon target. XLZD can reach a 3$\sigma$ discovery potential half-life of 5.7$\times$10$^{27}$ yr (and a 90% CL exclusion of 1.3$\times$10$^{28}$ yr) with 10 years of data taking, corresponding to a Majorana mass range of 7.3-31.3 meV (4.8-20.5 meV). XLZD will thus exclude the inverted neutrino mass ordering parameter space and will start to probe the normal ordering region for most of the nuclear matrix elements commonly considered by the community., Comment: 29 pages, 7 figures

This report describes the experimental strategy and technologies for a next-generation xenon observatory sensitive to dark matter and neutrino physics. The detector will have an active liquid xenon target mass of 60-80 tonnes and is proposed by the XENON-LUX-ZEPLIN-DARWIN (XLZD) collaboration. The design is based on the mature liquid xenon time projection chamber technology of the current-generation experiments, LZ and XENONnT. A baseline design and opportunities for further optimization of the individual detector components are discussed. The experiment envisaged here has the capability to explore parameter space for Weakly Interacting Massive Particle (WIMP) dark matter down to the neutrino fog, with a 3$\sigma$ evidence potential for the spin-independent WIMP-nucleon cross sections as low as $3\times10^{-49}\rm cm^2$ (at 40 GeV/c$^2$ WIMP mass). The observatory is also projected to have a 3$\sigma$ observation potential of neutrinoless double-beta decay of $^{136}$Xe at a half-life of up to $5.7\times 10^{27}$ years. Additionally, it is sensitive to astrophysical neutrinos from the atmosphere, sun, and galactic supernovae., Comment: 32 pages, 14 figures

We study the Pythagoras numbers $py(3,2d)$ of real ternary forms, defined for each degree $2d$ as the minimal number $r$ such that every degree $2d$ ternary form which is a sum of squares can be written as the sum of at most $r$ squares of degree $d$ forms. Scheiderer showed that $d+1\leq py(3,2d)\leq d+2$. We show that $py(3,2d) = d+1$ for $2d = 8,10,12$. The main technical tool is Diesel's characterization of height 3 Gorenstein algebras., Comment: 14 pages, 1 figure

We present an argument (for a cross disciplinary audience) to explain the Dunbar scaling hierarchy for social groups. Our analysis is based on the Promise Theory of trust, and basic dimensional analysis. We derive a universal scaling relation, and pinpoint how groups form from the seeding of individuals by relative alignment, which continues until the costs associated with group contention outweigh the benefits in a detailed balance scenario. We identify an `energy' parameter for this balance that has the semantics of trust in a social setting. Subject to partial efficiency of maintaining aligned intentions, we can calculate a series of compatible rates that balance growth with entropy., Comment: A significant rewrite of an earlier arXiv:2402.00598

The seven-gluon two-loop full-color Yang-Mills amplitude is presented in a compact analytic form where we use the methods of four-dimensional unitarity cuts to obtain the polylogarithmic pieces and augmented recursion to obtain the rational pieces. Furthermore, an $n$-point form for the full-color polylogarithmic piece is presented. We use these results to probe for potential relations amongst the two-loop partial amplitudes., Comment: two attached Mathematica files

We introduce the Faetar Automatic Speech Recognition Benchmark, a benchmark corpus designed to push the limits of current approaches to low-resource speech recognition. Faetar, a Franco-Proven\c{c}al variety spoken primarily in Italy, has no standard orthography, has virtually no existing textual or speech resources other than what is included in the benchmark, and is quite different from other forms of Franco-Proven\c{c}al. The corpus comes from field recordings, most of which are noisy, for which only 5 hrs have matching transcriptions, and for which forced alignment is of variable quality. The corpus contains an additional 20 hrs of unlabelled speech. We report baseline results from state-of-the-art multilingual speech foundation models with a best phone error rate of 30.4%, using a pipeline that continues pre-training on the foundation model using the unlabelled set.

Different approaches to using data-driven methods for subgrid-scale closure modeling have emerged recently. Most of these approaches are data-hungry, and lack interpretability and out-of-distribution generalizability. Here, we use {online} learning to address parametric uncertainty of well-known physics-based large-eddy simulation (LES) closures: the Smagorinsky (Smag) and Leith eddy-viscosity models (1 free parameter) and the Jansen-Held (JH) backscattering model (2 free parameters). For 8 cases of 2D geophysical turbulence, optimal parameters are estimated, using ensemble Kalman inversion (EKI), such that for each case, the LES' energy spectrum matches that of direct numerical simulation (DNS). Only a small training dataset is needed to calculate the DNS spectra (i.e., the approach is {data-efficient}). We find the optimized parameter(s) of each closure to be constant across broad flow regimes that differ in dominant length scales, eddy/jet structures, and dynamics, suggesting that these closures are {generalizable}. In a-posteriori tests based on the enstrophy spectra and probability density functions (PDFs) of vorticity, LES with optimized closures outperform the baselines (LES with standard Smag, dynamic Smag or Leith), particularly at the tails of the PDFs (extreme events). In a-priori tests, the optimized JH significantly outperforms the baselines and optimized Smag and Leith in terms of interscale enstrophy and energy transfers (still, optimized Smag noticeably outperforms standard Smag). The results show the promise of combining advances in physics-based modeling (e.g., JH) and data-driven modeling (e.g., {online} learning with EKI) to develop data-efficient frameworks for accurate, interpretable, and generalizable closures., Comment: 12 pages, 5 figures, 1 table

Circadian disruption contributes to adverse effects on sleep, performance, and health. One accepted method to track continuous daily changes in circadian timing is to measure core body temperature (CBT), and establish daily, circadian-related CBT minimum time (Tmin). This method typically applies cosine-model fits to measured CBT data, which may not adequately account for substantial wake metabolic activity and sleep effects on CBT that confound and mask circadian effects, and thus estimates of the circadian-related Tmin. This study introduced a novel physiology-grounded analytic approach to separate circadian from non-circadian effects on CBT, which we compared against traditional cosine-based methods. The dataset comprised 33 healthy participants attending a 39-hour in-laboratory study with an initial overnight sleep followed by an extended wake period. CBT data were collected at 30-second intervals via ingestible capsules. Our design captured CBT during both the baseline sleep period and during extended wake period (without sleep) and allowed us to model the influence of circadian and non-circadian effects of sleep, wake, and activity on CBT using physiology-guided generalized additive models. Model fits and estimated Tmin inferred from extended wake without sleep were compared with traditional cosine-based models fits. Compared to the traditional cosine model, the new model exhibited superior fits to CBT (Pearson R 0.90 [95%CI; [0.83 - 0.96] versus 0.81 [0.55-0.93]). The difference between estimated vs measured circadian Tmin, derived from the day without sleep, was better fit with our method (0.2 [-0.5,0.3] hours) versus previous methods (1.4 [1.1 to 1.7] hours). This new method provides superior demasking of non-circadian influences compared to traditional cosine methods, including the removal of a sleep-related bias towards an earlier estimate of circadian Tmin., Comment: 21 pages, 2 figures

The training phase of deep neural networks requires substantial resources and as such is often performed on cloud servers. However, this raises privacy concerns when the training dataset contains sensitive content, e.g., face images. In this work, we propose a method to perform the training phase of a deep learning model on both an edge device and a cloud server that prevents sensitive content being transmitted to the cloud while retaining the desired information. The proposed privacy-preserving method uses adversarial early exits to suppress the sensitive content at the edge and transmits the task-relevant information to the cloud. This approach incorporates noise addition during the training phase to provide a differential privacy guarantee. We extensively test our method on different facial datasets with diverse face attributes using various deep learning architectures, showcasing its outstanding performance. We also demonstrate the effectiveness of privacy preservation through successful defenses against different white-box and deep reconstruction attacks., Comment: 16 pages, 16 figures, 6 tables

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

A long-standing question in automatic speech recognition research is how to attribute errors to the ability of a model to model the acoustics, versus its ability to leverage higher-order context (lexicon, morphology, syntax, semantics). We validate a novel approach which models error rates as a function of relative textual predictability, and yields a single number, $k$, which measures the effect of textual predictability on the recognizer. We use this method to demonstrate that a Wav2Vec 2.0-based model makes greater stronger use of textual context than a hybrid ASR model, in spite of not using an explicit language model, and also use it to shed light on recent results demonstrating poor performance of standard ASR systems on African-American English. We demonstrate that these mostly represent failures of acoustic--phonetic modelling. We show how this approach can be used straightforwardly in diagnosing and improving ASR., Comment: Proceedings of Interspeech 2024

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random neural network whose hidden weights and biases are sampled from a probability distribution. Only the final output layer is fit to data. In randomized algorithms like RFR, the hyperparameters that characterize the sampling distribution greatly impact performance, yet are not directly accessible from samples. This makes optimization of hyperparameters via standard (gradient-based) optimization tools inapplicable. Inspired by Bayesian ideas from GPR, this paper introduces a random objective function that is tailored for hyperparameter tuning of vector-valued random features. The objective is minimized with ensemble Kalman inversion (EKI). EKI is a gradient-free particle-based optimizer that is scalable to high-dimensions and robust to randomness in objective functions. A numerical study showcases the new black-box methodology to learn hyperparameter distributions in several problems that are sensitive to the hyperparameter selection: two global sensitivity analyses, integrating a chaotic dynamical system, and solving a Bayesian inverse problem from atmospheric dynamics. The success of the proposed EKI-based algorithm for RFR suggests its potential for automated optimization of hyperparameters arising in other randomized algorithms.

This paper examines the extent to which large language models (LLMs) have developed higher-order theory of mind (ToM); the human ability to reason about multiple mental and emotional states in a recursive manner (e.g. I think that you believe that she knows). This paper builds on prior work by introducing a handwritten test suite -- Multi-Order Theory of Mind Q&A -- and using it to compare the performance of five LLMs to a newly gathered adult human benchmark. We find that GPT-4 and Flan-PaLM reach adult-level and near adult-level performance on ToM tasks overall, and that GPT-4 exceeds adult performance on 6th order inferences. Our results suggest that there is an interplay between model size and finetuning for the realisation of ToM abilities, and that the best-performing LLMs have developed a generalised capacity for ToM. Given the role that higher-order ToM plays in a wide range of cooperative and competitive human behaviours, these findings have significant implications for user-facing LLM applications.

We study the convex hull of a set $S\subset \mathbb{R}^n$ defined by three quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take nonnegative linear combinations of the defining inequalities of $S$. We call such inequalities aggregations. We introduce a new technique relating aggregations to properties of the spectral curve, i.e. the curve defined by the vanishing of the determinant polynomial, and utilizing known spectral sequences (Agrachev and Lerario, 2012). We find new families beyond those identified in (Dey, Mu\~noz, and Serrano, 2022; Blekherman, Dey, and Sun, 2024), where the convex hull is defined by aggregations. We also prove a characterization of the emptiness of the projective variety defined by $3$ homogeneous quadratics in terms of the spectral curve generalizing results of (Agrachev, 1988)., Comment: 30 pages, 6 figures

Machine learning is playing an increasing role in hydrology, supplementing or replacing physics-based models. One notable example is the use of recurrent neural networks (RNNs) for forecasting streamflow given observed precipitation and geographic characteristics. Training of such a model over the continental United States (CONUS) demonstrated that a single set of model parameters can be used across independent catchments, and that RNNs can outperform physics-based models. In this work, we take a next step and study the performance of RNNs for river routing in land surface models (LSMs). Instead of observed precipitation, the LSM-RNN uses instantaneous runoff calculated from physics-based models as an input. We train the model with data from river basins spanning the globe and test using historical streamflow measurements. The model demonstrates skill at generalization across basins (predicting streamflow in catchments not used in training) and across time (predicting streamflow during years not used in training). We compare the predictions from the LSM-RNN to an existing physics-based model calibrated with a similar dataset and find that the LSM-RNN outperforms the physics-based model. Our results show that RNNs are effective for global streamflow prediction from runoff inputs and motivate the development of complete routing models that can capture nested sub-basis connections., Comment: 32 pages, 11 figures; submitted in HESS (EGU) with CCBY license

We present a simple argument using Promise Theory and dimensional analysis for the Dunbar scaling hierarchy, supported by recent data from group formation in Wikipedia editing. We show how the assumption of a common priority seeds group alignment until the costs associated with attending to the group outweigh the benefits in a detailed balance scenario. Subject to partial efficiency of implementing promised intentions, we can reproduce a series of compatible rates that balance growth with entropy.

Human communities have self-organizing properties in which specific Dunbar Numbers may be invoked to explain group attachments. By analyzing Wikipedia editing histories across a wide range of subject pages, we show that there is an emergent coherence in the size of transient groups formed to edit the content of subject texts, with two peaks averaging at around $N=8$ for the size corresponding to maximal contention, and at around $N=4$ as a regular team. These values are consistent with the observed sizes of conversational groups, as well as the hierarchical structuring of Dunbar graphs. We use the Promise Theory model of bipartite trust to derive a scaling law that fits the data and may apply to all group size distributions, when based on attraction to a seeded group process. In addition to providing further evidence that even spontaneous communities of strangers are self-organizing, the results have important implications for the governance of the Wikipedia commons and for the security of all online social platforms and associations., Comment: Expanded method section and changed the title to be more specific and informative

It has been generally assumed in the automatic speech recognition (ASR) literature that it is better for models to have access to wider context windows. Yet, many of the potential reasons this might be true in the supervised setting do not necessarily transfer over to the case of unsupervised learning. We investigate how much context is necessary to achieve high-quality pre-trained acoustic models using self-supervised learning. We principally investigate contrastive predictive coding (CPC), which we adapt to be able to precisely control the amount of context visible to the model during training and inference. We find that phone discriminability in the resulting model representations peaks at around 40~ms of preceding context, and that having too much context (beyond around 320 ms) substantially degrades the quality of the representations. Surprisingly, we find that this pattern also transfers to supervised ASR when the pre-trained representations are used as frozen input features. Our results point to potential changes in the design of current upstream architectures to better facilitate a variety of downstream tasks., Comment: Repository at https://github.com/sdrobert/scpc. This work has been submitted to the IEEE for possible publication

This paper introduces an effective solution for retrofitting construction power tools with low-power IoT to enable accurate activity classification. We address the challenge of distinguishing between when a power tool is being moved and when it is actually being used. To achieve classification accuracy and power consumption preservation a newly released algorithm called MiniRocket was employed. Known for its accuracy, scalability, and fast training for time-series classification, in this paper, it is proposed as a TinyML algorithm for inference on resource-constrained IoT devices. The paper demonstrates the portability and performance of MiniRocket on a resource-constrained, ultra-low power sensor node for floating-point and fixed-point arithmetic, matching up to 1% of the floating-point accuracy. The hyperparameters of the algorithm have been optimized for the task at hand to find a Pareto point that balances memory usage, accuracy and energy consumption. For the classification problem, we rely on an accelerometer as the sole sensor source, and BLE for data transmission. Extensive real-world construction data, using 16 different power tools, were collected, labeled, and used to validate the algorithm's performance directly embedded in the IoT device. Experimental results demonstrate that the proposed solution achieves an accuracy of 96.9% in distinguishing between real usage status and other motion statuses while consuming only 7kB of flash and 3kB of RAM. The final application exhibits an average current consumption of less than 15{\mu}W for the whole system, resulting in battery life performance ranging from 3 to 9 years depending on the battery capacity (250-500mAh) and the number of power tool usage hours (100-1500h).

We introduce a new zero resource code-switched speech benchmark designed to directly assess the code-switching capabilities of self-supervised speech encoders. We showcase a baseline system of language modeling on discrete units to demonstrate how the code-switching abilities of speech encoders can be assessed in a zero-resource manner. Our experiments encompass a variety of well-known speech encoders, including Wav2vec 2.0, HuBERT, XLSR, etc. We examine the impact of pre-training languages and model size on benchmark performance. Notably, though our results demonstrate that speech encoders with multilingual pre-training, exemplified by XLSR, outperform monolingual variants (Wav2vec 2.0, HuBERT) in code-switching scenarios, there is still substantial room for improvement in their code-switching linguistic abilities., Comment: Accepted by ICASSP 2024 (v2)

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point.

We characterise possible identities among the two-loop partial amplitudes of gluon scattering in Yang-Mills theory. We use known amplitudes in an exhaustive search to identify potential new relations. We find two candidate relations which may extend to all-$n$ amplitudes.