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Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,700 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 27 pages, 6 figures

The research was commissioned by the National Association of School-Based Teacher Trainers (NASBTT) and Universities' Council for the Education of Teachers (UCET) to estimate the costs and possible impact on teacher supply of introducing a new Teacher Student Loan Reimbursement (TSLR) scheme. Under a TSLR scheme, the government pays back any student loan repayments a teacher made in the previous year provided they are still teaching in a state school and are in the first ten years of their career. The report presents analysis modelling the possible impact on teacher retention of introducing a TSLR scheme. We also compared the value for money of a TSLR scheme to other financial incentives designed to improve teacher supply, namely bursary increases and early-career retention payments (ECRPs). The research suggests that a TSLR scheme could prove a cost-effective option for policymakers alongside ECRPs, particularly when bursaries are already at a high level. Key findings: (1) Our modelling estimates that introducing a TSLR scheme in 2025/26 for all teachers who are in their first ten years since qualifying would lead to an increase of around 2,100 teachers in the first year of the programme; (2) The cost per additional teacher-year gained was lowest for bursaries, where a subject had no existing bursary (around £9,000) or where the existing bursary was low (around £10,000 per additional teacher-year for an existing bursary of £10,000). This suggests that a policy approach of first raising bursaries where they are low is likely to be most cost effective; and (3) The cost per additional teacher-year gained was similar for TSLRs and ECRPs (around £12,500). Both were also very similar to the cost per additional teacher-year where bursaries are already around £30,000. This suggests that where there is already a high bursary (e.g. maths and physics currently attract a £28,000 bursary) it is worth focusing on incentivising retention.

We introduce COU: Common Objects Underwater, an instance-segmented image dataset of commonly found man-made objects in multiple aquatic and marine environments. COU contains approximately 10K segmented images, annotated from images collected during a number of underwater robot field trials in diverse locations. COU has been created to address the lack of datasets with robust class coverage curated for underwater instance segmentation, which is particularly useful for training light-weight, real-time capable detectors for Autonomous Underwater Vehicles (AUVs). In addition, COU addresses the lack of diversity in object classes since the commonly available underwater image datasets focus only on marine life. Currently, COU contains images from both closed-water (pool) and open-water (lakes and oceans) environments, of 24 different classes of objects including marine debris, dive tools, and AUVs. To assess the efficacy of COU in training underwater object detectors, we use three state-of-the-art models to evaluate its performance and accuracy, using a combination of standard accuracy and efficiency metrics. The improved performance of COU-trained detectors over those solely trained on terrestrial data demonstrates the clear advantage of training with annotated underwater images. We make COU available for broad use under open-source licenses.

Genestier--Lafforgue and Fargues--Scholze have constructed a semisimple local Langlands paramterization for reductive groups over equicharacteristic local fields. Assuming a version of the stable twisted trace formula for function fields, we prove the surjectivity of this parameterization for split groups in sufficiently large characteristic.

Electroencephalograms (EEG) are invaluable for treating neurological disorders, however, mapping EEG electrode readings to brain activity requires solving a challenging inverse problem. Due to the time series data, the use of $\ell_1$ regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of $\ell_1$ regularization, $\ell_2$-based approaches such as sLORETA are used in practice. In this work, we formulate EEG source localization as a graphical generalized elastic net inverse problem and present a variable projected algorithm (VPAL) suitable for fast EEG source localization. We prove convergence of this solver for a broad class of separable convex, potentially non-smooth functions subject to linear constraints and include a modification of VPAL that reconstructs time points in sequence, suitable for real-time reconstruction. Our proposed methods are compared to state-of-the-art approaches including sLORETA and other methods for $\ell_1$-regularized inverse problems.

A key requirement of any separable quantum state is that its density matrix has a positive partial transpose. For continuous bipartite quantum states, violation of this condition may be tested via the hierarchy of negative-partial-transpose (NPT) based entanglement criteria introduced by Shchukin and Vogel [Phys. Rev. Lett. 95, 230502 (2005)]. However, a procedure for selecting the optimal NPT-based criterion is currently lacking. Here, we develop a framework to select the optimal criterion by determining the level of confidence of criteria within the Shchukin and Vogel hierarchy for finite measurement number, environmental noise, and the optimal allocation of measurement resources. To demonstrate the utility of our approach, we apply our statistical framework to prominent example Gaussian and non-Gaussian states, including the two-mode squeezed vacuum state, the quanta-subtracted two-mode squeezed vacuum state, and the two-mode Schr\"odinger-cat state. Beyond bipartite inseparability tests, our framework can be applied to any Hermitian matrix constructed of observable moments and thus can be utilized for a wide variety of other nonclassicality criteria and multi-mode entanglement tests., Comment: 23 pages, 3 figures

We study the effect of providing information to agents who queue before a scarce good is distributed at a fixed time. When agents have quasi-linear utility in time spent waiting, they choose entry times as they would bids in a descending auction. An information designer can influence their behavior by providing updates about the length of the queue. Many natural information policies release "sudden bad news," which occurs when agents learn that the queue is longer than previously believed. We show that sudden bad news can cause assortative inefficiency by prompting a mass of agents to simultaneously attempt to join the queue. As a result, if the value distribution has an increasing (decreasing) hazard rate, information policies that release sudden bad news increase (decrease) total surplus, relative to releasing no information. When agents face entry costs to join the queue and the value distribution has a decreasing hazard rate, an information designer maximizes total surplus by announcing only when the queue is full., Comment: 21 pages

Conducting levitated mechanical experiments in extreme conditions has long been the aim of researchers, as it allows for the investigation of new fundamental physics phenomena. One of the great frontiers has been sending these experiments into the micro-g environment of space, with multiple proposals calling for such a platform. At the same time, levitated sensors have demonstrated a high sensitivity to external stimuli which will only improve in low-vibrational conditions. conditions This paper describes the development of a technology demonstrator for optical and magnetic trapping experiments in space. Our payload represents the first concrete step towards future missions with aims of probing fundamental physical questions: matter-wave interferometry of nanoparticles to probe the limits of macroscopic quantum mechanics, detection of Dark Matter candidates and gravitational waves to test physics beyond the Standard Model, and accelerometry for Earth-observation., Comment: 12 pages, 4 figures, 2 tables. Comments welcome

As scientific facilities transition toward high-throughput, data-intensive experiments, there is a growing need for real-time computing at the edge to support autonomous decision-making and minimize data transmission bottlenecks. Department of Energy (DOE) initiatives emphasize the development of heterogeneous computing architectures that integrate machine learning (ML) models with specialized hardware such as FPGAs, GPUs, and embedded systems to meet the demands of next-generation experiments. These advances are critical for facilities such as X-ray free-electron lasers (XFELs), where high-repetition-rate experiments produce terabyte-scale datasets, requiring real-time analysis and control. To address this challenge, we introduce DCIFR, a deep learning framework optimized for edge processing and high-speed X-ray diagnostics at SLAC's Linac Coherent Light Source (LCLS). DCIFR leverages a hybrid neural architecture, combining convolutional neural networks (CNNs), bidirectional long short-term memory (BiLSTM) networks, and residual neural networks (ResNets) to denoise sinograms, classify X-ray sub-spikes, and extract phase separation with attosecond precision. The model achieves a phase extraction accuracy of 0.04652 radians (29.6 attoseconds at 1.2 um streaking wavelength) with inference latencies of 168.3 us and throughput exceeding 10kHz. Designed for deployment on heterogeneous architectures, DCIFR reduces computational overhead and supports future AI-driven feedback loops for ultrafast experiments. This work demonstrates the potential of edge AI and hardware acceleration to drive scalable, autonomous data analysis in next-generation DOE scientific facilities.

We report the confirmation of TOI-6324 b, an Earth-sized (1.059 $\pm$ 0.041 R$_\oplus$) ultra-short-period (USP) planet orbiting a nearby ($\sim$20 pc) M dwarf. Using the newly commissioned Keck Planet Finder (KPF) spectrograph, we have measured the mass of TOI-6324 b 1.17 $\pm$ 0.22 M$_\oplus$. Because of its extremely short orbit of just $\sim$6.7 hours, TOI-6324 b is intensely irradiated by its M dwarf host, and is expected to be stripped of any thick, H/He envelope. We were able to constrain its interior composition and found an iron core mass fraction (CMF = 27$\pm$37%) consistent with that of Earth ($\sim$33%) and other confirmed USPs. TOI-6324 b is the closest to Earth-sized USP confirmed to date. TOI-6324 b is a promising target for JWST phase curve and secondary eclipse observations (Emission Spectroscopy Metric = 25) which may reveal its surface mineralogy, day-night temperature contrast, and possible tidal deformation. From 7 sectors of TESS data, we report a tentative detection of the optical phase curve variation with an amplitude of 42$\pm$28 ppm., Comment: 16 pages, 5 figures, 2 tables

A proposal for the CEPC ECAL is a highly-granular scintillating crystal design that uses SiPMs to measure physics signals from photons. Radiation damage to the silicon will impair the performance of the calorimeter due to dark noise, which will affect the reconstruction capabilities of the calorimeter system. This paper presents a simulation study assessing the effect of radiation damage of SiPM dark noise on the response from calorimeter to electrons due to changing fluence and temperature. It was observed that dark noise significantly degrades the linearity of response, with up to 45% error in reconstructed energy for a 1 GeV shower at a fluence of $1 \times 10^{10}\mathrm{cm}^{-2}$. The stochastic and noise resolution terms was observed to remain stable, increasing only by 0.2% and 1% respectively in the range $1 \times 10^{7}-1 \times 10^{10}\mathrm{cm}^{-2}$ fluence. Under the assumption of no irradiation, the influence of dark noise with temperature in the normal operating range of the calorimeter system was estimated to be negligible.

Motor skill acquisition in fields like surgery, robotics, and sports involves learning complex task sequences through extensive training. Traditional performance metrics, like execution time and error rates, offer limited insight as they fail to capture the neural mechanisms underlying skill learning and retention. This study introduces directed functional connectivity (dFC), derived from electroencephalography (EEG), as a novel brain-based biomarker for assessing motor skill learning and retention. For the first time, dFC is applied as a biomarker to map the stages of the Fitts and Posner motor learning model, offering new insights into the neural mechanisms underlying skill acquisition and retention. Unlike traditional measures, it captures both the strength and direction of neural information flow, providing a comprehensive understanding of neural adaptations across different learning stages. The analysis demonstrates that dFC can effectively identify and track the progression through various stages of the Fitts and Posner model. Furthermore, its stability over a six-week washout period highlights its utility in monitoring long-term retention. No significant changes in dFC were observed in a control group, confirming that the observed neural adaptations were specific to training and not due to external factors. By offering a granular view of the learning process at the group and individual levels, dFC facilitates the development of personalized, targeted training protocols aimed at enhancing outcomes in fields where precision and long-term retention are critical, such as surgical education. These findings underscore the value of dFC as a robust biomarker that complements traditional performance metrics, providing a deeper understanding of motor skill learning and retention.

Passive imaging through optical obscurants is a promising application for mm-wave sensing. We have thus developed the Superconducting Kinetic Inductance Passive Radiometer (SKIPR), a 150 GHz polarization-sensitive photometric camera optimized for terrestrial imaging using a focal plane array with 3,840 kinetic inductance detectors (KIDs). We present a full description of the instrument design, with a particular emphasis on the cryogenic system based on a Gifford-McMahon cryocooler with a two-stage Adiabatic Demagnetization Refrigerator and a dedicated 1.59 m crossed Dragone telescope with an altitude/azimuth mount. We include a detailed lab-based characterization of the KIDs, which results in a determination of their superconducting resonator parameters and optical properties. We also present in situ measurements from the telescope, including point-spread functions and noise characterization. In sum, we find that SKIPR performs as expected, providing diffraction-limited imaging with detector noise performance set by the random arrivals of photons from the ambient background. There is minimal variation in detector characteristics over the full SKIPR focal plane array, and the overall detector yield is 92 per cent.

This paper provides a combinatorial characterisation for generic forced symmetric rigidity of bar-joint frameworks in the Euclidean plane that are symmetric with respect to the orientation-reversing wallpaper group $\mathbb{Z}^2\rtimes\mathcal{C}_s$, also known as $pm$ in crystallography, under a fixed lattice representation. Corresponding results for the wallpaper groups $cm$ and $pg$ follow directly from this. The method used also provides an inductive construction for the corresponding gain graphs, in terms of Henneberg-type graph operations., Comment: 22 pages

We measure radial stellar age gradients in the relatively isolated gas-rich dwarf irregular WLM, combining JWST NIRCam and NIRISS imaging with six archival Hubble fields over semi-major axis equivalent distances of 0$\lesssim$R$_{SMA}$$\lesssim$4 kpc ($\lesssim$3R$_{hl}$). Fitting lifetime star formation histories (SFHs) to resolved color-magnitude diagrams (CMDs), radial age gradients are quantified using $\tau_{90}$ and $\tau_{50}$, the lookback times to form 90\% and 50\% of the cumulative stellar mass. We find that globally, the outskirts of WLM are older on average, with ($\delta$$\tau_{90}$, $\delta$$\tau_{50}$)/$\delta$R$_{SMA}=$(0.82$^{+0.10}_{-0.10}$, 1.60$^{+0.23}_{-0.22}$) Gyr/kpc (stat.), in good agreement with simulations. However, we also detect an azimuthal dependence of radial stellar age gradients, finding that stars on the leading edge of WLM (relative to its proper motion) are both younger and have a flatter age gradient compared to the trailing edge. This difference persists over 0.6$\lesssim$R$_{SMA}$$\lesssim$3.2 kpc ($\sim$0.5$-$2.5R$_{hl}$) and lookback times up to $\sim$8 Gyr, and is robust to assumed stellar evolutionary model. Our results are consistent with star formation triggered by ram pressure stripping from a circumgalactic and/or intergalactic medium, suggested by recent HI observations. If confirmed, processes typifying dense environments, such as ram pressure stripping, may be more relevant to the evolution of isolated galaxies than previously thought., Comment: ApJ in press. 23 pages, 8 figures, 3 tables

In this paper we show that a generalized version of the Nikoli puzzle Slant is NP-complete. We also give polynomial time algorithms for versions of the puzzle where some constraints are omitted. These problems correspond to simultaneously satisfying connectivity and vertex degree constraints in a grid graph and its dual., Comment: 9 pages, 12 figures. Appeared at the Canadian Conference on Computational Geometry 2024 (CCCG 2024)

Objective motor skill assessment plays a critical role in fields such as surgery, where proficiency is vital for certification and patient safety. Existing assessment methods, however, rely heavily on subjective human judgment, which introduces bias and limits reproducibility. While recent efforts have leveraged kinematic data and neural imaging to provide more objective evaluations, these approaches often overlook the dynamic neural mechanisms that differentiate expert and novice performance. This study proposes a novel method for motor skill assessment based on dynamic directed functional connectivity (dFC) as a neural biomarker. By using electroencephalography (EEG) to capture brain dynamics and employing an attention-based Long Short-Term Memory (LSTM) model for non-linear Granger causality analysis, we compute dFC among key brain regions involved in psychomotor tasks. Coupled with hierarchical task analysis (HTA), our approach enables subtask-level evaluation of motor skills, offering detailed insights into neural coordination that underpins expert proficiency. A convolutional neural network (CNN) is then used to classify skill levels, achieving greater accuracy and specificity than established performance metrics in laparoscopic surgery. This methodology provides a reliable, objective framework for assessing motor skills, contributing to the development of tailored training protocols and enhancing the certification process.

Machine learning models assume that training and test samples are drawn from the same distribution. As such, significant differences between training and test distributions often lead to degradations in performance. We introduce Multiple Distribution Shift -- Aerial (MDS-A) -- a collection of inter-related datasets of the same aerial domain that are perturbed in different ways to better characterize the effects of out-of-distribution performance. Specifically, MDS-A is a set of simulated aerial datasets collected under different weather conditions. We include six datasets under different simulated weather conditions along with six baseline object-detection models, as well as several test datasets that are a mix of weather conditions that we show have significant differences from the training data. In this paper, we present characterizations of MDS-A, provide performance results for the baseline machine learning models (on both their specific training datasets and the test data), as well as results of the baselines after employing recent knowledge-engineering error-detection techniques (EDR) thought to improve out-of-distribution performance. The dataset is available at https://lab-v2.github.io/mdsa-dataset-website.

In an era of increasingly capable foundation models, job seekers are turning to generative AI tools to enhance their application materials. However, unequal access to and knowledge about generative AI tools can harm both employers and candidates by reducing the accuracy of hiring decisions and giving some candidates an unfair advantage. To address these challenges, we introduce a new variant of the strategic classification framework tailored to manipulations performed using large language models, accommodating varying levels of manipulations and stochastic outcomes. We propose a ``two-ticket'' scheme, where the hiring algorithm applies an additional manipulation to each submitted resume and considers this manipulated version together with the original submitted resume. We establish theoretical guarantees for this scheme, showing improvements for both the fairness and accuracy of hiring decisions when the true positive rate is maximized subject to a no false positives constraint. We further generalize this approach to an $n$-ticket scheme and prove that hiring outcomes converge to a fixed, group-independent decision, eliminating disparities arising from differential LLM access. Finally, we empirically validate our framework and the performance of our two-ticket scheme on real resumes using an open-source resume screening tool.

Hybrid traffic laws represent an innovative approach to managing mixed environments of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs) by introducing separate sets of regulations for each vehicle type. These laws are designed to leverage the unique capabilities of CAVs while ensuring both types of cars coexist effectively, ultimately aiming to enhance overall social welfare. This study uses the SUMO simulation platform to explore hybrid traffic laws in a restricted lane scenario. It evaluates static and dynamic lane access policies under varying traffic demands and CAV proportions. The policies aim to minimize average passenger delay and encourage the incorporation of autonomous vehicles with higher occupancy rates. Results demonstrate that dynamic policies significantly improve traffic flow, especially at low CAV proportions, compared to traditional dedicated bus lane strategies. These findings highlight the potential of hybrid traffic laws to enhance traffic efficiency and accelerate the transition to autonomous technology., Comment: 12 pages, 7 figures, 3 tables

Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ of on $G$. We then show that the foliation $\F$ is Riemannian and minimal. This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic., Comment: arXiv admin note: text overlap with arXiv:2308.15971

We develop a fast algorithm to calculate the Artin-Mazur height (equivalently, the quasi-$F$-split height) of a Calabi-Yau hypersurface, building on the work in arXiv:2204.10076. We provide a implementation of our approach, and use it to show that there are quartic K3 surfaces of any Artin-Mazur height over $\mathbb{F}_{5}$ and $\mathbb{F}_7$., Comment: 18 Pages, 7 figures

We present an alternative procedure for defining infra-red counterterms within dimensional regularisation for use in the $R^*$ procedure. The counterterms are given by simple closed expressions, and lead to the standard MSbar UV counterterms., Comment: 41 pages, uses tikz, references added, minor LaTex error corrected

Sparse Autoencoders (SAEs) provide potentials for uncovering structured, human-interpretable representations in Large Language Models (LLMs), making them a crucial tool for transparent and controllable AI systems. We systematically analyze SAE for interpretable feature extraction from LLMs in safety-critical classification tasks. Our framework evaluates (1) model-layer selection and scaling properties, (2) SAE architectural configurations, including width and pooling strategies, and (3) the effect of binarizing continuous SAE activations. SAE-derived features achieve macro F1 > 0.8, outperforming hidden-state and BoW baselines while demonstrating cross-model transfer from Gemma 2 2B to 9B-IT models. These features generalize in a zero-shot manner to cross-lingual toxicity detection and visual classification tasks. Our analysis highlights the significant impact of pooling strategies and binarization thresholds, showing that binarization offers an efficient alternative to traditional feature selection while maintaining or improving performance. These findings establish new best practices for SAE-based interpretability and enable scalable, transparent deployment of LLMs in real-world applications. Full repo: https://github.com/shan23chen/MOSAIC.

We give a new construction of the incipient infinite cluster (IIC) associated with high-dimensional percolation in a broad setting and under minimal assumptions. Our arguments differ substantially from earlier constructions of the IIC; we do not directly use the machinery of the lace expansion or similar diagrammatic expansions. We show that the IIC may be constructed by conditioning on the cluster of a vertex being infinite in the supercritical regime $p > p_c$ and then taking $p \searrow p_c$. Furthermore, at criticality, we show that the IIC may be constructed by conditioning on a connection to an arbitrary distant set $V$, generalizing previous constructions where one conditions on a connection to a single distant vertex or the boundary of a large box. The input to our proof are the asymptotics for the two-point function obtained by Hara, van der Hofstad, and Slade. Our construction thus applies in all dimensions for which those asymptotics are known, rather than an unspecified high dimension considered in previous works. The results in this paper will be instrumental in upcoming work related to structural properties and scaling limits of various objects involving high-dimensional percolation clusters at and near criticality., Comment: 36 pages, 3 figures

Ordinal variables, such as on the Likert scale, are common in applied research. Yet, existing methods for causal inference tend to target nominal or continuous data. When applied to ordinal data, this fails to account for the inherent ordering or imposes well-defined relative magnitudes. Hence, there is a need for specialised methods to compute interventional effects between ordinal variables while accounting for their ordinality. One potential framework is to presume a latent Gaussian Directed Acyclic Graph (DAG) model: that the ordinal variables originate from marginally discretising a set of Gaussian variables whose latent covariance matrix is constrained to satisfy the conditional independencies inherent in a DAG. Conditioned on a given latent covariance matrix and discretisation thresholds, we derive a closed-form function for ordinal causal effects in terms of interventional distributions in the latent space. Our causal estimation combines naturally with algorithms to learn the latent DAG and its parameters, like the Ordinal Structural EM algorithm. Simulations demonstrate the applicability of the proposed approach in estimating ordinal causal effects both for known and unknown structures of the latent graph. As an illustration of a real-world use case, the method is applied to survey data of 408 patients from a study on the functional relationships between symptoms of obsessive-compulsive disorder and depression., Comment: 22 pages, 4 figures (plus 16 pages of appendices)

Machine learning algorithms have enabled high quality stereo depth estimation to run on Augmented and Virtual Reality (AR/VR) devices. However, high energy consumption across the full image processing stack prevents stereo depth algorithms from running effectively on battery-limited devices. This paper introduces SteROI-D, a full stereo depth system paired with a mapping methodology. SteROI-D exploits Region-of-Interest (ROI) and temporal sparsity at the system level to save energy. SteROI-D's flexible and heterogeneous compute fabric supports diverse ROIs. Importantly, we introduce a systematic mapping methodology to effectively handle dynamic ROIs, thereby maximizing energy savings. Using these techniques, our 28nm prototype SteROI-D design achieves up to 4.35x reduction in total system energy compared to a baseline ASIC., Comment: Accepted as a full paper by the 2025 EDGE AI FOUNDATION Austin

We present a machine-learning-based workflow to model an unbinned likelihood from its samples. A key advancement over existing approaches is the validation of the learned likelihood using rigorous statistical tests of the joint distribution, such as the Kolmogorov-Smirnov test of the joint distribution. Our method enables the reliable communication of experimental and phenomenological likelihoods for subsequent analyses. We demonstrate its effectiveness through three case studies in high-energy physics. To support broader adoption, we provide an open-source reference implementation, nabu., Comment: 4 pages + references, 1 figure

We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called $p$-conductance learning that generalizes the $p$-Laplace and Poisson learning methods by introducing an objective reminiscent of $p$-Laplacian regularization and an affine relaxation of the label constraints. This leads to a family of probability measure mincut programs that balance sparse edge removal with accurate distribution separation. Our theoretical analysis connects these programs to well-known variational and probabilistic problems on graphs (including randomized cuts, effective resistance, and Wasserstein distance) and provides motivation for robustness when labels are diffused via the heat kernel. Computationally, we develop a semismooth Newton-conjugate gradient algorithm and extend it to incorporate class-size estimates when converting the continuous solutions into label assignments. Empirical results on computer vision and citation datasets demonstrate that our approach achieves state-of-the-art accuracy in low label-rate, corrupted-label, and partial-label regimes., Comment: 29 pages, 7 figures

As language models master existing reasoning benchmarks, we need new challenges to evaluate their cognitive frontiers. Puzzle-solving events are rich repositories of challenging multimodal problems that test a wide range of advanced reasoning and knowledge capabilities, making them a unique testbed for evaluating frontier language models. We introduce EnigmaEval, a dataset of problems and solutions derived from puzzle competitions and events that probes models' ability to perform implicit knowledge synthesis and multi-step deductive reasoning. Unlike existing reasoning and knowledge benchmarks, puzzle solving challenges models to discover hidden connections between seemingly unrelated pieces of information to uncover solution paths. The benchmark comprises 1184 puzzles of varying complexity -- each typically requiring teams of skilled solvers hours to days to complete -- with unambiguous, verifiable solutions that enable efficient evaluation. State-of-the-art language models achieve extremely low accuracy on these puzzles, even lower than other difficult benchmarks such as Humanity's Last Exam, unveiling models' shortcomings when challenged with problems requiring unstructured and lateral reasoning.

Next token prediction has been the standard training objective used in large language model pretraining. Representations are learned as a result of optimizing for token-level perplexity. We propose Continuous Concept Mixing (CoCoMix), a novel pretraining framework that combines discrete next token prediction with continuous concepts. Specifically, CoCoMix predicts continuous concepts learned from a pretrained sparse autoencoder and mixes them into the model's hidden state by interleaving with token hidden representations. Through experiments on multiple benchmarks, including language modeling and downstream reasoning tasks, we show that CoCoMix is more sample efficient and consistently outperforms standard next token prediction, knowledge distillation and inserting pause tokens. We find that combining both concept learning and interleaving in an end-to-end framework is critical to performance gains. Furthermore, CoCoMix enhances interpretability and steerability by allowing direct inspection and modification of the predicted concept, offering a transparent way to guide the model's internal reasoning process.

This paper addresses the challenge of occluded robot grasping, i.e. grasping in situations where the desired grasp poses are kinematically infeasible due to environmental constraints such as surface collisions. Traditional robot manipulation approaches struggle with the complexity of non-prehensile or bimanual strategies commonly used by humans in these circumstances. State-of-the-art reinforcement learning (RL) methods are unsuitable due to the inherent complexity of the task. In contrast, learning from demonstration requires collecting a significant number of expert demonstrations, which is often infeasible. Instead, inspired by human bimanual manipulation strategies, where two hands coordinate to stabilise and reorient objects, we focus on a bimanual robotic setup to tackle this challenge. In particular, we introduce Constraint-based Manipulation for Bimanual Occluded Grasping (COMBO-Grasp), a learning-based approach which leverages two coordinated policies: a constraint policy trained using self-supervised datasets to generate stabilising poses and a grasping policy trained using RL that reorients and grasps the target object. A key contribution lies in value function-guided policy coordination. Specifically, during RL training for the grasping policy, the constraint policy's output is refined through gradients from a jointly trained value function, improving bimanual coordination and task performance. Lastly, COMBO-Grasp employs teacher-student policy distillation to effectively deploy point cloud-based policies in real-world environments. Empirical evaluations demonstrate that COMBO-Grasp significantly improves task success rates compared to competitive baseline approaches, with successful generalisation to unseen objects in both simulated and real-world environments., Comment: 14 pages, 11 figures, https://combo-grasp.github.io/

For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least $\Omega(k^2)$. We find that initialization routines are not a bottleneck for this case. Instead, it is critical to improve the speed of Lloyd's local-search algorithm, particularly the step that reassigns points to their closest center. Attempting to improve this step naturally leads us to leverage approximate nearest-neighbor search methods, although this alone is not enough to be practical. Instead, we propose a family of problems we call "Seeded Approximate Nearest-Neighbor Search", for which we propose "Seeded Search-Graph" methods as a solution., Comment: 29 pages, 8 figures

Recent deep learning-based image completion methods, including both inpainting and outpainting, have demonstrated promising results in restoring corrupted images by effectively filling various missing regions. Among these, Generative Adversarial Networks (GANs) and Denoising Diffusion Probabilistic Models (DDPMs) have been employed as key generative image completion approaches, excelling in the field of generating high-quality restorations with reduced artifacts and improved fine details. In previous work, we developed a method aimed at synthesizing views from novel microscope positions for mastoidectomy surgeries; however, that approach did not have the ability to restore the surrounding surgical scene environment. In this paper, we propose an efficient method to complete the surgical scene of the synthetic postmastoidectomy dataset. Our approach leverages self-supervised learning on real surgical datasets to train a Single-Step Denoising Diffusion-GAN (SSDD-GAN), combining the advantages of diffusion models with the adversarial optimization of GANs for improved Structural Similarity results of 6%. The trained model is then directly applied to the synthetic postmastoidectomy dataset using a zero-shot approach, enabling the generation of realistic and complete surgical scenes without the need for explicit ground-truth labels from the synthetic postmastoidectomy dataset. This method addresses key limitations in previous work, offering a novel pathway for full surgical microscopy scene completion and enhancing the usability of the synthetic postmastoidectomy dataset in surgical preoperative planning and intraoperative navigation.

In 2018, by Ramsey and Hoffman theory, Koolen, Yang, and Yang presented a structural result on graphs with smallest eigenvalue at least $-3$ and large minimum degree. In this study, we depart from the conventional use of Ramsey theory and instead employ a novel approach that combines the Bose-Laskar type argument with Hoffman theory to derive structural insights into $\mu$-bounded graphs with fixed smallest eigenvalue. Our method establishes a reasonable bound on the minimum degree. Note that local graphs of distance-regular graphs are $\mu$-bounded. We apply these results to characterize the structure for any local graph of a distance-regular graph with classical parameters $(D,b,\alpha,\beta)$. Consequently, we show that the parameter $\alpha$ is bounded by a cubic polynomial in $b$ if $D \geq 9$ and $b \geq 2$. Also we show that $\alpha \leq 2$ if $b =2$ and $D \geq 12$.

Probabilistic programming methods have revolutionised Bayesian inference, making it easier than ever for practitioners to perform Markov-chain-Monte-Carlo sampling from non-conjugate posterior distributions. Here we focus on Stan, arguably the most used probabilistic programming tool for Bayesian inference (Carpenter et al., 2017), and its interface with R via the brms (Burkner, 2017) and rstanarm (Goodrich et al., 2024) packages. Although easy to implement, these tools can become computationally prohibitive when applied to datasets with many observations or models with numerous parameters. While the use of sufficient statistics is well-established in theory, it has been surprisingly overlooked in state-of-the-art Stan software. We show that when the likelihood can be written in terms of sufficient statistics, considerable computational improvements can be made to current implementations. We demonstrate how this approach provides accurate inference at a fraction of the time than state-of-the-art implementations for Gaussian linear regression models with non-conjugate priors, hierarchical random effects models, and factor analysis models. Our results also show that moderate computational gains can be achieved even in models where the likelihood can only be partially written in terms of sufficient statistics.

We report the masses, sizes, and orbital properties of 86 planets orbiting 55 stars observed by NASA's K2 Mission with follow-up Doppler measurements by the HIRES spectrometer at the W. M. Keck Observatory and the Automated Planet Finder at Lick Observatory. Eighty-one of the planets were discovered from their transits in the K2 photometry, while five were found based on subsequent Doppler measurements of transiting planet host stars. The sizes of the transiting planets range from Earth-size to larger than Jupiter (1-3 REarth is typical), while the orbital periods range from less than a day to a few months. For 32 of the planets, the Doppler signal was detected with significance greater than 5-sigma (51 were detected with >3-sigma significance). An important characteristic of this catalog is the use of uniform analysis procedures to determine stellar and planetary properties. This includes the transit search and fitting procedures applied to the K2 photometry, the Doppler fitting techniques applied to the radial velocities, and the spectral modeling to determine bulk stellar parameters. Such a uniform treatment will make the catalog useful for statistical studies of the masses, densities, and system architectures of exoplanetary systems. This work also serves as a data release for all previously unpublished RVs and associated stellar activity indicators obtained by our team for these systems, along with derived stellar and planet parameters., Comment: 156 pages, 86 planets, 55 stars, 104 figures, 48 tables. Accepted to ApJS

In this paper, we introduce WorldSense, the first benchmark to assess the multi-modal video understanding, that simultaneously encompasses visual, audio, and text inputs. In contrast to existing benchmarks, our WorldSense has several features: (i) collaboration of omni-modality, we design the evaluation tasks to feature a strong coupling of audio and video, requiring models to effectively utilize the synergistic perception of omni-modality; (ii) diversity of videos and tasks, WorldSense encompasses a diverse collection of 1,662 audio-visual synchronised videos, systematically categorized into 8 primary domains and 67 fine-grained subcategories to cover the broad scenarios, and 3,172 multi-choice QA pairs across 26 distinct tasks to enable the comprehensive evaluation; (iii) high-quality annotations, all the QA pairs are manually labeled by 80 expert annotators with multiple rounds of correction to ensure quality. Based on our WorldSense, we extensively evaluate various state-of-the-art models. The experimental results indicate that existing models face significant challenges in understanding real-world scenarios (48.0% best accuracy). We hope our WorldSense can provide a platform for evaluating the ability in constructing and understanding coherent contexts from omni-modality.

We consider the set ${\mathcal C}_Q$ of Farey fractions $d/b$ of order $Q$ with the property that there exists a matrix $\left( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \right) \in \operatorname{SL}(2,{\mathbb Z})$ of trace at most $Q$, with positive entries and $a\ge \max\{ b,c\}$. We prove that the elements of ${\mathcal C}_Q$ are distributed with respect to the probability measure $(1/\log (4/3)) (1/8 - x/4 + 1/(1+x) -1/(2+x) )$ and that $({\mathcal C}_Q)_Q$ has a limiting gap distribution as $Q\rightarrow \infty$., Comment: 13 pages

Piezoelectric resonators are a common building block for signal processing because of their miniature size, low insertion loss, and high quality factor. As consumer electronics push to millimeter waves frequencies, designers must increase the operating frequency of the resonator. The current state-of-the-art approach to increase the operating frequency is to decrease the thickness of the piezoelectric film to shorten the acoustic wavelength or to use higher order modes. Unfortunately, maintaining high crystal quality typically requires thicker piezoelectric layers. Thinner layers suffer from higher defect densities and increased surface damping, which degrade the electromechanical coupling and quality factor. While acoustic high order modes can also increase operating frequency, the electromechanical coupling rapidly decreases with increasing mode number. Here, we overcome these limitations by utilizing a piezoelectric stack of three layers of lithium niobate with alternating crystallographic orientations to preferentially support higher order modes and thereby enhance the electromechanical coupling without degrading the quality factor. Our approach improves the figure of merit of millimeter-wave acoustic resonators by roughly an order of magnitude greater compared to state-of-the-art piezoelectric resonators above 60 GHz. This concept of alternating crystallographic orientations facilitates a new path to develop millimeter wave resonators with high figures of merit, low insertion loss, and miniature footprints, enabling new applications in millimeter wave signal processing and computing.

Scene graphs have emerged as a structured and serializable environment representation for grounded spatial reasoning with Large Language Models (LLMs). In this work, we propose SG-RwR, a Schema-Guided Retrieve-while-Reason framework for reasoning and planning with scene graphs. Our approach employs two cooperative, code-writing LLM agents: a (1) Reasoner for task planning and information queries generation, and a (2) Retriever for extracting corresponding graph information following the queries. Two agents collaborate iteratively, enabling sequential reasoning and adaptive attention to graph information. Unlike prior works, both agents are prompted only with the scene graph schema rather than the full graph data, which reduces the hallucination by limiting input tokens, and drives the Reasoner to generate reasoning trace abstractly.Following the trace, the Retriever programmatically query the scene graph data based on the schema understanding, allowing dynamic and global attention on the graph that enhances alignment between reasoning and retrieval. Through experiments in multiple simulation environments, we show that our framework surpasses existing LLM-based approaches in numerical Q\&A and planning tasks, and can benefit from task-level few-shot examples, even in the absence of agent-level demonstrations. Project code will be released.

We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is restricted to deterministic classifiers. In contrast, we perform a theoretical analysis of an extension to this setting that allows the learner to produce a randomised classifier. We show that, under certain conditions, the optimal randomised classifier can achieve better accuracy than the optimal deterministic classifier, but under no conditions can it be worse. When a finite set of training data is available, we show that the excess risk of Strategic Empirical Risk Minimisation over the class of randomised classifiers is bounded in a similar manner as the deterministic case. In both the deterministic and randomised cases, the risk of the classifier produced by the learner converges to that of the corresponding optimal classifier as the volume of available training data grows. Moreover, this convergence happens at the same rate as in the i.i.d. case. Our findings are compared with previous theoretical work analysing the problem of strategic classification. We conclude that randomisation has the potential to alleviate some issues that could be faced in practice without introducing any substantial downsides.

Gaussian process (GP) bandits provide a powerful framework for solving blackbox optimization of unknown functions. The characteristics of the unknown function depends heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we propose two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) and HyperPrior GP-TS (HP-GP-TS). We theoretically analyze the algorithms and establish upper bounds for their respective regret. In addition, we demonstrate the effectiveness of our algorithms compared to the alternatives through experiments with synthetic and real-world data., Comment: 16 pages, 12 figures

Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries. Understanding the benefits of symmetry on the statistical and numerical efficiency of learning algorithms is an active area of research. In this work, we show that symmetry has a pronounced impact on the rank of kernel matrices. Specifically, we compute the rank of a polynomial kernel of fixed degree that is invariant under various groups acting independently on its two arguments. In concrete circumstances, including the three aforementioned examples, symmetry dramatically decreases the rank making it independent of the data dimension. In such settings, we show that a simple regression procedure is minimax optimal for estimating an invariant polynomial from finitely many samples drawn across different dimensions. We complete the paper with numerical experiments that illustrate our findings.

In this research-in-progress paper, we apply a computational measure correlating with originality from creativity science: Divergent Semantic Integration (DSI), to a selection of 99,557 scientific abstracts and titles selected from the Web of Science. We observe statistically significant differences in DSI between subject and field of research, and a slight rise in DSI over time. We model the base 10 logarithm of the citation count after 5 years with DSI and find a statistically significant positive correlation in all fields of research with an adjusted $R^2$ of 0.13., Comment: 6 pages, 3 figures, submitted to ISSI 2025, research in progress paper

(ABRIDGED) We use galaxy-galaxy lensing to investigate how the dark matter (DM) haloes and stellar content of galaxies with $0.012 \leq z \leq 0.32$ and $10 \leq \log_{10}(M_\star/\mathrm{M}_\odot) \leq 12$ change as a result of the merger process. To this end, we construct two samples of galaxies obtained from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS), comprising 1 623 post-mergers and $\sim$30 000 non-merging controls, that live in low-density environments to use as our lenses. These samples are weighted to share the same distributions of stellar mass, redshift, and geometric mean distance to a galaxy's three nearest neighbours to ensure differences in the lensing signal are due to the merger process itself. We do not detect a significant difference in the excess surface density profile of post-mergers and non-merging controls with current data. Fitting haloes composed of a point-like stellar mass component and an extended DM structure described by a Navarro-Frenk-White profile to the lensing measurements yields, for both samples, halo masses of $M_\text{halo}\sim 4\times10^{12}\,\mathrm{M}_\odot$ and a moderately negative correlation between $M_\text{halo}$ and concentration $c$. . . . Extreme merger-induced starbursts, in which more than 60 percent of the stars are formed in the burst, are ruled out at the 95 per cent confidence level. Although we do not find merger-induced differences in the DM haloes and stellar content of galaxies with our current data, application of our methods to upcoming surveys that are able to provide samples $\sim$10$\times$ larger than our current catalogue are expected to detect the weak-lensing signatures of mergers and further constrain their properties., Comment: 10 pages, 7 figures, 1 table. Submitted

Measuring the properties of planets younger than about 50 Myr helps to test different planetary formation and evolution models. NASA's Transiting Exoplanet Survey Satellite (TESS) has observed nearly the entire sky, including a wide range of star-forming regions and young stellar clusters, expanding our census of the newborn planet population. In this work, we present the discovery of the TIC 88785435 planetary system located in the Upper-Centaurus Lupus (UCL) region of the Scorpius-Centaurus OB association (Sco-Cen) and a preliminary survey of the planet population within Sco-Cen. TIC 88785435 is a pre-main sequence, K7V dwarf ($M_\star = 0.72M_\odot$, $R_\star = 0.91R_\odot$, $T_\mathrm{eff}$ = 3998K, V = 11.7 mag) located within the bounds of UCL. We investigate the distribution of rotation periods measured from the TESS long-cadence data and the Halpha and Li abundances from the spectra of TIC 88785435. TESS long-candence data reveal that TIC 88785435 hosts a transiting super-Neptune ($R_b = 5.03R_\oplus$, P = 10.51 days), TIC 88785435 b. Ground-based follow-up validates the planetary nature of TIC 88785435 b. Using the TESS data, we perform a preliminary survey to investigate how TIC 88785435 b compares to the population of newly born planets located within Sco-Cen., Comment: 15 pages, 9 Figures, submitted to AJ

Using molecular dynamics simulations of a binary Lennard-Jones model of glass-forming liquids, we examine how the decay of the normalized neighbor-persistence function $C_{\rm B}(t)$, which decays from unity at short times to zero at long times as particles lose the neighbors that were present in their original first coordination shell, compares with those of other, more conventionally utilized relaxation metrics. In the strongly-non-Arrhenius temperature regime below the onset temperature $T_{\rm A}$, we find that $C_{\rm B}(t)$ can be described using the same stretched-exponential functional form that is often utilized to fit the self-intermediate scattering function $S(q, t)$ of glass-forming liquids in this regime. The ratio of the bond lifetime $\tau_{\rm bond}$ associated with the terminal decay of $C_{\rm B}(t)$ to the $\alpha$-relaxation time $\tau_\alpha$ varies appreciably and non-monotonically with $T$, peaking at $\tau_{\rm bond}/\tau_\alpha \simeq 45$ at $T \simeq T_{\rm x}$, where $T_{\rm x}$ is a crossover temperature separating the high- and low-temperature regimes of glass-formation. In contrast, $\tau_{\rm bond}$ remains on the order of the overlap time $\tau_{\rm ov}$ (the time interval over which a typical particle moves by half its diameter), and the peak time $\tau_\chi$ for the susceptibility $\chi_{\rm B}(t)$ associated with the spatial heterogeneity of $C_{\rm B}(t)$ remains on the order of $\tau_{\rm imm}$ (the characteristic lifetime of immobile-particle clusters), even as each of these quantities varies by roughly $5$ orders of magnitude over our studied range of $T$. Thus, we show that $C_{\rm B}(t)$ and $\chi_{\rm B}(t)$ provide semi-quantitative spatially-averaged measures of the slow heterogeneous dynamics associated with the persistence of immobile-particle clusters.

Large-momentum effective theory (LaMET) provides an approach to directly calculate the $x$-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton's momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness $\xi$ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for $[-1+x_0,-\xi-x_0]\cup[-\xi+x_0,\xi-x_0]\cup[\xi+x_0,1-x_0]$, where $x_0$ is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.

We present an update on the analysis of semileptonic $B\rightarrow D^{(*)}$ decays at non-zero recoil. Our computation employs $2 + 1 + 1$ FNAL-MILC ensembles with highly improved staggered quark (HISQ) action for sea and light valence quarks, while the bottom quark is treated using the clover action in the Fermilab interpretation. Simulations are performed across several lattice spacings, ranging approximately from $\sim 0.15$ fm to $\sim 0.06$ fm, and for various quark masses. We will present an overview of the analysis and show some preliminary results for the form factors.