Papers

Tone languages constitute over 50-70% of the world's languages, but the vast majority are low-resource, lacking the large transcribed corpora needed for automatic tone classification. Existing datasets are typically collected at the sentence level, whereas field linguists require fine-grained syllable-level annotations. We propose ToneCL, a lightweight contrastive learning framework for few-shot syllable-level tone classification. We simulate low-resource conditions on Mandarin and Vietnamese, limiting labeled data to tens of examples per tone class. ToneCL is pretrained on unlabeled speech with augmentations that preserve tonal identity, then fine-tuned on few-shot examples. Experiments show our method consistently outperforms baselines, achieving 91.6% on six-speaker Mandarin at 10 shots. Cross-lingual transfer is also effective: pretraining on Vietnamese and fine-tuning on Mandarin reaches 91.0% accuracy at 10 shots. Ablation confirms that frequency band rejection is the most critical augmentation.

We study the finite spectra of the syllogistic logic with cardinality comparisons $S^\dagger(card)$. Since the language does not contain conjunction at the sentence level, we consider the spectrum of a theory $\Gamma$, namely the set of positive integers $n$ for which $\Gamma$ is satisfiable in an $n$-element model. We give a complete classification of these spectra: besides the empty set, every $S^\dagger(card)$-spectrum is either an eventual tail of the positive integers or an eventual tail of the positive even integers. We then consider the extension of $S^\dagger(card)$ by Boolean connectives at the sentence level and show that the collection of its spectra forms the topology generated by the spectra of the original language.

We study the squared Rayleigh-residual functional on complex projective space and its negative gradient flow. For an arbitrary complex matrix, every positive-residual critical point has a strictly descending tangent direction; consequently, the local minima are precisely the eigenlines. For normal matrices, we describe the critical set in terms of circles through spectral points and identify the amplitude dynamics with a replicator equation whose payoff matrix has rank at most four. This gives explicit logarithmic first integrals and a reduced representation of interior trajectories. We compute transverse escape rates near critical components and analyze how polynomial reweighting changes unstable coordinates. Finally, we distinguish local saddle trapping from concentration of Haar-distributed initial states and derive the density of the filtered ensemble. Numerical examples with random spectra and a Jordan block illustrate convergence, nonmonotone Rayleigh motion, and the improvement of finite-time spectral exploration by low-degree random polynomial filters.

In cavity optomechanics, the standard large-detuning regime is commonly described by retaining only the radiation-pressure interaction, while higher-order mirror–field interactions are assumed to be negligible. This approximation, however, fails to provide a microscopic explanation for the vacuum-mediated heat transfer observed between the mechanical membranes in the experiment of Fong, et.al.,[Nature 576, 243 (2019)], whose physical origin has remained under active debate. Here, using a fully quantum model, we show that the neglected higher-order optomechanical interactions naturally generate phonon-phonon coupling and quantitatively account for the observed energy exchange within the standard optomechanical framework. Building on this microscopic description, we further propose a protocol in which phonon-phonon interaction drives a cyclic process enabling net work extraction. Our results establish the fundamental role of higher-order optomechanical interactions and provide a microscopic framework for describing next-generation optomechanical experiments beyond the linear approximation.

Children with autism spectrum disorder (ASD) have social-emotional deficits that lead to difficulties in recognizing emotions as well as understanding and responding to social interactions. This study presents EMooly, a tablet game that actively involves caregivers and leverages augmented reality (AR) and generative AI (GenAI) to enhance social-emotional learning for autistic children. Through a year of collaborative effort with five domain experts, we developed EMooly that engages children through personalized social stories, interactive and fun activities, and enhanced caregiver participation, focusing on emotion understanding and facial expression recognition. Compared with a baseline, a controlled study with 24 autistic children and their caregivers showed EMooly significantly improved children's emotion recognition skills and its novel features were preferred and appreciated. EMooly demonstrates the potential of AI and AR in enhancing social-emotional development for autistic children via prompt personalizing and engagement, and highlights the importance of caregiver involvement for optimal learning outcomes.

How circumplanetary disks (CPDs) capture and retain solids is central to constraining the timescale for formation of rocky satellites and interpreting submillimeter continuum observations around giant planets. Here, we investigate the transport of gas and dust from the circumstellar disk into the CPD, using PDS 70 as our fiducial example. Based on observation-driven parameters, we perform high-resolution 3D adaptive mesh refinement (AMR) hydrodynamic simulations including a multifluid dust component to study dust accretion onto planets with masses of 1 $M_\mathrm{J}$ and 2.5 $M_\mathrm{J}$. We find that the pressure maximum at the gap edge imposes strong, size-dependent dust filtration, drastically lowering the solid content of the accreting flow. The net dust-to-gas mass ratio of the material accreting onto the planet is reduced by roughly two orders of magnitude relative to the outer disk. Only small grains ($\lesssim 61 \mu$m for the 1 $M_\mathrm{J}$ case and $\lesssim 10 \mu$m for the 2.5 $M_\mathrm{J}$ case) are able to accrete efficiently onto the CPD. Despite this filtering, we show that a continuous inflow of small grains can still deliver sufficient mass to build the observed PDS 70 c CPD or a Galilean-like satellite system within a few million years. Because more massive planets more effectively prevent the accretion of large grains, the dust that reaches the CPD is dominated by small particles with low millimeter-wave opacities. Consequently, in the absence of grain growth, interpreting millimeter continuum measurements of CPDs around massive giant planets may require invoking larger total dust masses than typically assumed.

Understanding how electronic correlations reshape topological states remains a central challenge in quantum materials. Here we investigate the uranium ferromagnet UPS using magnetotransport, angle-resolved photoemission spectroscopy, thermodynamic measurements, and first principles calculations. Resonant photoemission reveals narrow U-$5f$ spectral weight at the Fermi level coexisting with broad incoherent states, consistent with the itinerant/localized duality characteristic of uranium $5f$ electrons. The anomalous Hall conductivity reaches approximately $4.5\times10^{2}\,\Omega^{-1}\mathrm{cm}^{-1}$, yet does not simply follow the ordered magnetic moment. Temperature dependent photoemission reveals relatively little change across $T_C=118$~K, followed by a pronounced redistribution of low-energy $5f$ spectral weight below approximately 90~K. First-principles calculations identify a symmetry protected Weyl crossing with pronounced Berry curvature and yield an intrinsic anomalous Hall conductivity of approximately $9.6\times10^{2}\,\Omega^{-1}\mathrm{cm}^{-1}$. These results demonstrate that magnetic order, correlated electronic reconstruction, and anomalous Hall transport develop over distinct but overlapping temperature ranges, revealing how strong correlations reshape topological transport in a uranium Weyl semimetal.

Dexterous grasping requires deciding where to grasp, reaching the target, and maintaining stable contact. We connect these stages through a compact three-point interface that separates global geometric reasoning from local contact control. Given object geometry and optional language commands, our framework samples contact triples from a precomputed grasp-affordance heatmap. A model-based reactive controller tracks the object, avoids collisions, and guides the hand toward the selected contacts. In the final centimeters, a Reinforcement Learning (RL) policy uses proprioceptive feedback to refine and stabilize the grasp despite reaching and perception errors. It observes only finger joint states and its recent actions, with no target points, visual observations, or object geometry, so a single policy is shared across objects and grasp configurations. In simulation, we compare grasp-and-lift success against squeeze and end-to-end baselines, characterize reaching convergence, and demonstrate grasp steering; hardware demonstrations on two training objects and one unseen object illustrate the full pipeline. Our modular framework uses geometry to guide the reach and local feedback to secure the grasp.

When an LLM supplies an argument a user could not produce, how can the user decide whether to accept its claim? Inspired by interactive proofs, we pair a computationally unbounded LLM prover with a resource-bounded human verifier. The verifier checks requested details without seeing the LLM's internals; passed checks accumulate evidence toward an acceptance threshold. Given task-supplied bounds on false passes and human checking errors, we prove anytime-valid soundness against adaptive provers: the probability of ever accepting a false claim is at most a chosen error level. For a true claim, acceptance within the budget has probability at least the product of per-round probabilities that the LLM responds adequately and the human checks correctly, provided the threshold is reachable in time. Each additional check guards against false claims but gives a true claim another chance to fail. Which review lengths meet both error targets depends on the verifier's effort, cognitive load, expertise, and fatigue. With equal resources, we identify conditions under which the bounds certify a review by local checks but not a one-shot check. In LLM-only simulations on GPQA Diamond and Humanity's Last Exam, whether answers accepted without revision were more accurate varied by task and model pair.

Whole-slide pathology images (WSIs) contain gigapixel-scale visual content, creating a major scalability challenge for slide-level multimodal large language models (MLLMs). Existing approaches process thousands of patch tokens and typically apply compression only after slide encoding, leaving multimodal attention computationally expensive. We introduce SLICEChat, a slide-level MLLM that integrates progressive token pruning within a hybrid Mamba–Transformer slide encoder. Mamba layers enable efficient long-range propagation, while Transformer layers preserve global interactions as the sequence is progressively shortened. Between stages, language-supervised, region-aware pruning removes spatially coherent low-utility regions under a controlled keep-rate schedule, producing compact slide representations before multimodal fusion. On SlideBench VQA, SLICEChat achieves 79.84% accuracy on TCGA and 59.09% on BCNB cohorts, outperforming prior slide-level pathology MLLMs, and achieves the highest overall WSI-Bench metrics. It also provides competitive memory usage and the inference latency among the evaluated models. These results demonstrate accurate and computationally efficient multimodal reasoning over gigapixel WSIs.

Tantalum carbide (TaC) thin film ”virtual” substrates are a highly desirable material for $\text{Al}_{0.5}\text{Ga}_{0.5}\text{N}$ vertical power electronics devices due to lattice matching, thermal expansion matching, and metallic conductivity. However, the material has not been demonstrated to support $\text{Al}_{x}\text{Ga}_{1-x}\text{N}$ layers of variable composition $x$, limiting the range of device applications. We present a method to achieve tunable rock salt $\text{Ta}\text{C}_{x}\text{N}_{1-x}$ virtual substrates via a face-to-face annealing of TaC thin films in an $\text{N}_2$ atmosphere. The results suggest that annealing temperatures below $1600\,^{\circ}\text{C}$ promote partial uptake of nitrogen onto carbon and anion vacancy sites to form rock salt $\text{Ta(C,N)}$ with intermediate anion compositions. At temperatures $\ge 1600\,^{\circ}\text{C}$, nitrogen primarily occupies the anion sublattice and the crystalline quality and surface morphology simultaneously degrade coincident with the formation of secondary phases. This study demonstrates the growth and processing parameters necessary to make tunable lattice constant virtual substrates for $\text{Al}_{x}\text{Ga}_{1-x}\text{N}$ from $x = 0.5\text{-}1$, enabling vertically conducting power electronic devices with reduced defect density at high Al-content.

We establish Dirichlet–Neumann bracketing for the Dirichlet eigenvalues of $\psi(-\Delta)$ on bounded Lipschitz domains, where $\psi$ is an arbitrary complete Bernstein function. The eigenvalues lie between $\psi$ applied to the corresponding Neumann and Dirichlet eigenvalues of the Laplacian. Both inequalities are strict whenever $\psi$ admits no meromorphic continuation to $\mathbb C \setminus \{0\}$. The proof uses quadratic forms, operator monotonicity, and an analysis of equality in resolvent comparisons. Applying the bracketing to intervals and balls gives a unified proof of simplicity of interval eigenvalues and antisymmetry of second eigenfunctions in balls under the same condition on $\psi$. For fractional powers, these recover results of Fall, Ghimenti, Micheletti and Pistoia for the interval, and of Fall, Feulefack, Temgoua and Weth and, independently, Benedikt, Bobkov, Dhara and Girg for the ball. The argument extends these conclusions to a broader class of nonlocal operators.

Context. In wide-field surveys, the main challenge is not just classifier sensitivity, but the overwhelming number of false positives. Searching for strong lenses among millions to bilions of galaxies produces many contaminants, making the bottleneck for follow-up inspection and building statistically useful lens samples. Aims. We aim to improve the purity of strong-lens candidate selection in KiDS DR4 by combining several classifiers. The objective is to retain high completeness for known candidates while substantially reducing the fraction of non-lenses. Methods. We trained convolutional, Transformer-based, and hybrid classifiers, including Li ResNet+, Swin Transformer variants, Swin-MLP, and DemiLensNet. Their probabilistic outputs were combined at score level using averaging and a generalized mean consensus. The models were tested on simulated KiDS-like lens images and then evaluated on real KiDS DR4 lens candidates embedded in a non-lens sample. Results. On the simulated test set, ensembles show no advantage over the best single models. On the mixed real KiDS test set, the arithmetic mean reduces the false-positive rate at 90% completeness from 0.016-0.020 (the range spanned by the two best individual models) to 0.011 for the seven-model ensemble. The generalized mean reduces it further, to 0.007. Applied to the full LRG and BG samples at the same 90% completeness level, the generalized mean reduces returned candidates by roughly 50% for LRGs and 70% for BGs, relative to the best single model. After visual inspection, we obtain 170 new high-quality candidates (24 Class A and 146 Class B), together with 1706 Class C candidates. Conclusions. Our results demonstrate that the generalized mean consensus of an ML ensemble strategy provides a practical route to reducing the visual inspection workload while preserving a high recovery rate of promising strong-lens candidates.

Evaluation of Computer-Use Agents (CUAs) is often limited to the final deliverables they create (at the end of hundreds of steps) and assessed with functional verifiers, as seen in OSWorld. However, such evaluation of end-state performance lacks transparency into how and why agents fail in various tasks, obfuscating critical insight for subsequent improvement. For instance, agents that err during keyboard inputs would require a different mitigation strategy from those that fail to precisely provide click-based inputs on the graphical UI. We introduce OSWorld-Pro: a set of over 300 tasks containing over 2800 subgoals to enable the procedural evaluation of CUAs grounded in over 67,000 human annotations. We use robust human-aligned LLM-Judges to evaluate the fulfillment of OSWorld-Pro subgoals and thereby reveal the progress that models make throughout a series of sequentially dependent subgoals. Our findings reveal that OSWorld-Pro is challenging even for state-of-the-art LLMs, with top performers like Claude Opus 5 achieving only 75.7% vs. 83.4% on OSWorld. Furthermore, we identify critical process-focused failure modes of various models (e.g. subgoal-irrelevant actions and click-based mistakes) to provide insights to improve performance and efficiency of CUAs.

In DNA data storage, racetrack memories, and packet networks, data are written as many short strands of fixed length. The receiver knows where each strand begins and ends, and deletions occur only inside a strand. The relevant limit for such systems is the block capacity $C_N(d)$, the largest mutual information between a length-$N$ input and the output of a binary deletion channel with deletion probability $d$. Because the boundaries are known, $C_N(d)/N$ is never smaller than the classical capacity $C(d)$. Computing $C_N(d)$ is hard because the input takes $2^N$ values. For $0\le d<1$, we show that the optimal input is unique, gives positive probability to every string, and is unchanged by complementing or reversing the strings. We then introduce the optimized run distribution (ORD), which assigns one probability to each number of runs; it is optimal for $N\le3$ and is solved with a numerical optimality certificate up to $N=16$. For longer strands, an exact recursion for the output distribution gives unbiased rate estimates, and an empirical Bernstein inequality turns them into confidence intervals. Within the statistical precision, a one-parameter Markov input performs as well as the best inputs found. For strands of 100-200 bits, known boundaries increase the rate by up to 0.026 bits per symbol beyond the best certified upper bound on the capacity of the unsegmented channel. Via Fano's inequality, the block capacity also bounds the rate of any code that uses a single strand; in the tabulated case, this bound is tighter than the best known finite-length bound for strands longer than about 90 bits. Conversely, block rates yield lower bounds on $C(d)$; at $d=0.1$, the bound is within $1.1\times10^{-4}$ bits/use of the best certified lower bound. Finally, InfoNCE estimates, even with the optimal critic, empirically lose most of their ability to rank inputs as the strand length grows.

The constraints for the effective local gauge groups stemming from the causal action principle for causal fermion systems are reviewed. The constraint which are quadratic in the gauge potentials (coming from the so-called bilinear logarithmic terms) are shown to make a connection between the structures of Lie algebras and Clifford algebras. This connection is worked out systematically starting from general chiral potentials corresponding to the gauge group $\mathrm{U}(N) \times \mathrm{U}(N)$. The general results are illustrated in various examples.

A confining dark sector modeled after quantum chromodynamics provides a well-motivated framework for strongly-interacting dark matter. We show that dark vector mesons in a confining dark sector can be resonantly produced in high-energy neutrino scattering on the cosmic neutrino background, generating a distinctive absorption feature in the cosmic neutrino energy spectrum. Unlike conventional attenuation effects, this feature directly reflects the mass spectrum of dark resonances and can therefore serve as a spectroscopic signature of a strongly-interacting dark sector. We find that a broad range of dark-sector parameter space is within the reach of future neutrino telescopes, including IceCube-Gen2 Radio. Our proposal thus turns the cosmic neutrino background into a target for discovering dark-sector resonances, while simultaneously providing a novel probe of dark sector interactions with neutrinos.

We establish an exact composition principle for spherical immersions coupled through coefficient profiles and norm-preserving bilinear maps. Under explicit mixed orthogonality, the spherical mean curvature vector splits into orthogonal input and profile contributions. The composition is minimal if and only if every input is minimal and the profile is $W$-minimal for the induced monomial weight. Tensor iteration allows weighted profiles to serve as inputs in further compositions. At fixed weights, Hsiang–Lawson reduction and Kapouleas–McGrath doubling yield closed embedded $W$-minimal profiles. When the effective exponents tend to infinity in positive limiting proportions, Gaussian transfer produces interior coefficient profiles from closed embedded self-shrinkers that are nondegenerate modulo rotations. The number of distinct corresponding profiles is bounded below by the Lusternik–Schnirelmann category of the rotation orbit.

We built a node that grounds a replaceable language model in a maintained ontology corpus, then asked what its successful-looking evaluation could support. Across ten models, grounding raised target-name recall from 0.265 unaided to about 0.92. A copy baseline, the recall a verbatim copy of the shown context already achieves, scores 0.964, and every model sits 0.022 to 0.067 below it. Copying therefore scores higher on this limited recall measure, which does not assess whether answers are better. The comparison tests what a recall score establishes; it does not test whether reasoning occurred, because a reasoned answer and a copy score alike when the answer name is already in context. We report exposure accounting (four counts classifying each gold item by whether the context exposed it and the answer recovered it) and a model-judged audit of 423 sampled item observations. A separate paired production study found a model-judged quality gain of +0.27 [+0.11, +0.45] on a 0-5 scale. Operational studies found failures that recall alone would not show: rephrasing questions out of the graph's vocabulary cut exposure from 0.964 to 0.328, yet the absence-keyed fallback would have fired on only 2 of 506; and inserting extracted facts degraded judged pages in every arm, so that step was disabled. Five-arm controls show that any well-formed on-corpus block beats no context but do not establish that the specific content matters, and no matched comparison against flat-text retrieval was run. The corpus is public and largely LLM-generated, which establishes neither training exposure nor novelty. Each study has its own outcome measure. Where gold derives from the injected corpus, we recommend reporting the accounting beside quality judgements, not in place of them.

We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.

Artificial intelligence (AI) registers and inventories aim to make governmental AI visible, but their institutional scope, schemas, and reporting practices construct different representations of public-sector AI. We compare 8,368 records from country-specific and transnational inventories covering 72 countries. Across 23 harmonized fields, registers shared a descriptive core but rarely requested information about appeals, risks, legal bases, or external evaluation. We found that broad schemas often contained substantial missingness, schema similarity showed no significant patterned convergence, and multiple sources covering the same jurisdictions overlapped only selectively. Based on these findings, we synthesize a layered visibility framework that shows how register records reflect disclosure arrangements and why interoperability requires shared concepts, clear definitions, and preserved provenance.

Hybrid AI-physics climate modeling aims to improve coarse (~100km-resolution) Earth system models by learning to parameterize subgrid processes from high-fidelity data. However, this so far mostly involves local-in-time, diagnostic parameterizations, in which the subgrid state depends only on the current coarse state with no memory of previous states, which is unrealistic for processes such as convection that have intrinsic persistence. To address this, we enhance local-in-time parameterizations by learning prognostic variables that compactly carry important, additional past information where no explicit sub-grid information is available. First we compress past information into a low-dimensional latent space using an autoencoder, which then informs a neural network trained to parameterize targeted subgrid-scale processes. We then replace the autoencoder with symbolic equations that govern the time evolution of the latent variables, yielding additional prognostic memory variables that can be integrated alongside the resolved atmospheric state. We evaluate this approach on two systems: the Lorenz-96 model (online) and surface precipitation from high-resolution atmospheric simulations (offline). A forced multivariate linear ordinary differential equation recovers most of the added value achieved by the autoencoder-based approach in both experiments. Benchmarked against diagnostic parameterizations without memory, our memory-informed approach improves climate statistics and temporal structure, including a realistic diurnal cycle of tropical land precipitation.

In high-stakes decision-making applications of large language models (LLMs), practitioners require not only accurate LLMs but also uncertainty estimates for their predictions. Existing approaches to uncertainty estimation for LLMs require access to log-probabilities output by the model or require fine-tuning access. However, many industrial LLM products use closed-source API models, and many such API models like GPT do not return log-probabilities and may not allow fine-tuning. We introduce Pinocchio, an external calibrator that estimates the correctness of responses from black-box API models. Trained jointly on responses from seven LLMs, it achieves 0.862 AUROC predicting the correctness of held-out responses from those same models, and shows zero-shot transfer to thirteen unseen models across eight organizations. Our model needs only a single forward pass to generate an uncertainty estimate and requires no access to the target model's logits, weights, or internal states. A lightweight text only 0.8B checkpoint matches our largest model's AUROC. We release code for adding uncertainty estimation to existing repos in only two additional lines of code.

We prove a structure theorem for numerical semigroups H that are almost symmetric and almost complete intersections. We show that a row-factorization (RF) matrix of H must possess a highly regular structure, which we call a cascade matrix. Consequently, the defining ideal I_H of the semigroup ring k[H] also exhibits a highly regular structure, derived from this cascade matrix. Both the RF-matrix and the binomial minimal generating set of I_H are unique. Conversely, this structure completely characterizes almost symmetric almost complete intersection numerical semigroups: to every cascade matrix M we associate a monoid H and, whenever this is a numerical semigroup, we prove that H is pseudo-symmetric, almost complete intersection, and has M as RF-matrix. As a consequence of our study, we obtain several key results. 1) Rigidty: if an almost complete intersection semigroup is almost symmetric, then it is forced to have odd embedding dimension and to be pseudo-symmetric. This result is a “next step” after Kunz's theorem, which states that an almost complete intersection semigroup is never symmetric. 2) Huneke-Ulrich structure: the toric ideal can be realized as the ideal of entries of an alternating matrix multiplied by a vector of variables, and this yields the licci property. 3) Cascade polynomials: for each odd positive integer e, we construct a multivariate squarefree polynomial P_e with integer coefficients, arising from a cascade matrix of variables. We provide an enumerative interpretation of its coefficients, thereby proving their non-negativity. 4) Herzog–Watanabe question: we prove that every minimal relation of an arbitrary numerical semigroup H can be obtained by subtracting two rows in some RF-matrix of H, affirmatively answering a 2019 question by Herzog and Watanabe.

Counterfactual image generation answers questions about how a subject would have looked under retrospective, hypothetical scenarios. Recent methods have improved perceptual quality, identity preservation and faithfulness to an underlying causal model, but their adoption in healthcare is limited by scarce annotated data, distribution shift between datasets, and mismatches between pretrained generative models and those required for counterfactual inference. We propose specialisation, a data and parameter-efficient framework for adapting pretrained, non-causal generative models into causal mechanisms under distribution shift. Based on this framework, we train a radiology counterfactual image generation model, called RadCF, using latent flow matching. We validate our approach on three chest X-ray datasets spanning different dataset shifts, data volumes, and counterfactual questions, associated with challenging, highly-localised interventions. Our results show that RadCF and specialisation improve counterfactual soundness over existing methods while being data and parameter efficient, and that the resulting counterfactuals can detect and mitigate shortcut learning in a downstream medical classifier. Code is available at https://github.com/GSK-AI/RadCF/.

Bimatrix games may have an exponential number of mixed Nash equilibria if both dimensions of the game are allowed to grow. Bounds on their maximal number give structural insights that have been used to construct hard-to-solve games. We show new sharp or asymptotically sharp bounds on the (polynomial) number of equilibria for generic games where one dimension of the game is fixed and the number of strategies of the other player grows. These results go beyond the hitherto studied square games. Our methods employ combinatorial properties of polytopes, and recent obstructions that relate to the graph of those polytopes. For $n\ge5$, we construct $3\times n$ games that have all $2n+1$ vertices of the best-response polytope as equilibrium strategies, proved using a simple case of the 4-color theorem for planar graphs. Generic $4\times 5$ games are shown to have at most 17 equilibria, using computer calculations with existing datasets for all combinatorial types of the relevant polytopes. For $d\times n$ games, we construct games where all but a fraction of $O(1/n)$ of the maximum number of vertices are equilibrium strategies.

In automated clinical coding, where the label space spans tens of thousands of diagnosis and procedure codes, models are currently evaluated against a single gold annotation, treating any deviation as error. But we find when two teams code the same 110 ACI-Bench encounters, they agree on only 73% of codes (Jaccard similarity) for the same note; even after an independent clinical audit removes erroneous codes, agreement rises only to 77%. Is that gap error or something systematic? We model the systematic component as coding style $\psi$, a coder- or site-specific policy over what to code and how much to document, and recast coding as $p(\mathrm{code}\mid\mathrm{note},\psi)$, estimating $\psi$ with a 10-dimension rubric. If style were noise, conditioning on it would do nothing. Instead, across five datasets a model conditioned with a data-matching style raises ICD F1 by up to 26 points and an extreme mismatched one lowers it by up to 21. Four prompt based coding methods spanning 39-49 F1 converge to 52-56 once style is supplied (All p<0.05). Much of what single-gold evaluation charges to model error is recoverable, unmodeled style.

In multi-agent social settings, model reliability varies across relationships. Beyond inferring what others will do, an agent must calibrate how confidently those inferences should guide policy selection for each relationship. An agent may maintain a well-validated model of one partner, a fragile model of another, and a model under revision for a third; collapsing these into a single confidence estimate loses information relevant to policy selection. We therefore formalize affective precision as a relationship-specific metacognitive estimate of confidence in the current partner model. Each partner's behavioral evidence updates a local confidence estimate that modulates policy precision during selection, regulating how strongly current beliefs are expressed in policy rather than changing the content of those beliefs. Simulations in a multi-partner graded trust game show that partner-local affective precision influences behavior primarily through policy commitment rather than direct improvement of partner-state inference. Because the mechanism tracks partner-response predictability rather than realized payoff, greater confidence produces sharper policy commitment without necessarily producing higher rewards. Under abrupt shifts in social behavior, confidence accumulated from previously reliable predictions can remain behaviorally active after the relationship changes, showing that confidence revision can lag behind social change. Finally, varying precision gain and priors produce distinct trust-calibration dynamics, showing how confidence accumulation and revision depend on model parameters. Together, these results show how relationship-specific affective precision can distinguish social prediction from social policy commitment.

Recent foundation models are moving toward native multimodal Vision-Language Models (VLMs), making VLMs a central form of next-generation foundation models. However, their large language backbones make edge deployment difficult due to high memory footprint and memory-bound autoregressive decoding. Weight-only post-training quantization is a practical solution, but pushing VLMs to extreme low bit-widths remains challenging: existing rotation-free methods suffer from outliers at 2-3 bits, while rotation-based methods improve accuracy at the cost of additional runtime overhead. We propose SPHQuant, a rotation-free spherical weight-only quantization framework for VLMs. Instead of quantizing weights directly in Cartesian coordinates, SPHQuant decomposes each 8D weight vector into coordinate signs, radius, and a positive unit direction. This representation isolates outlier magnitude into the radius while keeping directions bounded and statistically regular. Based on this insight, SPHQuant allocates extra precision to the radius to mitigate accuracy degradation induced by outliers. It further uses a compact positive-direction codebook and fine-tunes codebook entries through angular parameterization to preserve the unit-sphere constraint. We also design a hardware-friendly GEMV kernel that keeps the direction codebook small enough for shared-memory lookup and packs radial bits efficiently. Experiments show that SPHQuant matches the performance of state-of-the-art extreme low-bit quantization methods while improving decode throughput over QTIP by 30.3% on RTX A6000. Code will be released in https://github.com/Pushazf/SPHQuant.

Trapped ions excited to high-lying electronic states, so-called Rydberg states, open new opportunities for quantum simulation and quantum computing. Generally, the fidelity of quantum coherent operations critically depends on the longevity of Rydberg states. However, scaling laws predict that the lifetimes of Rydberg states in singly charged alkaline-earth metal ions are 16 times shorter, compared to their neutral atom counterparts. Here, we show that this is not generally the case. We report an anomalous lifetime enhancement of certain low angular momentum ionic Rydberg series by factors larger than eight. The anomaly is present at both zero and finite temperature, although it is caused by different mechanisms. At zero temperature, the anomalously enhanced lifetimes are caused by accidental cancellations of the relevant dipole transition matrix elements, while at room temperature the anomaly originates from the enlarged energetic separation of ionic Rydberg levels with respect to neutral-atom levels.