Papers

LLM orchestration investigates how an orchestrator coordinates a group of autonomous agents to achieve common goals or maximize collective welfare. The agents are typically heterogeneous, each holding a private preference that it pursues but does not reveal. Inferring such hidden preferences from behavior has been a subject of long-standing research in game theory and multi-agent systems. The core challenge lies in maintaining a belief over every agent's preference and updating it from the agents' observed actions. Existing LLM orchestrators carry that belief as prompt text with no explicit update rule. This lets early errors persist and propagate rather than be corrected. We therefore propose HARP (Heterogeneous-preference Agent oRchestration via Preference inference), a novel framework that moves the belief out of the prompt. Specifically, HARP maintains one numeric posterior per agent over a finite set of candidate preferences and updates it in closed form by Bayes' rule. The language model supplies only actions and per-candidate likelihoods, so estimation is decoupled from its reasoning. We prove that HARP attains the same $\tilde O(\sqrt K)$ Bayesian regret as explicit joint inference when the factorization is exact. Furthermore, HARP\textsuperscript{+} augments planning with a bonus for actions that distinguish the candidates, so inference continues even when the optimal action is uninformative. Empirical results on three substrates, ranging from payoffs the preferences fully determine, through payoffs that depend on more than them, to scales where explicit joint inference is infeasible, demonstrate that HARP\textsuperscript{+} is the strongest non-oracle method across the class our theory identifies.

This paper investigates the stability of steady transonic shocks with constant states in rectangular nozzles under small three dimensional perturbations of the external force and the exit pressure. Mathematically, the problem can be formulated as a nonlinear free boundary problem for a hyperbolic-elliptic coupled PDE system. One of the key difficulties lies in the arbitrary location of the background shock, which may lead to multiple shock solutions for the same external force and exit pressure under perturbations, revealing the instability of the background shock. We reformulate the steady Euler equations in terms of deformation and vorticity to effectively decompose the hyperbolic and elliptic modes. Linearizing the reformulated system and the Rankine-Hugoniot conditions at background transonic shocks, we find that the class of nonzero horizontal external forces helps to uniquely determine the shock location, where the conservation of mass plays a critical role. A delicate iteration is developed to establish the existence and structural stability of transonic shock solutions. Our analysis shows that the stability mechanisms of steady transonic shocks in flat and divergent nozzles are quite different in many aspects.

We propose a scalable roto-reflection-group-equivariant vision transformer based on windowed group-convolutional self-attention and a hierarchical feature architecture. We demonstrate that our approach can be scaled to group-equivariant vision transformers (ViTs) with millions of parameters and large datasets with practically sized images, i.e., ImageNet. The code and pretrained weights for the proposed Hierarchical Windowed Roto-reflection Equivariant ViTs (REViT-v2) are available at https://github.com/kc-ml2/revit.

Time-resolved photometry from large surveys can yield rotation periods for huge numbers of asteroids, but only if the reliability of each period is assessed automatically, since sparse and irregular sampling produces many false periodogram minima. We present an improved method that determines asteroid rotation periods with a Fourier series whose order is chosen for each object individually. This has substantial advantages over lower order methods, especially when unique solutions for the spin period cannot be reliably determined. In such cases, the method reports the set of alternative periods together with the corresponding probability estimates. We apply the improved spin period determination method to the NSF-DOE Vera C. Rubin Observatory Data Preview 2 (DP2) catalog of solar system objects and determine reliable periods for a large sample of asteroids. Among them we find 66 super-fast rotators, which spin faster than the classical 2.2 h spin barrier. Two of them are remarkable: asteroids 491384 and 566130 are both larger than 2 km, yet they complete a full rotation in only about five minutes. To survive such a fast spin, they must have significant internal cohesion. At a diameter of about 2.5 km, asteroid 491384 is the largest ultra-fast rotator known so far.

While AI weather models now rival operational forecasts, how they represent the atmosphere internally remains an open question: feature attribution reveals which input patterns matter, not what the model computes or how it combines information internally. We train sparse autoencoders (SAEs) on GraphCast to uncover its learned concepts, using atmospheric rivers as our phenomenon of focus. Both standard and Matryoshka SAEs show GraphCast computes atmospheric river intensity, measured by integrated vapor transport (IVT), as a stable internal variable, despite IVT being neither an input nor a target. In contrast to the unstructured concept retrieval of the standard SAE, the Matryoshka SAE orders concepts by importance and exposes their relations. Atmospheric river concepts persist across depth and direct interventions confirm causality. This method offers a way to find internal variables and determine which of them the model actually relies on, which is a prerequisite for asking whether those variables remain meaningful as the phenomenon changes under a warming climate.

Quantitative imaging pipelines can produce precise but systematically different measurements of the same object. We present an empirical reliability assessment of three-dimensional mitochondrial morphometry that connects representation bias, a controlled processing intervention, correction transfer, and resolution sensitivity. Using 2,720 development objects from the 3D Mitochondria Shape Library for Optical Microscopy, we find that occupancy-derived volumes exceed reference mesh volumes by 3.665% on average despite an intraclass correlation coefficient of 0.994. Boundary analysis identifies an outward label displacement of 0.00304 normalized units. In a controlled label-pipeline reimplementation, removing the depth offset reduces volume error in all 55 analyzed objects by a mean of 1.57 percentage points, approximately 45% of mean reproduced inflation; the source of the remainder is not isolated. A frozen regression using occupancy-derived features reduces median absolute percentage error from 3.481% to 0.664% in 2,728 previously unused objects from the same resource. However, its calibrated error bound covers only 92.1% overall and 49.2% in a low-occupancy subgroup, demonstrating that accuracy and uncertainty transfer must be evaluated separately. In 550 rat-cortex objects from the MitoEM resource, coarsening in-plane spacing from 8 to 24 nanometers changes median surface area by minus 10.60% and sphericity by plus 11.76%, despite a rank correlation of 0.994. These results provide quantitative checks for distinguishing processing-induced descriptor changes from candidate biological differences, without establishing biological invariance or cross-source correction transfer.

We test the idea proposed by Laporte & Orkney that $\omega$ Centauri ($\omega$Cen) is the central nuclear star cluster of the Gaia-Sausage-Enceladus galaxy (GSE) which got dislodged by the bar. We run a series of simulations in time-evolving bar potentials with present-day pattern speeds within Portail et al's $\Omega_{b}=39\pm3.5\,\rm{km\,s^{-1}\,kpc^{-1}}$ and rate of slow-down $\dot{\Omega}_{\rm b}= 4.5 \pm 1.4 \,\rm{km \,s^{-1}\,kpc^{-1}\, Gyr^{-1}}$ to study how bar resonances modulate the angular momentum and energies of both GSE-debris and $\omega$Cen's location in $(E,L_{z})$ space. We find that the retrograde $3:2$ resonance is capable of inflicting changes of $\Delta E\approx0.4\times10^{5}\,\rm{km^{2}\, s^{-2}}$, $\Delta L_{z}\approx0.3-0.5\times10^{3}\, \rm{km \, s^{-1}\, kpc^{-1}}$ within timescales of $\Delta t\approx 0.5-1\,\rm{Gyr}$, well within the bar's lifespan $t_{\rm{bar}}\approx10-8\,\rm{Gyr}$. These results are independent of the choice of potential or modelling. We uncover a sample of N-rich stars with metallicities $-2.0<[\rm{Fe/H}]<-1.0$ and aluminium enrichments consistent with $\omega$Cen. In ($E,L_{z}$) space, the map reveals a corridor of trailing N-rich stars clustered about the region connecting $\omega$Cen to the GSE's debris centroid, matching $\omega$Cen's past predicted track. This provides the best evidence yet that $\omega$Cen is the nuclear star cluster of the GSE. Using M54 and $\omega$Cen's chemistry we show that neither first nor second generations follow general galaxy-wide scale chemical enrichment trends. This is empirical evidence that GC chemical trends are a cluster-scale physics problem, not a galaxy-wide one.

Aerospace electrical-design revisions can contain multiple genuine changes, although an engineering request may authorize only a subset. Propagating every detected difference can therefore produce overly broad impact reports. We present LOGIC, a controlled benchmark and evaluation framework in which locally deployable language models ground a request in a deterministic candidate-change inventory before selected changes are propagated through a typed electrical traceability graph. This separation permits candidate-selection errors to be distinguished from downstream propagation errors. LOGIC contains 168 scenarios, including 144 selection and 24 abstention cases. We evaluate three 7–8B models against intent-agnostic, lexical, and structured-evidence methods, with an oracle-root upper bound. On 96 explicitly anchored selection cases, gate-only structured evidence achieves candidate F1 of 1.0000, compared with 0.9677 for token-lexical matching. On 12 relational-paraphrase cases, token-lexical F1 is 0.1772 and gate-only F1 is 0.0000, compared with 0.5000–0.6400 for the large language models. Model grounding degrades as candidate inventories grow from 4 to 64 changes, while affected-element and typed-path accuracy remain comparatively stable when frozen selections are replayed over graphs of approximately 1K to 100K nodes. Strict evidence gating suppresses false positives but can remove correct semantic selections. An exploratory evidence-empty abstention policy raises strict abstention accuracy to 0.6667 for all three models and reduces unsafe-report rates to 0.1667, while decreasing answerable-case coverage by 16.0–27.1 percentage points. Four of six conflicting requests remain unsafe for each model. These findings support combining literal evidence and language-model reasoning with engineering review when intent cannot be established reliably.

The world's first Compton scattering measurements on a $^3$He target were performed to probe neutron electromagnetic polarizabilities. Differential cross sections were measured at laboratory angles of $40^\circ$, $55^\circ$, $90^\circ$, $115^\circ$, $150^\circ$, using circularly polarized, quasi-monoenergetic photon beams at weighted mean energy values of 61.5 and 97.1 MeV from the High Intensity $\gamma$-ray Source at the Triangle Universities Nuclear Laboratory. Comparisons with chiral effective field theory show good agreement at 97.1 MeV but over-prediction at 61.5 MeV, motivating further theoretical development.

In cooperative Multi-Agent Reinforcement Learning (MARL), agents are often trained under concurrent participation, while in many tasks some agents act earlier and leave task-relevant information that becomes useful to agents participating later. We study this setting as staggered participation (SP), which introduces a cross-time, cross-agent learning dependency because an early action may affect the return through the information it provides and the later policy that uses it. Learning under SP therefore requires both identifying what information is useful for future decisions and learning how later agents should use it. We propose Staggered Participation Learning (SPL), a training-time augmentation that addresses these two parts with prospective acquisition supervision for earlier agents and outcome-supervised receiver learning for later agents. We evaluate SPL across multiple policy-based MARL backbones, environments, and staggered-participation patterns. Across 60 MPE/RWARE backbone setting comparisons, SPL achieves higher observed mean task completion in every case, with an average difference of 14.1%. The gains also extend to eight-agent teams and a physics-based UAV-UGV environment in Isaac Lab, providing evidence across algorithmic, temporal, and embodied settings.

When a feasible plan is obtained whose quadratic transport cost is known to be close to the optimal cost, we try to determine how close the feasible plan is to the true optimal map under mild density and moment conditions. The source and target may be unbounded or have non-compact supports. We show that for a source with density in $L^p$ and an $n$-th moment, let $s=1-1/p$ and $\eta=sn/[n+(d-1)s]$. Under the target constraint $\int |y|^m[\log(e+|y|)]^\beta\,d\nu\leqslant1$, the worst-case class-uniform conditioning has a sharp modulus comparable to \[ t^{\eta(m-2)/[m(1+\eta)-\eta]} [\log(e/t)]^{-\beta(2+\eta)/[m(1+\eta)-\eta]}, \] whenever $t>0$ is small. This holds for $m\geqslant2$ and $\beta\geqslant0$. When $m=2$, every $\beta>0$ gives a sharp logarithmic modulus, whereas the $m=2,\,\beta=0$ extreme has no vanishing modulus. The matching lower bound is verified for both the squared map error and barycentric projection error. The sharp map error bounds allow us to directly derive quantitative stabilities of common source Brenier maps without passing through potential estimates, thereby avoiding loss of information. These stabilities strictly improve the corresponding results of Delalande-Merigot \cite{delalande2023quantitative} and Letrouit-Mérigot \cite{letrouit2026gluing} under identical or weaker settings, particularly no convexity of the source support or bounds of the source density are assumed.

Cassini synthetic aperture radar (SAR) images reveal the dunes, plains, and lake basins of Titan, providing an instance of representations learned from Earth imagery for planetary terrain classification. Cross-domain Evaluation of Earth-to-Titan Transfer Using SAR (CETUS) compares features from DINOv2, DOFA and CROMA with classical image measurements and features from an untrained vision transformer on the U.S. Geological Survey's Cassini SAR mosaic. The classifiers learn terrain labels from an expert geomorphological map and predict those labels in geographically separate Titan regions. Under logistic regression settings, pretrained encoders achieve higher mean macro F1 than the combined classical features. Encoder rankings change when feature scaling, optimization, and regularization change together. Further training on Titan improves DINOv2 performance, degrades DOFA performance, and leads to mixed results for CROMA under the tested settings. Architectural and input processing differences prevent these comparisons from isolating the effect of pretraining. Classifier fitting and performance on individual terrain classes matter when assessing representation transfer for planetary mapping. Since the map draws partly on the same radar observations, the scores measure agreement with expert interpretation.

Character error rate (CER) computed by automatic speech recognition (ASR) is widely used as an intelligibility reward for reinforcement learning (RL) post-training of text-to-speech (TTS) systems. For Japanese, however, orthographic CER introduces a representation mismatch for pronunciation-oriented optimization: distinct kanji readings may collapse to the same orthographic representation, while equivalent pronunciations may admit different orthographic forms. We instead compute CER in the kana domain using a kana-transcribing ASR model and reference readings (Kana-CER). Under matched group relative policy optimization (GRPO) conditions, Kana-CER reduces target-kanji reading error by approximately 26% relative to the orthographic CER reward, while maintaining comparable orthographic CER and similar speaker similarity and objective speech quality. It also reaches its best validation performance in substantially fewer optimization steps (4k vs. 18k). We further observe severe output elongation under unregularized Kana-CER optimization, which is substantially suppressed by KL regularization.

Boundary value problems for systems of conservation laws, including inviscid compressible flows, arise naturally in physical models such as shallow water flow in a canal, where fluid may leave the domain through the boundary. In contrast to the Cauchy problem, the inviscid limit is highly sensitive to the underlying viscous model: different viscous regularizations may select different effective boundary conditions for the limiting system. In this paper, we show that small BV solutions of the one-dimensional compressible barotropic Euler equations arise as inviscid limits of the barotropic Navier-Stokes system for the outflow boundary problem. We work with the physically meaningful effective boundary condition selected by the Navier-Stokes system for the limiting Euler solutions. Moreover, going beyond smooth flows or a fixed class of Riemann solutions, our stability results apply to small BV solutions exhibiting general wave patterns and complicated configurations generated by interactions with the outflow boundary, including reflected shocks.

Modern space missions require trajectory design methods capable of efficiently adapting to diverse mission objectives and operational constraints. Despite the maturity of non-convex trajectory optimization techniques, their broader adoption remains limited by the substantial domain expertise required to tailor problem formulations across varying mission scenarios. Recent advances in large language model (LLM) reasoning and agentic AI coding capabilities offer a promising pathway to improving the accessibility of advanced trajectory optimization techniques. This paper introduces PLUTO (Plain Language Understanding for Trajectory Optimization), an interactive trajectory design framework that integrates agentic AI coding tools within a sequential convex programming (SCP) architecture. The proposed system maps high-level semantic inputs to well-defined mathematical constraints while preserving a structured representation suitable for SCP. These constraints are processed through an auto-convexification pipeline and incorporated directly into executable optimal control formulations, thereby systematically connecting user intent and trajectory generation. Visual constraint verification and scenario parameterization further support an intuitive environment for trajectory design across a wide range of application scenarios. Within an evaluation of 50 natural-language rendezvous mission prompts spanning 10 constraint types, PLUTO generated a trajectory for every prompt, and 94% of the resulting trajectories satisfied both the quantitative and qualitative requirements of the mission intent. Ultimately, this work explores the potential of agentic AI to bridge the gap between advanced optimization algorithms and engineer-focused trajectory design workflows.

In-context learning (ICL) adapts frozen large multimodal models (LMMs) to new tasks from a few demonstrations (demos), but re-encodes them at every query, where each demo image adds up to hundreds of visual tokens. Demo-free methods remove this cost with a compact task state. However, they add it at locations searched per task or at every decoder layer, where task parameters grow with depth. Moreover, inserted tokens or keys cannot change how the original prompt divides its attention within a layer. To address these issues, we propose Structured Task Adaptation via Embeddings (STAVE), which replaces demos with two task-specific vectors added to existing input embeddings. Specifically, a readout vector updates the answer-producing tokens and a context vector updates the other structural token groups. Both are trained with answer labels on prompts with and without demos. We justify these design choices theoretically using a first-order analysis of the loss and a margin bound. Extensive experiments on six LMMs and five large language models show that STAVE matches or outperforms state-of-the-art methods on multimodal tasks with far fewer task parameters and surpasses 15-shot ICL and prior task vectors on 18 text tasks, all at zero-shot inference cost.

The rapid integration of electric vehicles (EVs) into the transportation system has introduced a new class of load into power distribution systems (PDS), i.e., EV charging demand (EVCD). The spatiotemporal variability of EVCD poses fundamental challenges for distribution system operators (DSOs), particularly in ensuring secure and reliable network operation. Accurately representing EVCD as a parameter within the distribution optimal power flow (DOPF) problem is a prerequisite for reliable, cost-efficient PDS operation, yet no universally accepted modeling framework has emerged. The existing contributions span a wide spectrum of assumptions, mathematical formulations, and solution paradigms. This article presents a systematic review of methods and models employed to represent EVCD within DOPF frameworks from the DSO's operational perspective. The existing EVCD modeling methods are classified into two primary categories based on EVCD representation: deterministic models and uncertainty-aware models. The two main categories are further divided into several subcategories. This paper aims to provide a comprehensive review on models for integrating EVCD into PDS operation and planning.

In clinical practice, agreement among independent experts is treated as evidence of reliability, and multi-round consensus has become a core mechanism of agentic medical question-answering systems. When such a system must decide whether to trust its own answer, the prevailing signal is again agreement, now among the sampled answers. But agreement is a fragile proxy for correctness. A system can be unanimously wrong, returning the same incorrect answer on every sample, and on these questions agreement-based signals carry no information. The cause is that these signals read only the final state of the consensus and discard how it was reached. Agreement that was reached by resolving disagreement with evidence looks identical, at the end, to agreement that was present from the first sample because every sample shares one misconception. ProbeGuard is a certified abstention framework that bases the abstention decision on how the consensus formed. Process features trace agreement trajectories, minority persistence, and retrieval saturation. For unanimous votes, rationale semantic entropy checks whether the reasons behind the vote cohere, and an active probe retrieves counter-evidence and measures whether the consensus survives. A stratified Learn-then-Test calibration then converts these scores into a distribution-free bound on selective risk. We evaluate ProbeGuard on three medical QA benchmarks and a hard-frontier reference, with a published multi-round agentic RAG substrate, against six abstention baselines. On MedQA, 13.4% of unanimous votes are wrong, and no agreement-based signal can flag them. Process signals raise the discrimination of correct from incorrect consensus from chance to 0.696 AUROC. The certified rule answers six in ten unanimous-layer questions at an observed selective risk of 9.0%, and nine in ten once in-domain calibration data accumulate.

Dense 3D mapping with semantic understanding is essential for robotic perception in complex environments. Recent 3D Gaussian Splatting-based mapping approaches enable high-fidelity geometry and efficient open-vocabulary perception, but typically represent semantics as unstructured feature fields that limit object-centric reasoning. In contrast, 3D scene graphs explicitly model objects and their relationships for structured reasoning, but are commonly constructed from sparse geometric representations that do not fully exploit dense semantic maps. In this work, we present OpenSplatGraph, a unified framework that constructs persistent 3D scene graphs directly from an online Gaussian-based open-vocabulary semantic map. The proposed framework augments the dense semantic map with a reliability-aware semantic field that maintains lightweight observation statistics for confidence-aware, query-conditioned object extraction. Extracted object instances are associated with persistent graph nodes, allowing object attributes and relationships to be incrementally updated across observations and queries. By tightly coupling dense semantic mapping with persistent object-centric representations, our framework supports both language-guided object grounding and structured relational reasoning while preserving the geometric fidelity of Gaussian-based mapping. Comprehensive evaluations on standard 3D scene understanding benchmarks and real-world robotic experiments demonstrate that OpenSplatGraph achieves competitive performance for online open-vocabulary perception and downstream robotic tasks. Project page: https://csiro-robotics.github.io/OpenSplatGraph.

Quantum Darwinism explains classical objectivity through redundant environmental records of a system's pointer states. We show that these records can be established through an intermediate measurement apparatus without direct system–environment interactions. Using exact analytical solutions of quantum circuit models, we compare system monitoring with apparatus monitoring, where the environment interacts only with the apparatus. During encoding, system–apparatus correlations decrease as system–environment correlations grow. Without noise, both models yield identical accessible pointer information and redundancy, while the discord accounts for their different mutual information. The reliability of these records depends on where noise acts. Apparatus bit flips introduce errors shared by successive records, limiting the information recoverable even from the complete environment. In contrast, larger fragments can mitigate independent noise on environment qubits after encoding. Dephasing in the pointer basis leaves the record information unchanged in the model considered. These results extend the description of quantum Darwinism to indirect measurements and clarify the conditions for reliable environmental records.

The Jx-Jy Blume-Capel model, with and without an external magnetic field, is investigated using the Monte Carlo method. Our aim is to verify the location of the tricritical point, examine the existence of reentrant behavior, and study the magnetocaloric properties of this specifically designed system. In the non-field case, the critical temperature given by the Monte Carlo simulations is lower compared to the conventional antiferromagnetic square lattice. When an external magnetic field is applied, we observed signs of a one-dimensional spontaneous symmetry-breaking phase in the mixed-states regime, which is counterintuitive with secondary specific-heat peak. We take the snapshot of this state and elucidated the underlying mechanisms using mean field theory in the field of spin-1 spinor Bose-Einstein condensate . Regarding reentrant behavior, we confirmed its occurrence as the magnetic field varies, but only when the temperature is kept constant. Temperature-dependent reentrant behavior could not be identified within this system. Finally, we examined the magnetocaloric properties and found no evidence of first-order phase transitions within the region of the considered phase-transition point. Although both inverse and direct magnetocaloric effects are present and related to the mixed state, we identified that the relevant phase transitions are all of the second order.

Feed-forward novel view synthesis methods achieve strong generalization from posed multi-view inputs, but scaling them to large input view sets remains challenging. Transformer-based approaches that jointly process all input-view tokens incur rapidly increasing computation and memory as the number of views grows, while simple view subsampling discards potentially useful observations. We introduce Anchor-Integrated Multi-View Synthesis (AIMS), a scalable framework that decouples the number of available observations from the number of views processed by the global synthesis model. AIMS selects a fixed set of spatially distributed anchor views using farthest point sampling, groups nearby observations around each anchor, and uses a lightweight learnable integrator to fuse their information into enriched anchor representations. This allows additional observations to contribute to synthesis while keeping the downstream global view budget fixed. Evaluations on RealEstate10K and ScanNet demonstrate a favorable quality–efficiency trade-off against transformer-based and Gaussian-based baselines. AIMS achieves 29.41 dB and 17.73 dB PSNR on the two datasets, respectively, with rendering averaging 7.24 ms per view.

Complementary Feature Domains (CFD) theory characterizes predictive value as a context-indexed contribution system induced jointly by representations and their realization family. We show that Shannon-information preservation does not imply preservation of this contribution system: an invertible representation transformation can leave target information unchanged while altering predictive contribution under a restricted decision family. We formalize the resulting transition through a CFD contribution defect that measures how contextual contributions change under controlled recoding. For bounded Lipschitz utility, we show that each coalition utility shift is bounded by the behavioral distance between the attainable action sets before and after recoding; consequently, every contextual contribution defect is bounded by the sum of the corresponding coalition incompatibilities. Exact behavioral closure yields invariance, while increasingly accurate compensation yields restoration. A controlled ECG experiment illustrates the mechanism: a nonlinear bijective recoding preserves the information in a frozen time-frequency representation but changes accuracy under a fixed affine learner; applying the exact inverse restores all tested coalition accuracies. The result separates information preservation from realization-dependent contribution and provides a quantitative transition law for multi-representation prediction.

We establish curvature-based bounds for the $p$-capacity of convex domains and related capacity–area inequalities. Let $K$ denote the Gauss–Kronecker curvature of $\partial\Omega$. In Euclidean space, if $ 0<K_-\leq K\leq K_+, $ then, for every $1<p\leq \frac{n+1}{2}$, $$ \operatorname{Cap}_p\left(B(K_+^{\frac{1}{1-n}})\right) \leq \operatorname{Cap}_p(\Omega) \leq \operatorname{Cap}_p\left(B(K_-^{\frac{1}{1-n}})\right). $$ The lower comparison remains valid for the full range $1<p<n$. Moreover, the exponent range in the upper comparison is optimal in general: when $n\geq 4$ and $\frac{n+1}{2}<p<n$, the upper comparison may fail. Thus $p=\frac{n+1}{2}$ is the critical exponent for the curvature-radius upper comparison. Under the pinching condition $ \frac{K_-}{K_+}=\rho\in (0, 1], $ we further obtain an explicit scale-invariant capacity–area lower bound for every $1<p<n$. In the special case $n=3$ and $p=2$, $$ \frac{\operatorname{Cap}_2(\Omega)} {\sqrt{|\partial\Omega|}} \geq \frac{4\sqrt{\pi}\,\rho^{1/4}} {1+\sqrt{\rho}}, $$ which implies the Pólya–Szegö inequality whenever $$ \rho\geq \rho_*:= \left( \frac{\pi^2-4-\pi\sqrt{\pi^2-8}}{4} \right)^2 \simeq 0.15484. $$ On a Cartan–Hadamard manifold with $\operatorname{Sec}\leq -k^2<0$, we obtain a $p$-capacity lower bound retaining all principal curvatures of the boundary, together with corresponding Gauss–Kronecker curvature estimates and a rigidity characterization of the equality case by a warped-product exterior geometry.

Large language models (LLMs) have the potential to meet a key goal in economics: a quantitative model of household decision making, across a variety of settings. Yet existing evaluations cover few surveys and outcomes, and do not study how households adjust to changing economic conditions. We introduce a new evaluation, HouseholdBench, which unites 6 U.S. household surveys and 32 prediction tasks spanning numeric, categorical and probabilistic outcomes, related to consumption, income, labor, expectations, and housing. Using past behavior, demographics and macroeconomic conditions, the tasks test whether LLMs predict behavior, including how households adjust to changes in various policies. We evaluate 13 proprietary and open-weight LLMs against a no-change baseline and a gradient-boosted tree model. Most LLMs outperform the no-change baseline, including for policy response tasks – with the best model lowering error for numeric outcomes by 12.2%. Across most tasks, gradient-boosted trees rank first; leading proprietary LLMs approach their performance, but open-weight models lag. LLMs exhibit systematic over- and underprediction across different tasks. We identify methods that enable a 4 billion parameter open-weight model to match proprietary models' performance: fine-tuning and aggregating 16 predictions per observation. Improvements generalize to policy-response tasks, which are excluded from fine-tuning. We release our datasets, code, and leaderboard on our website: https://jn-huang.github.io/householdbench

Learning an ensemble of GFlowNets to sample from a discrete target distribution has become a common approach for achieving better state space exploration and convergence than that of a monolithic sampler. However, these methods often add a substantial runtime overhead to the base model, and their conceptual connection remains elusive. To address this, we first propose a general-purpose theoretical framework for describing a mixture of GFlowNets, which we specialize into continuously (CI) and discretely indexed (DI) collections. On the one hand, we show CI GFlowNets can be interpreted through the lens of a random features expansion, provably boosting the sampler's expressivity in graph-structured tasks and reducing learning instability via spectral shifting. On the other hand, we demonstrate DI GFlowNets encompass prior approaches for GFlowNet training and provide the foundation for the newly proposed Stratum-Conditioned (SC) GFlowNets. This method, which is inspired by the Doob's h-transform of Markov chains, decomposes the state space according to a prescribed modular function and restricts each component to sample from a distinct subset of it. Importantly, SC GFlowNets support centralized and component-wise embarrassingly parallel training, and we show both of them significantly speed up learning convergence and mode coverage without introducing any non-negligible extra computation.

Image-guided surgery (IGS) depends on accurate tracking of surgical instruments to provide real-time navigation relative to anatomical structures. Commercial stereo infrared trackers are accurate but prone to occlusion and cost-prohibitive for many settings. This work presents LARK, a multi-camera optical tracking system using commodity RGB hardware and multi-view redundancy and fusion. We develop and evaluate two complete tracking methods: multi-view monocular pose fusion and multi-view triangulation. Both methods are assessed under varying occlusion levels using a precision-machined grid and an anatomical head phantom, and compared against a gold-standard stereo infrared system. With five cameras and adaptive Kalman filtering, LARK achieves median target registration errors of 0.64 mm for point localization with triangulation and 0.73 mm for trajectory tracking with pose fusion on the machined grid. Camera-subset experiments show graceful degradation in adaptive pose-fusion accuracy as fewer views remain available. With tracking hardware costing under $1,000 USD, LARK provides a low-cost platform for image-guided surgery research. Hardware designs and software are publicly available at https://nist.mni.mcgill.ca/software/ , and datasets at https://nist.mni.mcgill.ca/data/ .

Goal-directed molecular design has advanced rapidly, yet a substantial proportion of designed molecules remain difficult to synthesize in practice, limiting their real-world utility. Prior synthesizability-aware methods either project generated molecules back to synthesizable analogs that deviate from the intended target, or optimize directly in discrete synthesis spaces that lack a continuous landscape for efficient search. We argue that this limitation mainly comes from the search space rather than the optimizer. To address this, we propose RouteFlow, a framework that reformulates synthesizable molecular design as a search over a continuous route latent space, where each latent maps back to a complete synthesis route and synthesizability is inherently preserved. To navigate this space, we adopt reward-guided flow matching as an efficient sampler that steers toward high-property regions. Since reward optimization may push latents off the manifold of real synthesis routes, where decoding becomes unreliable, we further introduce a cycle-consistency mechanism to stabilize fine-tuning. Across 16 optimization tasks from Therapeutic Data Commons, RouteFlow achieves the best sample efficiency among synthesizability-aware baselines, with the best synthetic accessibility and the highest retrosynthesis success rate. Our results also confirm that the proposed cycle-consistency reliably keeps optimization on-manifold while improving target properties, supporting effective synthesizable molecular discovery.

Recent progress in tabular foundation models suggests that training on synthetic tasks can substantially improve in-context learning capabilities, with overall performance largely depending on how well models can infer task-specific predictive relationships from the available context during inference. In this paper, we introduce TAFFY, a tabular foundation model with an In-Context Diversity Prior and a Task-Conditioned Looped Transformer that strengthen this ability. Specifically, to construct each synthetic pretraining context, the In-Context Diversity Prior samples from multiple related environments derived via controlled interventions and distribution shifts on a shared causal process. This in-context diversity encourages the model to learn a more comprehensive and task-specific representation. Moreover, the Task-Conditioned Looped Transformer iteratively and selectively applies a shared group of Transformer blocks to refine contextual representations, with a task-conditioned gate modulating the final hidden-state update. This enables task-adaptive iterative refinement. Together, these components encourage the model to identify predictive relationships from contextual contrasts during pretraining and dynamically modulate context integration for each task. Across six classification and five regression benchmark datasets, TAFFY attains the lowest average rank.

Vision-Language-Action (VLA) models have become a major paradigm for Vision-and-Language Navigation (VLN). However, in safety-critical facilities, invisible risks such as radiation or temperature spikes cannot be detected by an RGB camera, and handling each risk is expensive, requiring a new encoder, new data, and model retraining. We propose Physics-Guided Visual Prompting (PG-VP), a plug-and-play multimodal perception module that instead reuses what a frozen VLA model already does well: avoiding visible obstacles. Given a proximal radiation or thermal source, PG-VP performs a physics-guided risk assessment to determine the avoidance direction and overlays a corresponding virtual obstacle that moves across consecutive frames (Dynamic Visual Prompting). The navigation policy then naturally detours around this invisible hazard. The identical virtual obstacle is used regardless of hazard type, so the visual prompting pattern remains fixed as sensors are added. When no hazard is detected, nothing is rendered, and the policy behaves exactly as it would without PG-VP. We evaluate PG-VP on OmniNav using the val-unseen splits of R2R-CE and RxR-CE, where it guides the policy toward intended low-risk actions in 84.9% and 83.2% of cases, at a cost of 6.8 and 7.9 percentage points in navigation success rate. We further test it with distinct scenarios on a real robot in the presence of actual thermal and radiation sources, all without any retraining. The real test shows that PG-VP effectively avoids these invisible hazards, improving worst-10% average trajectory safety by 63.45% and 32.59% against thermal and radiation sources, respectively.