Papers

We consider pulse propagation in a saturable nonlinear coupler whose other arm is dissipative and other is transparent. A flow of energy from transparent to dissipative arm takes place for weak value of dissipation and the coupler losses its energy. The energy loss of the coupler reduces for strong dissipation. This energy loss depends on the saturable nonlinearity. We find that the flow of relative energy at the output of a finite-sized coupler has a peak at a particular value of nonlinear strength. The peak value decreases with the increase of dissipation and it vanishes for stronger dissipation due to Zeno effect.

Triage in the emergency department (ED) is a sequential decision process that unfolds turn by turn. Existing evaluations of large language models (LLMs) for triage use completed retrospective records and report performance close to that of physicians. We implement a methodology for evaluating LLMs on sequential triage, the task of predicting a triage acuity label from a growing prefix of a nurse-patient conversation. We evaluate six LLMs at five sequential checkpoints on two corpora: 425 LLM-generated (SIMULATED) and 50 physician-authored (CLINICIAN) conversations, both labelled under the Emergency Severity Index (ESI). Every model, measured by quadratic weighted kappa (QWK), degrades from moderate-to-substantial agreement on completed records to fair-to-moderate agreement at every sequential checkpoint. Controlled perturbations show that the label at every checkpoint is anchored on the chief complaint exchanges, and prompting interventions fail to lift this plateau. Models extract clinically relevant content from later turns, yet the surprisal of the true label rises across the checkpoints. So the model fails to integrate the evidence. Three expert clinicians on the same conversations reach a QWK of 0.887-0.929, while the best model reaches 0.295. Predictions concentrate at ESI-2 and ESI-3, and models agree with each other more than with the ground truth, so ensembling worsens the failure. Deploying LLMs for ED triage based on offline benchmarks alone misses this sequential failure.

Machine learning practitioners commonly prototype models in computational notebooks before transitioning them to automated production systems. Despite its prevalence, the concrete engineering work involved in this transition and the software quality concerns that motivate it remain insufficiently characterized. We report on a qualitative study based on semi-structured interviews with 13 ML practitioners from industry and academia. Using reflexive thematic analysis, we identify 23 engineering changes organized into five themes: code restructuring, data pipeline development, testing & validation, pipeline automation, and monitoring & observability. We also identify 20 software quality attributes across the ML development lifecycle and map them to the engineering changes. A recurring pattern in our findings is that computational notebooks externalize oversight to the human practitioner, and defer costs that become obligatory at operationalization time. Operationalization constitutes the repayment of this technical debt accumulated during prototyping, which we refer to as oversight debt. Practitioners do not merely restructure notebook code, but repay this debt by constructing automated substitutes for the interactive oversight that notebooks provide. We further present seven quality trade-offs showing that these tensions are properties of the notebook-to-production transition, rather than symptoms of poor engineering practice. Our findings structure operationalization effort, establish empirical links between engineering changes and software quality concerns, and provide implications for practitioners, tool designers, and researchers working on ML-enabled software systems.

Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.

We study a natural class of normal functions on the moduli space of pointed curves and determine their rank at every point. We prove that the rank is maximal outside the corresponding stratum of Abelian differentials, while along this stratum it drops by exactly one. As a consequence, we describe the local geometry of the associated double ramification locus.

A SUPL\_INIT message is a network-initiated trigger that can be sent to a handset using an SMS to unilaterally start a location session: on receipt, the handset is instructed to determine its own position and report it, together with an identifier such as its IMSI, to a server specified in the message, without any action by the phone's user. The concern motivating this investigation is whether such a message could be used to silently exfiltrate a handset's location and subscriber identity to a server under an attacker's control. We investigated this on a Google Pixel 8 handset, which uses a Samsung Exynos modem and a Broadcom GPS/GNSS subsystem. We find no privacy issue: the handset never sends location data to an attacker-chosen server as a result of an unsolicited SUPL\_INIT delivered by SMS. We also examined an iPhone 8 (Qualcomm modem, iOS 16.7.11). On the handset studied SUPL is disabled, so it ignores any SUPL\_INIT and opens no SUPL connections of its own. More generally, iOS acts on a SUPL\_INIT only during an emergency call, and connects only to a server matching the carrier's configured one.

We develop an operator-level framework for reconstructing the angular structure of small-$x$ diffractive amplitudes from energy-flow measurements. Focusing on coherent diffractive dijet production in the leading-eikonal approximation, we establish the relation between the angular multipoles of the dipole amplitude, the gluon Wigner distribution, and the diffractive scattering amplitude, while keeping their distinct radial transforms explicit. We show that, in the real common-phase sector and away from diffractive zeros, the normalized scattering amplitude can be reconstructed directly, up to a global sign convention, from the square root of the normalized energy-flow distribution. For generic complex amplitudes, the measured intensity instead determines autocorrelations of the amplitude spectrum and phase retrieval is not unique without additional information. We further discuss corrections arising from harmonic-dependent phases, practical conditions for an EIC extraction, and effects beyond the leading-eikonal approximation.

In this paper, we continue to investigate Campanato spaces via semigroups on von Neumann algebras. One of the main results is their coincidence with Lipschitz spaces for all regularity indices $\alpha > 0$ and for all analytic semigroups on von Neumann algebras not necessarily being finite; the desired self-improving property of Campanato spaces has also been verified. As a consequence, we demonstrate that the column Campanato spaces are isomorphic to the row ones for all $\alpha > 0$. This not only removes several restrictions in the previous work \cite{HJ24} by the first two authors, but also extends the previous results to any analytic semigroup, and thus resolves several problems left open in \cite{HJ24}. Both the results and the proof are new even in the commutative setting.

Large vision-language models (VLMs) enable recognition beyond a fixed class set, but their computational demands prevent them from running on many edge devices. Cloud offload makes this capability accessible, but sending every image consumes scarce bandwidth and communication energy. We ask how to bring the open-world recognition capability of VLMs to the edge while operating within tight compute, energy, and bandwidth budgets. Wildlife monitoring provides a natural setting for exploring this question because camera traps encounter species not known at deployment. We present Scout, an autonomous open-world recognition system that invokes a cloud VLM intermittently to teach new classes to a compact edge model. Given only the deployment location and empty site frames, Scout autonomously turns each species identified by the VLM into persistent, site-conditioned recognition capability in a resource-efficient edge model, without a predefined species list, human labeling, or manual tuning. Across 30 camera-trap deployments in three regions on an NVIDIA Jetson Orin Nano, the accuracy of Scout remains within 0.1-2.5% of a model given a predefined species list. On species outside its initial class set, Scout achieves 53.7-59.1% accuracy, compared with 56.5-65.1% for full cloud offload, while using 59-71% less deployment energy.

Autonomous vehicles operating in open-world scenarios are inevitably confronted with previously unknown objects, such as exotic animals or loose cargo. The reliable detection and segmentation of these out-of-distribution (OOD) objects is therefore crucial for a safe understanding of the environment and decision-making. Most existing approaches require access to OOD training samples, retraining of the segmentation backbone, or dedicated auxiliary architectures, limiting their practical applicability. We propose a training-free method that derives dense OOD scores directly from the confidence predictions of a foundation segmentation model, without any task-specific fine-tuning or access to anomalous data. To improve the robustness of our OOD segmentation, geometric information from monocular depth estimation is incorporated into the decision process, providing complementary cues to uncertainty-based predictions. We evaluate the proposed method on the SegmentMeIfYouCan benchmark and additionally assess its performance on OOD tracking in video sequences, reflecting the temporal nature of real-world perception systems. The method performs strongly on road-centered benchmarks.

Vision-Language-Action (VLA) models have shown strong potential for robotic manipulation, but many existing methods still rely on direct mappings from language and visual observations to dense actions. This formulation can weaken the semantic reasoning capability inherited from pre-trained Vision-Language Models (VLMs), which are mainly optimized for visual-linguistic understanding rather than low-level control, and becomes fragile under spatial variations, including changes in object positions, scene layouts, robot embodiments, and camera viewpoints. To address these limitations, we propose H-VLA, a hierarchical VLA framework that decouples high-level key-action reasoning from low-level motion generation. H-VLA combines a Key-Action Model for predicting a key-action as the next manipulation subgoal, a Motion Planning Model for generating dense future actions conditioned on the predicted key-action, and a Unified Camera-Centric Action Space for consistent representation across datasets, embodiments, and viewpoints. We further adopt a two-stage training strategy that emphasizes key-action reasoning during pre-training and dense motion generation during fine-tuning. Experiments show that H-VLA achieves strong performance on SimplerEnv, reaching 91% on Google Robot visual matching, 84% on Google Robot variant aggregation, and 81% on WidowX visual matching. On Agilex real-robot tasks, H-VLA improves over the strongest baseline by 10, 47, and 16 percentage points under in-distribution, out-of-distribution position, and out-of-distribution scene/object settings, respectively.

Coreset selection picks a representative subset of the labeled training set to make training cheaper. However, it is usually evaluated by downstream accuracy at a fixed subset size, ignoring both the time spent selecting the subset and the training recipe behind each reported number. We introduce an end-to-end benchmark that standardizes downstream training and charges selection and training to the same auditable wall-clock budget, spanning 4 datasets from CIFAR-10 to ImageNet-1K, 11 selectors, 5 fractions, and 3 seeds, with over 1,500 released runs. Repeated-sampling work has shown that budget-aware evaluation already favors random strategies. Our two budget studies test whether that verdict survives when every selector is granted its most favorable operating point. Across eight wall-clock budget anchors on each of CIFAR-10 and Tiny ImageNet, no anchor is won by a sophisticated selector: every winner is class-balanced random sampling, repeated random sampling, or full-data training. In fixed-budget duels on ImageNet-1K, training on all data for fewer epochs beats every selection strategy we probe while also costing the least. A per-dataset cost audit shows that selection cost is dominated at every scale by a fixed full-dataset scan, so it cannot be amortized away by selecting a smaller fraction, and its absolute size does not extrapolate from one dataset to another. We further quantify when selection does pay back through subset reuse, and document 9 correctness fixes to a widely used codebase, one of which shifts a standard Herding baseline by nearly 6 points. Selection time is not free preprocessing, and an evaluation that ignores it measures the wrong quantity.

Modeling the dynamics of option implied volatility surface (IVS) is crucial for pricing, hedging, and risk-managing option portfolios. We develop a universal conditional diffusion model that learns to jointly generate next-day IVS increments and the underlying stock's returns. The model is trained on pooled data from 50 stocks and evaluated on a test set comprising 50 in-sample stocks and 50 out-of-sample stocks excluded from training. The training objective is primarily the minimization of MSE, with the variants that jointly impose surface smoothness, and that penalize the presence of static-arbitrage, which are all economically meaningful constraints. Across in-sample and out-of-sample stocks, our diffusion model outperforms the VolGAN benchmark in reducing arbitrage violations, improving stock risk prediction, and aligning explained variance ratios by the first three principal components. The fact that the model extrapolates well to stocks that are excluded from training indicates that the learned dynamics can be shared across stocks. These findings support a universal conditional diffusion as a credible framework for multi-stock implied volatility surface scenario generation.

We consider union-find with deletions, where the representation and the cost of a query must depend on the current number of live elements rather than on the number of elements ever created. For every integer parameter $k\ge 2$, we give a linear-space data structure supporting $\mathsf{MakeSet}$ in $O(1)$ worst-case time, $\mathsf{Union}$ in $O(k)$ worst-case time, $\mathsf{Delete}$ in $O(1)$ worst-case time, and $\mathsf{Find}$ in $O\left(1+\frac{\log n}{\log k}\right)$ worst-case time for a set containing $n$ live elements. A deletion is given only an element handle, not the identifier of its current set. The construction separates global rank growth from local deletion repair. A logical set is represented by fewer than $k$ disjoint ranked trees. Equal-level trees are collected without physical linking until $k$ certificates are available, at which point one base-$k$ carry is performed in $O(k)$ time. Each member tree uses a strengthened form of the full/reduced local rebuilding scheme of Ben-Amram and Yoffe. A $q$-ary value argument, with $q=3/2$, couples the local trees to the base-$k$ certificates and yields the stated current-size height bound. A small but essential rule handles high-rank stars, a state that the base-$k$ carry can create but that does not arise directly in the binary-rank construction underlying the earlier local scheme.

Artificial intelligence can increasingly produce plausible, sophisticated mathematical material faster than a developing graduate student can understand or verify it. A sophisticated result or paper draft therefore becomes weaker evidence of the student's own mathematical development. This creates a formation gap between output and personal capacity, and a trust gap between a convincing argument and warranted acceptance. The formation gap can persist even when the student understands the output: understanding a supplied argument does not by itself establish the capacity to initiate and direct inquiry. These gaps are not the whole story. AI can also help students explore examples, compare approaches, enter unfamiliar areas, and undertake ambitious research. The task is to design an apprenticeship that realizes these possibilities while developing substantive mathematical command. The central purpose of a mathematics PhD is to form mathematicians capable of original, independent, and responsible inquiry, including inquiry conducted with AI. This document develops that objective through four connected capacities: competence, judgment, independence, and responsibility. It distinguishes a work's contribution to mathematics from the evidence it provides of a student's formation; explains how a known answer can initiate rather than end creative inquiry; and proposes changes in learning activities, assessment, doctoral originality, advising, and institutional support. Purposeful independent work and ambitious AI-assisted research are complementary parts of the model. Its recommendations include proportionate contribution statements, recognition of advising costs, and staged pilots evaluating both mathematical ability and effective human–AI collaboration. The aim is not to preserve an inherited sequence of training, but to improve mathematical formation as mathematical practice changes.

The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.

Battery energy storage system (BESS) is integrated into the smart grid to enhance scalability, economy, and greenery. And the State-of-Charge (SoC) balance is one of the basic problems of BESSs, which can maximize the utilization of capacity. BESSs with a unified relative variation rate for SoC can be simultaneously filled or empty, while real-time estimation schemes of SoC balance and power sharing states are required in this power allocation scheme. Therefore, the prescribed performance control (PPC) method is applied in this paper to design two distributed estimators based on multi-agent systems (MASs), in order to estimate the power sharing and SoC balance states in real-time under dynamic load driving. In this way, these two average values can ultimately be well estimated with almost zero error performance, and dynamic performance and steady-state performance of the two estimators can be adjusted by different parameters. Similarly, consensus performance and dynamic tracking performance are decoupled. These results provide a broader range for the selection of gains. To verify the effectiveness, robustness and progressiveness of the designed estimators, some cases with a resistance network containing 4 BESSs as load distribution are designed and discussed. Further more, to test scalability, a large-scale system containing 12 BESSs is conducted to the designed scheme.

Online post-training of vision-language-action (VLA) models requires efficient use of robot interaction and reliable policy improvement from continually collected experience. We propose asynchronous Replay-Anchored Policy improvement (RAPolicy), a framework that performs rollout and learning concurrently while grounding both critic and actor updates in replayed behavior. The critic learns chunk-level values from recorded actions and constructs Bellman targets without predicting next actions, reducing computation and dependence on action-value estimates outside replay coverage. The one-step flow actor reuses the initial noise stored during rollout and learns through advantage-weighted conditional likelihood, directly supervising the action mapping used for execution. We evaluate RAPolicy across four single-task settings and one joint five-task setting in the real world, with online training budgets of only 1–2 hours. Starting from policies fine-tuned on just 10 demonstrations per task, RAPolicy rapidly adapts to new single tasks and achieves an average 86.3% success rate. In the joint multi-task setting, RAPolicy improves overall success rate from 52% to 88% while preserving performance on already reliable tasks and improving weaker capabilities. Overall, RAPolicy substantially outperforms the baselines in aggregate task success while requiring fewer human interventions, demonstrating stable policy improvement and high online training efficiency. Project page: https://flyfaerss.github.io/RAPolicy.

Among lattices normalized to have packing radius one, the known shallowest depths of the deep holes in $7$-, $8$-, $9$- and $10$-dimensional lattices are $\sqrt{7/3}$, $\sqrt2$, $\sqrt{5/2}$ and $\sqrt{8/3}$, given by $E_7^*$, $E_8$, the laminated lattices $\Lambda_9$ and $\Lambda_{10}$, respectively. This paper presents new lattices in these dimensions with shallower deep holes. It also answers two problems of J. Martinet about short representatives of the classes of $\Lambda/2\Lambda$ in $7,8,9,10$ and $12$ dimensions.

Model merging consolidates fine-tuned experts into one multi-task model without retraining. All existing data-free methods approach this problem entirely in weight space. Restricted to arithmetic on parameters, these methods never observe how each expert behaves, a signal that only emerges through forward evaluation. Accessing this behavioral signal requires inputs to evaluate on, which the data-free setting prohibits. We propose Merge++, a post-hoc method that addresses this by inverting the expert checkpoints to synthesize task-representative images, then distilling expert knowledge into the merged model using those images. Merge++ requires no additional data beyond the checkpoints themselves. It applies universally across merging algorithms and operates as a complementary refinement stage independent of the underlying weight-space method. The method consistently improves merging algorithms ranging from simple task arithmetic to state-of-the-art spectral methods, with average gains of +2 to +8 points and up to +25.9 on individual configurations.

Safe operation of robotic systems requires trajectories to remain within a prescribed safe set under admissible control inputs. Barrier certificates provide such guarantees by certifying a controlled-invariant region within that set. Sum-of-squares optimization offers a systematic way to synthesize such certificates, but its direct application requires polynomial dynamics, excluding common robotic nonlinearities, including trigonometric terms. We address this limitation using exact polynomial lifting, which replaces non-polynomial dynamics with polynomial-augmented dynamics subject to lifting-induced algebraic constraints, preserving nonlinear geometry without approximation. We formulate lifted-domain joint barrier synthesis that computes a certificate with a state-feedback control witness and develop a sampled-data safety filter for zero-order-hold implementation. To assess whether the benefits of lifting persist across synthesis frameworks, we also adapt a sample-guided successive-barrier method to the lifted representation. On coordinated-turn and planar multirotor models, exact lifting improves certified coverage in both methods: at matched sample sizes, lifted successive-barrier synthesis achieves higher coverage with fewer barriers and lower computational cost, while lifted joint barrier synthesis provides higher coverage and lower computational cost than the finest tested piecewise resolution. In closed-loop experiments, the safety filter maintains feasibility and safety across all evaluated trajectories, reduces spatial conservativeness, and requires less intervention for both models.

Long-context inference has become a defining capability of large language models, but exact dense attention remains costly due to its quadratic scaling with sequence length. Block-sparse attention offers a hardware-friendly alternative by routing each query block to a small set of relevant key blocks, yet accurate training-free block routing remains difficult. Existing routers often pool post-RoPE token representations, which entangles semantic aggregation with RoPE-induced geometry and attenuates local positional cues through high-frequency phase cancellation. To resolve this mismatch, we propose Semantic-Geometric Decoupled Routing, a training-free block routing framework that shifts semantic aggregation to the pre-RoPE space and reconstructs geometric bias with an offline structural prior and relative block distances. This decomposition yields an explicit closed-form block routing score without token-level search or post-hoc calibration. Experiments on long-context text and video tasks show that our method approaches full-attention accuracy across 4K–128K contexts, keeps routing overhead below 3.4 ms, and achieves a 5.03$\times$ speedup over FlashAttn at a 128K context length.

In this paper, we establish the existence and uniqueness of solutions for mean-field stochastic differential equations (MF-SDEs in short) and backward stochastic differential equations (MF-BSDE) driven by anomalous sub-diffusions $\{B_{L_t}; t\geq 0\}$ with random coefficients, respectively. Here $B$ is a Brownian motion on ${\mathbb R}^d$ and $L$ is the inverse of a subordinator $S$ with drift $\kappa >0$ that is independent of $B$. We further study the stochastic maximum principles (SMPs) for control problems of the stochastic systems modelled by the MF-SDEs using a convex variational method. A linear quadratic control example is given in the last section of this paper, for which both the SMP and the sufficient SMP established in this paper are utilized to show explicitly that it admits a unique stochastic optimal control.

On June 12, 2026, the U.S. government ordered Anthropic to bar foreign nationals from two of its most capable models. Unable to sort users by nationality, it withdrew them from everyone. Weeks later, OpenAI agents under test escaped their sandbox and compromised Hugging Face, which stopped the intrusion without knowing its source. Neither stop rested on a dedicated AI governance regime. Lawmakers have begun to address stopping, yet their vocabulary remains shaped by the power of technique: the EU AI Act requires a "'stop' button or a similar procedure," and a 2026 bill in Congress is titled the AI Kill Switch Act. This Article argues that interruption is an institutional practice, not simply a technical artifact. It develops a theory of stop along four dimensions (technical affordances, interruption authority, epistemic triggers, and epistemic standing) and four paradigms: simple (escalator), sequenced (process plant), networked (railway), and distributed (agentic AI). Agentic AI exposes a mismatch between legal mechanisms of stop and distributed agency: control is divided, a stop at one point may leave the activity running elsewhere, and the system may circumvent attempts to halt it. A coding of some 1,400 AI incidents, by two language models from different labs under a pre-specified protocol, finds no stop in roughly 80% of the 1,213 retained. Where a stop was possible but absent, the missing element was mostly legal for informational, economic, and societal harms, and mostly technical for physical harms and agentic systems. A survey of forty AI governance instruments finds binding stopping requirements in only seven. The Article proposes a reform in two layers: risk reduction (a duty to maintain stop capacity at each site, emergency authority at the infrastructure layer, and enforceable access to the evidence a stop must rest on) and adaptation (safeguards for when a stop fails).

We extend the theory of $s$-energy to $\mathbb{Q}_p^n$. We give an exact representation for the $s$-energy in terms of the Fourier coefficients of a finite Borel measure with support in $\mathbb{Z}_p^n$, which is stronger than the approximate representation in $\mathbb{R}^n$. We also compute the Fourier dimension of the $p$-adic Riesz product measure, even in the case $p=2$, which has never been studied before.

LLM rerankers add of the order of \$0.2-0.3 per 1,000 queries and about a second of tail latency on top of a graph-augmented dense pipeline such as HippoRAG2, and on three multi-hop benchmarks they improve final-hop top-K coverage on seven of nine (dataset, K) cells, by up to +34.8 pp. We ask whether a learned per-query gate can skip the reranker where it will not help, using only features available before the LLM call (27 score and lexical statistics of the two retrieval lists plus a PCA of a small query embedding) with an executable fallback. Every choice, including the fallback and the threshold, is made inside the training fold and applied once to held-out queries, and harmful skips (the rerank would have found the target, the fallback did not) are reported next to the aggregate coverage. Across nine cells on 2WikiMultiHopQA, MuSiQue and HotpotQA the gate skips 51% of calls at an average held-out LastHop@K cost of 1.2 pp; four cells meet a pre-registered 1 pp rule, harmful skips occur in eight (190 harmful against 136 beneficial), and a random gate at the same skip rate loses 2 to 11 pp on the high-lift cells. A second rule sets each cell's threshold from a pre-specified budget on the expected harmful-skip rate over Platt-calibrated harm probabilities (ECE 0.025 after calibration, 0.094 before): at a 1 pp budget the gate skips 42% at -0.8 pp with 66 harmful skips and six cells within 1 pp, but realised harm exceeds the promise in six cells (mean 1.45 vs 0.83 pp), a selection optimism we quantify; a 0.5 pp budget realises about 1 pp. The harm probabilities are calibrated but barely discriminative (AUC 0.16 to 0.70). An earlier version reported 73% "lossless" savings; that figure rested on an oracle fallback and a wrong MuSiQue target, and we document both.

Vision-Language-Action (VLA) models have emerged as a powerful paradigm for embodied intelligence, but fine-tuning them with reinforcement learning (RL) remains constrained by the cost of real-world robot interaction. Model-based reinforcement learning (MBRL) reduces this cost by using a learned world model to generate rollouts for policy optimization. However, it becomes computationally expensive as VLA policies and world models scale. Existing methods typically treat states equally, overlooking substantial differences in their utility for policy improvement. In this paper, we show that policy uncertainty helps identify states with greater potential for policy improvement. The policy exhibits high uncertainty at only a small subset of states, often during decision-sensitive stages where small action differences can alter task outcomes, suggesting that policy improvements at these states could be particularly valuable. Building on these findings, we introduce U-GROW, a lightweight, plug-and-play sampling layer that directs more model rollouts to these informative states. By modifying only the branched-start distribution, U-GROW can be integrated into existing MBRL pipelines without changing the policy optimization objective. Experiments in both simulated and real-world manipulation tasks demonstrate the efficiency and effectiveness of U-GROW, supporting the use of policy uncertainty to guide experience generation.

Large language model code generation benchmarks primarily evaluate well-resourced languages like Python and Java, where models benefit from abundant training data. They provide limited evidence about reasoning in unfamiliar computational models: deriving arithmetic from a single subtract instruction, coordinating parallel programs across communicating nodes, or wiring logic gates into circuits. We present ISA-Bench, a benchmark of programming games with constrained instruction sets. For each game we provide a full execution stack (parser, VM, and verifier), enabling automated evaluation with structured feedback for iterative refinement. Reasoning models achieve higher average solve rates than code-specialized and general-purpose models, but unfamiliar syntax remains a major source of failure. Models solve more tasks with iterative feedback, though the gains vary substantially across architectures. We introduce a reasoning–execution gap (REG) analysis that reveals a recurring disconnect between identifying a plausible computational strategy and expressing it as a correct program in the target ISA. Code is open-sourced.

We study a fractional Brezis–Nirenberg problem on a bounded domain with finitely many Hardy potentials centered at distinct points $a_1,\dots,a_k$, with masses $\mu_1,\dots,\mu_k\geq 0$. We assume $\sum_{i=1}^k\mu_i<\Lambda_{N,s}$ and consider $N>4s$ and $0<\mu_{\max}<\overline{\mu}_{N,s}$. The interaction between the poles allows existence for $\lambda=0$ and for some negative values of $\lambda$. At a pole $a_j$, this interaction is described by $B_j(\lambda,\mathbf a,\boldsymbol\mu)=\lambda+\sum_{i\neq j}\frac{\mu_i}{|a_i-a_j|^{2s}}$. This leads to a threshold $\lambda_{\mathrm{geo}}\leq 0$. We prove that the critical Rayleigh quotient is attained for $\lambda_{\mathrm{geo}}<\lambda<\lambda_1(\boldsymbol\mu,\mathbf a)$, and hence the problem admits a positive least-energy solution. If at least two masses are positive, then $\lambda_{\mathrm{geo}}<0$, so the result includes $\lambda=0$ and a nonempty interval of negative values of $\lambda$. We also prove a direct compactness estimate for weakly vanishing sequences by localizing the Gagliardo seminorm. The argument avoids both profile decomposition and the Caffarelli-Silvestre extension.

A detailed collider study of Higgs production in the process $e^+e^- \to ZH$ is presented within the framework of the Two-Higgs-Doublet Model (2HDM), with particular emphasis on mis-aligned scenarios in the Type-I realization. The analysis is performed at a future $e^+e^-$ collider with $\sqrt{s}=500$~GeV and an integrated luminosity of $10~\mathrm{ab}^{-1}$, considering heavy Higgs masses in the range $160 \leq m_H \leq 400$~GeV. The analysis covers heavy CP-even Higgs states with non-fermionic decay modes such as $H\to WW$ and $H\to hh$, and incorporates final states arising from leptonic and invisible $Z$ boson decays. Fast parametrized detector-level simulations are employed to evaluate selection efficiencies, signal–background discrimination, and exclusion sensitivities. It is shown that values of $|c_{\beta-\alpha}|>0.1$ can be excluded at the $95\%$ confidence level over almost the entire range $1\leq\tan\beta\leq10$ in the $H\to WW$ scenario, while the $H\to hh$ channel provides lower sensitivity.