Papers

Safe navigation against obstacles that can actively maneuver within bounded capabilities remains challenging: robust control barrier function methods typically treat obstacle actions as generic disturbances, while differential-game approaches are computationally expensive for online navigation. We propose an adversarially robust geometric certificate that accounts for the worst-case effect of admissible obstacle maneuvers directly in the safe-set geometry through a closed-form contraction of the certificate parameters. The construction exploits a structural property of line-of-sight (LoS) certificates: the robot and obstacle actions enter the certificate through a common state-dependent geometric gain. This gain cancels in the worst-case comparison, reducing the differential game to a direct comparison between obstacle maneuvering capability and the weaker of the robot's longitudinal and steering authorities. Instantiated on the parabolic certificate, the construction yields Adversarially Robust Dynamic Parabolic Control Barrier Functions (AR-DPCBF), for which we establish sufficient conditions for forward invariance of the contracted safe set against all admissible obstacle maneuvers under kinematic bicycle dynamics with bounded inputs. When the obstacle capability is unknown, a sliding-window estimator supplies a high-probability upper bound, allowing the guarantee to be retained with the corresponding coverage probability. We further formulate soft and buffered variants to recover feasibility in dense environments. Simulations across obstacle capabilities, densities, and capability mismatch show substantial reductions in barrier violations and collisions and demonstrate that pointwise robustification of the barrier derivative cannot substitute for contraction of its geometry.

Prospective memory allows an agent to retain an intention tied to a future condition, but the stored intention does not reveal whether that condition currently holds. Checking it may require web access, multi-step tool use, and paid calls. Existing systems decide when intentions require attention, but do not allocate the resulting observations under a shared budget. We introduce the first resource-allocation formulation for the external observations required by stored intentions under a shared episode budget. BudgetPM offers two policy variants that share a hard-budget executor. BudgetPM-Static uses a lightweight Logistic scorer to learn whether a check improves the current decision. BudgetPM-Sequential distills full-episode hindsight schedules into a lightweight policy that decides when to spend or reserve capacity using only pre-query information at deployment. We evaluate BudgetPM against two public memory-agent systems, five matched controls, and four hand-designed monitoring or budget-adaptation rules. Across two benchmarks and three backbones, BudgetPM-Static outperforms adapted Mem0 and PMA workflows. On PM-Bench, its Logistic scorer reaches competitive quality–cost operating points alongside higher-capacity scorers and retains 99.9–100% of unconstrained quality with 42–54% fewer observations. Under severe scarcity and the same hard caps, BudgetPM-Sequential exceeds the strongest tested natural monitoring schedule by 1.92–2.58 Set F1 points. It reaches the same Set F1 and on-time recall with 16–33% fewer observations. Matched attribution, exact-cost analysis, and a fixed-budget load intervention link this gain to competition between present and future opportunities. These results yield a demand–capacity design rule: local gating works when capacity covers demand, while future-aware supervision adds value when observations compete across time.

The Wagner-Preston theorem states that every inverse semigroup can be embedded into an inverse semigroup of partial bijections on some set. However, this embedding does not respect lattice operations in the natural ordering. In this paper, we show that an abstract pseudogroup can be faithfully represented by partial bijections on a set if and only if its frame of idempotents is spatial. More generally, we show that any abstract pseudogroup can be faithfully represented by partial homeomorphisms on a locale.

Fine-grained visual perception enables vision-language models to distinguish subtle attributes and ground their answers in visual evidence. In high-resolution scenes, processing the whole image at greater resolution spends visual tokens on irrelevant content, while isolated crops can lose the context needed to interpret the selected evidence. We introduce EviViT, a lightweight attachment that learns where a pretrained vision transformer should acquire detail. Human visual-search traces supervise a question-conditioned evidence density, which guides regional re-reading from the original pixels and the allocation of visual tokens. A sparse, coordinate-aware bridge then connects the regional features to the global scene, allowing the host to interpret precise evidence in context. Learned with the host backbone frozen, the attachment serves both the base model and compatible post-trained descendants without refitting. Experiments across nine hosts show consistent gains in average fine-grained accuracy. Matched-budget comparisons further show that EviViT outperforms global-only processing at every tested token ceiling while using fewer visual tokens.

Triangular transport maps provide a flexible approach to sampling-based probabilistic modeling, including density estimation, generative modeling, and Bayesian inference. They transform an unknown target distribution into a simpler reference through a monotone triangular map. The map structure is defined by a variable ordering and sparsity pattern, which together encode a directed acyclic graph. Map quality can depend strongly on this structure, yet finding a good structure is computationally expensive because each candidate generally requires fitting a different map. A central challenge is therefore to learn density and structure jointly, while keeping computation manageable as dimension grows. We introduce Self-Structuring Transport Maps (SSTM), which learn the map, ordering, and sparsity jointly. We use SoftSort to learn the variable ordering and $L_0$ gates to learn the sparsity, while preserving a triangular structure. To keep the map scalable, we use a monotone BatchEnsemble that shares one weight matrix across all map components through rank-one adapters. Across synthetic and real data, jointly learning the structure and map gives better density estimates than estimating the structure first. When the structure is identifiable from the density, SSTM matches the density performance of a map fitted with the true structure and outperforms autoregressive flows. On large datasets, SSTM is competitive with autoregressive flows.

Cross-linguistic effects are a central topic in bilingual first-language acquisition. Artificial learners can help investigate L1-L2 interactions by enabling controlled comparisons across language combinations and learning conditions. Recent work explores this direction by training bilingual language models under developmentally plausible constraints. However, human and model learners still diverge in fundamental ways, with one major difference being input modality: children learn primarily from spoken input, whereas language models are typically trained on orthographic text. To reduce this gap, researchers have trained models on phonemic representations of speech. In this work, we combine these research directions to train bilingual BabyLMs with phonemic input. We keep English fixed as the L2 and vary the L1 across German, Swedish, Persian, and Basque, selected to represent contrasting combinations of syntactic and phoneme-inventory distance from English. Our results show stronger L1-related variation in grammatical learning trajectories under phonemic than orthographic input, while early lexical differences align with phoneme-inventory similarity.

Implicit electric field conjugation (iEFC) is an efficient, model-free wavefront control technique for dark hole creation. Its model-free nature, relying on calibration with real data rather than a synthetic model of the instrument, makes it uniquely versatile and highly attractive. It has been successfully demonstrated in a variety of environments, both in the laboratory and on-sky, using different experimental platforms and coronagraphs. A common characteristic of these demonstrations is that the resulting DHs exhibit moderate to large inner working angles and wide fields of view, often extending over several tens of $\lambda/D$. Here, we report the first demonstration of iEFC at small angular separations, achieving a DH spanning 1 to 4 $\lambda/D$ on a segmented pupil in H-band under laboratory conditions. This combination of aggressive IWA and reduced FoV highlights the uniqueness of the SPEED facility (segmented pupil experiment for exoplanet detection). SPEED is a high-contrast imaging testbed designed for extremely large telescopes (ELTs), developed in the context of the ELT/PCS instrument (planetary camera and spectrograph), currently in pre-phase A. Its small-IWA coronagraph, an APCMC (apodized pupil complex mask coronagraph), and its multi- and out-of-pupil-plane deformable mirror (DM) architecture are specifically optimized for DHs at very small IWAs, down to the diffraction limit. Our results demonstrate (i) that widely separated out-of-pupil DMs are well suited to generating DHs with IWAs down to 1 $\lambda/D$, and (ii) the effectiveness of iEFC, when combined with the SPEED wavefront control architecture, for high-contrast imaging with segmented telescopes. Ultimately, these results pave the way toward meeting the stringent high-contrast requirements of ELT-class instruments, opening new opportunities for exoplanet detection at unprecedented angular resolutions.

Recent approaches to reinforcement learning (RL) post-training for large language models increasingly remove the critic to reduce training instability and memory overhead. Even where a critic is trained, it is discarded once training ends, although it has learned to predict outcomes. We revisit this trend and show that a pretrained critic's ability to predict future outcomes can make it a valuable asset for efficient long-horizon reasoning. First, we find that instability in critic-based RL for long chain-of-thought reasoning is largely an optimization artifact: keeping policy updates small and low in variance restores stable convergence. Second, a well-pretrained critic estimates the posterior probability of eventual success from later trajectory states and unfinished prefixes. Its predictions provide outcome-derived, dense, per-prefix learning signals that, during policy optimization, require neither completed rollouts, step-level annotations, nor external reward labels. Building on this insight, we introduce Reward-Free Policy Optimization (RFPO), which repurposes a single calibrated, frozen critic as a rollout-level reward, a value baseline for generalized advantage estimation, and a success forecaster for unfinished prefixes. We further show that binarizing the debiased score stops the policy from exploiting the critic's length bias. Binarized, RFPO matches supervised PPO without a single label in the training loop, while cutting compute and memory overhead. This makes RFPO well suited to long-horizon reasoning tasks, where outcomes arrive late and generation dominates cost: because rollouts can be rewarded before they finish, training no longer has to pay for waiting on every trajectory to complete. Our findings challenge the prevailing critic-free paradigm and establish critic-based, reward-free optimization as a scalable and computationally efficient path for LLM post-training.

We give a deterministic algorithm for Free-Flood-It on rectangular grids $P_k\square P_n$ with at most three colors. For every fixed height $k$, it computes the minimum number of moves and an optimal sequence in $N^{O(k^2)}$ time, where $N=kn$. This resolves the previously open three-color case on complete $3\times n$ boards. The proof uses a representation of flooding strategies as paintings by connected regions. We show that an optimal painting can be chosen so that its regions form a rooted tree with strong restrictions on the colors along ancestral paths. These restrictions make the part of the tree visible in any fixed-size connected window admit only polynomially many descriptions. The remaining common ancestors may form an arbitrarily long chain. We retain that chain on a stack and use a finite context-free recurrence to minimize the total painting cost without enumerating all possible stack contents. Connectivity information at the boundary ensures that the resulting local descriptions assemble into one valid global painting. The argument also applies to graphs supplied with an ordering into connected layers of bounded size, provided every edge lies within one layer or joins consecutive layers. A family of three-row boards shows that the unbounded ancestor chains handled by the algorithm are necessary even for optimal paintings. For any fixed height and palette size, we also give a deterministic EPTAS and a randomized sampling variant with an explicit failure-probability bound. These approximation results use a separate algorithm with single-exponential dependence on the move budget.

This document presents input from the U.S. Muon Collider Collaboration to the SCAC Facilities Subcommittee. It outlines the scientific motivation for a future Muon Collider, the R&D and demonstration program needed to establish its feasibility, and its relevance to U.S. facilities planning for 2026-2036. It also discusses opportunities for leveraging existing U.S. capabilities, developing the accelerator workforce, and building synergies with other DOE programs and international efforts.

Accurate perceptual quality assessment is essential for evaluating and optimizing spatial audio, where perceived quality depends on both signal fidelity and inter-channel spatial relationships. However, subjective evaluation is costly, while existing perceptual models are often trained for limited channel configurations and cannot be directly applied to higher-channel-count audio. This raises the question: how can pretrained perceptual knowledge be effectively reused for multichannel spatial audio? Using 5.1-channel audio, we study four levels of multichannel integration: signal, prediction, latent, and feature and propose two learned approaches: latent-level aggregation of spatial-group representations and the feature-level Feature-Band Group Attention (FGAtt), which adaptively fuses spatial groups at the feature level before perceptual processing. Across five 5.1-channel test sets, FGAtt achieves the strongest over- all performance, demonstrating the effectiveness of feature-level adaptation for reusing pretrained perceptual knowledge

We revisit the role of appearance modeling in 3D Gaussian Splatting (3DGS) and show that limited expressiveness in view-dependent reflectance is a key driver of representation redundancy. In standard 3DGS, low-order spherical harmonics (SH) are used, restricting the splats' ability to model high-frequency directional effects, which is typically compensated by increasing the number of splats. We propose NRF-GS: Neural Residual Fields for Gaussian Splatting, a hybrid representation that replaces per-splat SH-bases with a shared neural residual field. Each Gaussian encodes a compact set of appearance features and a lambertian base color, while a lightweight global scene-level MLP predicts view-dependent residuals conditioned on viewing direction, distance, and per-splat features. This formulation enhances directional reflectance modeling by combining diffuse per-splat reflectance representations with a shared global function for high-frequency details, enabling both higher expressiveness and parameter sharing across splats. Our key insight is that by accurately capturing high-frequency directional reflectance, especially in specular regions, the GS-representation becomes more expressive, reducing the need for geometrically redundant splats. As a result, NRF-GS achieves comparable or better rendering quality while reducing the number of Gaussians by up to 50%, and produces visibly improved specular and high-frequency details.

DANCo (Dimensionality from Angle and Norm Concentration) jointly calibrates nearest-neighbor distance and angular statistics and consistently reaches state-of-the-art accuracy on clean intrinsic-dimension (ID) benchmarks. Practical data, however, introduce neighborhood-relative noise and sample-amplitude heterogeneity that can distort these geometric signals. We reformulate DANCo componentwise, retaining separate distance and angular discrepancy curves so that the source of an estimate can be identified and interpreted. For the distance component, we derive a closed-form Kullback-Leibler divergence for the generic-order ratios of the generalized ratios ID estimator (Gride); when both angular parameters are matched (Full), Gride reduces mean percentage error from $27.7\%$ to $17.6\%$ at noise equal to $40\%$ of typical neighbor spacing on 24 manifolds. For the angular component, two sampling regimes motivate aligning mean direction while retaining concentration matching (Profiled). On a Gaussian scale mixture with generating dimension 70 embedded in 100 dimensions, profiling raises the Minimum Neighbor Distance (MiND) estimate from $22.8$ to $66.7$, while removing the known amplitudes restores MiND-Full to $71.9$; the control thus attributes the Full shortfall to amplitude heterogeneity. On CIFAR-10 and ImageNet, amplitude-reducing normalizations move angular location toward the references and narrow the Full-Profiled gap, an observational counterpart to the controlled mixture. Across four pretrained convolutional neural networks, Gride-Profiled, the two-nearest-neighbor estimator (TWO-NN), and the maximum-likelihood estimator (MLE) exhibit similar rise-and-fall profiles, while Full-Profiled differences identify the layers most sensitive to angular calibration.

Generalized reaction-diffusion systems encompass diverse transport mechanisms and coupled reaction kinetics. A central question for neural PDE solvers is what should be learned so that a common interface can accommodate phase-field and degenerate transport, local reactions, and multispecies coupling. We propose the Neural Constitutive Laws–Mass-Compression-Transport (NCL-MCT) Solver, which learns PDE-specific constitutive responses while retaining temporal evolution in a shared MCT integrator. Transport is represented through mobility and thermodynamic driving force, and reaction through relative reaction rates. These constitutive responses depend on the current density rather than explicitly on the initial condition or elapsed time, motivating their reuse across different initial conditions and time horizons. The same interface supports velocity-data supervision and known-law supervision, neither of which requires time integration during training. When constitutive laws are known, supervision can be evaluated on independently sampled density fields, enabling trajectory-free constitutive learning without generating solution trajectories. Across seven systems, separately trained constitutive modules share the same interface and MCT integrator and achieve relative rollout $L^2$ errors of $10^{-4}$ to $10^{-2}$. Tests with unseen initial-condition families and an extended time horizon assess reuse beyond training conditions, while separate experiments demonstrate trajectory-free constitutive learning. These results support constitutive responses as an effective learning target for a shared neural PDE framework.

We study the $\mathrm{v}$-numbers of ordinary and symbolic powers of the facet ideal and the Stanley–Reisner ideal of a chessboard complex. Exact formulas are established for the $\mathrm{v}$-numbers of ordinary and symbolic powers of the Stanley–Reisner ideal, as well as symbolic powers of the facet ideal. Furthermore, we show that the $\mathrm{v}$-number function of the ordinary powers is asymptotically linear.

Long-horizon LLM agents require reinforcement learning methods that can assign credit to intermediate decisions under sparse and delayed rewards. Existing group-based methods such as GRPO and GiGPO alleviate this issue by comparing rollout returns or repeated anchor states, but they still fail when the compared returns have no variation. We identify this failure mode as zero-credit failure: during early training, many failed rollouts contain useful prefixes, yet existing methods assign them no task-discriminative advantage. To address this issue, we propose Milestone Viability Potential Policy Optimization (MVPO), a potential-routed policy optimization algorithm that learns from viable failure prefixes. MVPO estimates prefix potential over Union-Find viability regions, repairs zero-credit groups with potential-difference advantages, and attenuates the potential branch according to relative performance progress. Experiments with Qwen2.5-1.5B-Instruct show that MVPO outperforms eight strong baselines, including GRPO and GiGPO. Under the same training length, MVPO improves over the GiGPO baseline by +4.4 success points on ALFWorld and +5.3 on WebShop, while adding only 0.16%-0.20% advantage-construction overhead.

Stochastic resetting can generate strong correlations in many-body systems through a shared fluctuating environment. Here, we investigate how such dynamically emergent correlations (DEC) coexist with intrinsic (direct) interactions in a weakly repulsive Bose-Einstein condensate described within the Gross-Pitaevskii framework. The condensate undergoes free expansion from an initial Thomas-Fermi state and is stochastically reset to this initial state at a constant rate. We show that the resetting protocol drives the system into a unique nonequilibrium steady state and obtain its density profile, edge statistics, and full counting statistics analytically. The steady-state density retains an inverted-parabolic form within the core, while developing exponentially decaying tails outside it. We further show that resetting induces nontrivial fluctuations of the condensate edge and particle number, yielding exact scaling forms for the edge distribution and the full counting statistics. Our results provide a tractable setting for exploring the interplay between intrinsic repulsive interactions and attractive DEC generated by a common stochastic environment in quantum many-body systems.

The rapid, unpredictable advancements in AI system capabilities has seen regulators take adaptive and experimental approaches to policymaking. Established in other domains as instruments balancing regulation with innovation, regulatory sandboxes are seen as solutions for AI regulation. However, analyses mostly focus on the legal and institutional design of AI Regulatory Sandboxes (AIRSes). With the legal framework leaving the socio-technical interpretation to stakeholders, this creates a gap on the sense-making required to fulfill the AIRS purpose. In this paper, we approach this by designing a Boundary Negotiating Artifact as a way to mediate meaning in AIRSes. Through Research-through-Design we iteratively develop a tool, providing an interface for the different stakeholders to collaborate in AI assessment. We then position it as technical backbone in established AIRS frameworks, structuring the collaborative sense-making of the involved stakeholders. We further report the insights gained from our design process leaving the qualitative evaluation for future work.

Schmelzer and Hastie prove that Markowitz's Critical Line Algorithm and the LASSO path trace the same curve. This companion note checks that result numerically with a stock LASSO solver, lars\_path from scikit-learn, and no portfolio software. It covers long–short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Every corner the path returns meets its own optimality conditions to about $10^{-13}$ and agrees with independent quadratic-programming solvers, on factor models of up to 500 assets, on the Fama–French size and book-to-market portfolios, and on daily returns of 494 S&P~500 stocks. Called naively, the long-only path stops at the maximum-Sharpe portfolio. One shift of the response, by an amount computed in advance, lets a single call reach the minimum-variance portfolio. The script, its checks, the Fama–French returns and an R cross-check are published, with a locked environment, so that anyone can repeat them.

We present Waypoint 1.5, a real-time diffusion world model for interactive video generation on consumer-grade hardware. Unlike general video diffusion models, interactive world models (iWMs) must respond to dense user controls under strict latency and throughput constraints. Waypoint 1.5 is pre-trained on 100,000 hours of diverse, control-aligned video game data across hundreds of games, and generates playable video conditioned on full keyboard and mouse input. The model includes two resolution variants that run across a wide spectrum of consumer hardware. To characterize this unique setting, we distinguish rendered FPS, latent FPS, and control rate. We describe the data pipeline, architecture, training methodology, and runtime system behind Waypoint 1.5. We evaluate interactivity through latency and throughput. Finally, we discuss the safety and ethics considerations unique to iWMs.

Momentum-dependent symmetry actions can turn the even-integer constraint of a $2\mathbb{Z}$ classification of topological insulators and superconductors into an odd-integer constraint without changing the symmetry algebra. For internal and order-two crystalline symmetries in up to four spatial dimensions, we derive parity relations between the Chern or winding number of a gapped Hamiltonian and topological invariants of its momentum-dependent antiunitary symmetry matrices. Whenever the symmetry action enforces odd parity, any symmetry-preserving gapped phase must be topologically nontrivial. Using cellwise actions, which are represented by momentum-independent matrices in a fixed unit-cell basis, as a reference, we determine how locality constrains the realization of odd topological numbers. Explicit model constructions and no-go theorems distinguish three cases: odd values can be realized by finite-range symmetry actions, can be realized by exponentially decaying quasilocal actions but not by finite-range actions, or are impossible in finite-dimensional Bloch systems.

Language model agents can be improved by updating their model weights or refining the harness that guides task execution. These components are coupled: weight updates change how the model uses the harness, while harness updates change the trajectories used for training. We propose VACE, Validation-Gated Alternating CoEvolution, which alternates agentic reinforcement learning with trajectory-driven harness refinement. After each RL stage, VACE reuses the collected trajectories to propose a harness revision and evaluates the incumbent and candidate with the updated model held fixed. The candidate guides subsequent training only if it improves validation performance. With Qwen3.5-9B, VACE achieves 45.26% test accuracy on OfficeQA and a mean partial-credit score of 75.19% on AutomationBench, exceeding weight-only RL by 6.43 and 9.09 percentage points and ungated alternation by 4.59 and 6.95 points, respectively. Across 44 harness proposals, 17 reduce validation performance at the updated checkpoint and are rejected before subsequent RL training, highlighting the importance of validation gating.

Open-source reasoning models provide unequal access to reasoning capability across languages. When a model can solve a problem but cannot deliver a complete solution in the user's language, language becomes an access barrier rather than merely a source of performance variation. We audit Qwen3 checkpoints on competition-mathematics tasks in eleven languages. Across the ten non-English languages, only 15.4-17.9% of problems receive a correct, terminating solution with visible reasoning in the requested language in any of 16 samples, compared with 92.9% in English. To identify the source of this disparity, we evaluate thirteen endpoints from one model family, spanning released checkpoints, multilingual supervised fine-tuning (SFT) at two scales, controlled SFT ablations, and three reinforcement-learning (RL) reward formulations. We jointly track correctness, language adherence, termination, and delivery efficiency. The dominant bottleneck shifts across post-training stages. Released models often reason in English. Multilingual SFT restores target-language reasoning, but accuracy declines across multilingual, English-only, and single-language SFT runs, showing that this cost is not specific to multilingual mixing; non-English reasoning traces additionally become prone to non-terminating loops. RL restores termination in both arms at no cost in accuracy, but only the arm whose reward includes a language term delivers: rewarding correctness alone returns the model to English. Together, these stages establish a constructive post-training path from English-pivoted capability to multilingual reasoning that is reliably delivered.

This work is concerned with the numerical computation of Gross-Pitaevskii ground states using the tensor train (TT) format. We regard the problem as the minimization of the Gross-Pitaevskii energy functional under a unit mass constraint, and propose a first-order Riemannian optimization scheme that preserves both the mass constraint and the low-rank representation throughout the optimization, by operating on the manifold of unit-norm functions of fixed TT-rank. On this manifold, we derive the energy-adaptive Riemannian gradient and show how to compute it efficiently in the TT format. Spatial discretization is performed using a spectral method with numerical integration, which allows the required computations to be carried out efficiently while preserving the low-rank format. The method is shown to substantially reduce computational time compared to full-rank computations, while maintaining accuracy for both single- and multicomponent Gross-Pitaevskii equations.

This paper extends the formalism of stochastic path-space thermodynamics by systematically expanding the space of thermodynamic variables with a spectrum of boundary and relative functionals of random processes. Generalizing the approaches introduced in preprints arXiv:2607.24078 and arXiv:2609.08477, we investigate the fluctuation statistics of a one-dimensional Ornstein-Uhlenbeck process with an asymmetric linear drift and a step penalty potential at the origin, which models the waiting phase of a molecular Brownian motor. Utilizing the Feynman-Kac formalism and the parabolic cylinder theory, a numerical scheme based on matching logarithmic derivatives via the secant method is constructed. A high-precision eigenvalues of the effective Hamiltonian is obtained, which define the cumulant generating function. We formulate a modified path-space fluctuation theorem of the Gallavotti-Cohen type for the conjugate drift current at a fixed integral occupation time of the system in the dissipative half-plane. The physical and thermodynamic significance of the new variables is elucidated. A combination of "residence time" and "integral current" functionals is applied to describe an ion channel sensitive to mechanical or electrical stimuli.

Preserving particle number and spin helps quantum circuits target molecular electronic states, but does not guarantee access to every state with the required quantum numbers. We determine which additional operations, combined with spin-independent orbital rotations connecting all spatial orbitals, generate every real state-space rotation within each complete subspace of fixed particle number $N$, total spin $S$, and spin projection $M_S$. We consider spin-free molecular calculations in real orbitals, without an additional spatial-symmetry restriction, and continuously tunable operations that preserve particle number, full spin symmetry, and real amplitudes. Below the maximal-spin limits set by the electron and hole numbers, repeated singlet-pair transfer between any two fixed spatial orbitals is sufficient. On nontrivial maximal-spin boundaries, pair transfer vanishes, and an additional generator built from one- and two-electron terms is sufficient exactly when its action in the target subspace is not a linear combination of orbital-rotation generators. The minimum number of spatial orbitals needed by one additional generator is two in the interior and three on nontrivial boundaries, even when terms involving more than two electrons are allowed. Both minima are attained using only one- and two-electron terms. The three-orbital optimum rotates two orbitals according to the occupation of a third, and its unitary factors exactly into eight commuting Pauli rotations. Molecular benchmarks show that this operation removes the observed boundary energy-error plateaus, while sparse interior constructions attain the prescribed energy accuracy with fewer compiled CNOT gates in selected fixed-orbital comparisons.

Multimodal sentiment analysis integrates textual, acoustic and visual cues, yet current language-model-based fusion methods typically leave prediction-layer branch allocation implicit. We introduce Branch-Calibrated Multimodal Language Fusion (BC-MLF), which explicitly models prediction-layer branch allocation through a Branch-Calibrated Task Head (BCHead), complemented by Fusion Token Contrastive Learning (FTCL) for sentiment-aware fusion-token regularization. FTCL organizes mean-pooled fusion-token representations according to continuous sentiment affinity, while BCHead combines fusion, text and audiovisual predictions through a lightweight sample-adaptive constrained mixture. Without modifying the fusion backbone, BC-MLF consistently improves the reproduced DeepMLF baseline and achieves the strongest results among the compared methods on CMU-MOSEI and CH-SIMS across classification and regression metrics. The controlled ablations show that sample-adaptive prediction-layer branch allocation consistently outperforms static branch aggregation. Code is available at https://github.com/sunyulin0421/BC-MLF.

Partially entangled thermal states (PETS) provide semiclassical families of black-hole microstates prepared through heavy shell insertions. We extend this shell-state framework and propose three-boundary partially entangled thermal states (PETS$_3$) by replacing the two-index insertion data with a trivalent junction tensor. The corresponding bulk three-boundary booklet geometry is constrained semiclassically by the Israel junction condition, allowing us to identify candidate symmetric and mixed-orientation branches. We verify the self-consistency of this construction by counting states in the symmetric all-black-hole sector. Using a heavy-operator probe, we further estimate the detection-to-universal ratio to be $Z_D/Z_U \simeq 3$, twice the two-boundary value of $3/2$. These results suggest that a fine-tuned probe localized on one boundary can test the proposed three-boundary shell state and potentially distinguish it from its two-boundary counterpart.

Vehicle-infrastructure cooperation can complement onboard sensing with broader and more informative observations of the traffic environment, providing valuable support for end-to-end autonomous driving. However, existing cooperative driving methods mainly exploit roadside information to enhance the representation of the current scene, while the future consequences of prospective driving actions are rarely modeled explicitly. This limits the ability of the planner to anticipate how its decisions may interact with the evolving traffic environment. To address this issue, we propose V2X-WAM, a cooperative world action model that tightly couples cooperative scene understanding, action generation, and future-world reasoning. V2X-WAM constructs a reliability-aware spatiotemporal representation from vehicle- and infrastructure-side observations, while compressing infrastructure information into a compact quantized message for efficient communication. Based on the resulting cooperative representation, a multimodal planner generates prospective trajectories, which explicitly condition future occupancy and dynamic-flow prediction. The predicted world consequences are then fed back to refine the planned trajectory, forming a closed interaction between action and future-world evolution. Experiments on a large-scale real-world cooperative driving dataset demonstrate that V2X-WAM consistently improves planning accuracy and safety over representative end-to-end cooperative driving methods, while achieving stronger future-world prediction and substantially lower communication overhead. Ablation studies further validate the effectiveness of the proposed design.

The rapid growth of submissions and reviewing workload has accelerated the use of large language models (LLMs) in peer review. Prior studies suggest that LLM-based reviewers can penalize content perturbations, such as overclaiming, indicating a certain degree of reliability. Yet these conclusions are largely based on a narrow set of perturbation strategies instantiated with static templates, providing limited evidence of actual reliability. In this paper, we construct a three-level evaluation framework covering perturbations to surface presentation, argumentative logic, and value judgment. Experiments on representative LLM-based reviewers reveal two limitations of static evaluation: stratified vulnerability, where perturbation effects depend on whether the paper's original review score is high or low, and perturbation undercoverage, where a single template misses vulnerabilities exposed by diverse realizations. To address these limitations, we propose SCOPE-Fuzzer, a strategy-aware fuzzer that combines feedback-driven strategy selection with adaptive mutation of paper content. By iteratively probing reviewers with dynamic perturbations, SCOPE-Fuzzer consistently uncovers vulnerabilities overlooked by static evaluation and other baselines.