arXiv:2607.15113v1 Announce Type: new
Abstract: In the online graph exploration problem, a single agent needs to visit every vertex of an initially unknown graph, which is learned over time in an online fashion, and return to its starting position. We prove that the competitive ratio of this problem is at least 4, improving on the previously best known lower bound of 10/3. A key ingredient of our proof is showing that several restrictions can be imposed on the agent's behavior without affecting the competitive ratio. As a byproduct, we also obtain that certain graph properties, such as the triangle inequality or being subcubic, can be assumed without affecting the competitive ratio.
Science Journals
arXiv:2607.14846v1 Announce Type: new
Abstract: Current voice AI benchmarks typically evaluate isolated capabilities such as speech intelligibility, word error rate, or text-based dialogue quality, but they rarely test whether systems harness the acoustic information that distinguishes spoken language from its textual representation. To this end, we introduce the Real World Voice EQ Bench, a multidimensional benchmark for evaluating voice AI across text-to-speech (TTS), speech-to-speech (STS), speech understanding (SU), and automatic speech recognition (ASR). Our evaluations indicate that performance is highly dimension-specific. For TTS, naturalness, expressiveness, identity stability, and reliability are largely independent evaluation dimensions. For STS, access to audio does not guarantee use of vocal affect, and some agents remain largely transcript-driven. For SU, models perform unevenly across paralinguistic tasks. For ASR, real world accent, emotion, noise, and conversational conditions expose failures that are not captured by established clean-speech benchmarks. Together, these results show that voice AI should be evaluated as a profile of acoustic, expressive, interactional, and robustness capabilities rather than by a single aggregate score.
arXiv:2607.14877v1 Announce Type: new
Abstract: Reachability is the most fundamental logical objective, yet it is notoriously difficult to learn in reinforcement learning settings: even for Markov decision processes, PAC learning of reachability is impossible without additional assumptions. This difficulty also holds in turn-based stochastic games (TBSGs), where two adversarial players interact on a finite state space. In this work, we consider turn-based stochastic games with reachability objectives. For such settings, adversarial learning, in which players are adversarial even in the learning phase, is impossible. Therefore, the goal is to consider learning, in which both players learn the unknown model together. In this spirit, previous literature on PAC learning in TBSGs considers (a)~public information shared by both players; and (b)~centralized learning, which means that players share the same learning algorithm. In this work, our contribution is two-fold. First, we relax these strong assumptions and ensure learning: (i)~with private information not shared with the other player; and (ii)~decentralized learning where the players do not share the same learning algorithm. To the best of our knowledge, this work is the first positive result for decentralized and private information learning of TBSGs with reachability objectives. Second, we introduce a game-theoretic generalization of the Expected Conditional Distance (ECD) parameter, which measures the expected length of reaching the target set. We establish a polynomial-sample complexity bound with respect to the number of states, actions, ECD parameter, and inverses of error tolerance and failure probability.
arXiv:2605.17644v2 Announce Type: replace
Abstract: The particle representation model (PRM) and interacting particle representation model (IPRM) describe homogeneous turbulence through orientation-conditioned structural states. In their original form, the conditional state is organized by the unit spectral direction, while the radial spectral coordinate is integrated out. We introduce a scale-conditioned Ray-Column extension in which the spectral vector is decomposed into orientation and radial wavenumber, and the conditional structure state is projected onto finite radial bands.
The formulation starts from the continuum spectral tensor and is then reduced to the ray-packet ensemble sums used in the implementation. The bands are projections of an orientation-wavenumber tensor density and retain scale-conditioned structural populations for closure evaluation. The rapid dynamics remain ray-packet resolved, while the nonlinear slow and terminal closure coefficients are evaluated from band-aggregate structure tensors formed by integrating over orientation and wavenumber within each band. The present reference closure omits conservative cascade modeling among bands.
A reference closure is built from PRM rapid kinematics, band-local effective-gradient response, slow rotational randomization, and an active large-scale enstrophy (LSE) terminal-drain map. In the active-LSE closure, the misalignment-sensing factor Psi_fd regularizes the LSE structure-to-dissipation map; the Ray-Column formulation evaluates this map on band-aggregate structural populations. The model is assessed in irrotational strain, homogeneous shear, elliptic-streamline, and rotating-shear configurations. The rotating-shear comparison with filtered LES data illustrates the payoff of retaining band information: filtered or low-pass observables can be formed before scale information is lost in the one-point reconstruction.
arXiv:2607.14998v1 Announce Type: new
Abstract: This paper suggests the adoption of a novel inversion in AI ethics: instead of asking how humans should treat artificial superintelligence (ASI), it examines how future sentient ASI may morally consider and evaluate humanity. We are not only designing intelligent systems but also shaping the initial conditions under which those systems form judgments about us. The paper proposes a preliminary set of post-human moral principles that may govern sentient ASI actions. The implication is that technical design choices (some are suggested), humanity's moral behaviour, and the essence of what it means to be human, may influence humanity's long-term standing in a post-ASI world.
arXiv:2607.14967v1 Announce Type: new
Abstract: Most existing approaches to AI-Generated Text Detection (AIGTD) treat documents as static objects and base their decisions on aggregate statistics or globally compressed embeddings. However, this perspective overlooks the inherently dynamic nature of autoregressive generation, where content evolves progressively through the latent space. In this paper, we reformulate AIGTD as the problem of distinguishing between latent generation trajectories. Instead of relying on static representations, we model how textual representations evolve across the sequence. To this end, we propose Geometric Trajectory and Contrastive Learning (GTCL), a framework that segments the document into ordered local units, encodes each unit in an embedding space, and constructs a structured and sequence-level representation. GTCL then applies contrastive learning to these trajectories to learn geometric regularities associated with the autoregressive generation. Evaluations performed on three different benchmarks and several approaches show that GTCL outperforms detection baselines consistently, which implies that explicitly modeling sequential dynamics provides robust discriminative signals across models and domains. These results suggest that modeling trajectory differences could improve detection and open up a dynamic direction that has been underexplored in previous AIGTD literature.
arXiv:2607.14989v1 Announce Type: new
Abstract: Large language models are increasingly evolving from text generators into general agents capable of understanding user requests, invoking external tools, and completing complex tasks through interaction. However, existing agent benchmarks often focus on limited scenarios, tool ecosystems, or interaction formats, making it difficult to systematically characterize model capabilities across heterogeneous application settings. We introduce OmniaBench, a benchmark for evaluating general agents across diverse scenarios with explicit state spaces. We derive application-oriented scenario knowledge from app stores, product documents, industry resources, Web retrieval, and human refinement, forming a hierarchical taxonomy that spans ToC, ToB and ToE with 90 level-1 and 354 level-2 domains. Based on this taxonomy, we construct executable environments and synthesize single-turn and multi-turn tasks through four complementary routes: DAG, DAG-S, Solver, and Program. OmniaBench further introduces a ten-dimensional capability taxonomy and eight compositional atomic difficulty factors to support fine-grained evaluation and analysis. The resulting dataset contains 1,431 tasks, together with a challenging subset of 644 tasks designed to reduce evaluation cost and mitigate potential contamination of the full set after public release. The bench presents substantial challenges to current frontier models, with even Claude-Sonnet-5 and GPT-5.6-Sol achieving Overall Pass@1 scores of only 58.54 and 57.14, respectively. Further analyses reveal clear differences across domains and capabilities, as well as persistent limitations in planning, constraint maintenance, and adaptive correction. OmniaBench provides a broad and diagnostic benchmark for characterizing the capability boundaries of general agents.
arXiv:2607.14895v1 Announce Type: new
Abstract: Reasoning language models (RLMs) have demonstrated impressive performance in domains such as mathematics and coding. These domains permit reliable verification of model outputs, which is important for enabling the reinforcement learning that drives RLM performance gains. However, training RLMs on domains that lack reliable verifiers remains challenging. Meanwhile, for both verifiable and unverifiable domains, large amounts of unused supervised fine-tuning data with human-written solutions exist. In this work, we show that these data can be used efficiently to further improve RLM performance. For this, we first use classic instruction tuning, supervised fine-tuning without reasoning traces, on the RLM. Next, we merge our instruction-tuned model with the original reasoning model, recovering its reasoning behavior on the target domain. Our extensive evaluation demonstrates that our technique improves RLM performance in both verifiable and hard-to-verify domains, including coding and text summarization, while preserving RLM capabilities across other domains. Importantly, our method is highly cost-effective, enabling such improvements for less than USD $3.
arXiv:2607.15003v1 Announce Type: new
Abstract: The deployment of autonomous cyber-physical systems in safety-critical environments requires closed-loop control strategies (i.e., policies) that are not only performant but also provably safe and robust. While learning-based methodologies such as Reinforcement Learning offer flexible and scalable approaches to automatically synthesize such controllers, they typically lack the formal guarantees necessary for safe deployment. To bridge this gap, we propose a novel simulation-based methodology to automatically synthesize policies with formal guarantees regarding performance, safety, and robustness specifications. Specifically, given a set of properties to verify, a confidence parameter $\delta$ and an allowable failure probability $\varepsilon$, our method guarantees that the synthesized policy comes with a certificate: with confidence at least $1 - \delta$, the probability of encountering a scenario where the given properties are violated is at most $\varepsilon$. We demonstrate the feasibility of our approach by developing SMC-ES, an algorithm that integrates Evolutionary Strategies with Statistical Model Checking-based verification. We evaluate SMC-ES on a suite of continuous control tasks using Gymnasium and Safety Gymnasium testbeds. Results show that, at the price of a sustainable increase in computational cost, our algorithm provides formal guarantees regarding performance, safety, and robustness specifications, while performing competitively against leading model-free Deep Reinforcement Learning (DRL) and Safe-DRL baselines.
arXiv:2607.15004v1 Announce Type: new
Abstract: Dynamic target tracking is essential for Unmanned Aerial Vehicles (UAVs) operating in complex urban environments, where both the target and the camera viewpoint change continuously. Existing Vision-Language-Action (VLA) policies can track visible targets effectively, but their performance often degrades when buildings, vegetation, or roadside objects block the line of sight. During sustained occlusion, a policy may lose the target state, execute actions toward an incorrect region, and amplify this error through subsequent observations until re-acquisition becomes impossible. To this end, we present CosFly-VLA, a spatially aware VLA model that jointly grounds the target, estimates its visibility, and generates continuous flight actions through a structured prediction interface. To train this policy, we use a large-scale recipe over diverse data sources. Spatially Grounded Continued Pretraining (CPT) on a 500k mixed pool injects UAV-view depth, distance, and 3-D spatial reasoning. A three-stage Curriculum-based Supervised Fine-Tuning (SFT) process then specializes the tracker through multi-head warm-up followed by two-stage curriculum learning over natural and hard / long-occlusion data. Chain-of-Thought (CoT) training subsequently teaches recovery-oriented reasoning traces before structured answers. Finally, a closed-loop Reinforcement Learning (RL) stage optimizes tracking behavior with a multi-component reward covering stand-off tracking, grounding quality, collision avoidance, and task success. Relative to OpenVLA, CosFly-VLA-0.8B reduces open-loop Average Displacement Error (ADE) by 34.1% on seen-test and 35.3% on unseen-test. Closed-loop optimization improves Success Rate (SR) by 29.8% and 2.5%, respectively. These results demonstrate progress from visible-frame imitation toward spatially grounded action-closed-loop control, evaluated under a shared oracle state history.
arXiv:2607.15016v1 Announce Type: new
Abstract: Ensuring robot safety in unknown, dynamic environments is a fundamental requirement. It involves inferring the states of an unknown and time-varying number of moving objects from noisy, incomplete measurements. We address safe control under the induced multi-object state uncertainty with a risk-aware belief control barrier function (BCBF) framework. The uncertainty is captured by a random finite set (RFS) belief, estimated by a sequential Monte Carlo probability hypothesis density (SMC-PHD) filter that represents it with a set of particles. Building directly on these particles, we construct a nonsmooth BCBF, establish forward invariance of the safe set under continuous prediction, and derive an explicit condition under which discrete updates preserve safety. Simulation and real-world underwater experiments demonstrate the effectiveness and efficiency of the proposed approach.
arXiv:2607.14937v1 Announce Type: new
Abstract: Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts. Such an understanding could help to strip down overladen FM architectures to their bare essence and expose the minimal requirements for in-context learning in the DS domain. Toward this goal, here we iteratively reduce a recent powerful SOTA model for DS reconstruction, DynaMix (Hemmer & Durstewitz, 2025), to a minimal interpretable two-parameter form, which we call DynaBase. DynaBase produces forecasts through a linear blend of the current latent state and the nearest in-context neighbor and its temporal successor. Surprisingly, despite its extreme simplicity, DynaBase produces highly competitive zero-shot DS reconstructions across chaotic and cyclic systems, with a negligible parameter load, many orders of magnitude below that of other FMs. Even more, this extreme simplicity permits direct model optimization on DS reconstruction measures, as well as closed-form one-step analytical solutions on prediction MSE. Theoretical and empirical analysis of DynaBase further leads to a 1-parameter family of maps, with the context-parroting algorithm of (Zhang & Gilpin, 2026) recovered at one end, and chaotic (divergent but bounded) behavior at the other. We further show how different training strategies lead to models either optimal for short-term prediction or for DS reconstruction. Thus, DynaBase not only exposes the minimal mechanisms required for producing zero-shot DS reconstruction, but also reconciles within an accessible mathematical frame divergent observations in the literature.
arXiv:2607.15035v1 Announce Type: new
Abstract: Principal component analysis (PCA) is optimal for the linear reconstruction of Gaussian data, a foundational property underlying its central role in algorithms and signal processing. Its nonlinear analogue, however, is notoriously subtle: in 2011, Mallat and Zeitouni conjectured that the Karhunen--Lo\`eve (KL) basis remains optimal even when the retained coordinates are chosen adaptively per sample, a property that would theoretically justify the ubiquitous pipeline of PCA followed by sparse thresholding. In this paper, we establish a $1+O(1/\sqrt{d})$-approximate version of the retained-energy form of the Mallat--Zeitouni conjecture, showing that the KL basis is within this factor of the optimal basis. This dimension-free comparison depends only on the number of retained coordinates and shows that the possible advantage of optimizing over all orthonormal bases vanishes as $d$ grows. It complements the universal-constant reconstruction-error comparison of Litvak and Tikhomirov (Ann. Appl. Probab., 2018), while providing a comparison naturally suited for algorithmic analysis. Our proof rests on a clean, conceptual reduction: we relax arbitrary rotations to a deterministic threshold bound via Schur--Horn majorization, and identify the remaining loss with the correlation gap of the rank-$d$ uniform matroid over Gaussian level sets.
arXiv:2607.15036v1 Announce Type: new
Abstract: Navigating dynamic and crowded environments presents significant challenges for quadruped robots due to severe sensor occlusion and unpredictable human motion. Existing approaches face a trade-off: model-based methods, such as Velocity Obstacles (VO), theoretically guarantee safety but rely on accurate obstacle motion estimates that often fail in dense crowds, while end-to-end learning methods offer robustness but lack motion prediction capability of obstacles, leading to collisions or conservative behaviors. To solve this, we propose VOP-Nav, a novel navigation system that combines the geometric safety of VO with the agile adaptability of end-to-end learning. Using only local onboard observations, our system avoids explicit obstacle detection and tracking pipelines. The VOP-Net processes multi-frame LiDAR data to implicitly encode dynamic constraints and predict a safe velocity region derived from Velocity Obstacle theory. Importantly, the VO predictions serve a dual role: they are used as input to the navigation policy during inference and as a reward signal during training to encourage safe motion. Evaluations in Isaac Gym demonstrate that VOP-Nav achieves higher success rates than all baselines while balancing locomotion speed and collision avoidance. Real-world deployment on a Unitree Go2 quadruped robot further validates the system's robustness and efficiency in complex indoor and outdoor dynamic environments.
arXiv:2607.15038v1 Announce Type: new
Abstract: We present Wan-Streamer v0.3, which reframes our native-streaming interaction model under a single organizing view: a video is a world plus an event stream. The world is the persistent context in which a video unfolds, including the environment, scene, subjects, ambient acoustic conditions, voice characteristics, and other relatively stable conditions. The event stream is everything that changes over time within that world, including scene or environmental changes, subject behavior, speech, and other sounds. This yields a general-purpose pretraining task over large amounts of real video: given a world and incoming input, predict how the world moves, changes, and responds in real time. The resulting competence can be specialized to a broad family of real-time downstream tasks. We instantiate it on real-time full-duplex audio-visual interaction, where the event stream is the agent's speech together with free-form behavior. Functionally, the model's multimodal understanding process is vision-language-action-like: it maps multimodal user input to language-form speech and behavior actions. Wan-Streamer v0.3 preserves the v0.2 operating point: 640x368 video at 25 FPS, a 160 ms streaming unit, approximately 200 ms model-side response latency, and approximately 550 ms total interaction latency under a 350 ms bidirectional network budget.
arXiv:2607.15047v1 Announce Type: new
Abstract: Mild Cognitive Impairment is a critical early stage of cognitive decline that frequently precedes Alzheimer's disease, yet its automated detection from neuropsychological drawing tests remains fundamentally constrained by data scarcity, class imbalance, and diagnostic ambiguity near clinical boundaries. Existing methodologies attempt to bypass these constraints using computationally expensive, fully fine-tuned hybrid architectures that relegate spatial explainability to a post-hoc approximation rather than an intrinsic model property. We propose a parameter-efficient framework utilizing frozen DINOv2-Small model adapted via three modality-specific learnable prompt tokens while Operating with 1.19 million trainable parameters, each token serves as a query in a shared cross-attention layer over the source image patch tokens. Crucially, spatial explainability is achieved directly through these attention maps; as a structural consequence of the architecture. Then task-conditioned embeddings fused via an attention module to quantify modality-level importance per subject. To handle boundary ambiguity, a MoCA-adapted focal loss introduced that integrates continuous cognitive scores into the training target, loss modulation, and adaptive sample weighting, strictly generalizing standard soft-label approaches. Under stratified five-fold cross-validation, the proposed architecture yields an MCI-class F1 of 0.641 and an AUC of 0.795, outperforming the computationally heavier ResViT baseline by 0.110 in MCI-class F1.
arXiv:2607.15101v1 Announce Type: new
Abstract: The kinetics of protein-ligand binding systems are increasingly recognized as a key determinant of drug efficacy, yet remain far harder to compute than binding affinities. Existing kinetics methods either bias the dynamics along a collective variable (CV), demanding careful system-specific CV design, or use path sampling, which keeps the dynamics unbiased but can struggle to converge rates out of deep free-energy wells and often relies on hand-engineered descriptors. By combining the `best of both worlds', we propose a method to compute accurate kinetics for general ligand-unbinding problems at modest computational expense and minimal fine tuning, building on the AI for Molecular Mechanism Discovery (AIMMD) path sampling framework. To avoid the need for feature engineering, we opt for modelling the committor with a single descriptor-free, equivariant graph neural network shared across all systems. We also partially flatten deep bound-state wells with a static, basin-restricted bias potential. This improves convergence by lifting the path sampling state boundary out of regions, where the committor is hard to learn, while leaving the reactive region strictly unbiased. Across host-guest and protein-ligand systems spanning roughly 17 orders of magnitude in residence time, the method robustly recovers rates in line with reference and experimental values. Simultaneously, and without further sampling, it also reconstructs the underlying unbinding mechanisms. We additionally find that accurate rates do not require globally accurate committor models, allowing for efficient kinetics estimation even in a low-data training regime. Requiring little system-specific setup, our approach offers an efficient and broadly generalizable route to binding kinetics, and its shared committor architecture lays crucial groundwork for probing structure-kinetics relationships across ligand series in drug discovery.
arXiv:2607.15138v1 Announce Type: new
Abstract: A method is presented for the translation of acoustic field data from a source to a target region. Field data are represented as spherical harmonic expansions on spheres surrounding the source and target regions respectively and expansions are translated using a ``point and shoot'' method using the Kirchhoff-Helmholtz integral to carry out an axial translation from one sphere to the other. The principal motivation for the method is its use in a time-domain Fast Multipole Method, and test cases reflective of this application are presented. The method converges to six digits for appropriate values of parameters and computational effort scales approximately as $N^{2}$ where $N$ is the order of spherical harmonic expansion for the field data.
arXiv:2607.15054v1 Announce Type: new
Abstract: Multimodal Large Language Models (MLLMs) have demonstrated substantial promise in spatial understanding. Existing works typically incorporate prior knowledge extracted from a pre-trained foundation model to further enhance the spatial awareness of MLLMs. In this paper, we first reveal that when integrating diverse foundation models into MLLMs, different models provide complementary spatial priors that benefit different tasks. Motivated by this, we propose $\textbf{ViPS}$, a novel multi-model prior framework designed to fully unleash the potential of incorporating multiple $\textbf{Vi}$sual $\textbf{P}$riors from diverse models into MLLMs for $\textbf{S}$patial understanding. Specifically, ViPS introduces an Efficient Prior Proxy to generate multiple foundational priors with minimal inference overhead, and a Dynamic Prior Fusion mechanism to achieve harmonious and context-aware prior fusion and injection from the prior proxies. Extensive experiments demonstrate that ViPS successfully harmonizes diverse visual priors, establishing new state-of-the-art performance across multiple complex spatial reasoning and 3D spatial understanding benchmarks. Project page: https://visual-ai.github.io/vips
arXiv:2607.14997v1 Announce Type: new
Abstract: Language-conditioned quadrotor flight requires a policy to ground semantic goals, anticipate the visual consequences of ego-motion, and output control references that remain smooth and dynamically executable under rapidly changing first-person views. Existing aerial vision-language navigation and vision-language-action methods commonly use discrete actions, high-level waypoints, or instantaneous velocity commands, which provide limited supervision about how flight actions change future observations. We present AeroAct, an action-centered world-action model (WAM) for quadrotor navigation. To the best of our knowledge, AeroAct is the first WAM instantiated and demonstrated for real-world aerial flight. The model adapts a pretrained video diffusion Transformer to predict local trajectory-action chunks from egocentric visual history, proprioception, and language. Future first-person frames are used during training as dense consequence supervision, while deployment directly decodes actions without generating future video. To obtain aligned visual, state, language, and dynamically feasible action data, we build a DiffAero-based pipeline with complementary Isaac Lab and 3D Gaussian splatting renderers. We further introduce a low-cost handheld collection device that couples camera observations with motion estimates to recreate flight-like egocentric trajectories, and a self-guidance procedure that improves temporal consistency across overlapping trajectory chunks. Closed-loop simulation and real-world experiments show that temporal visual context improves target tracking and object-search performance, and that WAM-based policies can be executed on a physical quadrotor.
arXiv:2607.15024v1 Announce Type: new
Abstract: The least-squares splitting algorithm for the Monge-Amp\`ere equation has been used successfully in computations for several years, but a convergence theory for fully discrete splitting schemes of this type has remained unavailable. In this work, we introduce and analyze a finite element framework for smooth solutions of the Dirichlet Monge-Amp\`ere equation in two dimensions. The proposed schemes combine a discrete Hessian reconstruction with a local projection onto the determinant constraint. Under a discrete Miranda-Talenti estimate and standard approximation properties of the Hessian reconstruction, we prove local convergence of the iterative scheme and optimal-order convergence of its limit to the exact solution in an $H^2$-type norm. We verify the estimates for conforming $C^1$ schemes, including the Argyris element, and for $C^0$-interior penalty and DG schemes of degree at least three; quadratic $C^0$-interior penalty and DG schemes are also covered when $|u|_{H^3(\Omega)}$ is sufficiently small. To the best of our knowledge, these discretizations have not previously been proposed or analyzed for least-squares splitting methods. Numerical experiments confirm the theoretical convergence rates.
arXiv:2607.15041v1 Announce Type: new
Abstract: Weakly-supervised RGB-D Salient Object Detection (SOD) is explored to reduce the heavy burden of pixel-level annotations. But scribble annotations lack the structure and details of objects, resulting in inaccurate saliency maps. In this paper, we propose a novel scribble-supervised RGB-D SOD method, consisting of a Segment Anything Model (SAM)-driven pseudo annotation generation method (\emph{SAM-PAG}) and a state space interaction-based conditional diffusion model (\emph{$S^2$Diff}). Specifically, SAM-PAG is tailored to address the issue of sparse supervision information. In SAM-PAG, we adopt the advanced SAM to expand sparse scribbles to dense pixel-level pseudo annotations through the dual-branch structure and the consistency of segmentation masks. In $S^2$Diff, we adopt the diffusion model to iteratively refine the noisy saliency maps with the guidance of conditional information, generating accurate saliency maps. Naturally, the core of our $S^2$Diff lies in the acquisition of conditional features and the denoising of saliency maps. For the former, we employ a cross-modal conditional generation module to interweave cross-modal features through frequency integration and implicit-explicit state space interaction, effectively achieving global conditional features. For the latter, we employ a context injection module to mitigate noise interference and to enhance object information with the conditional context. With the close cooperation of SAM-PAG and $S^2$Diff, our method outperforms relevant scribble-supervised methods and achieves competitive performance compared to fully-supervised methods on seven datasets. The code and results of our method are available at https://github.com/Switch457/WeakS2Diff_SOD.
arXiv:2607.15087v1 Announce Type: new
Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving forward and inverse partial differential equations (PDEs), but conventional real-valued PINNs (RV-PINNs) often suffer from spectral bias, limited expressivity, and reduced accuracy for high-frequency, oscillatory, and phase-dependent dynamics. In this work, we propose a generalized split complex-valued physics-informed neural network (SCV-PINN), in which network parameters and latent representations are defined in the complex domain. The framework employs split complex-valued activation functions by independently applying standard real-valued activations to the real and imaginary components, providing numerical stability, computational efficiency, and improved approximation capability. This formulation enables simultaneous learning of amplitude and phase information, enhancing the representation of nonlinear and oscillatory systems. Extensive ablation studies evaluate different split activation functions and collocation sampling strategies. The proposed framework is validated on forward and inverse PDE benchmarks including Burgers, Allen-Cahn, Korteweg-de Vries, nonlinear Schrodinger, Helmholtz, Poisson, Kovasznay flow (Re = 20), lid-driven cavity flow (Re = 100), the Lorenz system, inverse Burgers, inverse Navier-Stokes (Re = 100), and a three-dimensional Navier-Stokes Beltrami flow. For the Beltrami benchmark, SCV-PINN achieves a relative L2 error of 4.07 x 10^-5. Numerical results consistently demonstrate lower relative L2 errors and more accurate parameter identification than RV-PINNs and several existing PINN variants. The proposed SCV-PINN provides a robust and generalized extension of standard PINNs for complex-valued, multiscale, oscillatory, high-dimensional, and real-valued nonlinear PDEs.
arXiv:2607.15088v1 Announce Type: new
Abstract: Large Faraday rotations can be generated by circular birefringence of atomic samples in an axial magnetic field in the vicinity of atomic resonance lines. The Faraday angle is a function of the magnetic field strength, the optical density of the atomic sample which may be varied by changing the temperature of the atomic gas, and of course the optical detuning from the transition frequencies. More generally, magneto-optical effects in atomic samples include circular dichroism in addition to birefringence, resulting in a modification of the ellipticity as well as the polarisation alignment. Usually such effects are investigated for homogeneous linear polarisations, but the mechanisms apply also to polarisation structures such as vector vortices. We investigate the effect of optical activity of a rubidium vapour in the Hyperfine Paschen-Back regime, for the example of an azimuthally polarised input light beam. We show that for low atomic densities, circular birefringence dominates over dichroism, and azimuthal polarisation is rotated towards radial polarisation. The rotation angle increases with increasing optical densities. At high vapour temperatures, dichroism becomes more and more relevant, leading to intricate variations of both alignment and ellipticity.
arXiv:2607.15097v1 Announce Type: new
Abstract: All-in-one image restoration aims to recover clean images degraded by multiple corruption types using a single unified model. Existing methods typically rely on image-level prompts or shared guidance to handle diverse degradations. However, such a paradigm becomes inadequate when degradations are spatially heterogeneous or even coexist in mixed forms within a single image. Yet spatially adaptive guidance alone is not sufficient, since accurate restoration also requires each spatial query to reliably aggregate complementary information from local neighborhoods and global contexts. To this end, we propose QuReC, a unified framework for all-in-one image restoration. QuReC consists of a Degradation-Guided Query Reconstruction Module (DQRM) and a Local-Global Response Calibration Module (LGRCM). Specifically, DQRM matches each spatial query against a degradation prototype space to reconstruct a query-specific degradation-aware representation, thereby providing fine-grained spatially adaptive restoration guidance. To further stabilize this query-wise matching process, we introduce a weakly supervised prototype matching learning strategy to improve optimization stability and degradation semantic consistency. Meanwhile, LGRCM performs local-global dual-branch aggregation and calibrates the aggregated responses with learnable priors, improving the reliability of feature aggregation and the coordination between local detail modeling and global context modeling. Extensive experiments demonstrate that QuReC achieves superior performance on multiple all-in-one image restoration benchmarks. The code is released at https://github.com/zhoushen1/QuReC.