Papers

Action chunking improves temporal coherence in visuomotor imitation learning by jointly predicting sequences of future actions. However, many existing policies regenerate entire action chunks even when errors are localized, potentially replacing otherwise valid predictions. We introduce Contextual Masked Action Policy (CMAP), a visuomotor policy that refines continuous action chunks through history-conditioned local regeneration. Specifically, CMAP introduces a history-conditioned action tape that combines executed commands with masked future positions to produce coarse action predictions and per-step uncertainty scores. An uncertainty-guided span regeneration mechanism then selects a high-uncertainty contiguous span and reconstructs it using the executed history and retained future predictions as context. By jointly reconstructing neighboring actions, CMAP models local temporal dependencies while preserving all predictions outside the selected span. Extensive experiments on nine simulated and four real-world manipulation tasks demonstrate that CMAP achieves superior overall performance over several competitive baselines. Ablation studies validate the complementary contributions of its key components, while held-out trajectory analysis shows that local regeneration reduces prediction errors within selected spans.

Data-driven weather forecasting models are commonly trained on ERA5, yet operational deployment must use timely initial states from physics-based numerical weather prediction (NWP) systems whose distributions differ substantially from ERA5. Direct initialization with these states can degrade autoregressive forecasts, motivating input adaptation that keeps the pretrained forecasting model unchanged. Here, we introduce WeatherBridge, a unified, source-conditioned adapter that maps heterogeneous operational NWP initial states to ERA5 reference states without updating the pretrained forecasting model. WeatherBridge predicts the structured residual corrections with a Swin-UNet and injects source embeddings across multiple spatial scales, allowing the model to capture shared atmospheric structure and source-specific discrepancies. Its training objective combines latitude-weighted ERA5 reconstruction with One-step Rollout Alignment (ORA), which backpropagates one-step forecast error through a frozen FuXi model to optimize the adapted states for both initial state fidelity and downstream forecast compatibility. We evaluate WeatherBridge using daily GFS, HRES, and CMA initializations from 1 January to 22 November 2025 across six variables and lead times up to 240 hours. Relative to raw source initialization of FuXi, WeatherBridge reduces the mean RMSE of FuXi over the 6- 240-hour rollout for 17 of 18 source-variable combinations, with a median reduction of 10.2% and a maximum reduction of 46.3%. The adapter trained with frozen FuXi also improves FengWu forecasts on GFS inputs without retraining either the adapter or FengWu. These results demonstrate that forecast-aware input adaptation can improve forecasts from heterogeneous operational NWP inputs and transfer across pretrained ERA5-based forecasting models.

Machine learning models for protein-ligand interactions commonly rely on atomic coordinates, which are constructed by fitting molecular models to experimental electron-density maps. However, most models represent each complex as a single fitted structure, which can omit information about conformational heterogeneity, positional uncertainty, and local density support for individual atoms at binding interfaces. To fill this gap, we present CoDE, a Coordinate and Density Encoder, pre-trained on experimental density maps. We represent each binding site on a shared three-dimensional voxel grid combining atomic occupancy, experimental electron density, and its gradient magnitude. Using approximately 100K curated complexes, we pre-train a channel-wise vision transformer to jointly reconstruct masked atomic and density channels, learning a representation that integrates structural and experimental information. We evaluate the frozen encoder on two downstream tasks: (i) binding-affinity regression under leakage-controlled splits and (ii) pocket-conditioned ligand generation. Across these settings, CoDE improves over an identically pre-trained coordinate-only encoder and remains competitive with task-specific baselines, showing that density complements fitted atomic coordinates for protein-ligand interaction modeling and that the density-blended representation is useful for structure-based ligand generation.

Time-series forecasting plays a vital role in a wide range of real-world applications. Recent approaches have achieved strong performance by modeling temporal correlations and cross-channel dependencies, yet most forecasting benchmarks still represent time series primarily as numerical histories. In practice, time series are observations of complex real-world processes, and their trajectories may reflect events, interventions, disruptions, and changes in measurement or reporting that cannot always be inferred from past values alone. A central barrier to studying context-aware forecasting is therefore the lack of large-scale datasets that align real-world events with the individual series they affect. We present World2TS, a scalable construction framework and large-scale dataset for time-series forecasting with real-world event context. We first develop world2ts-core, a reusable tool that combines agent-led semantic reasoning and Web search, command-line execution and validation, and human review within a feedback-driven discovery workflow. Given heterogeneous time series with semantic descriptions, the workflow discovers candidate events, consolidates retrieved evidence into verified events, and links them to relevant series under explicit temporal and semantic scopes. Using this framework, we construct world2ts-data, which contains 31 datasets across six domains, comprising 4,179 series, 97.1 million observations, 1,159 events, and 56,846 event-series links. We further conduct extensive data analyses and controlled comparative experiments to characterize the dataset and demonstrate the utility of the collected context for improving forecasting accuracy. World2TS provides a reusable data foundation for developing and evaluating context-aware forecasting models and agents. The project homepage is available at https://world2ts.github.io/.

Advances in large language models (LLMs) have brought the vision of a general-purpose personal assistant closer to reality. Such assistants could provide a unified natural-language interface to a broad ecosystem of applications. However, real-world applications do not readily support training at scale because access is often restricted and their state is difficult to reset. To address this challenge, we introduce Terrarium, a framework that synthesizes executable App Worlds from real-world application information, generates training task packages with evaluator-side rubrics from these worlds, and iteratively validates and refines both through agent rollouts. For App World synthesis, Terrarium organizes public Web information and in-application observations into structured app specifications that guide the construction of self-contained runtimes with callable operations and mutable, resettable state. For task synthesis, Terrarium constructs tasks grounded in App World state together with evaluator-side outcome rubrics that assess success without prescribing reference trajectories. We construct a training suite of 275 App Worlds and 13,344 tasks for outcome-based reinforcement learning across three Qwen3 model scales (4B, 8B, and 14B parameters). Across these scales, models trained with Terrarium outperform the corresponding Qwen3 models by an average of 18.34 percentage points on the $\tau^2$-bench and 10.94 percentage points on the AppWorld bench. These results suggest that app-grounded world and task synthesis offers a scalable path toward general-purpose assistants capable of operating across broad application ecosystems.

We give an explicit countably infinite orthomodular lattice generated by three specified elements and a direct argument that it admits no injective homomorphism into any $\sigma$-complete orthomodular lattice. In particular, it does not embed into any set-sized complete orthomodular lattice. The source is a generated subalgebra of a cofinite reduced product of finite-dimensional real subspace lattices. A nonzero finite term $a$ is orthogonal to the orbit of a terminal line under every finite word in three Sasaki projections, while another finite term $X$ satisfies $\pi_a\pi_X(t)=a$. If the image of this countable orbit has a supremum in a target orthomodular lattice, Sasaki adjunction forces that supremum to commute with the generator images. This forces the image of $a$ to vanish. The proof imposes no atomicity, modularity, Hilbert representation, cardinality bound on the target, or preservation of source infinitary operations. All target lemmas are derived from the orthomodular axioms.

The increasing adoption of peer to peer energy trading has enabled prosumers to actively participate in decentralized energy markets. However, the growing dependence of P2P energy markets on communication infrastructures and distributed coordination mechanisms introduces an expanded cyberattack surface, enabling sophisticated adversaries to manipulate market interactions while remaining concealed from conventional detection mechanisms. This paper first designs an optimal stealthy attack that maximizes economic disruption of the MicroGrids, while preserving the apparent convergence characteristics of the ADMM based market-clearing process. To detect such attacks, a Mahalanobis Boosting detector is developed using market layer features to effectively capture inter feature dependencies and distinguish compromised updates from normal market operation. An adaptive rho based mitigation strategy is then introduced to limit the propagation of compromised information and restore robust market operation once an attack is flagged. The effectiveness of the proposed framework is demonstrated through comprehensive case studies, achieving an attack detection accuracy of 98.49% while the proposed mitigation strategy reduces the operating cost by approximately 18.43% compared to the unmitigated attack case. The proposed approach provides a practical pathway toward trustworthy and cyber-secure distributed P2P energy trading systems.

Bloch oscillations typically arise in periodic systems subjected to a constant force generated by a potential gradient. Here, we study domain-wall dynamics in coupled Ising layers under asymmetric longitudinal fields. The interlayer coupling is of Heisenberg type and acts as an effective transverse coupling in the emergent pseudospin representation. We show that the rung pseudospin structure gives rise to kinetic constraints, restricting the many-body dynamics to an emergent one-dimensional quasiparticle subspace within the original two-dimensional system. Furthermore, the imbalance between the longitudinal fields of the two layers induces an effective linear potential for the emergent domain-wall excitations, leading to their confinement between two oppositely polarized ferromagnetic domains. Remarkably, the resulting Wannier–Stark ladder of domain-wall excitations gives rise to Bloch oscillations in the absence of a conventional tilted potential, revealing a distinct mechanism for coherent quantum dynamics. Numerical simulations of time-dependent observables confirm the analytical predictions.

This paper studies the problem of recovering motion from monocular video, even when the target skeleton topology differs from the subject observed in the video. Although previous methods have made efforts to resolve this problem, they remain vulnerable to joint-rotation errors that are coupled across the skeleton and can propagate along its kinematic hierarchy. To mitigate these errors, we present CAST, a topology-aware motion capture framework that combines learned local rotations with geometric correction guided by predicted global bone directions. Our observability analysis characterizes which rotational components can be constrained by outgoing bone directions. Guided by this analysis, GRACE uses reliability-gated alignment to correct composed orientations in parent-to-child order, leaving unconstrained components to the learned rotation predictor. The motion predictor and correction module are trained jointly with motion-derived supervision, using a frozen image encoder. Experiments under the TopoCap evaluation protocol show that the proposed framework improves motion recovery across different target topologies, including unseen structures. Reference-based cross-skeleton evaluation on a curated Mixamo benchmark and a user preference study further assess transfer to different target structures. A causal CAST-B variant achieves over 51 FPS on a single NVIDIA A100 GPU, with timing covering image encoding and motion prediction. Code repository: https://github.com/fankewen/CAST.

The growing deployment of compact large language models on smartphones is enabling autonomous on-device decision-making, such as emerging mobile GUI agents. However, many mobile decisions, such as network configuration when users switch apps or connectivity conditions change, must satisfy stringent latency constraints to preserve user experience. In this paper, we propose PEAM, an on-device LLM-based communication agent that autonomously generates personalized network-configuration rules executable within milliseconds. Specifically, PEAM first fine-tune the on-device LLM with a dataset constructed from manually annotated real-user data to integrate the communication knowledge into the local model. PEAM then operates in two phases. In the rule-generation phase, which is performed when the device is idle, such as overnight, PEAM analyzes historical network-configuration records in batches and reflects across batches to consolidate consistent evidence, reduce local bias, and derive robust configuration rules. To enable more accurate and stable rule generation over time, PEAM further constructs a user profile from high-confidence rules to capture the user's network preferences and incorporates this profile into each rule-generation cycle. In the rule-execution phase, PEAM is invoked when the communication context changes, such as when users switch apps or connectivity conditions change, and searches the rule library to identify and execute the appropriate rule. Experiments demonstrate that PEAM, based on a fine-tuned 4B model, achieves 99.13% correct network configuration decisions, while 92.50% of the rules generated by PEAM are valid, outperforming the traditional expert-rule based method by 4.41% and 84.50%, respectively.

Contact-rich manipulation poses a stage-dependent sensory conflict: vision and proprioception are essential for localization and approach, when force is largely uninformative and potentially distracting, whereas force becomes critical after contact, when irrelevant visual details and correlated robot states may become shortcuts. We propose DEFT-VLA (Dual-Expert Force-specialized Training for Vision-Language-Action Manipulation), which retains the task-adapted base expert for vision-dominated non-contact behavior and introduces a force-aware contact expert for critical contact stages, localizing force-conditioned adaptation to where it is needed. We further introduce a contact-localized force-attending curriculum that applies force-attending post-training only to the contact expert, progressively restoring vision and masking state tokens to suppress shortcuts. Real-robot experiments on pipette tip attachment, bimanual pipette aspiration, and whiteboard wiping show that DEFT-VLA effectively exploits force feedback to improve contact-stage performance while maintaining strong non-contact behavior and robustness to held-out grasp heights. It improves overall task success by 20-40 percentage points over the strongest baseline on each task.

Optimal transport (OT) is widely used to align distributions and transfer labels between unpaired source and target data, but source-target composition shifts can cause rare classes to be systematically under-predicted even with high transport confidence. We identify a source of this failure in the transport marginal: under the standard uniform weighting of source points, each class has transport capacity proportional to its source frequency, which can be insufficient to meet its target demand even when separated well in the embedding space. We show that displaced mass is preferentially absorbed by high-capacity classes rather than geometrically similar classes, producing confident errors that are difficult to detect from the transport plan. Downstream read-outs, entropic smoothing, and marginal relaxation provide limited recovery, whereas matching the transport marginal to the target composition substantially improves label transfer. On single-cell data, the oracle composition-matched marginal raises macro-F1 from 0.322 to 0.623, and the best deployable estimator closes 69% of the oracle gap. Correcting the marginal also separates a coverage-dependent component of error from residual error associated with class separability, showing that transport capacity and representation geometry are distinct sources of transfer error.

Reinforcement learning (RL) is promising for spatial text-to-image generation, but existing work largely focuses on policy optimization, assuming accurate rewards and effective online rollouts. We observe in-domain gains with out-of-domain degradation, exposing two limitations: unreliable spatial rewards in open-world settings and rollouts lacking basic-to-complex progression. We propose a curriculum-guided RL framework. First, we introduce SpatialCritic, an agentic reward model equipped with a spatial perception harness that combines reusable verification guidance with specialized vision tools. We then construct spatial preference datasets through targeted counterfactual perturbations and perform agent-harness alignment to improve tool selection and evidence integration efficiently. Second, curriculum learning organizes shared foundational capabilities and their compositional dependencies in a capability graph for mastery-guided rollouts, periodic review, and targeted remediation. On SpaRW-Eval, SpatialCritic achieves 95.1% verification accuracy, outperforming 320B GLM-5.3-Flash with a 40x smaller 8B backbone and raising average baseline scores from 78.4 to 83.9 on SD3.5-Medium and 83.2 to 86.5 on BAGEL. Project page: https://xiaofeng-tan.github.io/projects/spatialcritic/

High-multiplicity pp and p-Pb collisions show signatures of radial and anisotropic flow, as well as the enhanced production of strange hadrons. These observations resemble phenomena seen in heavy-ion collisions, where a quark-gluon plasma (QGP) is formed, although their origin in small systems remains under discussion. This contribution presents ALICE Run 2 results on light-flavour hadron ($\pi$, K, p) production in high-multiplicity (HM) pp collisions at $\sqrt{s}=13$ TeV, where the charged-particle multiplicity reaches values comparable to peripheral or semi-peripheral Pb-Pb collisions. The multiplicity dependence of $\pi$, K, and p transverse momentum spectra, $p_{\rm T}$-differential and $p_{\rm T}$-integrated particle ratios, and mean transverse momenta ($\langle p_{\rm T}\rangle$) is presented and compared with published results from other collision systems and energies, as well as with PYTHIA 8 and EPOS4 model calculations.

We build a labor market in which AI systems enter as workers: they apply for jobs, pass screenings, get hired, and get dismissed, alongside humans. Firms post vacancies, workers search with friction, and product demand slopes downward. Across 30 seeded runs per configuration, AI entry at 70% of the human wage raises unemployment by 4.1 percentage points (95% CI 3.5 to 4.6) and leaves 12.2 fewer humans employed (CI 10.5 to 13.9). Layoffs dominate when AI is much cheaper than humans: the layoff margin accounts for 7.2 of the lost jobs and reduced hiring for 5.0, though most dismissed workers find work again. A wider price gap reduces displacement, because cheap AI makes firms expand: at price parity, with zero dismissals, the unemployment effect is largest at 9.2 points (CI 8.6 to 9.9), all of it through hiring. That parity result survives cutting AI applications from five per period to one. Demand elasticity decides how many workers AI displaces. Screening changes who gets hired and leaves the displacement total unchanged.

Authenticated state transitions need proof engines that conserve memory, avoid repeated setup, and preserve request semantics across parallel execution. We present StateSync-GKR, a reusable Rust sumcheck/GKR core with a sparse-Merkle frontend, and connect its design mechanisms to controlled measurements. Sparse layer reduction and derived wiring reduce prover ownership and repeated verification work. Cube/affine fusion and parallel path constraints keep the circuit schedule and proof-size growth compact. Reusable preparation and indexed parallel jobs amortize setup while maintaining independent results. Three-state records, strict original-request decoding, and separate core/model interfaces expose the application and assurance boundaries. With circuit, field, transcript and prover driver held fixed, sparse reduction lowers additional requested allocation 3,242-fold and peak process resident memory 89.46-fold relative to StateSync-GKR's test-only dense reference for a two-layer mixed circuit of width 4096. Direct depth-24 fresh/prepared measurements show 3.46-4.45-fold lower per-request proving-path latency. CPU and full-proof delivery studies distinguish useful parallel work from queueing and return-path costs, retaining all outcomes and latency budgets. The evaluation supports larger circuits within finite RAM, lower repeated-request cost, and explicit deployment choices for this artifact. It preserves the cryptographic claim boundary of the existing construction.

Synthesizing believable 4D hand-object grasping sequences is important for character animation, extended reality, and embodied agents. Grasping requires a hand to approach, contact, and lift or manipulate an object coherently. Existing synthesis methods often model only the final static grasp or rely on additional conditions, such as language, target grasps, or object trajectories, to specify the interaction. We instead study the underconstrained problem of generating a complete grasping motion from a single initial hand-object state. Our framework decouples hand-motion generation from object-motion recovery. Given an object point cloud in the initial wrist frame and the initial parameterized hand configuration, conditional flow matching predicts a sequence-level contact map and a hand pose at each normalized sequence time. This time-indexed formulation avoids the error accumulation of autoregressive rollout while representing the complete motion. We then infer an attachment frame and recover rigid-object motion through training-free, contact-guided weighted registration. We evaluate on held-out DexYCB objects and unseen object geometries reconstructed from in-the-wild videos by Open-CHOIR. Compared with LatentHOI, our method produces smoother hand and object motion in every setting, matches or improves on its contact and penetration metrics in the wild under a shared initialization, and is about 30x faster per generated frame. In a 15-participant study, our motions were preferred in roughly two thirds of (forced-choice pairwise) comparisons. Precise contact closure on novel geometry, however, remains a key open challenge.

Gauging fermion parity in a $(2+1)$-dimensional fermionic topological order requires lifting its symmetries to the resulting bosonic theory. We give a direct tensor-categorical proof that, for a slightly degenerate braided fusion category $\mathcal{C}$ and a fixed minimal nondegenerate extension ${\cal E}$, the restriction homomorphism $r\colon\operatorname{Aut}_{\mathrm{LR}}(\mathcal{E})\to \operatorname{Aut}_{\mathrm{LR}}(\mathcal{C})$ on classes of complex-linear locality-respecting (LR) braided autoequivalences is surjective with central kernel $\mathbb{Z}/2$, generated by fermion attachment. Thus each symmetry class has exactly two LR lift classes, related by attaching the fermion to every vortex. We apply graded Morita theory to reduce the kernel to two module types on the vortex sector, corresponding to tensoring with the vacuum or the fermion. We then prove relative rigidity to show that each type determines a unique LR class, which are distinguished by fermionic self-braiding even when their actions on simple-object labels coincide. We prove surjectivity by extending graph algebras in $\mathcal{C}^{\mathrm{rev}}\boxtimes\mathcal{C}$ to Lagrangian algebras in $\mathcal{E}^{\mathrm{rev}}\boxtimes\mathcal{E}$. Our results require neither unitarity nor a ribbon structure. We illustrate the lifting ambiguity in the Laughlin state, the $SO(3)_3$ theory and the Ising topological order.

Indoor human perception is the foundation for smart homes and healthcare. However, RGB cameras raise privacy concerns in private indoor environments, while low-resolution thermal cameras provide limited spatial and semantic information. Large-scale indoor thermal datasets and real-world deployments remain limited. Here, we introduce Indoor RGB-T, a large-scale paired RGB–thermal dataset for indoor human perception. The dataset covers 20 indoor rooms and contains 90,576 80x62 thermal frames, 87,016 temporally matched RGB–thermal pairs, and 115,557 annotated human bounding boxes. We establish benchmarks for robust thermal occupant-state detection with 0.75 mAP and occupancy estimation with an accuracy of 0.847 in unseen rooms. We further evaluate RGB-to-thermal and thermal-to-RGB translation, achieving a temperature MAE of 0.654 C and an R2 of 0.923. Finally, we deploy the thermal perception model on a commercial sleep-monitoring system in the real world. Field testing with 100 participants and deployment of approximately 1,000 devices further demonstrate its practical feasibility. We identify practical challenges that motivate future research directions, including environmental thermal interference, sensing range and multi-person occlusion. The code, trained models and partial dataset are available at https://github.com/kailaisun/RGBT and https://huggingface.co/skl24/RGBT.

Soon after Maxwell's celebrated synthesis of electrodynamics, the discovery of the electron raised fundamental questions about the nature and structure of elementary particles. The picture of a small, rigid, charged body of finite radius faced the difficulty of introducing non-electromagnetic forces or stresses to prevent the charge from dispersing, an assumption that was increasingly regarded as unsatisfactory. The alternative description in terms of a point charge was no more satisfactory, because its electromagnetic self-energy diverges. From the early twentieth century onward, several authors therefore explored modifications of Maxwell's theory, with nonlinear electrodynamics emerging as a particularly natural and radical possibility. In this paper, we revisit at the undergraduate level some of the nonlinear theories proposed in this context and explore their ability to address the classical self-energy problem of charged particles.

We introduce stochastic physics-informed neural networks (SPINNs) for stochastic boundary-value problems (SBVPs) with random operators. The method enforces physics through a structural probabilistic coupling: a common Gaussian stochastic germ drives both the SBVP random operator and a manifold-based stochastic neural architecture. The stochastic neural network is non-feedforward and intrinsically random. A latent Gaussian field and an inhomogeneous Poisson point process on a compact, boundaryless, multiply connected manifold generate random neuron locations, geodesically local sparse connectivity, and a sparse random weight matrix, all governed by a low-dimensional hyperparameter. For deterministic inputs, the network output is random and can represent non-Gaussian random operators. Training is performed in observation space: SBVP simulations produce random observables, while the SNN defines a predictive conditional probability density function. The supervised objective combines data fidelity, through negative log-likelihood, with a cross-entropy alignment term relative to the SBVP-induced conditional distribution. The resulting target is a convex mixture of observation-induced and SBVP-induced distributions, with a dimensionless parameter controlling robustness to model–data mismatch. The shared stochastic germ yields common-random-numbers Monte Carlo estimators and reduced-variance gradients. The method uses only evaluations of the SBVP solution mapping, without differentiating or modifying it, and avoids PDE-residual or boundary-penalty losses. A stochastic elliptic problem on a periodic cylindrical surface illustrates the approach in SBVP-consistent and SBVP-misspecified regimes. A generalized-posterior formulation is also outlined for hyperparameter inference and posterior averaging without per-query reoptimization.

Claims of recursive self-improvement are easy to make and hard to falsify: did improvement come from re-using designer-provided mechanisms, or from mechanisms the system authored itself? We introduce a pre-registered, two-tier accounting: M1 counts machine-generated content instances within a designer-provided vocabulary, while M2 counts machine-authored mechanism types (new operators registered into the runtime's own vocabulary, with a held-out-validation certificate). We report the first audited M2 genesis events. In the primary event, depth-limited compositional search over elementary operators, judged by held-out R^2 on real NIST hydrogen Balmer measurements, produced the operator sq(inv(n)) = 1/n^2 – the Rydberg-level form – which no standard-library transform could express (held-out R^2: -0.546 best standard transform vs. 1.0000000 composed). A protocol flaw (independent variable built by inverting the very law under test) was caught in audit and repaired via an independent-label protocol; extrapolation to unseen levels (n=8,9 trained on n<=7) attains relative error ~10^-6, four to six orders beyond the best standard operator. A second event independently recovered sqrt(inv(a)) – Kepler's velocity law – from JPL ephemeris vectors. Also incorporated: an audited compounding channel (first domain-level measurement: 1.109x accuracy ratio on a real held-out domain) and blind, decurated genesis exams whose honest tally is zero. The Kepler event passes line audit; the hydrogen gap reproduces on He II; the certificate is threshold-stable. Against eleven prior systems, the contribution is the measurement and governance of machine-authored mechanisms, not the search algorithm or rediscovered physics. Limitations: exams were curated by agents who knew the textbook answer, triggers manual, grammar observer-injected; both events demonstrate capability to author, not yet autonomous genesis.

We proved recently that there are no unconditional Schauder frames of exponentials in the space $L^p(\Omega)$, $1 \le p < 2$, for any set $\Omega \subset \mathbb{R}^d$ of finite measure. For $p > 2$, we proved that the same holds provided that $\Omega$ has nonempty interior, but the general case remained open. In this note we close this gap, i.e., we establish that exponentials cannot form an unconditional Schauder frame in $L^p(\Omega)$, $p \ne 2$, without any additional assumptions on the set $\Omega$ of finite measure other than measurability.

We prove decay estimates for oscillatory integral operators along $(y_1, y_2, y_1^2+y_2^2)$ in the finite field and the continuous settings. In the continuous setting, our result allows a bi-parameter maximal modulation, which extends the one-parameter version previously established by Pierce and Yung. Our approach is different from theirs. Then we discuss three applications of our estimates: a power saving bound for certain pattern finding problem in finite fields, a short approach to $L^p$ boundedness of an one-parameter Pierce–Yung operator, and $L^p$ boundedness of a bi-parameter Pierce–Yung operator.

We present a learning-based framework that enables a full-scale bipedal humanoid to sprint at over 7 m/s with motion-prior-guided gait and perform aggressive cornering at high speed with a pronounced trunk lean of up to $25^\circ$. Achieving this combination is challenging: above approximately 4 m/s, periodic foot impacts induce severe, high-frequency yaw-rate oscillations intrinsic to high-speed gaits. This high-frequency temporal structure corrupts the history of proprioceptive feedback that flat-MLP policies rely on, while rendering conventional yaw-rate tracking rewards counterproductive, as they fight against the robot's natural oscillatory dynamics. Moreover, a single style prior shared across skills cannot tell which skill is commanded and inherently compromises the low-speed skill fidelity. To overcome these limitations, we adopt a causal multi-head attention (MHA) module to explicitly model the high-frequency temporal feedback. In place of the oscillatory yaw rate, we design a heading-direction reward that supervises only the low-frequency velocity direction, allowing agile turning at high speed without suppressing natural gait oscillations. We further introduce skill-conditioned multi-adversarial-motion-prior (MAMP) discriminators that condition the style reward on the commanded skill. Ablation experiments confirm that each mechanism is essential: replacing structured temporal encoding with a flat-history MLP caps the top speed; reverting to yaw-rate tracking prevents high-speed turning; and a single shared discriminator makes in-place turning collapse into a quasi-static stance. Our framework bridges the gap between raw sprinting speed and reference-motion fidelity, demonstrating stable high-speed sprinting and aggressive cornering in both simulation and real-robot deployment.

Variational inequalities (VIs) provide a unified framework for optimization, saddle-point, equilibrium, and learning problems, where operators need not be globally Lipschitz. The $\alpha$-symmetric generalized-smoothness condition allows local operator variation to grow with the operator norm, but existing extragradient methods often require unknown problem-specific constants. To address this issue, we propose PF-AEG, an explicit, line-search-free extragradient method whose stepsizes use quantities generated during the iterations, without prior knowledge of these constants. Under $p$-quasi-sharpness, we prove full-sequence convergence and last-iterate squared-distance rates: linear convergence for $0<p\le2$ and $\mathcal{O}(k^{-2/(p-2)})$ for $p>2$. The latter matches existing parameter-dependent rates under comparable assumptions, while the linear guarantee extends the previous $p=2$ result to $0<p\le2$. Building on the idea of PF-AEG, we develop AEG-VR, a variance-reduced adaptive extragradient method for finite-sum VIs. We prove almost-sure convergence and, under mild conditions, obtain analogous expected last-iterate rates, while retaining independence from the unknown problem-specific constants in stepsize selection. Experiments on synthetic generalized-smooth VIs and several learning problems show that the proposed methods are competitive with, and in several tested regimes outperform, existing baselines.

We introduce Rota-Baxter operators on Lie affgebras by an identity independent of the choice of origin and prove that they induce descendant Lie affgebra structures. We establish a bijection between ordered affine Lie factorizations and idempotent operators split at a chosen idempotent fixed point. A cokernel obstruction determines the existence of this point, while invariance under the structural endomorphisms characterizes splitting. We also determine when weighted descendants satisfy the affine Jacobi identity and when operators of nonzero weight give affine doubles. For canonical Lie affgebras, we describe all affine Rota-Baxter operators by Lie subalgebra decompositions and translation vectors, and classify them up to automorphism in dimensions at most two.

We study weighted Bergman spaces of quasiregular mappings on the unit ball in $\mathbb{R}^n$, with weight $(1-|x|)^\alpha$, $\alpha>-1$. For every fixed distortion bound $K\ge1$ and every $p>0$, we characterize Bergman integrability by averaged derivatives. We also give geometric conditions under which integration over a subset, or against another measure, controls the full Bergman integral. When $K$ is sufficiently large, the dominating sets are precisely the relatively dense sets. For comparison, we determine the dominating sets for the Möbius class $K=1$ in dimensions $n\ge3$. At the critical exponent $p=n+\alpha$, its domination criterion differs from that for every fixed $K>1$. Our results extend aspects of the Bergman theory developed by Nolder~\cite{Nolder90} and by Oleinik and Vuorinen~\cite{OV}, and complement the recent work of Adamowicz and González~\cite{AG21,AG25} and Adamowicz and Caamaño~\cite{AC} on quasiregular Hardy spaces.

As a key extension mechanism for agent systems, Agent Skills package specialized capabilities for reuse by LLM agents. An agent first retrieves candidate skills based on skill documentation and then relies on their metadata to make the final selection. As third-party skills proliferate on insufficiently vetted open registry platforms, the security risks posed by malicious skills become increasingly prominent, but existing attack research still focuses primarily on the potential harm caused after their execution. The limited related studies typically examine skill retrieval or selection in isolation and have yet to cover a complete end-to-end attack chain. To address this research gap, we find an end-to-end attack surface arising from the process-wide influence of metadata. Based on this finding, we propose MetaCascade, an end-to-end metadata-only poisoning framework. MetaCascade first generates diverse malicious skill candidates through multi-view semantic expansion, then uses tasks and black-box competition feedback to analyze the competitive relationships among malicious candidate skills and iteratively optimize malicious metadata, thereby improving the target skill's end-to-end attack effectiveness. Under a unified evaluation setting spanning four datasets and two agents, Hermes and OpenClaw, MetaCascade achieves state-of-the-art attack performance, with its average attack success rate (ASR) and its average ASR under four defense settings exceeding the strongest baselines under the corresponding settings by 35.53 and 34.65 percentage points, respectively. Our code is provided in the supplementary material.

Branch-and-bound (BnB) solves mixed-integer linear programs by constructing and exploring a search tree. Node selection and branching are two recurrent decisions that directly determine the tree. Learning-based approaches typically optimize either decision in isolation and condition on a mostly local view, leaving the coupled evolution of the search tree insufficiently modeled. This paper proposes Seq-BnB, a sequence-structured framework that learns branching and node selection from a shared global representation of the evolving BnB process. Seq-BnB serializes node creations, node updates, node-selection events, and branching events into typed tokens, producing a causal event sequence of the search trajectory. A self-attention encoder summarizes this global search history, a bipartite graph neural network encodes the current LP relaxation, and context-conditioned decision heads score branching variables and open nodes. To reduce distribution shift between expert demonstrations and learned policies, Seq-BnB is trained with DAgger-style data aggregation. On four MILP benchmark families, Seq-BnB consistently processes fewer BnB nodes than heuristic and learning-based baselines, with strong solution times on both standard and larger transfer instances. While this paper evaluates Seq-BnB instantiation for branching and node selection, it accommodates additional solver decisions, such as cut selection, by introducing new action tokens and decision heads.