Papers

Interpreting Earth system conditions is central to understanding environmental risks and informing decisions across weather- and climate-sensitive sectors. Existing multimodal weather systems primarily target task-specific prediction, generation, or question answering, while general-purpose alignment between Earth system data and language remains underexplored due to the limited availability of diverse language supervision grounded in meteorological conditions. To fill this gap, we introduce EarthAlign, a large-scale dataset with broad geographic coverage spanning 2000-2024 that combines 10 expert-curated natural event and disaster data sources with climatology-derived normal-weather samples. Each sample includes temporal and geospatial information and four grounded caption styles aligned with 63-variable ERA5 meteorological data. Building on EarthAlign, we introduce MeteoLIP, a dual-encoder framework for learning aligned meteorology-language representations. MeteoLIP incorporates MetTok, which uses a geolocation- and time-conditioned query to aggregate variable-specific patch embeddings into a compact sequence of meteorology tokens. To comprehensively assess Earth system multimodal representations, we introduce three downstream tasks: cross-modal retrieval, weather-condition classification, and physical variable estimation. Our experiments show that MeteoLIP improves upon the corresponding CLIP and SigLIP baselines across these tasks. Further analyses highlight the importance of meteorological input, temporal and geospatial conditioning, and multi-style supervision for meteorology-language alignment. Thus, EarthAlign and MeteoLIP provide a foundation for learning and evaluating language-aligned representations of Earth system data. Our code, dataset, and weights are publicly available at https://github.com/mbzuai-oryx/EarthAlign.

Direction-of-arrival (DOA) estimation can degrade markedly in impulsive noise, where methods relying on Gaussian or second-order statistical assumptions are particularly susceptible to large-amplitude outliers. This paper develops an adaptive DOA estimator that employs Gaussian kernel weighting to attenuate the influence of large prediction errors while adjusting the kernel bandwidth online according to a Kullback–Leibler (KL) divergence criterion. A sample-based approximation of the KL criterion yields a recursive bandwidth update that adapts the degree of outlier suppression to the observed error statistics rather than prescribing a fixed bandwidth a priori. The spatial-filter coefficients and kernel bandwidth are updated recursively, and the DOAs are recovered from the resulting spatial spectrum. Mean and mean-square analyses are developed under standard adaptive-filtering approximations to characterize the coefficient convergence and steady-state behavior. Simulation results under Gaussian-mixture impulsive noise demonstrate stable coefficient adaptation and improved DOA estimation accuracy over representative competing methods in several challenging operating regimes, with the most pronounced gains occurring at low-to-moderate signal-to-noise ratios. The results also indicate reduced sensitivity to the initial kernel bandwidth through online bandwidth adaptation.

Extreme rainfall can rapidly degrade road-network functionality (RNF), disrupting emergency mobility, accessibility, evacuation, logistics, and infrastructure restoration. Existing flood-transportation impact models are often difficult to deploy across regions because they rely on local calibration, intensive simulation workflows or target-region retraining. This study proposes G-R2R, a transferable spatiotemporal graph-learning framework that reframes rainfall-induced road-network disruption as a region-conditioned, topology-flexible graph forecasting problem for unseen transportation networks. The framework integrates ego-centered subgraph sampling, terrain-conditioned graph representation, region-conditioned dual-level static encoding, and dynamic rainfall-network feature learning. Static geographic and infrastructure attributes are fused with rainfall forcing and recent RNF states to forecast node-level RNF across heterogeneous road networks. G-R2R is evaluated using simulation-derived RNF sequences from ten flood-prone regions in Wenzhou, China, under unseen-region testing protocols. It outperforms representative forecasting baselines, achieving a stabilized MAPE of 2.33% and $R^2$ of 0.855 under the fixed unseen-region benchmark. Leave-one-area-out evaluation yields stabilized MAPE values of 2.30%-3.54%. Ablation analysis supports the contributions of the terrain-conditioned graph representation and dual-level static encoding. A historical-event replay of Typhoon Fitow further shows that G-R2R reproduces principal temporal trajectories and node-level spatial patterns of the simulation-derived RNF reference under observed rainfall forcing without target-region retraining. These results support rapid and transferable node-level RNF forecasting across the regional road-network domains represented in this study.

Horizon optimization in finite-horizon LQR treats the horizon $T$ as a decision variable and adds a penalty $wT$ to the cost. Recent composition-based methods evaluate all candidate horizons in $O(Nn^3)$, instead of the $O(N^2n^3)$ of one Riccati recursion per horizon, but they track the inverse cost-to-go $P^{-1}$ and therefore require every stage and terminal cost to be positive definite, whereas LQR requires only positive semidefiniteness. This excludes costs that leave some states unpenalized. In this work, we track instead the shifted inverse $\widehat{P}_k=(P_k+cI)^{-1}$, the inverse coordinate after a symplectic shear of the state-costate variables. Its domain contains every positive semidefinite Riccati matrix, and $P_k=\widehat{P}_k^{-1}-cI$ recovers the Riccati solution. We show that the shift can be absorbed into the stage coefficients of the inverse-coordinate composition, so the $O(Nn^3)$ search carries over, exact in exact arithmetic, subject to invertibility conditions. These hold for all small $c$ when the dynamics contract the unpenalized directions, fail for at most finitely many $c$ outside a degenerate case, and are certified per horizon at run time. In our experiments, diagonal loading $Q_k+\varepsilon I$ either left cost errors several orders of magnitude above those of the shifted chart or, for small fixed $\varepsilon$, selected the wrong horizon. The shifted chart with a fixed default $c$ selected the correct horizon on all tested instances, reporting long horizons as uncertified in one stress case.

Many applications in science and engineering require solving sparse Hermitian eigenvalue problems that are so large that even algorithms whose runtime scales linearly with the matrix dimension are unacceptably slow. Responding to this challenge, there is a growing body of work on sparsified iterative methods and submatrix selection methods that often perform well in practice. However, theoretical understanding of these methods is limited. In this paper, we take a step toward better understanding sublinear-time eigenvalue computation by analyzing the sparsified power method. We prove that the method approximates a leading eigenpair to a prescribed accuracy in a number of iterations comparable to the standard power method. The required number of retained nonzeros depends explicitly on the target accuracy, the initial overlap with the leading eigenvector, the compressibility of the leading eigenvector, and the relative spectral gap. When these quantities and the column sparsity are independent of dimension, the runtime is independent of dimension. In contrast, we show that a comparable worst-case guarantee cannot hold for a prototypical sparsified submatrix selection method. Submatrix selection is the approach of choice in many quantum chemistry applications. However, we show that, even with substantial initial eigenvector overlap, a single iteration of the method can produce a vector that is orthogonal to the leading eigenvector, after which the method cannot recover. Nevertheless, experiments on matrices from the SuiteSparse matrix collection and quantum chemistry problems illustrate the practical effectiveness of submatrix selection methods in a variety of domains despite these worst-case limitations.

Bismuth oxyselenide (Bi2O2Se) has emerged as a leading semiconductor candidate for next-generation electronics and quantum phenomena research. However, its strong ionic interlayer bonding of Se layers fundamentally restricts the full potential of this otherwise promising quasi-two-dimensional (2D) material. In this work, we demonstrate chlorine substitution as an effective strategy to introduce van der Waals gaps and modify the electronic structure of the system. Through comprehensive transport and angle-resolved photoemission spectroscopy (ARPES) measurements on Bi6O6Se2Cl2 single crystal, an optimal Cl-doping compound, we show that the key electronic features, including indirect band gap, high electron mobility, and carrier effective mass, are well preserved, while the 2D character of the system is sufficiently enhanced. First-principles calculations attribute this selective tunability to the unique spatial separation between conductive Bi-O layers and dopant Se/Cl layers, which enables independent optimization of interlayer coupling and intralayer transport. Remarkably, our theoretical calculations combined with experimental observations project a broad bandgap engineering across a wide range (0.8 ~ 3.5 eV) within the Bi2O2Se system. Our findings not only expand the application potential of Bi2O2Se-based materials in optoelectronics, nanoelectronics, and fundamental research but also highlight spatial decoupling as a viable strategy for modifying detailed electronic structure of quasi-2D quantum systems.

The flux variability of Active Galactic Nuclei (AGNs) is commonly modeled using the damped random walk (DRW), but increasingly rich multiband time-domain surveys motivate more flexible stochastic models that characterize variability beyond a single timescale and exploit dependence across bands. Multivariate continuous-time autoregressive moving average (MCARMA) processes extend the multivariate DRW to higher-order stochastic dynamics and provide a matrix-valued power spectral density for characterizing marginal variability and cross-band dependence. In a carefully selected Sloan Digital Sky Survey (SDSS) Stripe~82 sample, higher-order models are selected for 109 of 134 AGNs (81.3%), with substantial rather than marginal support in most objects; convergence diagnostics indicate that this fraction is conservative. The fitted models also reveal strong cross-band dependence that generally decreases with wavelength separation. Motivated by this richer structure, we investigate its recoverability under Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) observing conditions. Model-order recovery depends strongly on the underlying stochastic behavior as well as source brightness and observing cadence. Recovery is high across many of the simulated settings, but deteriorates when the characteristic features of higher-order variability become difficult to distinguish from the multivariate DRW. Additional simulations show that this loss of distinguishability can persist over a range of underlying variability behaviors. These results show that stochastic structure beyond the multivariate DRW is prevalent in our selected SDSS sample, while its recoverability with LSST depends on both observational conditions and the form of the underlying stochastic variability. The methodology is implemented in the Python package mcarma.

LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we establish two asymptotic results: (i) a local oracle property for the penalized regression, and (ii) a global oracle property for regressions with a penalty-level constraint. In particular, the latter guarantees a global solution that consistently estimates the true coefficients and enjoys oracle prediction performance. Simulation studies and an application to predicting the euro area unemployment rate show that FCP improves variable selection and out-of-sample prediction relative to LASSO.

We study random contingency tables obtained by conditioning a matrix of independent Poisson entries on its row and column sums. We identify such a table with the block counts of a random permutation drawn from a Gibbs measure of Mallows type, an exact coupling whose normalizing constants recover Barvinok's permanent identity. We use this correspondence to study the table at three scales. For finite dimensions, a transference principle compares the table with a matrix of independent Poisson entries whose means form the static Schrödinger bridge, the solution of a discrete entropic optimal transport problem. As the dimensions grow and the margins and prior means converge, the normalized histogram of the table converges to a limiting Schrödinger bridge at a quantitative rate. The fluctuations of the table around the bridge are characterized in two complementary ways. Linear statistics satisfy a central limit theorem for bounded test functions, with limiting variance equal to the squared $L^2$-distance, under the bridge, of the test function to the subspace of additively separable functions; as a process they converge to white noise with intensity given by the bridge, conditioned to have vanishing marginals. Spectrally, the limiting spectral distribution of the centered table is governed by a Dyson equation whose variance profile is the density of the bridge. The key ingredient is an asymptotic formula for the partition function of the Gibbs measure in terms of a Fredholm determinant given by the canonical correlations of the bridge. For Mallows-type random permutations, our results prove Pal's conjecture on the limiting partition function and Mukherjee's conjecture on the central limit theorem for linear statistics, both in greater generality.

We study autoregressive token generation through the notion of sequential samplers: A circuit that samples the next symbol only given the previous ones and possibly a small amount of state. We show that (1) a sequential sampler with $k$ bits of state can be simulated by a stateless one at a roughly $O(2^{k})$ size overhead; (2) efficient insertional sampling (Stern, Chan, Kiros, Uszkoreit, ICML 2019) is more powerful than efficient sequential sampling in any fixed order; (3) sequential samplers with small state cannot establish certain forms of covert cryptographic channels. Result (1), together with the pseudoentropy vs. sequential sampleability duality of Vadhan and Zheng (STOC 2012), characterizes efficient sequential sampleability with small state. Result (3) provides a potential safety mechanism against subliminal coordination among malicious LLM agents.

The focus of this article is to establish the existence portion of the Strauss conjecture for wave equations with spatially dependent scattering damping. In the current setting, the damping is not sufficiently strong to alter the critical Strauss exponent. In a subsequent study, the authors will consider the case of damping coefficients with critical decay where a shift of the Strauss exponent is expected. While several recent studies of the Strauss conjecture have relied upon weighted Strichartz estimates, here, instead, an approach that is based only on integrated local energy estimates, in particular those with both $r^p$ and ghost weights, is developed. This technique also applies to the problem for the free equation. Space-time Klainerman-Sobolev estimates provide the necessary decay to close the argument.

In this paper, by normalizing the trace-zero norm forms according to the parity of orders of definite rational quaternion algebras, we give an explicit formulation to the even Clifford correspondence followed by the reciprocity of ternary forms. We obtain an exact identity between ternary representation numbers and the number of elements of an order with prescribed reduced norm and trace, which applies to all orders without squarefreeness constraint on the reduced discriminant. Applications include a criterion for realizing ternary forms as trace-zero norm forms, a formula for traces of Brandt matrices in terms of representation numbers, and explicit theta series relations associated with local reciprocity. We also describe reciprocal orders and order chains, and interpret the ternary forms occurring in the congruent number problem through their associated quaternion orders.

Chiplet technology is a key approach for extending Moore's Law. However, its design process is constrained by two primary challenges: the scarcity of early-stage platforms for rapidly evaluating chiplet-based heterogeneous systems, and the complex relationships between design parameters and optimization metrics. To address these challenges, we propose a synergistic framework that integrates a Large Language Model (LLM) with Bayesian Optimization (BO), enabling architectural-level simulation and automated optimization for the 2.5D/3D CPU-GPU heterogeneous chiplets. We extend the open-source chiplet simulator to evaluate 3D designs by supporting graph topologies. Further, to enhance the exploration efficiency of BO, we introduce an LLM that generates high-quality policies to guide the optimization process, enabled by our proposed adaptive directional policy reasoning (ADPR) and an exploration gain-aware fine-tuning method. Finally, we use the policy-guided BO to perform an automated and efficient exploration of the complex chiplet design space. Experiments on 2.5D and 3D chiplet reveal that our framework improves design space exploration efficiency.

Axion quasiparticles introduce magnetoelectric coupling in topological materials, yet their optical signatures are intrinsically weak, severely limiting experimental detection and practical exploitation. Here, we demonstrate maximal optical chirality of axion quasiparticles by coupling them with degenerate quasibound states in the continuum (qBICs). By integrating three-dimensional topological insulators (3DTIs) with achiral photonic crystal slabs (PCSs), we reveal that axion quasiparticles induce an effective Zeeman effect that lifts the degeneracy of achiral qBICs in PCSs, splitting them into two nondegenerate high-Q chiral qBICs with maximally opposite chirality. These result in a more than 10^3- and 200-fold increase in the polarization conversion efficiency and Faraday rotation angle, respectively, compared to the intrinsic chiroptical response of bare 3DTI films. Moreover, circular dichroism and nonreciprocal optical responses are revealed as new key signatures for probing axion quasiparticles in 3DTI-PCS coupled systems. Our results provide a definitive route for observing axion quasiparticles and topological physics, while establishing a promising platform for controlling optical polarization, spin, phase, and nonreciprocal responses.

The Strauss conjecture concerns wave equations with power-type nonlinearities and seeks the optimal range of powers that admit global solutions for all sufficiently nice and sufficiently small initial data. In three spatial dimensions, it is well known that small data global existence is available provided that the power $p>p_c(3)=1+\sqrt{2}$, where $p_c(n)$ denotes the critical power in $n$-spatial dimensions. In the current article, the analogous problem is considered for damped wave equations where the damping coefficient is at the critical scaling. When $a$ denotes the constant multiple applied to the damping term, it is shown that the corresponding critical power is $p_c(3+a)$ provided that $a$ is sufficiently small.

Determining whether an image is AI-generated does not establish whether the situation it depicts is factually supported. We formulate Image Factuality Assessment: given an image and a generic verification instruction, a system returns a supported or refuted verdict with an evidence-grounded explanation. Without a supplied textual claim, the system must progressively refine factual questions during investigation and align external evidence with the specific situation depicted. We introduce EviLens, an expert-reviewed benchmark of 10,174 supported and refuted images from controlled construction and web collection, covering twelve factual error types and evaluating both verdict accuracy and evidence sufficiency. We develop EviScene, a multimodal ReAct agent that interleaves visual inspection, external retrieval, and evidence analysis, using new findings to refine its questions and revisit relevant image details. We train a compact policy with supervised fine-tuning on reviewed teacher trajectories, followed by privileged on-policy self-distillation applied to verified decisions from the policy's own investigations. On the 1,527-image test set, the trained Qwen3.5-9B agent achieves 79.05% balanced accuracy and a Strict Evidence Sufficiency Rate (SESR) of 52.26%, improving over the same-backbone base agent by 6.71 and 9.37 percentage points, respectively. Its SESR is the highest among the evaluated agents.Code, models, and data will be released at https://github.com/wangzian828/EVISCENE and https://huggingface.co/ZiAnwang/EviScene.

In these lecture notes we review some constructions and results on the relation between topology of the moduli space of stable curves and integrable systems of evolutionary PDEs.

Voice activity detection (VAD) sits in front of almost every streaming speech recognizer, yet the choice of detector is often made by feel rather than by measurement. We report a frame-level offline benchmark of three detectors on the test-clean split of LibriVAD-small: the neural TEN VAD, the neural Silero VAD and a simple RMS energy baseline. The evaluation covers 2,214 noisy utterances (about 7.1 hours) built from LibriSpeech, nine noise families and six SNR levels from -5 to 20 dB. At a 16 ms hop, TEN VAD reaches a ROC AUC of 0.917, an average precision of 0.968 and an F1 of 0.913. A sweep over 20, 30, 40 and 50 ms windows shows TEN to be almost insensitive to frame length (AUC 0.916 to 0.919), while RMS stays near 0.75 to 0.77. Silero matches TEN only near its native 32 ms input size and drops to 0.63 at 20 ms. We hypothesize that this is likely caused by our fixed-frame protocol rather than by the model itself. Zero padding, sub-chunk averaging and unreset model state are the likely factors, but we have not ablated them. In a per-condition breakdown of TEN, babble noise at low SNR stays close to chance. We also show that F1 at a fixed 0.5 threshold is a weak metric on this data, because a trivial all-speech detector already scores 0.854. All settings needed to reproduce the results are given in the paper.

Routing policies in Multi-Agent Systems (MAS) represent valuable intellectual property, yet their exposure through execution logs creates significant risks of unauthorized policy cloning. Existing agent watermarking methods protect intellectual property by modifying internal generation processes, such as perturbing token sampling distributions or injecting structural mutations into action trajectories, which may compromise task fidelity or suffer from limited transferability across heterogeneous platforms. To address these limitations, we propose Decision Uncertainty-Oriented Watermarking (DUOW), a lightweight framework that operates at the external decision layer without modifying model parameters or generated outputs. DUOW introduces a plug-and-play scoring mechanism that evaluates candidate agents from semantic and operational perspectives, identifies functionally redundant routing decisions, and selectively redirects choices among equivalent alternatives to embed ownership signals. By coupling watermark behaviors with utility-preserving routing decisions, DUOW enables cloned policies to retain ownership signals during policy imitation while increasing the difficulty of watermark removal. A confidence-driven adaptive threshold dynamically determines embedding opportunities, balancing watermark capacity and task fidelity under diverse routing contexts. Extensive evaluations on four multi-agent routing benchmarks demonstrate that DUOW preserves high task utility, achieves reliable ownership verification under up to 90% log erasure, and introduces negligible computational overhead, with an average per-step latency of 0.043 ms and total embedding overhead below 0.54 ms.

Current evaluations of multimodal unlearning typically focus on whether a model stops outputting target information. This surface-level criterion, however, masks two critical failure modes. First, knowledge suppression techniques often induce confabulation, leading the model to hallucinate facts about the unlearned subject. Second, refusal training merely alters observable behavior without erasing the underlying knowledge; such models might decline open queries but still identify correct answers under multiple-choice probing. To overcome these limitations, we propose Forget-Aware Self-Distillation (FASD). This method is designed to achieve honest ignorance, a state where the model genuinely loses the target knowledge and learns to acknowledge its absence. FASD separates these goals into two complementary channels. The behavior channel distills appropriate refusals from an ignorance-prompted copy of the model itself. Crucially, target tokens are masked from the teacher distribution to avoid accidentally reteaching the forgotten concepts. Simultaneously, the knowledge channel directly suppresses ground-truth answer spans independently of the model's generated responses. Experiments demonstrate that FASD successfully unlearns target knowledge, prevents information leakage in open-ended tasks, and preserves performance on retained data. The resulting model not only forgets the specified information but accurately recognizes the boundaries of its own knowledge. Code and data will be released upon publication.

Consider an unknown graph $G = (V,E)$ with vertex degrees $d_v$, accessed only by sampling uniformly random edges and querying the degrees of their endpoints. We study the query complexity of estimating the number of edges $m$ and the degree moments $M_s = \sum_{v \in V} (d_v)^s$ for fixed integers $s \ge 2$. In this model, [Beretta and Tětek, TALG 2024] estimate $m$ within relative error $\varepsilon$ using $O(\log n/\varepsilon^2+\sqrt n/\varepsilon)$ expected queries without knowing the number of vertices $n$, and [Bhattacharya and Pradhan, CIAC 2025] estimate $M_s$ using $O(n^{1-1/s}/\varepsilon^2)$ queries when $n$ is given. We show that the query complexity of both problems is governed by the matching number $\nu$ of $G$ (the maximum number of pairwise disjoint edges) rather than the number of vertices $n$, and that the dependence on $\varepsilon$ for degree moments can be polynomially improved. Our algorithms rest on a simple observation: the endpoints of a maximum matching cover every edge, so a random endpoint of a random edge falls on this set of $2\nu$ vertices with probability at least $1/2$. For every $\varepsilon\in(0,1]$, we give advice-free algorithms that estimate $m$ and $M_s$ within relative error $\varepsilon$ with probability at least $2/3$, without knowledge of $n$, $\nu$, or other graph parameters. Specifically, our algorithms use $O(\min\{\nu/\varepsilon, 1/\varepsilon^2+\sqrt\nu/\varepsilon\})$ expected queries for $m$ and $O(\min\{\nu^{1-1/s}/\varepsilon^{2/s}, \nu^{1-1/(2s-1)}/\varepsilon^{2/(2s-1)}\})$ for $M_s$. Finally, our lower bounds show that for every $k \ge 2$ and sufficiently small $\varepsilon$, these query complexities are optimal up to constant factors over graphs with matching number at most $k$.

Due to the high cost of hardware experiments, robot policies are predominantly evaluated by comparing their empirical performance on a limited number of hardware trials. However, finite-sample statistical uncertainty can lead to erroneous conclusions, especially when ranking multiple policies using a fixed batch of evaluation data. We propose AnyRank: a sequential method for multi-policy ranking that (i) adaptively allocates trials to hard-to-separate policies, (ii) provides (partial) rankings at any stopping time while bounding the probability of an incorrect ranking, and (iii) optionally exploits prior information to prioritize hardware evaluations more efficiently. This prior information could be informed from expert intuition, a small set of held-out hardware evaluations, or from policy rollouts in a simulator or an action-conditioned video world model. Notably, the prior can be imperfect; while a strong prior can provide efficiency gains on hardware, any inaccuracies in prior policy rankings do not invalidate the statistical assurances of AnyRank. We achieve the aforementioned properties through novel theoretical contributions that combine sequential testing with multiple-hypothesis graphical testing approaches. Experiments in simulation and real-world policy evaluation benchmarks show that AnyRank requires up to 50% fewer hardware evaluations compared to existing statistically rigorous approaches, while guarding against the incorrect rankings produced by heuristic methods used by state-of-the-art benchmarks.

Linear-optical platforms provide a promising route to demonstrate quantum computational advantage, particularly through the boson sampling problem. While a boson sampling system should be large enough to show the quantum advantage, the size of the boson sampling problem is often restricted by experimental constraints. In particular, as a boson sampling system is scaled up, experimental constraints can limit its effective problem size to permit efficient classical simulation. In this paper, we investigate the theoretical scalability bounds for boson sampling systems under practical experimental conditions, including photon loss, mode mismatch, and input state error. We employ non-negativity conditions for phase-space quasiprobability distribution functions to analyze these effects. In addition, we introduce two device-level metrics, the boson sampling score which measures the usable capacity of a given device and the boson sampling volume which provides a common hardware-level benchmark for comparing different platforms and assessing their access to an advantage-relevant problem size regime. Our results provide fundamental insights into the performance of boson sampling systems under realistic experimental conditions and offer practical guidelines for scaling up boson sampling systems.

In this work, we aim to develop an embodied MLLM agent that understands and solves embodied tasks by learning, abstracting, and reusing transferrable and generalizable behavioral patterns. To this end, we propose StateSkill, a new skill representation for embodied agents, which introduces the concept of "finite-state machines" into skill modeling for effective and efficient skill construction and learning. The core idea of StateSkill is to model embodied interaction experiences as a finite-state machine, where a skill is organized around a set of task-progress states, state transitions, and state-conditioned guidance, enabling embodied agents to dynamically adjust their skills as the task progresses while keeping skill contexts compact and stage-relevant. We further develop StateSkill-Evolve, an experience-driven evolution mechanism that iteratively refines StateSkill through retrospective analysis of new successful and failed state-guided trajectories. Upon this, we introduce StateGRPO, which integrates StateSkill evolution and model optimization via state-conditioned GRPO into a unified iterative learning loop, enabling state-conditioned skills and model capabilities to co-evolve and reinforce each other. Extensive experiments demonstrate the effectiveness of our proposed methods and trained model (i.e., StateSkill-Agent) across various embodied tasks.

We consider an elliptic Cauchy problem for the Poisson equation in which both Dirichlet and Neumann boundary data are prescribed only on a portion of the boundary, while no boundary conditions are available on the remaining part of the boundary. Such problems are severely ill-posed. In this work, we study the convergence of an iterative method based on the alternating imposition of Dirichlet and Neumann boundary conditions. We formulate the scheme within a Hilbert space framework, where a yet another alternation becomes apparent: each iteration can now be interpreted as an orthogonal projection onto an appropriate closed subspace. This perspective provides a transparent geometric interpretation of the algorithm and yields a concise convergence proof based on von Neumann's classical result on alternating (orthogonal) projections. In addition to elucidating the convergence of the method, this alternating projections perspective also offers a general rate of convergence in terms of the Friedrichs angle (between two closed subspaces). We point out by means of an example that such convergence rate estimate degenerates for the elliptic Cauchy problem under consideration.

We study products $B_{\alpha,m}^{(d)}B_{\beta,m}^{(d)}$ of Berezin transforms on generalized Fock spaces over $\mathbb C^d$. We establish a result for $m\neq2$: if $B_{\alpha,m}^{(d)}B_{\beta,m}^{(d)}$ coincides with another such product, then the weight parameters of the second product must be $(\alpha,\beta)$. As consequences, we characterize when two Berezin transforms commute and when the product of two Berezin transforms is again a Berezin transform.

The effective integration of features derived from RGB images and 3D point clouds presents a substantial challenge in the field of multimodal anomaly detection (MAD). Existing MAD methods typically rely on static fusion paradigms built upon frozen pre-trained encoders. While these frameworks facilitate spatial alignment, they lack the mechanism to establish latent semantic correspondence, thereby inducing cross-modal interference that degrades anomaly discriminability. To mitigate these limitations, this study proposes a Bidirectional Adaptive Transformers (BAT) framework, which constructs comprehensive and semantically aligned multimodal representations by leveraging complementary attributes across modalities. The BAT framework introduces a Bidirectional Feature Alignment (BFA) module, which employs a mutual predictive mechanism to bridge the gap between 2D textural patterns and 3D geometric structures. This bidirectional interaction explicitly enhances the textural granularity of point cloud descriptors while augmenting the spatial contextual awareness of RGB features. To ensure that the latent representations possess sufficient informational density for alignment, BAT incorporates a parameter-efficient adaptation architecture. By utilizing lightweight image and point cloud adapters, the framework facilitates specialized fine-tuning of pre-trained models, mitigating the information loss inherent in frozen encoders. Extensive experiments conducted on MVTec 3D-AD and Eyecandies confirm that BAT achieves state-of-the-art anomaly detection performance, significantly outperforming existing MAD methods.

Refining atomistic supercells against powder pair distribution functions (PDFs) requires optimizing many coupled atomic coordinates using a much smaller set of radial measurements. Reverse-mode differentiation makes gradients accessible for large systems, but standard first-order optimizers do not explicitly use coupled PDF sensitivities to precondition coordinate updates. We introduce a matrix-free, Fisher-geometric approach that pulls the information metric of the observation likelihood back onto atomic coordinates. The resulting update weights collective displacements according to their PDF response and experimental uncertainty. Under isotropic damping, the update is obtained by solving a damped linear system over $M$ PDF channels, using automatic differentiation to evaluate Jacobian–vector and vector–Jacobian products without constructing the full Jacobian or coordinate curvature matrix. For Gaussian measurement errors, the update recovers classical Levenberg–Marquardt refinement while avoiding dense coordinate-space factorization. The same computational framework accommodates correlated Gaussian errors and robust likelihood-based updates. This approach combines likelihood-aware collective updates with matrix-free backpropagation for direct second-order refinement of large atomistic supercells.

Navigating cluttered environments while carrying objects remains a challenging problem for quadruped robots. Compared with works that focused on load-aware locomotion adaptation to maintain gait stability, existing autonomous navigation systems generally ignore the influence of carried objects' geometries and use fixed footprint inflation, leading to overly conservative navigation. To fill this knowledge gap, we propose a two-phase load-aware navigation learning framework. In Phase 1, we train LOADNav, a load-aware navigation policy via reinforcement learning, enabling the robot to adapt its trajectory and clearance behavior according to the geometric size of the carried object. In Phase 2, we train CoGE, an online geometry predictor via imitation learning, which estimates unknown payload geometry from occasional contact events. We evaluate the framework in cluttered environments with loads of varying sizes and shapes. The results show that our navigation policy exhibits clear load-aware behaviors, and the online geometry predictor estimates object geometry from occasional contact events, refining its estimate and adapting the navigation behavior accordingly. Without requiring any prior knowledge of the payload, it narrows the gap to geometry-aware policies.

Given $n$ nonnegative integer weights $w_1, \ldots, w_n$ and an integer knapsack capacity $T$, the $\#$Knapsack problem asks to count the number of subsets $I \subseteq \{1, 2, \dots, n\}$ such that $\sum_{i \in I} w_i \le T$. A long line of research has been devoted to designing faster $(1 \pm \varepsilon)$-approximation algorithms for this \#P-hard problem. Until very recently, the best-known time complexity was $\tilde{O}\bigl(n^{2.5}/\mathrm{poly}(\varepsilon)\bigr)$, achieved by the randomized algorithm of [Dyer, STOC 2003] and the deterministic algorithm of [Gawrychowski, Markin, and Weimann, ICALP 2018]. The recent work by [Feng and Jin, SODA 2025] improved the randomized complexity to $\tilde{O}\bigl(n^{1.5}/\mathrm{poly}(\varepsilon)\bigr)$, leaving open the question whether this $n^{2.5}$ barrier could also be broken by a deterministic algorithm. In this work, we answer this question in the affirmative by presenting a deterministic $(1 + \varepsilon)$-approximation algorithm for \#Knapsack in $\tilde{O}\bigl(n^{2.4}/\mathrm{poly}(\varepsilon)\bigr)$ time. Our key technical innovation is to deterministically simulate the balancing technique, which was previously used in the literature of knapsack-type problems via random partitions and seemed to require randomization.