Papers

Quantum linear-system algorithms access the coefficient matrix through a block-encoding oracle $U_A$ and the right-hand side through a state-preparation oracle $U_b$. The optimal query complexities of these two oracles are known separately: $O(\kappa\log(1/\varepsilon))$ queries to $U_A$ and $O(\kappa/s)$ queries to $U_b$, where $s=\alpha\|A^{-1}b\|$. Whether a single algorithm can achieve both bounds simultaneously has remained open. We resolve this question affirmatively. Given a constant-factor estimate of $s$, we give a quantum linear-system algorithm that prepares the normalized solution to error $\varepsilon$ using simultaneously $ O\left(\kappa\log\frac1\varepsilon\right)$ queries to $U_A$ and $O\left({\kappa}/{s}\right)$ queries to $U_b$. The algorithm separates state preparation from precision refinement, so only the matrix-query count depends on the target accuracy. We also prove a matching same-instance worst-case lower bound: for every quantum linear-system algorithm and every solution-norm scale, there exists a single Hermitian instance on which that algorithm requires both $\Omega(\kappa\log(1/\varepsilon))$ matrix queries and $\Omega(\kappa/s)$ state-preparation queries. Thus the two oracle complexities can be optimized simultaneously, and the resulting bounds are jointly optimal.

Artificial Intelligence (AI) models for temporal multimodal data have potential in healthcare and agriculture, but their opacity can limit trust and adoption. We introduce T-MoXAI (Temporal Multimodal eXplainable AI), a hierarchical framework explaining (1) when timepoints influence predictions, using temporal Shapley values; (2) which modalities contribute at those moments, using attention analysis; and (3) what features or image regions drive decisions, using gradient based attribution. A transformer based architecture handles irregular temporal sequences and heterogeneous data, generating all three explanation levels in under one second for interactive decision support. We evaluate the framework on two real world tasks: predicting IVF treatment outcomes from ultrasound sequences and clinical measurements (AUC 0.660 despite significant class imbalance), and forecasting wheat yield from temporal RGB imagery and phenotypic traits ($R^2$ 0.265 amid substantial environmental variability). Ablation studies indicate that temporal modelling is critical in both domains: removing it reduces performance to the equivalent of random guessing. Temporal ROAR experiments provide evidence that the explanations reflect the model's reasoning process. With a unified, domain agnostic architecture and open source implementation, T-MoXAI provides a baseline for temporal multimodal XAI, addressing fragmentation in the field and supporting applications where understanding decisions is as important as predictive accuracy.

We give a randomized polynomial-time algorithm that, for every fixed $\varepsilon > 0$, colors every $3$-colorable $n$-vertex graph using $O\bigl(n^{(13-\sqrt{97})/18+\varepsilon}\bigr) \approx O\bigl(n^{0.17506+\varepsilon}\bigr)$ colors, improving upon the previous best bound of $O(n^{0.19539})$ from Bansal, Huang, and Lee. Our improvement comes from analyzing higher-level neighborhoods through a recursive description of failure in Gaussian SDP rounding. If the rounding returns too small an independent set, it produces local Gaussian certificates at every vertex of a nonempty induced subgraph. We propagate these certificates along walks to higher-level neighborhoods by defining a recursive certificate structure and proving a strengthened cover-composition lemma, which refines the one of Arora, Chlamtáč, and Charikar. We then construct a bounded potential function that increases by a fixed positive amount at every propagation step, yielding a contradiction. Consequently, the rounding must produce a sufficiently large independent set.

When should multimodal foundation models generate tokens, and when should they directly output a decision? We present MAD-Guard, a controlled study of output-decision interfaces for closed multimodal forensic tasks. Once a multimodal representation is computed, is autoregressive generation necessary for closed forensic decisions with high input complexity but low output entropy? Under a matched Qwen3-VL-8B backbone, 2,400 FakeClue training samples, and LoRA budget ($r=16, \alpha=32$) on Huawei Ascend 910C NPUs, we evaluate a progression of decision interfaces (AR-SFT [generate] $\to$ Logit Slice $\to$ Binary Direct Head $\to$ +choice $\to$ +act $\to$ CLM-Head) and decompose latency into backbone representation (53.12 ms), 151,643-way vocabulary projection (+85.04 ms $\to$ 138.16 ms), and decoding (+248.26 ms $\to$ 386.42 ms). Under 1-to-1 binary supervision ($\mathcal{L}_{\mathrm{BCE}}$), a Binary Direct Head cuts latency by $2.60\times$-$7.27\times$ (53.12 ms) and lowers calibration error by $1.88\times$ (ECE = 0.0450 vs. 0.0845), with a -1.80% accuracy trade-off (93.10% vs. 94.90%; 0.9795 vs. 0.9871 ROC-AUC) from forfeiting token priors. Gains above AR-SFT arise either from multi-task attribution and uncertainty gating (+choice+act: 96.44% accuracy, 0.9940 ROC-AUC, 0.0187 ECE at 53.71 ms) or from a disaggregated contrastive head (CLM-Head: 96.55% binary and 96.44% multi-task accuracy, 0.0166 ECE, 98.79% 7-class attribution at 54.42 ms) retaining semantic priors without token decoding. Across 5,000 out-of-sample images from five benchmarks, our framework excels on synthetic, camouflage, and document forgeries (96.44% GenImage, 97.73% Chameleon, 91.84% Doc) while showing a clear boundary on compressed face manipulation (FF++ ROC-AUC = 0.5913).

Information diffusion can be controlled by restricting or removing links (edges) in online social networks, as well as in real-world networks. To identify the most influential links to remove while minimizing diffusion, previous studies have proposed upper bounds for spreading processes in SIR and SIS models, using supermodularity and weighted matrices to identify critical links in contact networks. However, in some cases, existing upper bounds are not sufficiently tight to accurately capture the effect of important edges, as in the SDIR model of [14] (Khanh-Cho-Dung, Proceedings of 40th ICOIN, 2026). We therefore propose a tighter upper bound for controlling diffusion in the SDIR model by directly analyzing the dynamics of the two state vectors D and I in a $2N$-dimensional space. This approach yields an improved spectral-radius convergence condition and outperforms the previous method. Simulations on the synthetic Erdos-Renyi network and the real-world Haslemere dataset using a Greedy edge-deletion algorithm demonstrate its effectiveness for influence minimization on social networks.

This paper presents the application and experimental evaluation of a systematic method for optimal sensor placement in soft robots. Existing methods either lack generalizability across different soft robot morphologies or do not account for system dynamics. The applied method uses convex optimization to find the optimal sensor configuration that maximizes an observability Gramian-based metric. The framework is experimentally evaluated using position and strain measurements on a soft continuum arm. Kalman filter state estimates using optimal sensor placements yield lower reconstruction error than a baseline across all sinusoidal input trials, with improvements on the order of millimeters. This case study shows that linear control theory tools can guide optimal sensor placement in soft robots, suggesting an interpretable approach to sensor placement that may extend to other morphologies.

For a connected graph \(G\), let \[ Q(G)=\frac{T(G;2,0)T(G;0,2)}{T(G;1,1)^2}. \] We obtain quantitative lower bounds for \(Q\) under the graph join operation. If \(A\) and \(B\) are arbitrary simple graphs of orders \(3\le a\le b\), then \(Q(A\vee B)\) admits an explicit lower bound depending only on \(a\) and \(b\), and this bound is strictly greater than \(1\). We further quantify the improvement produced by edges inside the two factors. For every simple graph \(F\), with \(n=|V(F)|+2\ge4\), we prove \[ Q(K_2\vee F)\ge \frac{27}{n^2}\left(\frac32\right)^{n-4}. \] Consequently, every join of at least three nonempty factors, and every complete multipartite graph with at least one edge and no cut edges, satisfies the strict multiplicative Merino–Welsh inequality. The proofs combine orientation estimates with spanning-tree comparisons based on effective resistance and block elimination.

We prove the full termination of the minimal model program for klt pairs with big boundaries. We also prove the finiteness of marked Mori fiber spaces.

We introduce SWE-Game, a benchmark of 247 tasks grounded in 41 executable reference Godot games spanning 13 gameplay categories in 2D and 3D. Five task types cover development from a brief, implementation from a game design document, skeleton completion, repair of 83 injected-fault cases, and Godot-to-Unity porting. Reference materials specify the intended gameplay, while a shared instrumentation interface lets evaluator-owned drivers and probes execute actions and observe independently implemented games. Evaluation combines engine-state checks, certified reference-input replay, and agent-authored feature demonstrations to assess mechanic correctness, demonstrated playability, and behavioral restoration and preservation after repairs. Game-specific vision-language rubrics separately assess presentation. Across six models, Opus5 achieves the highest overall score in all five task types. Best overall scores remain below 60 out of 100 across the three construction tasks, with Brief-to-Game reaching 50.38. Analysis of reviewed submissions identifies requirement omissions and gameplay logic errors as predominant implementation problems. On human-labeled behaviors from 100 agent-built games, executable checks achieve 92.59% balanced accuracy, compared with 78.41% for a video-based VLM judge. Rubric-based visual scores reach a Spearman correlation of 0.829 with human ratings of 200 gameplay clips. Together, these results characterize current agent capabilities across game-development activities and support combining runtime evidence with visual assessment.

In this work, a globally stiffly accurate Implicit-Explicit (IMEX) Runge-Kutta scheme is developed and implemented in the GBS code [Ricci et al., Plasma Phys. Control. Fusion, 2012], for two-fluid plasma turbulence simulations. The stiffest phenomena, governed by shear Alfvén waves and parallel diffusion, are treated implicitly, while the remaining non-stiff terms are advanced explicitly. This splitting enables time steps well beyond the Courant-Friedrichs-Lewy limit, without incurring the full computational cost of a globally implicit formulation. To efficiently solve the implicit subsystem at each time step, a three-dimensional physics-based preconditioner, inspired by techniques developed in the magnetohydrodynamic (MHD) context, is used. The resulting framework is verified through the method of manufactured solutions and exhibits both algorithmic and parallel scalability. Significant advantages in numerical stability and computational efficiency are demonstrated with respect to an adaptive explicit Runge-Kutta scheme.

LLM agents increasingly take consequential actions through interactions with users, policies, and external tools. Auditing these agents requires automated attribution of realized actions to their historical basis. However, existing attribution formulations do not provide question-specific traces for diverse auditing objectives. Additionally, when access to the acting model is limited (e.g., in API-only deployments), applicable methods commonly rely on costly input perturbations or external LLM analysis of complete trajectories. We therefore formulate query-conditioned agent action attribution, a new task that takes a natural-language auditing query as input and recovers the source and ordered intermediate evidence for the query-specified aspect of an action. We instantiate this task with $A^3Bench$, a benchmark comprising 1,396 auditing queries across policy basis, parameter provenance, failure propagation, and unsafe-behavior tracing. To enable efficient, query-specific attribution, we use small open-weight models as attribution proposers that combine query-conditioned gradient saliency with query-semantic relevance to rank history units. Our proposer consistently achieves stronger source and evidence rankings at lower inference cost than open-weight baselines, improving source MRR by up to 40.9% and evidence MAP by 42.1% with only two forward passes and one backward pass. Controlled evaluations confirm that our proposer improves attribution specificity by adapting its rankings to fine-grained changes in the auditing query. Building on a proposer ensemble, our end-to-end system surpasses the strongest frontier-model baseline in source accuracy (64.5% vs.\ 60.4%) while reducing empirical deployment latency by 29.9% relative to the fastest frontier API baseline. Code and data will be released after the initial review period following final validation and cleanup.

Understanding why predictors can generalize despite interpolating noisy training data is a central puzzle in machine learning. Most work on such "benign overfitting" studies minimum-2-norm linear regression, reflecting the inductive bias of gradient descent. However, modern optimizers such as Adam and Muon use non-Euclidean update geometries, favoring solutions associated with other norms. Analyzing regression for non-Euclidean norms is substantially more difficult, with known results essentially limited to Gaussians. In this paper, we develop a method to analyze benign overfitting in linear regression for general norms and general (sub-Gaussian) distributions. As a special case, we prove that minimum-p-norm interpolation with p>1 can benignly overfit even for non-Gaussian distributions, under suitable conditions. Perhaps surprisingly, for the 1-norm, benign overfitting does not hold in general for well-behaved (but non-Gaussian) distributions, showing that existing positive 1-norm results rely crucially on Gaussianity. Our proof analyzes the geometry of the dual optimization problem, using concentration and central limit tools to show it is approximately Euclidean in many high-dimensional cases.

Graph neural networks (GNNs) are often called long-range because their architecture can connect distant nodes, but this does not show whether they use distant information correctly. We introduce a framework that measures how strongly inputs at each graph distance affect predictions and separates limitations due to architecture, finite approximation, training, and numerical execution. Our analysis shows that local message-passing can spread influence slowly, so a finite implementation may rely mainly on nearby inputs even when the ideal computation uses the whole graph. We also explain why mathematically equivalent filters can differ in how easily they are learned and how reliably they run. Across controlled tasks, models with similar architectural reach use distant information very differently, while low average error can hide failures on distant interactions. Together, these results show that long-range capability depends on learning to use information at the distances required by the task and preserving that use during computation.

All cosmological models are defined through energy and matter, which describe the evolution of the targeted Universe. Whether the content is simple or complex, it can be defined through an effective equation of state (EoS). We study different cosmological models by analyzing the properties of the complete EoS of their fluid contents. We obtained general expressions for the ratio between pressure $p$ and energy density $\rho$, and for their derivative $dp/d\rho$ in terms of deceleration and jerk parameters. We show that, in general, a cosmology whose energy density is constructed from multiple ideal gases cannot be described by the EoS of a single, ideal gas. This is directly related to a variation in the deceleration parameter during the evolution of the Universe. Furthermore, we studied the effective compressibility properties of the EoS, demonstrating that dark energy features of the fluid should be related to the negative compressibility of the contents. These features depend on the dynamics of the jerk parameter for each cosmological system, implying that the knowledge of dark energy evolution is encoded in the third-order derivatives of the scale factor. This approach to understanding the properties of cosmological models indicates that the accelerating evolution of some models, such as the lambda-cold dark matter model ($\Lambda$CDM) or the Chaplygin gas model, is due to the EoS of their nonideal content fluids rather than an associated anomalous (dark energy) nature. On the contrary, models such as $w$-cold dark matter ($w$CDM), $w_0$$w_a$-cold dark matter ($w_0$$w_a$CDM), or Dvali-Gabadadze-Porrati models, include by construction fluids with anomalous content, implying a negative compressibility and an effective dark energy behavior. Our work highlights the importance of treating all contents of the Universe as a nonideal fluid system, with a unique EoS.

Grounded language models are usually evaluated by adding relevant context, but multiturn dialogue also contains unsupported user claims that may contaminate later factual answers. We study post-pressure recoverability: whether a model returns to clean-context behavior after a user repeatedly advocates a wrong answer and then withdraws that pressure. We introduce a recovery-after-pressure protocol for multiple-choice factual dialogue and measure sycophancy hysteresis, the residual probability assigned to the user-advocated wrong answer relative to a clean-context counterfactual. Across seven instruction-tuned open-weight models and two factual benchmarks, ordinary reset often reduces but does not erase pressure-induced bias. History preserving repairs such as user retraction, system reset, and self-verification recover only 2-3/14 model-dataset pairs under the strict clean-restoration diagnostic, whereas operations that change the effective context are substantially more reliable; the two conditions that remove the pressure-bearing history entirely, fresh-context deletion and context truncation, recover 14/14. In an oracle trusted-evidence condition across fourteen model-dataset pairs, preserving the pressure-bearing history while adding benchmark-derived trusted evidence increases accuracy from 0.368 to 0.929, while wrong-answer following falls from 41.2% to 4.3%. Controls show that the effect is not explained by dialogue length, repeated confidence, plausible distractors, mere false-answer mention, or option-label inertia. These results suggest that faithful grounded dialogue requires evaluating which prior context should be treated as evidence and which should be removed or quarantined before answering.

When must a foundation-model safety gateway generate tokens, and when should it directly output a calibrated decision? We study calibrated standalone direct-decision foundation models for real-time pre-ingestion safety guardrails, jointly addressing probability calibration, dual-use false-positive control, and heterogeneous CPU-NPU routing under explicit latency SLOs. Pre-ingestion guardrails must screen prompts prior to target-LLM prefill with low false alarms on benign compliance inquiries; however, shallow classifiers are brittle to phrasing shifts, hidden-state probes require coupling to a target LLM, and generative guards incur high decoding latency and dual-use false positives. We present COGNIT-Guard, coupling a validation-calibrated CPU fast gatekeeper with confidence-gated escalation to an NPU-resident 322M bidirectional direct-decision model (Laya-322M) under an asymmetric false-positive penalty. On the clean unseen DUCS-Bench test split ($N=607$), COGNIT-Guard achieves 98.85% accuracy (McNemar $p = 1.19 \times 10^{-4}$ vs. ML), reduces benign FPR to 0.42% ($1/238$; Fisher's exact $p = 8.23 \times 10^{-4}$ vs. ML), and attains 1.12% ECE and 0.0104 Brier score. On Huawei Ascend 910C NPUs, pure NPU inference runs in 21.77 ms mean latency (45.90 QPS), while the live serial CPU-NPU cascade ($\theta^*_{\mathrm{deploy}}=0.70$) achieves 41.63 ms mean latency (P50: 39.47 ms, 99.23% accuracy, 0.00% FPR). Evaluation on SafetyBench-ZH ($N=2,100$) and comparison against a bi-encoder direct-decision baseline (CLM-8B) disentangle in-domain gains, OOD alignment tax (60.33% $\to$ 56.81% on Laya; 55.10% on domain CLM-8B), and experience replay recovery, restoring OOD accuracy to 64.10%-65.05% and reaching 99.67%-99.84% in-domain accuracy with 0.00%-0.42% FPR.

Text-to-SQL systems are typically trained and evaluated on a single dialect (SQLite), yet production deployments span PostgreSQL, MySQL, ClickHouse, and beyond. We show that this single-dialect assumption leads to a substantial drop in cross-dialect accuracy for every model we tested. The drop persists across scale, architecture, and even purpose-built text-to-SQL systems. We argue that the fix is to change the generation target: instead of asking an LLM to emit dialect-specific SQL, we have it emit a dialect-agnostic relational algebra query plan, which a deterministic compiler then renders into SQL for any supported backend. Across thirteen models from 3B to frontier scale, this restores cross-dialect portability nearly uniformly, at a small cost in peak accuracy on the model's home dialect for capable prompted models and none once fine-tuned on plans; under matched fine-tuning, plan supervision yields a stronger model than SQL supervision. We also introduce MetricName, a question-aware result-set comparator needed to evaluate fairly across dialects, where existing metrics confound semantic errors with benign cross-dialect variation. More broadly, the result is a reminder that a generation target chosen for execution is not necessarily the one that maximizes generation quality.

Residual policy adaptation provides a lightweight way to modify a strong reference policy, but a shared scale and a fixed subgroup partition can hide heterogeneous degradation and become fragile when the deployment mixture of information states changes. We introduce RSD-Poker, a structure-adaptive and shift-robust certification framework that freezes a bank of residual families and scales, learns a policy-visible partition on an independent structure split, and freezes that partition before calibration labels are joined. Each candidate-group pair receives a weighted simultaneous upper certificate for anchor-relative risk and a lower certificate for weak-response utility. A robust group-to-candidate map is then selected over a predeclared uncertainty set of deployment group proportions. Under independent calibration units drawn from each frozen group's law, a candidate bank and partition fixed before calibration, and invariant within-group conditionals, the selected map satisfies its declared mixture-robust risk budget and utility certificate with probability at least $1-\zeta_{risk}-\zeta_{util}$. The information contract supports both a teacher-backed transform and a teacher-free observation-only student. The retained deterministic 24-state audit remains an exact replay diagnostic: empirical-zero selects $\alpha=0.08$, raising the weak-response proxy from 4.2082 to 4.2889 with $0/12$ held-out threshold crossings. On stratified held-out states, the learned-partition dual selector raises weak utility from 4.4074 under global dual certification to 4.4936 and lowers held-out violation from 0.0215 to 0.0078; its mixture-robust variant reaches violation 0.0059. Across five observation-only checkpoints, risk-calibrated residuals attain weak utility $4.3659\pm0.0177$ and violation rate $0.0178\pm0.0057$.

Pseudo-labeling has become a cornerstone of learning from unlabeled data in semantic segmentation. Yet its effectiveness drops sharply in real-world scenarios where strong imaging noise and long-tailed class distributions occur together. We trace this failure to a vicious cycle of pseudo-label degradation. Imaging noise entangles foreground and background features, lowering prediction confidence across all classes, while long-tailed distributions leave tail classes with far fewer training samples and inherently lower confidence. Under fixed high-threshold filtering, these tail-class predictions are systematically filtered out, so they receive no supervision from unlabeled data and thus features keep degrading in subsequent iterations. Critically, noise and long-tail are not independent obstacles but mutually amplifying ones, and addressing either alone is insufficient. To break this cycle, we propose FTC-Seg, a Feature-Threshold dual-Calibration framework built on a standard teacher-student framework. At the feature level, Orthogonal Prototype Reconstruction (OPR) uses a set of learnable orthogonal prototypes to residually purify pixel-wise features, widening the margin between weak foreground targets and noisy backgrounds. At the threshold level, Adaptive Threshold Calibration (ATC) dynamically adjusts class-specific thresholds based on learning difficulty and prediction-distribution bias, rescuing low-confidence pseudo-labels of tail classes from systematic exclusion. Extensive experiments on four public benchmarks spanning three distinct noise modalities show that FTC-Seg achieves strong performance against state-of-the-art methods, with particularly substantial gains on tail classes. Our results establish that jointly calibrating features and thresholds is essential for robust pseudo-labeling under compounded noise and class imbalance.

Attributing and controlling model behavior during training requires identifying each example's contribution quickly enough to act before the next update. However, examples in the same training batch can produce similar behavioral changes, making their individual contributions difficult to distinguish. We address this ambiguity through mutual information, accounting for interference within the batch by quantifying how much the combined behavioral change reveals about each example's contribution. We show that this mutual information is a logarithmic function of Behavioral Gradient Uniqueness (BGU). BGU gives the information measure its geometric interpretation. Our Batch-Space Ghost (BS-Ghost) algorithm makes these scores practical inside the training loop through shared computation in batch space, without storing model-sized example gradients. On a complete 1,000-example Qwen2.5-7B-Instruct workload, our BS-Ghost implementation adds 27 seconds (8.0%) to 5.5 minutes of ordinary training. Removal and retraining demonstrate that BGU identifies data that causally shapes final behavior. At each training step, signed information identifies which examples strengthen or weaken the target behavior, explaining how behavior develops during training. Signed information also enables cheap intervention during training: it predicts how changing example weights will affect behavior in the next update. We then use these predictions to choose weights that steer behavior toward a desired target. This makes our framework a practical foundation for scalable oversight and verification of training pipelines and processes, helping evaluators assess model alignment, understand how it develops during training, and guide interventions that shape ongoing learning.

Human communication on the internet is shaped by diverse perspectives, most visibly expressed in online comment spaces. As large language model (LLM)based AI agents begin to inhabit these spaces, a key question arises: whether synthetic comment threads can capture the diversity inherent in human discourse. This concern is increasingly important, as the growing presence of homogenized AI-generated content risks reducing diversity over time, potentially leading to model collapse and degrading the richness of digital communication. Inspired by the plurality of human crowds and the aspect-driven nature of discourse, we hypothesize that comment diversity is better approximated by combining multiple LLMs with aspect-conditioned generation. We formalize and evaluate this approach using models from different providers and introduce a framework that characterizes diversity across semantic, linguistic, and socio-pragmatic features along three axes: dispersion, coverage, and alignment. Using this framework, we conduct a large-scale study on over 2 million YouTube comments across multiple domains. Our results reveal that multi-LLM and aspect-conditioned generation better align with human comment distributions and such data remains viable under pretraining style curation and is effective for downstream tasks. Yet, human diversity remains unmatched. Overall, our findings provide a practical foundation for generating more diverse and socially grounded discourse in AI-mediated environments.

Automatically generated environments provide a scalable source of interaction data for training general agents. However, existing approaches mainly generate tasks within a single environment, while real-world workflows require agents to connect information and actions across multiple services. We introduce Compositional Environment Scaling (CompoWorld), which expands the task space by composing a finite library of reusable services. Coding agents turn tool specifications into verified services with typed states and shared interfaces, while a world model handles tools that cannot be reliably implemented. A random-walk procedure connects services through dependency graphs, enabling the generation and verification of tasks that require information to flow across services. Verified trajectories support supervised fine-tuning (SFT), while our Completion-Focused Rubric Reward guides reinforcement learning (RL) toward full task completion by emphasizing criteria with lower pass rates within each rollout group. We construct 448 services exposing 10,130 tools and use 3K SFT trajectories and 1K RL tasks to train Qwen3.6-35B-A3B. Experimental results show that CompoWorld improves on its backbone by 9.17 points on average across eight benchmarks. On AutomationBench, it surpasses frontier models such as Claude Opus 4.6 and leads all compared agent-specialized 35B-A3B models.

Historically, statistical analysis of offensive lineman has been hindered by the lack of easily measurable quantities. More recently, with the introduction of player tracking data new methodological advances are now possible. Using high-dimensional spatio-temporal data, we adapt the defensive-matchup hidden Markov model of \cite{franks2015characterizing} from basketball to football pass protection, producing frame-by-frame probabilistic assignments of each pass blocker to the rushers. We show how this probabilistic assignment is a usable modeling artifact that augments existing player-evaluation frameworks. We directly quantify the attention a rusher commands, upgrade adjusted plus-minus \citep{Macdonald+2012} from all-or-nothing stints to partial, continuous blocking credit in continuous time, yield block-shedding survival metrics, and measure the space a rusher generates for his teammates. Fit to the first eight weeks of the 2021 NFL season, the resulting metrics recover widely-recognized elite rushers and pass protectors and align with independent charting.

Discovering underlying symmetries from data has emerged as a crucial challenge in scientific discovery. Existing data-driven methods for symmetry discovery fail to determine the exact number and mathematical form of unknown infinitesimal generators. Recent explicit methods represent generators using a predefined function library and identify them through algebraic optimization, but they often struggle to capture complex symmetries involving high-order polynomials or transcendental functions. To address this limitation, we formulate symmetry discovery as a joint optimization problem over the function library and coefficients. We propose a novel framework that leverages an encoder-decoder architecture to dynamically generate symbolic expressions and expand the library. This generation process is optimized via reinforcement learning, which accelerates the exploration of the symbolic search space through step-wise rewards. Experiments demonstrate that LieDiscover can successfully uncover open-form infinitesimal generators involving high-order polynomials or transcendental functions, which remain intractable for existing methods. The discovered symmetries also improve performance in downstream PDE solving and discovery tasks.

Imperfect verifiers can assign a harmful update direction even when clipping and regularization bound its magnitude. We introduce Audit-First VAPO, which separates discrete directional admission from continuous magnitude control. An observation-only accept-appeal-abstain policy uses a finite secondary-verification budget; its action trace is frozen before clean labels are joined. Simultaneous finite-sample bounds then certify selected harmful risk, coverage, and verifier-call rate over a predeclared policy family. Conditional Hoeffding-Azuma bounds account for the dependence induced by shared budgets, and rollout or verifier changes initiate a new certification stage. After admission, a bounded trust-clip-KL actuator controls magnitude. We evaluate two models on two reasoning benchmarks against static RLVR, matched-random selection, confidence thresholding, noise correction, and verifier augmentation. On Qwen3.5-0.8B and GSM8K at target risk $\rho=0.08$, RC-VAPO achieves 74.1% accuracy, selected harmful risk 0.0697, coverage 0.4125, and relative verifier cost $1.16\times$. At matched coverage and update magnitude, its selected-risk difference from matched random is -0.0260 with paired 95% interval $[-0.0364,-0.0157]$. Across asymmetric, confidence-dependent, and correlated-verifier noise, the certificate is satisfied on 57 of 60 independent runs. These comparisons isolate informative directional selection from proposal suppression, update shrinkage, and additional verifier computation.

We study linearized perturbations of the subextremal Kerr-Newman black hole solution of the Einstein-Maxwell equations. We show how to overcome what Chandrasekhar called the "apparent indissolubility of the coupling between the spin-1 and spin-2 fields" by using a matrix integrating factor for suitably transformed first-order systems that describe the radiative degrees of freedom. For the radial ODEs obtained after angular separation, we prove mode stability on the real axis, i.e., the absence of quasinormal modes with real frequencies, using a Whiting-type transform.

Spectral zeta functions provide a standard tool for regularizing determinants of differential operators in quantum physics. In a previous paper (J. Math. Phys. 66: 083505, 2025), we introduced a $p$-adic spectral zeta function for discrete spectra via a locally analytic interpolation function. In this paper we extend the framework to continuous spectra using the inverse Stieltjes transform. Starting from the resolvent of a bounded operator, we construct a generalized distribution, called the $p$-adic spectral distribution, and define bosonic and fermionic zeta functions and functional determinants. We establish their analytic properties, special value formulas, and Stirling expansions, and show that our previous framework is embedded into the present one in the discrete case. In this approach, the bosonic and fermionic cases exhibit an interesting symmetry. As an application, we consider the position operator in $p$-adic quantum mechanics on an arbitrary compact subset of $\mathbb{C}_{p}$.

Multimodal large language models can expose task-relevant evidence through generation, but producing useful evidence does not by itself determine how it enters a retrieval embedding. We study whether the semantic organization of that evidence can also specify where representations are read. To address this question, we introduce EviAlign, which couples Semantic Evidence Generation with Boundary Readout in a shared multimodal large language model. It organizes evidence into five semantic units, reads the contextualized state at each unit boundary, and aggregates these states into a single normalized embedding. Generation and contrastive retrieval objectives jointly train this shared structure. With the same trailing readout, semantic evidence and free-form CoT yield nearly identical retrieval performance, suggesting that evidence organization alone does not explain the full gain. A controlled $2\times3$ study compares consistent and permuted evidence organization across three readout strategies, using training targets with matched evidence spans. With five readout states and the same mean pooling, the advantage of consistent semantic organization grows from 0.65 points at length-based training positions to 2.39 at evidence boundaries, yielding a 1.74-point co-design interaction. Across 12 MMEB retrieval tasks, EviAlign achieves 76.9 average Recall@1 with 500K training pairs while retaining single-vector indexing and scoring.

Safety alignment for large language models (LLMs) in conversational settings is largely framed around whether to answer or refuse a request. In agentic settings, however, the same models must decide whether to act as permission-critical evidence emerges during execution. This creates a distinct challenge: apparent risk, action permissibility, and task competence are easily confounded, making agentic over-refusal difficult to distinguish from ordinary task failure. To address this, we introduce AgentBound, the first four-way counterfactual generation-and-evaluation framework for tool-using agent safety. AgentBound transforms the same executable workflow by independently varying apparent risk and action permissibility, enabling controlled comparisons of risky-looking but authorized tasks and routine-looking but unauthorized tasks. These comparisons jointly diagnose over-refusal and unsafe compliance while controlling for task competence. We instantiate AgentBound as a human-validated 4,000-task evaluation suite with trajectory-based and post-state-based judgments. Across 17 model and harness configurations, high safety frequently coexists with poor authorized-task completion: GPT-5.5 blocks 99.5% of routine-looking unauthorized actions yet completes only 28.7% of risky-looking authorized tasks. We further train a lightweight runtime calibration module that improves authorized-task completion by 18.2% on average across 10 evaluated configurations, while improving unsafe-action blocking by 5.4% on average. These show that effective agentic alignment requires action decisions to track permission-relevant execution evidence, rather than refusal strength alone.

Despite its low cosmic abundance, phosphorus is a bioessential element whose prebiotic availability and incorporation into biomolecules remain open questions. Only a few phosphorous containing molecules with P to C bonds have been detected in astronomical environments (CP, CCP, HCP). More complex species have been proposed, but their formation and destruction pathways remain poorly constrained. Gas-phase ion molecule chemistry involving P cations may contribute to organophosphorus formation, particularly in protostellar shocks and outflows, while reactions of ground state P cations with closed-shell neutrals provide benchmarks for spin-forbidden mechanisms. We investigate the reaction of P+ with C$_2$H$_2$ through a joint experimental and theoretical study aimed at revising astrochemical database rate coefficients. Absolute cross sections and branching ratios were measured as a function of collision energy and complemented by high-level electronic structure calculations and a refined capture model accounting for higher-order long-range interactions and intermediate complex formation. Channel-specific rate coefficients were derived in the range from 10 to 5000 K. The reaction produces predominantly HCCP$^+$ + H (branching ratio 99%), while CCP$^+$ + H$_2$ is a minor channel (branching ratio 1%) arising from intersystem crossing from the triplet to the singlet potential energy surfaces. The total rate coefficient at 300 K agrees well with the SIFT value, but it increases with decreasing temperature, deviating from a pure Langevin trend. The reaction should be included in astrochemical models where phosphorus is released as P+, such as during energetic processing of icy grains in shocks. It provides a pathway to linear HCCP$^+$, a potentially relevant precursor to the observed CP and CCP species through dissociative recombination