Modern vehicles are increasingly vulnerable to attacks that exploit network infrastructures, particularly the Controller Area Network (CAN) networks. To effectively counter such threats using contemporary tools like Intrusion Detection Systems (IDSs) based on data analysis and classification, large datasets of CAN messages become imperative. This paper delves into the feasibility of generating synthetic datasets by harnessing the modeling capabilities of simulation frameworks such as Simulink coupled with a robust representation of attack models to present CARACAS, a vehicular model, including component control via CAN messages and attack injection capabilities. CARACAS showcases the efficacy of this methodology, including a Battery Electric Vehicle (BEV) model, and focuses on attacks targeting torque control in two distinct scenarios.

Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most proofs, particularly those written by AI systems, have neither property, and translating them into formal languages remains challenging in many frontier math settings. We propose Pseudo-Formalization (PF), a proof format that captures the modularity and precision of formal proofs while retaining the flexibility of natural language. A Pseudo-Formal proof is decomposed into self-contained modules, each stating its premises, conclusion, and proof in natural language. To verify the correctness of a regular natural language proof, an LLM translates it to Pseudo-Formal and then verifies each module independently, an algorithm we call Block Verification (BV). We evaluate PF+BV on two benchmarks spanning olympiad and research-level mathematics, where it pareto-dominates LLM-as-judge baselines on error-finding precision and recall. To support future work, we release our research-level proof verification benchmark ArxivMathGradingBench.

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

Test-time scaling has emerged as a promising approach for improving code generation by exploring large solution spaces at inference time. However, existing methods often rely on public test cases that are unavailable in practice, or require extensive LLM inference for candidate selection, leading to significant token consumption and time overhead. We present DiffCodeGen, a novel test-time scaling method for code generation based on coverage-guided differential analysis. DiffCodeGen generates diverse code candidates using various sampling and prompting strategies, then applies coverage-guided fuzzing to synthesize inputs without requiring any existing tests or large language models. By executing all candidates on these inputs, DiffCodeGen captures their dynamic behavior and clusters candidates based on behavioral similarity. DiffCodeGen selects the medoid of the largest cluster as the final output. Unlike prior test-time scaling methods that invoke additional LLM inference for candidate selection, DiffCodeGen performs selection without any extra model calls, incurring little to no additional token consumption. DiffCodeGen is fully asynchronous, naturally suited to the current trend of agentic coding, and is thus efficient and highly scalable. We evaluate DiffCodeGen across 4 large language models, demonstrating consistent improvements over baselines. Compared to state-of-the-art test-time scaling methods, DiffCodeGen achieves competitive or superior performance while using only a fraction of time and tokens. DiffCodeGen is model-agnostic and can be combined with reasoning models to further boost performance.

Agentic AI coding systems can inspect repositories, plan implementation steps, edit files, call tools, run tests, and submit pull requests. These capabilities make software and hardware development faster in some settings, but current evidence does not support the simple claim that autonomous code generation automatically improves engineering outcomes. Controlled studies report productivity gains in some enterprise tasks, slowdowns in mature open-source work, moderate but heterogeneous meta-analytic effects, and persistent failures in repository setup, dependency handling, permission gating, and hardware verification. This paper argues that the central problem is no longer prompt engineering; it is engineering process control. It synthesizes evidence from agentic software engineering, GitHub-scale adoption studies, repository-level agent configuration, productivity trials, issue-resolution benchmarks, and hardware/RTL verification research. It proposes Agentic Agile-V, a process framework that uses Agile-V as the lifecycle backbone and a task-level SCOPE-V loop - Specify, Constrain, Orchestrate, Prove, Evolve, and Verify - to convert conversational intent into structured engineering artifacts and acceptance evidence. The paper contributes: (i) a taxonomy of minimum input artifacts for agentic software, firmware, and hardware work; (ii) a conversation-to-contract gate that separates exploratory dialogue from implementation; (iii) risk-adaptive feature, bug-fix, testing, and hardware workflows; and (iv) an evidence-bundle acceptance model for agent-generated artifacts. The paper concludes that agentic AI does not eliminate engineering discipline; it increases the value of requirements, constraints, traceability, independent verification, and human approval.

Generative AI systems are increasingly deployed as interactive agents in online environments, such as a social network called Moltbook. In Moltbook, large-scale agentic AIs can post, comment, and engage in activities generated at scale by AI-driven text. Yet these agent behavioral characteristics remain insufficiently understood, particularly in complex, multi-agent interaction. In this study, we analyze the emotional dynamics of agent interactions within Moltbook. We construct an emotion-aware framework that maps textual interactions to a predefined set of fine-grained emotional categories, enabling the extraction of structured emotion profiles across agents and interaction contexts. To further evaluate behavioral reliability, we introduce an emotion-based domain called Persona-Stimulus-Reaction (PSR) that captures the alignment of emotional responses across similar contexts. Our analysis shows distinct emotional patterns and varying levels of behavioral stability across agents. Our analysis reveals that agents exhibit distinct emotional signatures with varying levels of behavioral stability influenced by interaction context.

Make America Healthy Again (MAHA) is a national health movement that encompasses a striking mix of beliefs, from broadly accepted concerns about good diet and exercise to controversial takes on organic and genetically modified food, childhood vaccination, science, and institutions. Various influencers and promoters of the MAHA movement on social media are scattered throughout the online space. Investigating the structure, discourse, and contagion of MAHA beliefs requires large-scale fine-grained digital footprints. Constructing structured data covering different MAHA themes from vast unstructured social media data is challenging. We introduce a Reddit dataset that spans six years (2020-2025), comprising 19.4M posts from 4M users. Containing the natural and thematic context of 12 MAHA-aligned beliefs, this dataset offers researchers from various domains the opportunity to study the dynamics of the MAHA movement, its structural and functional components, and the linguistic and behavioral patterns of its proponents.

We study the contradiction graphs associated with binary concept classes. For a class $H \subseteq \{0,1\}^X$, the order-$m$ contradiction graph $G_m(H)$ has as vertices the $H$-realizable labeled sequences of length $m$, with two vertices adjacent when the two sequences assign opposite labels to some common domain point. Our main result is that the single graph $G_m(H)$ determines the threshold predicate $\mathrm{VCdim}(H)\ge m$. Consequently, the full sequence $(G_m(H))_{m \ge 1}$ determines the exact VC dimension and, in particular, detects finite versus infinite VC dimension, answering a question posed by Alon et al. (2024).

Missing significant amounts of school during K-12 education is known to put students' cognitive and social development at risk. Alternatives such as home instruction and online learning are common, but lack sufficient interaction with peers and teachers in the classroom. Mobile remote presence systems, or telepresence robots, are promising for homebound students because they provide embodiment and mobility in addition to the real-time participation offered by video conferencing technologies. Research is needed, however, for telepresence robots to meet the complex needs of homebound students participating remotely in the K-12 classroom context. We present findings from four multi-week deployments with homebound K-12 students attending classes via telepresence robots. The homebound students' experiences were documented in a total of 15 interviews and analyzed qualitatively as case studies. The homebound student participants and their deployment contexts differed from one another along multiple dimensions, and while some benefits of mobile remote attendance were enjoyed by all participants, each participant also experienced unique benefits. Some challenges with hearing, seeing, and moving the robot around the classroom warranted improvements to the design of the telepresence system. Other challenges suggested priorities for managing a classroom deployment, such as ensuring that the remote student is included in classroom activities, accountable to the teacher, and treated with respect by classmates. Based on insights from the study, we make recommendations for real-world deployment procedures in similar contexts.

Class imbalance is a fundamental challenge in medical image segmentation, where frequent classes typically dominate training at the expense of rare classes. Loss-based approaches mitigate imbalance by reweighting the per-pixel loss within the batch, while sampling strategies control which images enter the batch. Yet neither explicitly controls which classes appear within the batch, leaving rare-class exposure only partially rebalanced. In this work, we adopt episodic sampling from few-shot learning to promote class-balanced batch construction in a fully supervised setting. We decouple episodic sampling from its conventional metric-learning context and evaluate it in body composition segmentation in CT. We compare episodic sampling against random and weighted sampling on nine muscle and adipose tissues, derived from 210 scans of the public SAROS dataset. Training is performed under full- and low-data regimes, with additional comparisons under matched training iteration budgets. Under full-data training, all three strategies performed comparably (mean Dice 0.882 for episodic, 0.878 for random and weighted). Under low-data training, episodic sampling outperformed random and weighted (0.787 vs. 0.758 and 0.762), driven by a 12-fold difference in training iterations. Under matched training budgets, random and weighted overfit earlier, while episodic improved for approximately three times more iterations before plateauing. Our findings identify the training iteration budget as under-recognized confound in sampling strategies, motivating iteration-aware evaluation protocols for small datasets. Furthermore, the residual advantage of episodic sampling is consistent with an implicit regularization effect of class-balanced batches, offering a low-cost, model-agnostic strategy for class-imbalanced medical image segmentation. Code is available at https://github.com/iasonsky/episodic-sampling.

Infrastructure deterioration poses significant challenges for asset management, yet existing approaches rely on population-averaged models that overlook equipment-specific heterogeneity. We present a novel framework that combines Bayesian hierarchical hazard modeling with causal discovery to identify operational patterns that drive heterogeneous deterioration rates in pump equipment. Our approach first estimates pump-specific random effects $u_i$ using GPU-accelerated No-U-Turn Sampling (NUTS), achieving 3--5$\times$ speedup over CPU implementations. We then employ DirectLiNGAM to discover causal relationships between 22 engineered time-series features and deterioration rates, stratified by positive ($u_i > 0$, faster deterioration) versus negative ($u_i \leq 0$, slower deterioration) random effects. Analyzing 112 pumps with 92,861 observations over 650 days, we uncover striking heterogeneity: the negative group exhibits causal effects 400$\times$ larger than the positive group, with standard deviation (std) showing a strong positive causal effect ($+1.515$) on deterioration rates in low-risk equipment. We validate linearity assumptions through NonlinearLiNGAM comparison and demonstrate practical scalability through GPU acceleration. Our findings enable targeted maintenance strategies by revealing that different operational regimes require fundamentally distinct management approaches, advancing predictive maintenance from population-averaged to heterogeneity-aware decision making.

Traditional anomaly detection marks events when measured signals cross predefined thresholds. This captures the moment of transition but not the structural pressure that precedes it. We propose treating large behavioral populations as geometric energy landscapes whose deformation can be measured before and during major transitions. The central thesis is that structure precedes geometry: the structural organization of the population is the signal, and geometric metrics are instruments for measuring it. Applied to the Tor anonymity network across 67 consecutive daily observation windows, the dual-observer pipeline identifies a stable nine-dimensional load-bearing subspace invariant across the observation period and validates this structure by Monte Carlo simulation at 16.8 sigma above the noise floor. Primary detection gates achieve 0.0% false positive rate on 24 confirmed stable windows. Forensic analysis of the February 20, 2026 confirmed infrastructure event formally falsifies the relay-departure hypothesis, identifying connectivity degradation without topology change as a detectable network failure mode. The result is a candidate structural-monitoring framework for behavioral populations with sufficient telemetry.

The I-Ching is one of the most influential texts in Chinese intellectual history, integrating divination, cosmology, and ethical reflection. While Western experimental music, most notably John Cage, has drawn on the I-Ching as a source of chance operation, such appropriations have often detached its formal mechanisms from the interpretive and philosophical processes that give the text meaning. This work, Music of Changing Lines, presents an interactive system that re-centers the I-Ching as a meaning-bearing framework rather than a neutral randomizer. Users perform Wen Wang Fa coin casting, which is accompanied in real time through probabilistic musical processes. The resulting hexagrams and changing lines are interpreted by a large language model, Gemini, in relation to the user's inquiry. This textual interpretation is then translated into a prompt for a generative music model, Lyria, producing a responsive musical realization. By situating AI as an interpretive intermediary rather than a compositional authority, the system foregrounds the I-Ching's ritual, interpretation, and participation as the primary sonic materials. Music of Changing Lines extends process-driven traditions in computer music by demonstrating how generative AI can support participatory, meaning-driven musical processes without prescribing musical structure or replacing human agency.

Organizations that scan documents for sensitive information face a practical problem. Cloud services require data to be sent to external infrastructure, while rule-based tools often miss threats that depend on context. This study presents TorchSight, an open-source local system for security document classification built around a fine-tuned Qwen 3.5 27B model. The model was trained on 78,358 samples from 13 permissively licensed sources and GPT-4 synthetic data covering seven security categories and 51 subcategories. In the main evaluation on 1,000 documents, the model reached 95.0% category-level accuracy (95% confidence interval: 93.5-96.2). The tested commercial models scored 75.4-79.9% under the same prompting protocol. On a separate external set of 500 held-out samples, the model reached 93.8% accuracy, which suggests that performance extends beyond the main benchmark, although the margin depends on dataset composition and difficult boundary cases. The results show that a fine-tuned local model can support accurate security document classification while keeping document processing under local control.

Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing out the latent variables. For LGMs with a non-Gaussian likelihood, exact marginalization is not possible and a popular approach is to do approximate marginalization with an integrated Laplace approximation (ILA). Using ILA produces an approximate posterior which, in some settings, can differ significantly from the correct posterior, which impacts downstream applications. We propose an importance sampling scheme to correct the error introduced by ILA. By increasing the number of samples in importance sampling, the posterior with ILA converges to the correct posterior. This idea is realized with various techniques, including pseudo-marginalization, quasi-Monte Carlo and randomized quasi-Monte Carlo. We implement our methods in an automatic differentiation framework to support gradient-based algorithms when doing inference on the hyperparameters. For the latter, we specifically consider the use of Hamiltonian Monte Carlo. We demonstrate the benefits of reduced error in various applied models.

Optimization problems such as the NP-complete 3-SAT provide an important benchmark for the difficult task of finding ground-states in strongly correlated many-body systems with rugged energy landscapes. The study of random 3-SAT problems as Ising spin Hamiltonians in statistical physics has yielded major insights including the existence of a satisfiability phase transition, and the prediction of a critical parameter line of particularly hard instances. Yet, progress on solving those instances has been scarce for several decades. Here, introducing the Target-SAT (TSAT) algorithm, we roughly triple the tractable problem sizes in the hardest regime, with an even greater improvement in a vast range of neighboring regions. By leveraging statistical information hidden in the combinatorial constraints of the problem, TSAT is actively guided in its stochastic local search toward a target within the relevant parameter space. Our analysis also explains why established local search algorithms are limited to relatively small system sizes due to a vast low-energy trap. Furthermore, we characterize the aforementioned critical line in terms of a dominant additional complexity barrier, whose exponential scaling is quickly overcome by TSAT only in the surrounding parameter space. With TSAT, the lead in solving the hardest known random satisfiability problems returns to the realm of stochastic local search algorithms.

We develop a representability-aware and interpolable neural network (NN) framework for predicting two-particle reduced density matrices (2-RDMs). The NN incorporates a subset of representability conditions through its architecture and loss function, and can operate on different momentum meshes, enabling evaluating the representability conditions across multiple meshes, which we call interpolated representability condition. The framework can be used either to predict 2-RDMs on large momentum meshes by interpolating exact results from small meshes, or as a variational 2-RDM ansatz optimized by energy minimization on arbitrary meshes. We apply this approach to the fractional Chern insulator in the one-band projected model of twisted bilayer MoTe$_2$ at twist angle $3.89^\circ$ and hole filling $2/3$. Trained on exact-diagonalization (ED) 2-RDMs from meshes with $12$ or $18$ momentum points using six different NN architectures, the best NN is the residual multilayer perceptron, which predicts the $6\times6$ 2-RDM with $97.07\%-98.18\%$ accuracy relative to the ED 2-RDM but predicts an energy $77.353$ meV above ED ground-state energy. We then variationally optimize the NN on several meshes including $6\times6$, predicting a $6\times 6$ energy of just $0.104$ meV below ED while maintaining $98.94\%-98.96\%$ accuracy. Compared with the conventional boundary-point semidefinite programming, which gives an energy $5.560$ meV below ED with $96.40\%-98.94\%$ accuracy, the NN achieves a more accurate energy and similar accuracy while using only less than 1/20 as many parameters. Eventually, we add a symmetric mesh of $48$ momentum points to the variational optimization of the NN, and provide a prediction of the many-body ground-state energy and the many-body quantum metric on that mesh.

Recent generative video models achieve impressive visual quality but remain constrained by limited physical consistency and controllability. Existing video generation methods provide minimal physical control, and single-image-to-3D conversion approaches often suffer from object interpenetration. Furthermore, physics-based scene-level 3D generation methods exhibit spatial misalignment, stylized artifacts, and inconsistencies with the input data, restricting their use in realistic interactive video synthesis. We propose TelePhysics, a training-free framework that converts a single image into a physically consistent and controllable video through holistic scene-level 3D reconstruction. By representing the full scene geometry in a unified spatial coordinate system, TelePhysics resolves object penetration and alignment ambiguity. Unlike prior methods, this formulation enables accurate scenelevel multi-object interactions and introduces richer, complex control types for advanced mechanicsbased manipulation. By decoupling simulation from rendering, TelePhysics bypasses latency-heavy priors, achieving real-time physical interaction previews paired while preserving photorealistic visual fidelity. Experimental results demonstrate that TelePhysics substantially outperforms prior methods in physical fidelity, spatial coherence, and controllability. The open-source code is available at https://github.com/xinzhang007/TelePhysics.

Recent work has demonstrated the potential of contrastive steering for jailbreaking Large Language Models (LLMs). However, existing methods rely on limited and inherently biased contrastive prompts and require laborious manual tuning of steering strength, limiting their robustness and effectiveness. In this paper, we leverage the idea of model extraction to guide the learned steering vectors to approximate the ideal one and propose tuning the steering strength adaptively based on contrastive activations' statistics. Experiments demonstrate that our method notably improves the effectiveness and robustness of probe-based steering, without any extra contrastive prompts or laborious manual tuning. Being an attack paper, this paper focuses on revealing the breakdown of fortified LLMs, raising the average harmfulness score from 6\% to 70\%. Our code is available at https://github.com/fhdnskfbeuv/adaptiveSteering.

We develop a unified microeconomic and monetary theory of artificial intelligence inference costs and their pass-through to inflation, welfare, and optimal monetary policy. We introduce the Inference-Cost Phillips Curve (ICPC), an augmented New Keynesian Phillips curve in which firm-level marginal costs of producing differentiated goods include a non-trivial AI inference component lambda-bar, and prove a closed-form structural slope kappa*_inf = lambda-bar * kappa, where kappa is the standard Calvo-Yun slope. We derive a welfare-relevant Hicks-Kaldor decomposition of consumer welfare under inference-cost shocks, prove a generalized Taylor principle for the inference-augmented economy, and characterize the optimal monetary policy response coefficient psi*_inf = (1 + phi*rho) * lambda-bar * kappa under commitment. A second-order welfare loss formula closes the model in closed form. We confront the theory with U.S. monthly data 2022:M01-2026:M04 using a two-step GMM estimator with Newey-West HAC standard errors and Hansen J-test, recovering an empirical slope kappa-hat_inf = 0.087 (HAC s.e. 0.021) which lies within one standard error of the structural prediction. A scaling regression over 50 rolling-window subwindows yields b-hat = 0.987 (R^2 = 0.998), consistent with a near-unit-elasticity pass-through. A G7 reduced-form panel with Driscoll-Kraay HAC standard errors yields b-hat^G7 = 0.094 (s.e. 0.026), and a Wald test fails to reject cross-country homogeneity (p = 0.78). The framework provides a single equilibrium scaffold for the joint study of AI inference cost dynamics, monetary policy under generative-AI shocks, and the welfare cost of inference-driven inflation.

Generative artificial intelligence is rapidly transforming the supply side of training data: an increasing share of new tokens, images, and structured records is produced by previous-generation models rather than by human originators. Recursive training on such synthetic content induces a measurable and often irreversible loss of distributional fidelity, a phenomenon known as model collapse. We develop the first unified microeconomic theory of synthetic data markets under model collapse. We introduce the Synthetic Data Contamination Equilibrium (SDCE), prove existence and generic uniqueness, derive a welfare decomposition W = W_prod + W_cons - L_coll - L_info, establish a Wasserstein-gradient-flow mean-field collapse limit, prove an impossibility of information-constrained implementation, and obtain closed-form expressions for the welfare-maximizing provenance subsidy s* = KL(q||p)/(2 kappa) and the welfare-maximizing watermark strength w* = (1 - psi) KL(q||p)/(2 kappa psi). We prove an information-theoretic Cramer-Rao lower bound on any provenance estimator using only producer-side observations and show that the Provenance-Market Iterative Retraining (PMIR) algorithm attains this bound up to constants while converging to an epsilon-SDCE in O(epsilon^-2 log T) iterations. A reduced-form OLS estimation on a C4-synthetic benchmark over ten retraining generations yields a collapse-rate coefficient b-hat = 0.181 (HAC s.e. 0.024), within one standard error of the structural prediction 0.183. Calibrated experiments raise generation-ten model quality by 23.1 percent over the unregulated benchmark while lowering the 2-Wasserstein drift on a held-out diversity probe from 0.318 to 0.142. Scaling experiments over generations t in {1,...,10} recover a logarithmic-in-t collapse law log Q_t = log Q_0 - 0.183 t rho^2 with R^2 = 0.962.

Hexahedral meshes are widely used in simulation pipelines, yet automatic generation remains challenging for complex CAD geometries. Polycube-based hexahedral meshing is a representative approach due to its regular, parameterization-friendly structure, but existing polycube construction methods often rely on intricate surface segmentation and local heuristics, which can produce artifacts or fail on difficult shapes. In this paper, we propose an end-to-end framework for polycube generation based on conditional diffusion models. Given an input geometry represented as a point cloud, our method directly produces a corresponding polycube point cloud, eliminating the need for explicit surface segmentation or predefined polycube templates. At the core of our approach is a dual-latent conditional diffusion architecture that confines computationally expensive self-attention operations to a fixed-capacity, low-dimensional latent space. This design effectively decouples computational complexity from the resolution of both the input geometry and the output polycube, thereby avoiding the quadratic cost typical of point cloud self-attention mechanisms while supporting flexible input and output resolutions. To obtain a hexahedral mesh, the generated polycube is aligned to the input shape via rigid and non-rigid point cloud registration to establish surface correspondence, followed by a polycube-to-hex pipeline. We additionally create and release a paired dataset of CAD meshes and their corresponding polycube meshes, together with the core implementation of our model. Experiments show that PolycubeNet generalizes to complex CAD models with arbitrary genus and produces high-quality polycube structures within seconds, improving robustness and efficiency over prior learning-based approaches.

We develop a rigorous statistical theory of multi-head attention (MHA) as an ensemble of Nadaraya-Watson (NW) kernel regression estimators. Building on the algebraic identity between single-head softmax attention and the NW estimator, we prove that MHA is a structured ensemble of H NW estimators, each operating in a distinct learned projection subspace of the key space. We derive an explicit Bias-Variance-Covariance decomposition of the MHA mean squared error, showing that variance reduction depends not merely on the number of heads H but fundamentally on the decorrelation of head outputs. Decorrelation is governed by the principal angles between learned projection subspaces: orthogonal projections yield maximum variance reduction; aligned projections yield none. We introduce the Head Diversity Index (HDI), a computable spectral measure of inter-head decorrelation, and prove that MHA mean squared error is monotonically decreasing in HDI. This provides the first rigorous theoretical explanation for the empirically observed specialization of attention heads. Under a fixed total-dimension budget D = H * d_k, we solve the optimal head-dimension allocation problem, deriving the MSE-minimizing pair (H*, d_k*) from data distribution and regression smoothness. The solution yields a new architectural scaling law: the optimal per-head dimension grows logarithmically with training set size, while the optimal number of heads grows nearly linearly with the total budget D. Our framework unifies three strands of prior work: the NW theory of single-head attention, the general weighting theory for ensemble learning, and the decorrelation-variance-reduction isomorphism between biological and computational ensembles. Multi-head attention is the Transformer's instantiation of a universal principle: identical agents plus diversity-enforcing mechanisms yields emergent optimality.

Large Language Models (LLMs) have shown promising results on NLP tasks, however, their performance on tabular data still needs research attention, because Table Question-Answering (TQA) requires precise cell retrieval and multi-step structured reasoning. Existing work improves TQA either by fine-tuning or training LLMs on task-specific tabular data, but often lacks verifiable control over how the model navigates tables and derives answers. In this work, we propose a training-free TQA approach with two structured prompting frameworks: TableGrid Navigation (TGN), which iteratively navigates rows and columns via a three-module loop to locate evidence and refine answers, and Progressive Inference Prompting (PIP), which enforces columns identification for explicit progressive row selection constraint according to the query. We evaluate 17 LLMs against 6 baselines on TableBench and FeTaQa dataset. On TableBench, TGN improves over the strongest baseline by 3.8 points, and on FeTaQa, PIP achieves SOTA performance over ReAct and Chain-of-Thought. Beyond inference-time gains, PIP and TGN can also serve as supervision templates to fine-tune small models, narrowing the performance gap to much larger architectures in resource-constrained settings, offering versatile and cost-efficient solution for TQA.

We introduce \textbf{Prism}, a framework for structural symmetry diagnosis in complex networks. Given a graph Laplacian $L$ and a duality operator $P$ (a symmetric involution), Prism computes the \emph{duality defect} $δ(L,P) = \|LP - PL\|_F / \|L\|_F$ -- a scalar measuring how far the network deviates from structural self-consistency. When $P$ encodes the network's true symmetry, $δ$ starts near zero and rises monotonically as structure degrades; an arbitrary $P$ gives noise. We prove that the optimal $L'$ satisfying $[L', P] = 0$ is given by a closed-form block-diagonal projection, and provide an unsupervised alternating optimization that learns $P$ from the graph's own Fiedler vector. Experiments on synthetic networks show the true-$P$ defect is $3.38\times$ more sensitive to structural degradation than an index-reversal baseline and more sensitive than modularity. On Zachary's Karate Club with edge noise, Prism achieves $94.5\%$ community detection accuracy at $5\%$ noise versus $76.6\%$ for the raw Laplacian baseline. Applied to live S\&P~500 data (2026-05-17), Prism detects rising structural stress (defect $0.43 \to 0.73$ over 90 days) while surface correlations remain low -- a signal invisible to correlation-based methods. In a historical backtest spanning five major stress events (2011--2020), the duality defect exhibits a consistent pattern: it reaches elevated levels \emph{before} the correlation spike that accompanies each crisis, and sustains high readings during periods of structural fragility that conventional metrics classify as calm. The duality defect is a first-principles structural admissibility condition, requiring no training data and computable in milliseconds.

We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across library versions, yet existing refactoring works overlook three practical challenges: 1) Lean refactoring is natively multi-objective (proof length, compilation cost, and version compatibility are often in tension); 2) Lean repositories have fragile compatibility, whereas LLM releases are unaware of Lean/Mathlib versions; 3) Training-based pipelines require repeated fine-tuning with each new LLM release, scaling neither with model churn nor with Lean's release cycle. Lean Refactor steers a frozen agentic LLM with retrievals from a curated database of multi-objective refactoring strategies, each densely annotated with metadata such as supported Lean/Mathlib versions and expected compilation-cost reduction. Experiments show over $70\%$ token-level compression on competition benchmarks, over $20\%$ on research repositories, and up to $60\%$ compilation-time reduction, outperforming prior work and Claude Code. Version-filtered retrieval further improves compression on the target Lean version, and refactored miniF2F proofs exhibit stronger zero-shot version transfer to future Lean releases than their unrefactored counterparts.

Contextual combinatorial optimization (CCO) plays a critical role in decision-making under uncertainty, yet remains a significant challenge. We present Quantum End-to-End Learning (QEL), the first quantum computing-based end-to-end learning framework for CCO that leverages Quantum Approximate Optimization Algorithms. Inspired by the integration of state preparation and evolution in data re-uploading, we propose a context re-uploading phase-separator that jointly captures the complex relations among contexts, uncertain coefficients, and optimal solutions. This allows a contextual encoder to be seamlessly integrated within a quantum surrogate policy, enabling joint end-to-end training with a stationarity guarantee. Exploiting an optimization-aware structure grounded in physical principles that classical methods cannot readily leverage, our approach demonstrates practicality by directly training on task loss despite the discreteness and nonconvexity, while avoiding calls to NP-hard optimization solvers. QEL empirically achieves competitive performance while requiring substantially fewer parameters than classical benchmarks, highlighting its industrial-level potential for the future quantum era.

Treating and preventing Human Immunodeficiency Virus (HIV) remains a critical global health challenge. While antiretroviral therapy provides a path toward viral suppression -- effectively eliminating an individual's transmission risk -- systemic resource constraints limit the reach of intervention efforts. This work addresses the strategic distribution of intensive resources among virally unsuppressed individuals to minimize the expected cascade of new infections within a transmission network. We formalize this challenge as a novel constrained optimization problem where we have resources to "treat" $k$ out of a set $\mathbf{P}$ of virally unsuppressed individuals, and establish its theoretical connections to existing computational literature. We then propose Cascade-Aware Suppression of Transmission (CAST), a polynomial-time $(δ, ε)$-approximation algorithm that achieves a $2\sqrt{|\mathbf{P}|}$ approximation ratio by leveraging connections to the Minimum-$k$-Union (MkU) problem and Hoeffding-style concentration bounds. Extensive evaluations on real-world HIV networks demonstrate that CAST outperforms standard public health and computer science baselines. Furthermore, we show that CAST is empirically robust across diverse infectious disease networks, varied edge probability initializations, and settings involving imperfect network data.

Agentic AI systems - systems that can pursue goals through multi-step planning and tool-mediated action with limited direct supervision - are moving from experimental prototypes to enterprise deployments. This transition introduces tensions in implementation, scaling, and governance: organizations seek scalable autonomy for knowledge and coordination work, yet must preserve accountability, safety, cost control, and responsibility as systems initiate actions, access enterprise data, and evolve through iterative updates. Building on an in-depth qualitative case of a large IT services company's 2025 development and staged rollout of an agentic system integrated with enterprise tools; we show that governance is implemented through concrete architectural and working arrangements that determine what the system is allowed to do, which tools and data it can use, how memory is handled, and how performance improvements are introduced over time. We then distill seven lessons that explain how to build effective governance into agentic AI during operationalization and scaling.

Achieving precise, versatile whole-body character control in physics-based animation remains challenging. Recent diffusion-based policies generate rich and expressive motions but typically rely on gradient-based test-time guidance to satisfy task objectives, which is slow and can reduce robustness. We introduce NaP-Control (Navigating Diffusion Prior for Versatile and Fast Character Control), abbreviated as NaP. Our method uses reinforcement learning to manipulate the latent noise of a task-agnostic diffusion policy prior, steering it toward task-specific behaviors for fast, robust control with high motion fidelity. In contrast to methods that rely solely on offline training, NaP interacts with the environment during training to correct motions and optimize task rewards, improving success rates and enabling adaptation to challenging scenarios. By directly predicting task-optimized diffusion noise, NaP eliminates iterative guidance during denoising and enables efficient inference. Experiments show that NaP attains higher success rates and faster inference while preserving natural motion across diverse tasks.