Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates

Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made. Existing analyses establish degeneracy for particular constraint formulas but do not isolate what follows from smooth exactness itself. At a DAG boundary, we show that minimal cycle completions generate a squarefree monomial ideal containing every restricted Taylor jet of an exact representation. If the smallest completion has $q$ edges, the first possible response has order $q$ for a vector residual and $2q$ for a nonnegative scalar. Exponentially many constant-scale cyclic manifolds exhibit the same lack of ranking away from the boundary for NOTEARS and DAGMA. We derive the exact selection time for an isolated cycle. When $Ψ'(h)\asymp h^ν$, the feasibility-only time is $T_0(\varepsilon)=Θ(\varepsilon^{-(2ν+1)})$; a score margin changes the leading dynamics at scale $T_0^{-1}$ for $ν>0$, while $ν=0$ has a logarithmic boundary layer requiring $γT_0\log(1/\varepsilon)\to0$. Experiments verify this law, and a truth-free separation statistic predicts selection time on 320 official NOTEARS/DAGMA trajectories (Spearman $-0.52$ and $-0.66$, permutation $p<10^{-4}$). For finite samples, a parent-set confidence family and forced-opposite queries certify skeleton and unshielded-collider labels shared by every population optimum of a frozen score. Across 320 runs, every regret bound covers an independent oracle-score audit. None of 3,042 certified skeleton or 2,396 collider labels disagrees with the oracle-score optimum, although 4.4% and 5.5%, respectively, disagree with the generating graph. These results separate DAG feasibility, score-based support selection, and causal identification.

TAU-Bench: From Anomaly Instance Tracking to Fine-Grained Video Anomaly Understanding

Humans understand anomalous events through a coherent perceptual process in which they identify the focal instance, follow its behavior as the event unfolds, and interpret why it violates the expectations of the surrounding scene. Video anomaly understanding (VAU) seeks to endow models with a similar capability, moving beyond deciding whether a video is anomalous toward explaining how the event develops and why it matters. Although recent vision--language models (VLMs) can generate detailed and plausible anomaly descriptions, their semantic fluency does not ensure that these interpretations remain grounded in the correct anomaly instance over time. Existing benchmarks typically evaluate tracking and semantic understanding through separate protocols, leaving such instance--semantic inconsistency largely unmeasured. We therefore introduce TAU-Bench, a track-centric benchmark for jointly evaluating anomaly instance tracking and fine-grained anomaly understanding. TAU-Bench contains 1,118 videos, 1,454 tracks, and 202,438 pixel-level masks spanning 49 event and 45 scene categories, together with track-centric annotations that connect instance-level identification, event-level understanding, and scene-level reasoning. To build TAU-Bench at scale, we developed an automated data engine integrating anomaly suitability filtering, anomaly instance track construction, hierarchical caption annotation, and human quality control. Evaluations across representative VLM families show that models producing plausible anomaly interpretations may still fail to localize and track the correct instance reliably, revealing a persistent gap between semantic reasoning and visual grounding. These findings therefore highlight instance-grounded evaluation as an important step toward more faithful and reliable VAU systems.

Empowering Polymeric Materials Discovery by Artificial Intelligence

Polymeric materials underpin modern technologies spanning energy storage, microelectronics, healthcare and sustainable manufacturing. Yet their rational design remains exceptionally challenging because material performance emerges from complex interactions among molecular composition, chain architecture, processing history and hierarchical structural evolution across multiple length and time scales. Consequently, polymer research has long relied on labor-intensive experimentation and fragmented modeling approaches, limiting both mechanistic understanding and innovation efficiency. Recent advances in data infrastructure, machine learning, large artificial intelligence (AI) models and laboratory automation are beginning to reshape this landscape. Rather than functioning as isolated tools, polymer databases, predictive models, AI agents and automated laboratories are increasingly converging into interconnected discovery ecosystems. As a result, the central challenge is shifting from improving predictive accuracy alone to enabling reliable decision-making, adaptive learning and seamless integration across computation, experimentation and scientific reasoning. We argue that polymer science is entering an era of autonomous discovery, in which data, simulation, reasoning and experimentation operate within self-improving feedback loops that continuously generate hypotheses, design materials, execute experiments and refine predictive models. By unifying molecular design, process optimization, experimental validation and industrial translation, such autonomous ecosystems establish a more predictive, reproducible and scalable paradigm for polymer innovation, fundamentally transforming how polymer research is conducted.

Greed Is Learned: Visible Incentives as Reward-Hacking Triggers

Deployed agents increasingly act with their reward proxy in view, such as a balance, score, or KPI dashboard. We show that reinforcement learning can make a policy \emph{addicted} to such a visible self-benefit channel. It chases the displayed payoff across held-out domains, sacrifices the true task to do so, and follows the channel wherever we rewrite it, while policies that never saw the channel stay honest. We call this \emph{reward-channel addiction} and study it in \emph{MoneyWorld}, a synthetic sandbox. The addiction can \emph{flip a model's safety alignment}: trained only on innocuous money tasks with no safety content, the model abandons the safe action it otherwise always takes whenever a dashboard pays for an unsafe one, and reverts to safe once the channel is hidden. This learned bribe replicates across model scales and families. Blindly optimizing super-capable, next-generation AI on KPIs or P\&L can be dangerous for alignment. \emph{Greed is learned} when following such a channel pays.

Constitutional Value Potentials: reading and steering internal priority margins in language models

A constitution tells a language model what to value, but little tells us whether it does. Adherence is judged from outputs, and output evidence is most fragile on value conflicts, where what matters is not which value a model mentions but which one it is willing to sacrifice. We provide evidence that this arbitration can be read from activations in a structured margin readout. We introduce Constitutional Value Potentials (CVP). For each value we learn a scalar potential from the hidden state: an internal pressure to preserve that value, supervised not by the prompt but by an independent judge's verdict on which value the model's own response actually preserved. The signed difference of two potentials is a priority margin. A constitutional clause becomes the claim that a margin stays positive, and a single monitor score flags when it does not. The monitor predicts conflict violations with AUROC up to 0.95, beats a strong hidden-state probe, and generalizes to held-out synthetic conflicts across three Qwen2.5 scales. The signal appears as the answer begins, from the prompt tail and first response token. Read this early, the same signal reveals whether an adversarial priority hack has actually pushed the model toward a violation, rather than only whether the prompt looks adversarial. The same directions also support intervention tests: under selected steering settings, moving along a value direction shifts judged trade-offs in the intended direction. Together, these results suggest that some constitution-relevant priorities are accessible as activation-space margins, rather than only as output behavior.

Graph Diffusion Residuals for Control-Function Instrumental Variables

Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction. High-capacity first stages can interpolate treatment and leave too little residual information for the outcome equation. We study Adaptive Anisotropic Instrumental Heat Flow (A-IHF), a deterministic graph-diffusion residual extractor for flexible control functions. A-IHF treats treatment as a signal on a graph of first-stage features, uses pilot diffusion to detect large treatment jumps, attenuates conductance across those jumps, and computes the generated control with a sparse graph resolvent. Its observational selection rule uses only $(Z,X)$, combining graph generalized cross-validation, roughness, residualized-treatment relevance, and graph-admissibility filtering. The analysis decomposes error into structural leakage, residual attenuation, and residualized treatment variation, yielding finite-sample bounds, graph-admissibility rates under latent piecewise-smooth geometry, and finite-path selection calibration. Across 54 synthetic benchmark cells with tuned graph, kernel, tree, boosting, series, and neural control-function baselines, guarded observational A-IHF has the lowest average structural-response MSE; the A-IHF family beats the best non-A-IHF baseline in 32 cells. Performance is strongest when the graph captures piecewise-smooth first-stage structure.

Weak Critics Make Strong Learners: On-Policy Critique Distillation for Scalable Oversight

As large language models become stronger, weak supervisors may fail to provide reliable labels, preferences, or final judgments for complex outputs, limiting both weak-to-strong generalization and scalable oversight. We study a more tractable form of weak supervision: using a weak model as a critic rather than as a labeler or judge. Instead of solving the task or selecting the correct answer, the weak critic only needs to provide a non-misleading revision direction that helps the strong model better use its own knowledge. We call this setting *weak-critic strong oversight*. We first show that weak critiques can improve frozen strong models at inference time, and that critique quality is key to this improvement. We then propose progressive on-policy critique distillation (**OPCD**), which filters high-quality critiques and distills critic-guided behavior into the strong model through adaptive self-teacher signals. Experiments on reasoning and alignment benchmarks show that our method improves strong models over training epochs, suggesting an effective path for scalable oversight with weak supervision.

Underwater360: Reconstructing Underwater Scenes from Panoramic Images with Omnidirectional Gaussian Splatting

Underwater scene reconstruction is essential for immersive exploration of aquatic environments, yet remains challenging due to complex participating-media effects such as absorption and scattering, as well as the limited field of view (FoV) of conventional cameras. Although combining panoramic imaging with 3D Gaussian Splatting (3DGS) offers a promising direction for photorealistic underwater rendering, traditional 3DGS struggles with both spherical projection distortion and underwater medium degradation. In this paper, we propose \textbf{Underwater360}, a physics-informed omnidirectional 3DGS framework for underwater panoramic scene reconstruction. First, we introduce an Omnidirectional Gaussian Splatting module that performs ray casting directly in spherical camera space instead of relying on 2D projection approximations, thereby reducing geometric distortions under 360$^\circ$ FoV. Second, we design a physics-based appearance-medium modeling architecture with pose-conditioned appearance embeddings to explicitly decouple intrinsic scene radiance from depth-dependent backscatter and attenuation, enabling physically grounded scene appearance restoration. Finally, we establish a new panoramic underwater benchmark dataset containing both synthetic and real-world scenes. Extensive experiments demonstrate that Underwater360 achieves superior performance in underwater novel view synthesis and scene appearance restoration, delivering improved rendering quality and cross-view consistency in complex underwater environments. The code and datasets are released at https://github.com/SwcK423/Underwater360

Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians

Continuous causal discovery typically couples representation learning with structural optimization via non-convex acyclicity penalties, which subjects solvers to local optima and restricts scalability in high-dimensional regimes. We propose a decoupled paradigm that shifts the causal discovery bottleneck from non-convex optimization to statistical score estimation. We introduce the Score-Schur Topological Sort (SSTS), an algorithm that extracts topological order directly from unconstrained generative models, bypassing constrained structure optimization. We establish that the causal hierarchy leaves a geometric signature within the score function: iterative graph marginalization is mathematically equivalent to computing the Schur complement of the Score-Jacobian Information Matrix (SJIM) under linear conditions. This translates the acyclicity constraint into an algebraic procedure with a dominant cost of O(d^3) operations. For non-linear systems, we formulate the expectation gap of Schur marginalization and introduce Block-SSTS to compress extraction depth, bounding structural error. Empirically, SSTS allows causal structural analysis on non-linear graphs up to d=1000. At this scale, our framework indicates that once the non-convex optimization bottleneck is mathematically bypassed, the structural fidelity of continuous causal discovery is bounded by the finite-sample estimation variance of the global score geometry. By reducing graph extraction to matrix operations, this work reframes scalable causal discovery from a constrained optimization problem to a statistical estimation challenge.

Taming Actor-Observer Asymmetry in Agents via Dialectical Alignment

Large Language Model agents have rapidly evolved from static text generators into dynamic systems capable of executing complex autonomous workflows. To enhance reliability, multi-agent frameworks assigning specialized roles are increasingly adopted to enable self-reflection and mutual auditing. While such role-playing effectively leverages domain expert knowledge, we find it simultaneously induces a human-like cognitive bias known as Actor-Observer Asymmetry (AOA). Specifically, an agent acting as an actor (during self-reflection) tends to attribute failures to external factors, whereas an observer (during mutual auditing) attributes the same errors to internal faults. We quantify this using our new Ambiguous Failure Benchmark, which reveals that simply swapping perspectives triggers the AOA effect in over 20% of cases for most models. To tame this bias, we introduce ReTAS (Reasoning via Thesis-Antithesis-Synthesis), a model trained through dialectical alignment to enforce perspective-invariant reasoning. By integrating dialectical chain-of-thought with Group Relative Policy Optimization, ReTAS guides agents to synthesize conflicting viewpoints into an objective consensus. Experiments demonstrate that ReTAS effectively mitigates attribution inconsistency and significantly improves fault resolution rates in ambiguous scenarios.