Papers

Learning EEG representations that generalize across cognitive tasks, subjects, and recording conditions remains a key challenge in electroencephalography (EEG) decoding. Recent advances in foundation models have improved EEG decoding performance, yet a fundamental open question remains: how to effectively interface neural signals with these models to enable multi-task learning across datasets. To investigate this question, we introduce BraVista, a visual-language framework that encodes multichannel EEG signals as structured images and enables multi-task learning through instruction-conditioned vision-language models (VLMs). Our approach relies on continued post-training of a general-domain VLM, leveraging its visual and linguistic priors to adapt to neural signals without a separate large-scale EEG-specific pretraining stage. We evaluate BraVista on four datasets spanning sleep staging, emotion recognition, cognitive workload classification, and abnormal EEG detection, showing strong performance across these tasks. Further analyses show that the choice of EEG-to-image representation is critical to performance. Moreover, through controlled perturbations of the EEG signal, we observe a gradual performance degradation under increasing noise, suggesting that the model relies on EEG-relevant information rather than superficial visual patterns. Together, these findings establish structured visual representations as an effective and scalable interface between neural signals and general-domain foundation models for unified multi-task EEG decoding.

We prove that the Laurent polynomial in $\mathbb{Z}[q^{\pm 1}]$ that is the top coefficient of the Links-Gould invariant of the boundary of a Seifert surface is multiplicative under arbitrary Murasugi sums of minimal genus Seifert surfaces. This extends a previous result of the second and third authors which only holds for plumbing, i.e. 4-Murasugi sum. Our technique relies on quantum supergroup themselves and PBW basis rather than the skein relations used in the previous work.

We introduce a non-orthogonal amplitude amplification (NOAA) method for hybrid continuous-variable- discrete-variable (CV-DV) quantum processors, where the available CV-assisted projector is not perfectly se- lective for the target state. We establish a bound on the achievable target-state fidelity, which is determined by the initial target-state amplitude and the selectivity of the accessible reflection operator. This bound limits the performance of NOAA in hybrid CV-DV systems. To mitigate this limitation, we propose using a squeezed CV ancilla to reduce the overlap between relevant CV states and a hybrid quantum signal processing (HQSP) filter to suppress errors arising from imperfect knowledge of the target eigenenergy. Numerical simulations show that, for small initial target-state amplitudes, our protocol achieves higher fidelity and efficiency than the repeat-until-success (RUS) method despite the presence of non-orthogonality. For large initial amplitudes, RUS is already efficient, and amplitude amplification provides little additional advantage.

Visual decoding from fMRI is typically siloed by participant and experiment, obscuring whether heterogeneous neural measurements can be organized within a common computational geometry. Here we introduce BRAID-fMRI (Brain Representation Alignment across Individuals and Datasets), a shared CLIP-supervised decoding framework. BRAID-fMRI uses a single ROI-wise Transformer with optional participant conditioning across eight visual-fMRI datasets comprising 93 dataset-specific participant entries, 430,007 single-trial responses and 162,839 unique stimuli. Regional brain activity is aligned with 512-dimensional CLIP ViT-B/32 representations using a multi-positive contrastive objective that treats repeated stimuli across participants and datasets as positives. BRAID-fMRI supports retrieval across seven evaluation datasets. On eight matched participant entries, it achieves 35.0 +/- 11.1% Top-10 accuracy, exceeding the observed mean accuracy of the two evaluated baselines - the MindEye-style pooled-CLIP decoder (27.1 +/- 5.1%) and ridge regression (21.1 +/- 9.1%) - and attaining the highest observed accuracy for seven of eight entries. In separately trained participant-agnostic models, expanding the source pool increased target-dataset holdout accuracy by up to 92.1% relative to the initial source-training condition. The learned space preserves graded semantic structure, while ablations and saliency highlight ventral and early visual cortex and category-specific motion and attentional systems. These results support scalable cross-dataset decoding into a common CLIP-aligned space, with model sensitivity concentrated in ventral and early visual inputs.

This paper develops novel smooth tests for structural changes in the innovation copula of multivariate dynamic models. We characterize deviations from copula constancy through a collection of generalized Fourier coefficients and test their joint significance. Under the null hypothesis, estimation of the dynamic parameters and the unknown marginals has no first-order estimation effect on the proposed statistics. Consequently, the feasible tests based on estimated residuals are asymptotically equivalent to their infeasible counterparts based on the unobserved innovations, yielding a desirable oracle property. Our proposed tests are asymptotically $\chi^2$-distributed and possess nontrivial power against local alternatives that approach the null at the parametric rate. To enhance the practicability of our methods, we further develop a data-driven procedure that automatically selects the truncation orders of the basis expansions. Unlike existing methods based on empirical copula processes or kernel smoothing, our tests require neither computationally intensive bootstrap procedures nor bandwidth selection. Extensive simulations demonstrate the satisfactory empirical size and power of our proposed tests. In particular, the data-driven test delivers substantial power gains under sparse alternatives, while remaining competitive under dense alternatives. Applications to exchange rates and stock returns further illustrate the practical usefulness of the proposed methods.

Learning from demonstrations (LfD) provides a framework for inferring unknown constraints from locally optimal, constraint-satisfying expert behavior. Existing approaches largely fall into two paradigms, constrained inverse optimal control (CIOC) and inverse constrained reinforcement learning (ICRL). CIOC exploits optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions but typically assumes known dynamics and structured constraint representations. Meanwhile, ICRL accommodates complex unknown constraints and unknown transition dynamics but often requires extensive online exploration, during which unsafe constraint violations may occur. In this work, we introduce Counterfactual KKT (CF-KKT), a constraint learning framework that leverages learned dynamics and locally optimal demonstrations to recover unknown constraints without requiring known dynamics or additional risky exploration, thereby combining the data efficiency and safety advantages of CIOC with the flexibility of ICRL. First, we use a locally learned differentiable dynamics model to impose KKT-inspired optimality conditions directly on the demonstrations. Second, we use the learned dynamics to generate reward-improving counterfactual behaviors near the demonstrations, revealing behaviors that would be preferable in the absence of the unknown constraint and thus providing synthetic infeasible data. When the constraint parameterization is known, the same learned-dynamics framework enables direct CIOC-based parameter recovery, and we characterize its sensitivity to dynamics misspecification. Across high-dimensional robotic control tasks, our approach learns neural constraint representations with improved safety and data efficiency relative to state-of-the-art offline ICRL baselines.

Let $m(p)$ be the least size of a subset of $\F_p$ with at least two elements for which every sum has two distinct representations as unordered pairs, allowing repetition. We prove that, for every prime $p\ge64$, \[ m(p)\ge2^{-80}\left(\frac{\log p}{\log\log p}\right)^2. \] The argument compresses the full integer collision lattice by unit-pivot elimination. A shared random sample and forests of bounded diameter give $O(\sqrt n+n/\log p)$ surviving coordinates of polynomial height for a minimal set of size $n$. A nonzero minor divisible by $p$ then gives the lower bound. We also construct weakly ternary-balanced seeds yielding \[ m(p)\le\frac{(\log p)^2}{2(\log3)^2} +\left(\frac1{4\log3}+o(1)\right) \frac{(\log p)^2}{\log\log p}. \] Consequently $m(p)=(\log p)^{2+o(1)}$ as $p$ tends to infinity through the primes. The constant-factor order of $m(p)$ remains undetermined.

LLM agents that interact with a user across many sessions accumulate histories that exceed their context window, so they store past interactions in an external memory and answer each question from a small set of retrieved records. Existing memory systems rank records by lexical or embedding relevance, yet the top-ranked memories can each be relevant while jointly omitting a complementary fact that the answer requires, especially for multi-session and temporal questions. Drawing on the distinction between relevance and sufficiency in legal evidence scholarship, we recast memory retrieval as constructing a sufficient memory set. To operationalize this view, we introduce a blinded LLM judgment over the retrieved set, together with Gold Hit and Turn Hit as evidence-coverage proxies. We then propose Budgeted Flat Reconstruction (BFR), which builds sufficient sets over a fixed flat memory store in two stages. Specifically, we first apply Formal Concept Analysis for Memory Selection (FCA-MS) to decompose the question into information requirements and select a compact candidate subset that jointly covers them. Then, we repeatedly acquire unseen records through deeper text search or complementary entity and session views, stopping when the budget is exhausted. Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems in both answer quality and evidence coverage. Specifically, on LongMemEval-S it raises judged accuracy from 72.4% to 82.2% and Turn Hit to 91.4%.

Genetic programming was conceived as a way of evolving solutions: the program is the answer, and fitness is the error of its own output. A substantial line of work instead makes the program an input to a separate learner, so fitness measures the learner's output rather than the program's. Which learner to attach matters, with no account of what decides it. What makes a target hard for genetic programming is how much nonlinearity the program must build by composing primitives; whatever nonlinearity the learner supplies, the program need not. The quantity to measure is therefore how much of a target's nonlinearity a learner can take over, though on continuous benchmarks it can only be estimated. Here we show that how much the program must still build is decided by which learner is attached, and is measurable on the programs themselves. Moving to Boolean domains, where a target's nonlinearity is exactly its Fourier degree, we tune that degree from one to six with everything else fixed. Conditioned on success, a linear learner forces the evolved program to the target's degree exactly, at one through six without exception over thirty runs per setting, while tree ensembles succeed with far simpler programs and four times as often. This gives the field two things: a learner can be chosen from a target's structure instead of its reputation for difficulty, and the degree of the evolved program is a diagnostic free to compute during any run. Our control target has lower degree than the parity problems yet gains nothing from a nonlinear learner, while targets reducible to a simple statistic gain a great deal. The latter comes with a warning: evolution internalises what the learner supplies in only four of sixty-three conditions, and grows more dependent on it in forty-four, so the more capable the learner, the less of the model is legible in the program.

Quantization-aware training (QAT) can recover much of the accuracy lost when large language models are compressed below four bits. Existing re- covery stages, however, are commonly optimized on fixed completions or teacher-generated answers, whereas the deployed quantized model condi- tions on prefixes generated by itself. Quantization errors can therefore move the model into states that are absent from offline recovery data. We introduce OnlineQAT, a two-stage framework that first obtains a usable low-bit initialization through block-wise QAT and then performs on-policy distillation (OPD) on student-generated responses. At each visited pre- fix, a frozen full-precision teacher provides a sampled reverse-KL training signal. On Qwen3-1.7B, OnlineQAT obtains the best average among the compared quantized methods: 57.28 at W3A16 and 32.52 at W2A16, im- proving over ReasoningQAT by 2.90 and 0.44 points, respectively. The results suggest that student-visited states provide a useful recovery signal beyond fixed-completion training, particularly at three bits.

Polarized neutron scattering has been widely used for studying magnetic orders in condensed matter. A typical setup for this technique is a triple-axis spectrometer with a ferromagnetic single-crystal monochromator and analyzer, which is suited for point-by-point measurements within the horizontal scattering plane. However, this setup cannot fully meet the demands of recent studies on complex magnetic orders with emergent cross-correlated phenomena. For instance, multiferroics, magnetic skyrmions, and other topologically nontrivial magnetic orders tend to have incommensurate magnetic modulation vectors running along various directions in reciprocal space, which cannot be captured by measurements restricted to the horizontal scattering plane. To overcome these limitations, we have developed an experimental setup combining a $^3$He neutron spin filter ($^3$He-NSF) and a two-dimensional (2D) detector, which enables us to analyze the polarization of neutrons scattered away from the horizontal plane. We also establish a data reduction procedure to convert the 2D intensity maps into three-dimensional intensity distributions in reciprocal space, correcting for the effect of imperfect $^3$He polarization. This method is applied to single-crystal diffraction measurements on the multiferroic material Mn$_3$WO$_6$, which exhibits complex incommensurate magnetic orders. We have successfully observed polarization-dependent intensities of out-of-plane incommensurate magnetic reflections, demonstrating the effectiveness of the present method for analyzing complex magnetic structures.

General image editors are asked to make a photo look as if it were taken at f/1.4, yet it is rarely checked whether the blur they add follows thin-lens optics. A physical aperture edit spreads blur across depth in thin-lens proportions and changes the blur when the aperture changes; prior evaluations check blur monotonicity, sharpness-trend correlation, effective-aperture error, or vision-language judgments, and none we found reports the two properties separately at known depths. In this pilot audit of two editors (Gemini~3.1 Flash Image and GPT-image-2.5) we compare against a rendered oracle: Blender Cycles scenes with true thin-lens depth of field, one blur-width estimator applied identically to oracle and editor outputs, and preregistered depth and aperture indices. In 24 texture scenes rendered in one three-panel geometry, accepted and measurable panels show f/1.4-to-f/2.8 width ratios, $\bar\sigma_{1.4}/\bar\sigma_{2.8}$, of 0.99–1.18 against 1.98–2.13 for the oracle, and ratios of pooled median Gaussian-equivalent near/far blur widths of about 1.18–1.25 (Gemini) and 0.97–1.05 (GPT-image) against 1.69–1.82. Preregistered black-box interventions show that qualitative wording changes blur strength by roughly 2–10 times, whereas a request for 2 versus 6 px changes it 1.1–1.3 times and no tested wording of the f-number meets the registered “followed” criterion. The depth compression appears in the original and reversed centre-focus layouts; with the focus on the near panel, the available-panel depth index reaches the registered threshold, and the aperture response stays attenuated in every layout tested. Scalar metrics adapted from published ones give oracle-like scores to synthetic editors whose proportions are compressed.

Tiled 3D Gaussian Splatting rasterizers often use one scene-wide contribution cutoff for tile enumeration, although content differs in its sensitivity to support truncation. TileSkipper selects a static per-Gaussian cutoff policy for a frozen checkpoint. Calibration renders measure candidate pair savings and an isolated-removal distortion proxy that accounts for front transmittance and background color. The method allocates cutoffs across 64 Gaussian groups and accepts policies only after complete renders on disjoint selection views. The exported policy uses one byte per Gaussian, with no parameter updates, additional kernel, or per-frame policy inference. Across 13 scenes from Mip-NeRF 360, Tanks & Temples, and Deep Blending, a fixed-policy AccuTile sweep gives dataset-macro speedups of $1.088\times$ at standard resolution and $1.238\times$ at 3840 pixels wide, with $-0.007/-0.023$ dB mean PSNR change. Six integrations with existing opacity-aware bounds yield $1.009\times$–$1.121\times$ compiler-only speedups. For four ports from $3\sigma$ rasterizers, we separately attribute the prior exact-bound transition and our incremental gain. Matched-quality ablations show modest gains over scene-global calibration and parity with per-Gaussian control; the standalone comparison with AdaGScale is regime-dependent.

Mixture-of-Experts (MoE) large language models decouple capacity from compute through sparse routing, but their large parameter count creates storage and serving challenges. We analyze three MoE compression families: expert pruning, expert merging, and weight reconstruction, and derive structural error bounds showing that pruning and merging can incur non-vanishing errors tied to routing and expert heterogeneity. In contrast, weight reconstruction avoids these structural costs by preserving expert structure and routing. Motivated by the analysis, we propose Shared Low-rank Basis Factorization (SLBF), a data-free weight reconstruction method that uses rank-$k$ bases shared among experts, enabling richer cross-expert sharing, faster convergence, and lower reconstruction error. A post-hoc gauge fixing removes redundant parameters at no representational cost. Across five MoE architectures spanning 16B to 122B parameters, SLBF consistently outperforms methods from all three compression families.

We construct CSS codes with three logical qubits whose logical CCZ gate is implemented by transversal physical $T/T^\dagger$ gates and whose distance is at least 3. These codes start with 8-divisible $X$-stabilizers defined by projective geometry, which guarantees $d_Z \geq 3$. A SAT solver then finds three $X$-logical operators compatible with the transversal CCZ. We build codes at thirteen block lengths from $n=48$ to $n=496$, with $d_Z=3$ or 4, and illustrate the method with the [[48,3,3]] code $Q_{48}$. Additionally, we prove that no CSS code with three logical qubits, $Z$-distance at least 3, and a quasi-transversal CCZ gate (transversal $T$ with a diagonal Clifford correction) exists below $n=39$. The [[47,3,3]] code of Jacinto et al. attains the minimum length in this class, as established by the classification of Wills, Jain, and Singh.

Benign overfitting is extensively studied when learning from a single high-dimensional input, but its behavior under heterogeneous input fusion remains largely unexplored. We study this question for minimum-norm linear interpolation under a heterogeneous Gaussian design, comparing two statistically dependent input blocks with their fusion while holding the underlying population task fixed. For regression, we identify a full-spectrum covariance certificate whose asymptotic status is independent of the cutoff threshold and prove that it is preserved by every positive-semidefinite joint covariance consistent with the two marginals. This protection is sharp, yet it does not extend to all benign regression problems: outside the certified regime, two benign marginals can have a harmful fusion. For one-sparse Gaussian classification, benignity in the regular regime is characterized by the balance between surviving predictive signal and nuisance contamination. Fusion can move these two quantities in opposite directions, and within this model class every marginal-to-joint benign/non-benign pattern is attainable. We further show that the same fused input can have qualitatively different effects on regression and classification. These results establish that benign overfitting under heterogeneous fusion is determined by the joint signal and spectral geometry created by input interaction, rather than by marginal benignity alone.

Data arrive sequentially, each associated with a null hypothesis. We develop testing procedures to locate intervals in which some null hypotheses fail, with false discovery rate (FDR) control. The new procedures are called sequential resetting procedures, and they are based on e-values and test supermartingales. We also develop a refined version of the procedures by dropping less informative data points before the block minimum of the test supermartingale in each rejection block. These procedures have explicit FDR bounds under two settings: a classic setting of independence and the more general setting of possible dependence across null data and non-null data. These FDR bounds are independent of the testing horizon, and the general one has anytime validity, but it has an extra logarithm factor compared with the standard FDR level. We present simulation studies and data experiments with applications of sequential resetting procedures to LLM watermark detection and financial backtesting.

We construct shallow neural networks with fixed Gaussian and tanh-difference activations on bounded Lipschitz domains $\Omega\subset\mathbb{R}^d$, $d\ge2$. For each $s>0$, explicit deterministic rules prescribe all hidden parameters independently of the target $u\in H^s(\Omega)$. At frequency resolution $M$, the $N_M\asymp M^d$ prescribed features span a linear space $V_M$. For every sufficiently large integer $N$, we choose $M\asymp N^{1/d}$ with $N_M\le N$ and construct a bounded linear operator $A_N:H^s(\Omega)\to V_M$ such that \[ \|u-A_Nu\|_{H^m(\Omega)} \le C N^{-(s-m)/d}\|u\|_{H^s(\Omega)} \] for every $u\in H^s(\Omega)$ and every integer $0\le m<s$, with $C$ independent of $u$, $N$, and $m$. Sobolev width lower bounds show that this rate is optimal among linear spaces of dimension at most $N$ chosen independently of the target. We use explicit spherical cubature nodes for the directions and Gauss-Legendre nodes or equispaced midpoints for the offsets. We show that the exterior offset margin can shrink to zero as $M\to\infty$ while preserving the approximation rate. A margin beyond $\sup_{x\in\Omega}|x|$ of order $M^{-1}\log M$ for the Gaussian and $M^{-1}(\log M)^2$ for the tanh difference suffices to truncate the ridge integral and remove exterior midpoint nodes. Numerical experiments in two and three dimensions examine $L^2$ and $H^1$ approximation.

Policy-based reinforcement learning (RL) approaches have produced promising results for autonomous cyber defense; however, they are sample-inefficient in settings where defenders must respond under delayed, partial observations with actions from large action spaces. While large language models (LLMs) may reason semantically about security state space, high latency and trust assumptions prevent attractive in-line deployment models. We introduce Ask the Expert, a training-time guidance framework which first summarizes hard cyber-defense states, then intermittently queries an LLM for host-level defensive recommendations via a constrained action interface, and finally transforms those recommendations into tiered reward shaping for use with PPO. Because the LLM is discarded after training, deployment is a pure RL policy. Across TTCP CAGE CC1 and CC2 and both attacker types, this asymmetric design improves sample efficiency over PPO and outperforms the evaluated potential-based reward shaping (PBRS) baselines, while retaining the strongest terminal mean and requiring no LLM dependency at deployment time.

Numerical relativity has a profound impact on gravitational theory and gravitational wave astronomy. In this work, we present a systematic study of the head-on collisions of multipule black hole systems within the framework of numerical relativity using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation. The numerical simulations of the dynamical evolution of gravitational fields are computed using the AMSS-NCKU code. We report numerical results for black hole collisions in several symmetric and non-symmetric configurations, in which the black holes are initially at rest and are described by Bowen-York type initial data. Our results suggest that black hole systems with perfectly symmetric configurations (e.g., black holes located at the vertices of a regular polygon or a regular polyhedron) impose strong constraints on the emitted gravitational waves, and no gravitational kick arises in these symmetric systems. For regular polygonal configurations, the radiation is dominated by the plus polarization of the $l=2$, $m=0$ mode. For regular polyhedral configurations, all the quadrupole modes with $l=2$ nearly vanish, and gravitational wave amplitudes are strongly suppressed to the order of $10^{-4}$ or below, which is in accordance with an analysis based on the quadrupole approximation. Gravitational radiations from $m \ne 0$ modes become non-negligible only when non-symmetric configurations are encountered. Keywords: Numerical Relativity, Black Holes, Gravitational Waves, N-Body Systems

Autonomous unmanned aerial vehicle (UAV) object search involves a closed loop of perception, decision-making, and action under partial observability. Urban environments pose several challenges: large search areas and narrow egocentric views limit coverage, dense 3D geometry constrains safe motion, and open-world instructions require identifying a specific target among distractors. Many existing methods mitigate partial observability through explicit maps or memory representations, yet remain largely reactive, reasoning over past observations without explicitly predicting future states. World models enable prospective reasoning through imagined rollouts. However, image-generating world models can incur high inference latency, while spatially grounded planning remains challenging for latent world models. We propose SearchWorld, a recurrent state-space world model that connects explicit spatial memory with value-guided imagination. The model maintains BEV exploration and obstacle memory and decodes a task-aware spatial value layer to guide search. A cognition-action network uses this learned spatial value prior to improve the policy through imagined rollouts, without training a separate scalar critic. Training progresses from world-model learning to expert imitation and imagination-based exploration refinement. On UAV-ON, SearchWorld improves the success rate to 23.8% (19.5% for the strongest published agent) and raises oracle success to 35.5%, while remaining robust on unseen scenes (19.9% success rate). By grounding imagination in explicit spatial representations, SearchWorld enables UAV agents to plan prospectively rather than react.

Blind Source Separation(BSS) is a fundamental problem in signal processing, aiming to separate multiple source signals from their mixtures without prior knowledge of the sources or the mixing process. Traditional approaches, such as Independent Vector Analysis (IVA) exploits statistical independence of sources. Recently, diffusion-based approaches have emerged as a promising alternative by leveraging powerful generative priors. Among them, ArrayDPS formulates BSS problem as a posterior sampling problem, and utilizes a pretrained speech diffusion model to guide the recovery of clean source signals. A key factor behind its separation capability is the multi-channel consistency (MC) objective, which enforces the estimated source signals to reconstruct the observed microphone mixtures through the estimated acoustic transfer functions. However, the number of microphones in the array is often limited, which constrains the performance of ArrayDPS. To address this issue, we propose VM-ArrayDPS, a novel method that augments the microphone array with virtual microphones with higher-SNR, these microphones can offer extra MC constraints to enhance the separation performance. Experimental results demonstrate that VM-ArrayDPS significantly outperforms ArrayDPS on both 2-speaker and 3-speaker datasets, showcasing the effectiveness of virtual microphone augmentation in improving BSS performance. We also did ablation studies to show the influence of the number of virtual microphones and weight of the MC objective brought by virtual microphones.

We unify Jones' representations of braid groups and the oriented Thompson's group by introducing the oriented dyadic braid group. This finitely generated group contains every braid group and the oriented Thompson's group. We construct an embedding of the oriented Thompson's group into this group such that taking braid closures recovers Jones' construction of oriented links. We also introduce the dyadic Temperley-Lieb algebra and construct a unitary representation of the oriented dyadic braid group extending the classical Jones representations of braid groups. Along the Thompson group's embedding, its distinguished matrix coefficient agrees with the corresponding coefficient of Jones' representation of the oriented Thompson's group.

The centroaffine Bernstein conjecture for hyperbolic centroaffine extremal hypersurfaces predicts that nonnegative Ricci curvature together with either Euclidean or centroaffine completeness forces the hypersurface to lie in Wang's class. We disprove it by systematically studying Calabi compositions: we develop a general geometric method for constructing complete centroaffine extremal hypersurfaces and apply it to construct two families that violate this rigidity. The first family is Euclidean complete but has incomplete centroaffine metric, nonnegative Ricci curvature, and positive Gauss curvature in dimension two; iterating the composition with a point gives examples in every dimension $n\ge2$. The second family is flat and complete in both metrics in dimension three, and iteration yields examples in every dimension $n\ge3$. Thus the centroaffine Bernstein conjecture fails under Euclidean completeness for $n\ge2$ and under centroaffine completeness for $n\ge3$.

We investigate birational automorphisms of hypersurfaces that preserve the projection from a point. Let $V \subset \mathbb{P}^{n+1}$ be an irreducible hypersurface of degree $d \ge 3$ with $\dim \mathrm{Sing}(V) \le n-2$, and let $\pi_P : V \dashrightarrow \mathbb{P}^n$ denote the projection from a point $P \in \mathbb{P}^{n+1} \setminus \mathrm{Sing}(V)$. Assume moreover that if $d = 3$ then $P \notin V$. We prove that any $\sigma \in \mathrm{Bir}(V)$ satisfying $\pi_P \circ \sigma = \pi_P$ extends uniquely to a projective transformation of $\mathbb{P}^{n+1}$. By combining the above projective lifting theorem with the theory of complex reflection groups, we investigate Galois and quasi-Galois points for the Fermat variety $F_d^n \subset \mathbb P^{n+1}$ of dimension $n$ and degree $d$. We show that, for $d \ge 4$, $F_d^n$ has exactly $n+2$ Galois points and, in addition, $d(n+2)(n+1)/2$ quasi-Galois points. When $d=3$, $F_3^n$ has exactly $n+2$ outer Galois points.

Infrared and visible (IR-VIS) image fusion integrates complementary multimodal information into a single fused image to support downstream vision tasks. However, existing methods are typically tailored to seen tasks within a fixed task set and struggle to generalize to unseen tasks, which restricts their applicability in real-world open-task scenarios. To address this issue, this paper proposes CRT-HMAR, a Causal Requirement Tracing-Guided Hierarchical Multi-Agent Regulation Framework for open-task-aware IR-VIS image fusion. CRT-HMAR introduces a Causal Requirement Tracing Task Localization mechanism, which actively intervenes in key image information and observes task-network response variations to map task-specific semantic preferences into image-level causal requirement maps. Based on these maps, a requirement analysis agent aggregates task-specific requirement knowledge to adaptively guide requirement-customized image fusion. Moreover, CRT-HMAR incorporates History-Analysis Multi-Objective Balancing and Task-Level-Correction Conflict Mitigation mechanisms, jointly constructing a hierarchical regulation chain of "requirement interpretation - task balancing - conflict mitigation". Through multiple collaborative agents, CRT-HMAR dynamically regulates key processes including open-task requirement modeling, multi-task balanced optimization, and gradient conflict mitigation. Extensive experiments on open-task scenarios involving five downstream tasks demonstrate that CRT-HMAR significantly improves generalization to unseen tasks while maintaining the performance and balance of seen tasks. Overall, CRT-HMAR shifts IR-VIS image fusion from task-oriented modeling toward requirement-oriented modeling, promoting its extension from closed-task settings to real-world open-task scenarios.

Automated quality inspection is essential for ensuring product reliability in manufacturing.While image-based methods effectively capture appearance-related defects, these methods are limited in detecting structural and geometric anomalies, motivating multimodal approaches incorporating 3D information. However, existing methods mainly rely on local patch-level representations, which often lead to unstable reconstruction errors even in normal regions. To address this limitation, we propose GRC-Net, which integrates a global-attention MLP to enforce global representation consistency across patch embeddings with a stable reconstruction module to improve reconstruction stability. The proposed method captures holistic contextual information through a global token and suppresses reconstruction noise by minimizing discrepancies between original and predicted embeddings. Experiments on MVTec 3D-AD and Eyecandies demonstrate that GRC-Net consistently outperforms existing methods at both image and pixel levels. Qualitative results further demonstrate reduced reconstruction errors in normal regions and more distinct reconstruction differences between normal and anomalous regions.

Multi-subject image generation requires rewards that verify whether requested attributes, actions, and relations hold for the specified reference subjects. Subject presence alone does not establish that the correct subjects participate in a requested interaction. We present reference-bound Visual Jev rewards that turn these visual decisions into generator training signals. Each subject-related question receives a positive label only when the requested condition and the relevant reference identities hold jointly. We construct fixed questions offline, train a Qwen3.5-4B verifier with binary supervision, and directly read Yes probabilities from its language-model head. Their mean supplies a GRPO reward while retaining individual judgments for inspection. Using 200 MICo-150K training tasks and 30 updates, the framework raises a GPT-5.4 composite score from 41.78 to 52.50 on a manually selected 897-task MICo-Bench subset; direct 27B rewards yield 51.84. Each reward is tested in one GRPO run, and offline human evaluation does not establish a statistically significant advantage over direct scoring. The study provides an initial implementation and evaluation of Visual Jev as a reference-bound reward for multi-subject image generation.

Automated insertion of board-to-board (BTB) connectors in 3C manufacturing requires both high visual accuracy and strong deployment robustness. This problem remains challenging because multi-variant connectors exhibit significant morphological and appearance variations, making stable cross-variant generalization difficult, while the mismatch between training and deployment under fixed-view inspection settings induces background spurious correlation and degrades real-world performance. To address these issues, this paper proposes MCFR, a Mask-Guided Coarse-to-Fine Regression framework for multi-variant BTB connector assembly. By introducing an object-aware mask prior and explicit photometric refinement, the proposed method suppresses background interference and improves alignment accuracy and robustness in practical deployment. Experiments on a self-constructed multi-variant dataset, a BTB batch insertion testbed, and a real smartphone assembly task show that MCFR consistently outperforms representative baselines and achieves an average real-world insertion success rate of 99.25%. These results demonstrate the effectiveness and practical potential of MCFR for automated assembly of multi-variant BTB connectors.

Video interactive storytelling enables viewers to actively steer how a video unfolds. However, once we allow viewers to intervene during generation, a new challenge arises: The viewer's request can have latent dependencies on both the grounding source and the current rendered video state. These dependencies may not be explicitly stated in any individual input, but emerge only when the source, rendered history, and new viewer intent are considered jointly. Existing interactive video generation systems primarily emphasize following viewer instructions, while source-grounded video generation methods focus on aligning generated content with an external narrative or knowledge source. This leaves a fundamental question underexplored: What context should a generation model ground on during interactive continuation, and how can heterogeneous, unstructured inputs be transformed into such grounding context? In this work, we formulate contextual grounding as the process of transforming heterogeneous input context into an executable constraint model for video generation. To address this challenge, we introduce VIS-Ground, which performs Structured Context Abstraction to recover grounded states and cross-context dependencies, Generation Constraints Induction to project relevant dependencies into candidate-specific constraints, and Constrained Video Generation to enforce these constraints through planning, verification, revision, and rendering. Across three video generation backbones, VIS-Ground consistently achieves the highest overall composite score, reaching an average absolute improvement of 10.3 points over the strongest per-backbone baselines. Detailed analysis further shows gains across both narrative and knowledge grounding, and reveals remaining challenges in dependency extraction, and faithful realization during video rendering.