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Large language models can produce fluent financial analysis, but fluency alone does not establish whether a report is suitable for institutional delivery. We introduce FinReportBench, an expert-grounded benchmark for measuring and improving institution-grade financial report generation. Expert review reveals recurring gaps in report identity, institutional components, source discipline, and visual delivery. We derive a 35-item rubric through expert partial orders, multimodal evidence, and audits of decision boundaries, covering deliverability, report identity, and institutional completeness. Starting from 10,000 balanced Chinese and English financial-research source records, we curate 244 bilingual tasks across three research objects and two input tiers. Each task separates the public query, reconstructed research trajectory, and hidden source packet. Three independent judge families reproduce the expert partial order at near-ceiling rates, showing that bounded, observable criteria support reliable evaluation. Across nine model families, basic deliverability is nearly saturated, while report identity and institutional completeness remain the primary bottlenecks. The largest cross-model gaps concern generation-trace control, information density, and data discipline rather than basic report framing. We then use benchmark-guided skill distillation to turn recurrent failures into reusable generation and self-review constraints. Across five model families, the evolved skill improves mean G1 by 33.85 points and mean G2 by 13.83 points over paired no-skill runs while preserving G0 for every pair. Code and benchmark artifacts are available at https://github.com/MisterBrookT/finreportbench.

UAV see-and-reach navigation requires an aerial agent to approach a language-specified target visible in its initial view and stop reliably near it. Existing methods typically map vision-language representations directly to action outputs without explicitly modeling intermediate fine-grained spatial decisions. This direct mapping causes semantic-control misalignment, leading to inconsistent maneuvers and unreliable termination. To address this issue, we propose DBFly, a vision-language waypoint prediction framework that introduces explicit vision-guided spatial deliberation before waypoint generation. Specifically, DBFly introduces a spatial maneuver decision chain that progressively performs target-direction anchoring, spatial diagnosis, and maneuver decision, enabling high-level maneuver intent to explicitly guide continuous waypoint generation. DBFly further constructs an implicit flight corridor by transforming the initial target-direction prior into a persistent geometric reference and deriving an online corridor state from the UAV's current position, thereby providing soft geometric guidance for spatial diagnosis and maneuver correction. In addition, DBFly develops a terminal-convergence-aware stopping strategy that characterizes terminal states through both target proximity and short-horizon motion convergence, enabling more reliable stopping near the target. Extensive experiments across seen, unseen-object, and unseen-scene test sets demonstrate that DBFly improves the success rate over the SOTA baseline by an average of 25.07 percentage points. The project homepage is available at https://xuefanfu.github.io/DBFly-Page.

Collaborative music agents need internal representations rich enough to support both understanding and generation, yet flexible enough for a workflow where the human retains agency. We present a hierarchical self-supervised ``world model'' for symbolic music: a 2.55M-parameter Swin V2 encoder trained on MIDI piano-roll images with JEPA-style objectives (pitch- and time-shift equivariance, masked embedding prediction, and a distributional regularizer), using no labels and no music-theory vocabulary. Probing the frozen embeddings shows that the level at which a musical property becomes decodable tracks its musical time scale: phrase boundaries are read off the coarsest levels, note density and harmonic detail off the finest. Temporal and phrase structure emerge from the self-supervised objectives alone, while harmonic content must be asked for; a small chord-supervision head raises joint chord recovery from .18 to .54, and key detection, which is never supervised, from .16 to .70. Following the Representation AutoEncoder paradigm, a conditional flow-matching model stands in for a trained decoder, flowing in pixel space from PCA-reduced conditioning: it reproduces a target window at pixel F1 $0.996$, and the same per-level conditioning dropout that controls how far variations stray also enables graphical prompting for masked inpainting with no inpainting-specific sampler. The pipeline runs on CPU producing a suggestion in $2.8$ s, or $0.6$ s on Apple MPS, which we demonstrate in a live interactive demo. In concert with an LLM-based brain, these capabilities supply the core of a collaborative music creation agent in service of, rather than in place of, human agency.

Diffusion transformers deliver strong image generation, but their training cost grows superlinearly with resolution. Recent work justifies training or sampling at reduced resolution on a spectral premise: at high noise, a downscaled latent preserves almost the full surviving signal. Whether a downscaled step also preserves the native training gradient signal, however, has remained unresolved. We reduce how that signal changes under downscaling to two terms: a noise-dependent term governed by the downscale ratio, which decays at high noise as the spectral premise predicts, and a σ-independent floor governed by the target grid's absolute token count, carried by the compute graph itself and removed by no noise level. The measured (route, σ) map corroborates the account and uncovers structure the spectral picture cannot express: on the 1024->768 route, a window (0.65 < σ< 0.95), predicted by no spectral criterion at any tolerance, where the downscaled gradient stays within a small margin of the native one. Training LoRA adapters with downscaled steps restricted to the routes and noise windows the map validates reduces training time by 14.6% at a fixed step budget while remaining near-native in weight space. Code is available at https://github.com/sorryhyun/anima_lora.

Vision-language systems combine images with retrieved text, but these sources can disagree or jointly fail to support an answer. Reliable models must identify the trustworthy source and abstain when neither is adequate. Existing post-training objectives score instances independently and therefore do not enforce coherent behavior under counterfactual evidence changes. We introduce CARGO-VL, a group-relative framework that optimizes matched variants covering aligned, image-correct, text-correct, and both-wrong (A/V/T/N) evidence states as one bundle. Its objective couples condition-wise correctness with transition rewards for answer invariance, source equivariance, and answer-to-abstention switching, while a primal-dual controller balances unsafe answers against excessive deferral. We also contribute XMC (eXtended Modal Conflict), a four-condition conflict training resource, and evaluate transfer on CMC-Bench and Modality-Bias. Across multiple seeds, CARGO-VL improves conflict handling, unsupported-answer avoidance, and modality balance over pointwise baselines. Ablations identify complementary benefits from relational transition signals and adaptive risk control, supporting counterfactual consistency as a practical objective for reliable multimodal evidence arbitration.

Long-form video understanding requires locating sparse, question-relevant evidence in long, multimodal videos. Real-world video distributions differ in modality-specific information density, content structure, and evidence patterns, causing fixed video-agent designs to incur redundant processing or fail when mismatched. Extending automated agent evolution from text to video is challenging because full long-video execution makes candidate validation expensive, failures propagate across coupled evidence-processing stages, and complex preprocessing, perception tools, and localization strategies make code-level updates difficult to implement reliably. We introduce MetaVideoAgent, a framework that automatically evolves a video agent for a target distribution. It profiles information density and evidence requirements from sparsely sampled frames and associated queries to guide initial design, then compresses localized failures into independently executable minimal validation tasks. It constructs evidence-grounded Gold Paths, audits Student trajectories, aggregates recurring failures across samples, and attributes them to responsible modules. A modular agent representation constrains each update to the primary responsible module and its necessary dependencies. We further introduce VA-EvoBench, covering eight video distributions with separate evolution and held-out splits. With four evolution iterations per distribution, MetaVideoAgent improves every initial agent and raises macro-average accuracy from 38.44% to 51.47%, at an average evolution cost of 3.54M tokens per distribution. The evolved agents outperform the strongest prior fixed-design video agent by 6.39 percentage points while using the fewest tokens and video frames per question among the compared video agents. We will release all code and data to support reproducible research.

Recent video models increasingly support generation, reference conditioning, and editing within a single model, yet typically expose them as separate operations over fixed inputs. Practical creation unfolds across multiple shots, requiring one model to generate from text, follow a reference, or edit source footage while maintaining shared history. We formalize this setting as interactive multi-shot video creation (IMVC) and introduce ContextMaster, a unified model with a role-aware context representation for these operations. An interactive model must retain access to an expanding history without allowing the context read cost at each denoising step to grow. ContextMaster combines reusable clean context states with fixed budget sparse context routing and uses ConstraintSink to keep task constraints visible. To address the dual challenges of sparse context access and inference with few denoising steps, we propose a two-stage privileged context distillation framework, which transfers full context behavior from a dense teacher through consistency distillation and then refines deployment rollouts with distribution matching. Experiments on the three primitive tasks demonstrate improved task fulfillment and consistency across shots over specialized baselines. User studies further validate flexibly composed workflows, while the model reaches 16 FPS on a single GPU.

Similes provide a compact and expressive way to describe visual characteristics in text prompts. Recent text-to-image models (t2i models) can produce visually compelling outputs from simile prompts, yet even frontier models frequently misinterpret the metaphorical vehicle and confuse it with the object. These systematic failures reveal a gap between figurative language and object-level visual grounding in t2i models. To investigate this issue, we propose a scalable evaluation framework for simile understanding. Our framework includes (1) a controlled simile dataset in which metaphorical vehicles are drawn from a predefined set of object-detectable categories and combined with diverse templates, (2) automatic grounding metrics based on YOLO (You Only Look Once) detection, and (3) text encoder layer analysis using Diffusion Lens to track how metaphorical vehicles emerge during generation. Experiments across architecturally diverse t2i models reveal consistent literalization failure patterns. We further discuss potential mitigation strategies for improving simile grounding in t2i models.

Video Anomaly Detection (VAD) is inherently challenging due to the scarcity of anomalies and the large visual variability in surveillance footage, including changes in lighting, viewpoint, and human appearance. To mitigate visual noise and address privacy concerns, recent work has shifted to pose-based VAD, which focuses on motion dynamics rather than raw video data. However, existing pose-based approaches model human behavior in continuous latent spaces, limiting their ability to learn compact motion patterns necessary for robust behavior analysis. We address this by proposing Vector-Quantized Video Anomaly Detection (VQ-VAD), a novel human-centric anomaly detection framework that learns discrete motion representations. VQ-VAD adapts Vector-Quantized GAN (VQ-GAN), originally developed for image generation, to operate on keypoint sequences and construct a motion codebook of normal behavior. Trained exclusively on normal motion sequences, VQ-VAD detects anomalies by identifying high reconstruction errors when an observed motion sequence cannot be mapped to the learned codebook. We conduct extensive experiments across three complementary evaluation settings, including in-domain, cross-domain, and cross-dataset generalization, on four anomaly detection benchmarks. VQ-VAD achieves strong in-domain accuracy (81.83% on HR-SHT [15]), effective cross-domain transfer from CMU Panoptic [14] (76.69% on HR-SHT [15] without retraining), and competitive cross-dataset robustness. The code base for this work is available at https://github.com/TeCSAR-UNCC/VQ-VAD.

The abundance of casually captured monocular videos and images on social media provides a valuable source for immersive content creation, where generating novel views from such sparse observations can greatly enhance user experiences. However, producing photorealistic and geometrically consistent views with precise camera control remains challenging when input coverage is extremely limited. Reconstruction-based approaches such as NeRF and 3D Gaussian Splatting (3DGS) deteriorate severely under sparse inputs and fail to explicitly handle occlusions. Generative methods ease data requirements but still struggle with large-baseline view synthesis due to inaccurate or implicit geometric guidance. To overcome these limitations, we introduce UniWorld-View, a unified framework for controllable large-baseline novel view synthesis from monocular inputs. UniWorld-View integrates explicit 3D guidance with generative diffusion modeling to enable precise camera control and geometrically consistent view generation. The geometric guidance is obtained through an occlusion-aware point cloud rendering strategy that resolves visibility ambiguities and provides accurate priors for diffusion-based synthesis. By coupling this rendering strategy with powerful video diffusion backbones, UniWorld-View achieves high-fidelity novel view generation even under extreme camera motions and wide-baseline changes, and can further provide multi-view videos for downstream dynamic 3DGS reconstruction. Experiments on the WorldScore benchmark and zero-shot NVS benchmarks demonstrate the effectiveness of UniWorld-View in controllability, geometric consistency, and visual fidelity.

Interactive video world models are essential for long-horizon planning and exploration, yet they suffer from compounding errors. Post-training methods such as reinforcement learning (RL) can improve these models, but they hit a verification bottleneck: for arbitrary action sequences, no ground-truth future state exists to measure long-term drift. Our key insight is that reversible action cycles make this verification possible: a sequence composed with its inverse must analytically return to the initial state, yielding annotation-free supervision on long-horizon correctness. Building on this, we introduce WorldCycle, a self-verifiable RL framework that constructs closed action cycles and their repeated executions from ordinary action sequences, and optimizes two complementary rewards: a spatial closure reward enforcing symmetry between mirrored forward and reverse segments, and a temporal consistency reward aligning states across repeated cycle executions. These rewards force the model to learn actions as consistent state operators rather than memorized temporal patterns, and extend naturally to out-of-distribution composite action cycles that the base model handles poorly. We further release CycleBench, a diagnostic benchmark for state-returning ability under complex action structures. WorldCycle reduces state returning drift by up to 44% and lifts composite-action accuracy nearly 4x over the base model, providing a vital foundation for physically grounded world models.

World action models (WAMs) built on video generation backbones are a rising recipe for robot learning, yet remain confined to tabletop manipulation. Mobile manipulation demands simultaneous locomotion and whole-body manipulation amid scene-scale dynamics, yet is still dominated by dynamics-blind visual encoders with hand-crafted coordination. We bridge this gap with MobileWAM, a mixture-of-transformers architecture that fuses a pretrained video diffusion transformer with a lightweight action expert through layerwise joint attention, translating internet-scale motion priors into whole-body control. To reconcile the heterogeneous dynamics of moving and manipulating, each feed-forward layer of the action expert becomes a three-expert mixture of shared, locomotion, and manipulation experts, softly routed by the motion intent in the action tokens. To densify supervision, we further propose Chain-of-Foresight (CoF): intermediate representations sequentially predict a chain of future latent chunks, each step conditioned on its predecessor. CoF pairs naturally with our decoupled video--action denoising scheme. At deployment, the WAM serves as a pure current-frame encoder; foresight acts only through gradients, so at inference the foresight chain and video generation are discarded, leaving only policy-level cost. MobileWAM surpasses state-of-the-art mobile manipulation policies on ManiSkill-HAB and fine-tunes to a real ARX Lift2 mobile manipulator across diverse tasks with strong generalization. Code will be released soon.

Video-to-audio (V2A) generation extends image-to-audio generation (I2A) by introducing consecutive frames that provide essential temporal cues for audio synthesis. However, existing conditional diffusion-based V2A methods typically enhance visual conditioning with additional audio-visual supervision, acoustic structure prediction, or reasoning from large multimodal models, requiring extra networks or strong inductive biases. Inspired by recent advances in visual representation learning, we introduce TD-V2A, which leverages temporal differences (TD) as the key representation that distinguishes V2A from I2A, enriching visual conditioning with minimal architectural modification. We first investigate TD at both the frame and feature levels to identify the most effective representation level at which TD complements visual representations. Based on these findings, we develop a hierarchically continual learning strategy and an annealed temporal differences guidance method to progressively learn and exploit TD information during diffusion training and sampling process, respectively. Extensive experiments on benchmark datasets demonstrate that effectively exploiting TD through our proposed framework significantly improves end-to-end V2A generation quality, even outperforming dedicated V2A representations such as contrastive audio-visual pretraining.

Action-conditioned world models aim to predict how visual environments evolve under an agent's actions. Yet future frames are often highly predictable from visual inertia and recurring motion patterns alone. This creates a shortcut: models can fit the data by exploiting statistical biases without making their visible dynamics meaningfully depend on the action. As a result, different actions may produce similar futures, while motion may persist even under zero action. The key question is how to reduce reliance on statistical shortcuts from dominating action-conditioned prediction. We argue that action control requires more than injecting action features; it requires enforcing consistency under counterfactual changes to actions and observations. Based on this insight, we introduce CoCo, a Counterfactual Consistency framework to enhance action controllability through two complementary constraints. Multi-step counterfactual consistency constrains reference, inverse-action, and zero-action rollouts, while action-spatial counterfactual consistency enforces consistent predictions under mirrored scenes and transformed actions. Together, they reduce reliance on statistical shortcuts from substituting for action-dependent dynamics. We further introduce Action Response Consistency (ARC) and Drift Energy (DE) to assess action controllability, together with Mini-SSMB for same-state, multi-action counterfactual evaluation. On Mini-SSMB, our full model achieved ARC_inv of 0.412 and ARC_ref of 0.483, while reducing DE by 17.07% relative to the baseline. On VP2 visual planning, it achieves the highest average success rate among SOTA models, at 73.1%. Experiments on BAIR and RoboNet further show that these gains preserve video prediction quality and transfer across model settings.

Instruction-based video editing (IVE) is an emerging field with broad applications, yet evaluating editing models remains challenging. Existing benchmarks suffer from two major limitations: limited task coverage inherited from image editing, which overlooks video-specific dimensions, and inadequate metrics that fail to measure instruction fidelity, allowing incorrect edits to receive high scores due to strong visual priors from the original video. To address these issues, we introduce a comprehensive and structured benchmark for IVE. Our benchmark decomposes editing tasks into multiple video-specific dimensions, including spatial, temporal, audio, and reference-based editing, extending beyond conventional frame-level evaluation. It also distinguishes explicit and implicit instructions and incorporates reasoning-based scenarios to better reflect real-world requirements. Furthermore, we propose an evaluation framework that assesses editing quality from four complementary dimensions: accuracy, preservation, realism, and consistency, using both human judgments and state-of-the-art vision-language models. To emphasize instruction fidelity, we introduce an accuracy-aware penalty mechanism that conditions other scores on accuracy, preventing visually plausible but incorrect edits from receiving inflated evaluations. Extensive experiments on representative open-source and commercial models show that current IVE models remain far from satisfactory. OmniEdit-Bench provides a comprehensive and reliable testbed for evaluating instruction-based video editing and offers insights into future research directions.

Despite the remarkable recent progress of video world models, social interaction between users and the characters within these worlds remains unsupported. To fill this gap, we present HelloWorld, a video world model that enables social interaction with in-world characters. With a single button press, users can prompt the on-screen character to respond toward the camera, e.g., turning to the viewer, waving, nodding, or speaking a short greeting. To make these interactions natural, we propose a self-distillation pipeline that finetunes the video generation model on data synthesized by itself. Each synthesized clip contains both social interactions and camera motion, allowing the model to learn camera-pose conditioning without degrading interaction quality. At inference, we further introduce a training-free module that determines when the interaction occurs. Upon a button press, it modulates the cross-attention masks of the DiT so that the interaction-related text prompt attends only to the frames within the press window, temporally localizing the character's response. We further build HelloWorldBench, a 400-sample benchmark with three social interaction metrics alongside three conventional metrics, for evaluation. Experiments demonstrate that HelloWorld surpasses a variety of baselines in interaction quality, while maintaining state-of-the-art picture aesthetics and camera-pose following. Project page: https://github.com/AlayaLab/HelloWorld

High-quality driving data are essential for autonomous-driving systems and generative world models. However, rare and safety-critical scenarios involving adverse weather, braking under low tire--road friction, and uneven road geometry are costly and risky to collect at scale. Existing video-generation and 3D Gaussian editing methods can modify weather appearance or road geometry, but typically do not couple these edits with tire--road interaction and vehicle dynamics. As a result, an edited video may retain its original trajectory even when the modified road condition should alter braking, wheel slip, load transfer, and ego-camera motion. We present muSync-GS, a physics-synchronized framework for driving video synthesis under adverse-weather and road-elevation hazards. A precipitation-derived road-surface condition jointly controls road appearance and tire friction, while a shared road-elevation profile drives both visible road-geometry editing and axle excitation. A calibrated vehicle model predicts speed, slip ratio, normal loads, and pitch for constructing the ego-camera trajectory and synchronized physical annotations. On 12 held-out CarSim cases spanning precipitation levels, brake inputs, and road-profile parameters, the model achieves mean case-wise RMSEs of 0.0273 m/s for speed, 0.0590 degrees for pitch, 0.0101 for slip ratio, and 26.61 N for per-wheel normal load. Together with the reconstructed-scene experiments, these results show that muSync-GS accurately reproduces vehicle responses under held-out controls while synchronizing them with controllable scene edits and ego-camera motion.

Diffusion policies are a powerful policy class for continuous control, but their iterative denoising process creates a substantial computational bottleneck. Reducing this cost requires adapting the number of denoising steps to the difficulty of each action while preserving task performance. We introduce Prefix-Optimal Generative Policies (POGP), a framework that learns a prefix value function at every intermediate denoising step through a Bellman-style recursion over the denoising chain. The prefix value function serves two purposes: it provides an auxiliary training objective that encourages intermediate outputs to become high-quality actions, and it enables a test-time stopping rule that terminates denoising when additional steps are unlikely to produce meaningful improvement. Across four MuJoCo environments and comparisons with 12 baselines, POGP reduces the required number of denoising iterations by approximately 2.7-fold while retaining near-full task performance. Compared with state-of-the-art dynamic diffusion baselines, prefix training also improves final task performance by approximately 3.5%. These results indicate that supervising intermediate denoising steps is useful not only for adaptive early stopping, but also as an auxiliary objective that improves the learned policy.

Gradient descent has been of particular interest in modern machine learning beyond sole focus on optimization. Implicit bias emerging from optimization, though not being encoded by the learning objective, often prevents from overfitting to spurious patterns. A typical instance is the max-margin implicit bias of a linear classifier, widely established for exponentially tailed loss functions. Even after having a given dataset separated, the parameter vector continues to evolve towards the max-margin direction asymptotically along the gradient descent dynamics. This phenomenon corroborates a frequent empirical observation of "train longer, generalize better." However, the max-margin convergence is an asymptotic phenomenon, and what is worse, this asymptotic convergence rate is significantly slower than pure convex optimization. Even so, the parameter vector along gradient descent dynamics commonly correlates with the max-margin direction positively (though not exactly) within considerably fewer iterations than the asymptotic rate. By shedding another light on this classical problem, this work aims to understand the mechanism of this early-stage alignment phenomenon. Our theoretical results demonstrate that the parameter vector weakly aligns with the max-margin direction within $O(\exp(\exp(-δ)))$ iterations, where $δ>0$ is the permissible alignment error, which is shown to be tight. By tracking the radial and tangential flows, our proof operates on the alignment dynamics directly with dataset geometry and gets rid of the asymptotic expansion, which is a key insight to establishing faster weak alignment.

Face inpainting with diffusion models has recently achieved impressive visual quality, yet preserving identity fidelity under significant occlusion and conflicting text guidance remains a major challenge. To address this issue, we present Reference Semantic Inpainting for Face (ReSem-Face), a cascaded diffusion framework that introduces an explicit identity-conditioned semantic prior for multi-reference face inpainting. Our approach distills representative identity features from multiple references to reconstruct missing semantic regions, which then guide the diffusion process through a multi-stream conditioning architecture. This design provides strong semantic constraints when pixels are absent and stabilizes identity reconstruction while remaining compatible with prompt-driven edits. Experiments on CelebAHQ-IDI-5 and VGGFace2 demonstrate that ReSem-Face yields more reliable identity-preserving completion under severe semantic masks and improves text-controlled editing quality compared with representative baselines.

Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data. In this study, we propose a fundamentally different, unified approach to atmospheric data assimilation. We use latent video flow-matching to sample temporally consistent trajectories from a prior trained using ERA5 reanalysis (69 variables over an 8-day window). We also use posterior sampling to assimilate real observation sources, such as those from the NOAA Integrated Global Radiosonde Archive and the Integrated Surface Database. Because the prior generates a continuous trajectory, it naturally propagates information between observed and unobserved frames. Therefore, we can perform various DA tasks, such as filtering and smoothing, simply by changing the observed frames. Moreover, we generate full-state ensemble forecasts directly from sparse observations, achieving performance competitive with state-of-the-art observation-to-forecast models.

Modern diffusion and flow-based models are increasingly moving toward few-step, latent-free generation to bypass the computational overhead of multi-step sampling and the reconstruction bottlenecks of external autoencoders. We propose the Interval Denoiser, a theoretically rigorous framework for latent-free generation. Derived directly from the flow matching ODE, it establishes an exact analytical mapping for intermediate trajectory states. Unlike prior formulations, our prediction is shown to reside on a low-dimensional manifold across any time interval, making the regression tractable for a network operating directly on pixels. Furthermore, by avoiding empirical algebraic substitutions, our formulation correctly isolates the pure time derivative to prevent biased gradient evaluations and ensure exact first-order optimization. By analyzing this objective, we equip our framework with residual clipping and a time-sampling curriculum, enabling effective long-interval training and improving few-step performance. Trained from scratch on ImageNet 256x256, our model achieves an FID of 4.55 in one step (1-NFE) and 3.98 in two steps (2-NFE) without perceptual losses.

The Subspace Constrained Mean Shift (SCMS) algorithm is a popular nonparametric method for extracting density ridges, which serve as a low-dimensional representation of high-dimensional data. It is a widely held belief in the literature that SCMS trajectories converge to the classical density ridge, which we call the "static ridge", defined via the density gradient and the eigenvalues and eigenvectors of the density's Hessian. In this paper, we demonstrate that this assumption does not hold in general, as the static definition fails to account for the rotation of the trailing eigenspace along the continuous flow of the algorithm's underlying vector field. To resolve this, we propose a paradigm shift by introducing the "stable ridge", a novel geometric structure defined through the lens of dynamical systems and the Jacobian of the projected density gradient. We prove that this stable ridge is the true theoretical target of the SCMS algorithm. Building upon this foundation, we develop a generalized SCMS framework utilizing a constant step size, establishing its uniform R-linear convergence and topological surjectivity onto the stable ridge. We further derive the rates of convergence for estimating the stable ridge in terms of the Hausdorff distance. Finally, we expose that the original SCMS algorithm suffers from polynomial-time computational complexity, which is caused by implicitly coupling the step size to the smoothing bandwidth via the Mean Shift operator, and demonstrate how our generalized framework provides a statistically consistent and more efficient solution.

We study asynchronous optimization for finite-sum eigenspace computation in heterogeneous distributed systems. The theoretical foundations for asynchronous eigenspace computation remain scarce, with existing approaches offering limited coverage of dynamics directly on the Grassmannian under stale information. In this paper, we propose a Grassmannian incremental aggregation method that refreshes only arriving components and reuses cached gradients, retaining low per-update cost without global synchronization. The method employs an extrinsic polar update that preserves the intrinsic subspace geometry without requiring parallel transport of stale tangent vectors. Our analysis establishes a tight angle-dependent gradient-dominance characterization of the objective and a basin-invariance property for stale aggregated updates. These yield two-phase linear convergence, comprising an explicit broad-basin regime and a sharper local regime, with constants controlled by component spectral spreads. Experiments on serial and distributed PCA demonstrate improved sample efficiency and wall-clock convergence over representative baselines.

On-policy distillation (OPD) has become an effective approach for consolidating multiple task-specialized image generation models into a single student. However, existing OPD methods optimize the student mainly to match the teacher's output velocity, making the teacher the upper limit of the optimization objective. While output-level supervision alone leaves the student's blockwise representation evolution underconstrained, which weakens the transfer of capabilities that must be progressively developed across layers. We propose STEP-OPD, an on-policy distillation framework for image generation that extends the student's learning target beyond the teacher and introduces explicit constraints on its internal representation evolution. Instead of treating the teacher as the final target, we use the velocity difference between each task-specific teacher and the shared base model as a direction for further learning and add a scaled version of this difference to the teacher velocity. In addition, we align the direction and magnitude of representation changes between the student and teacher, enabling the student to learn how representations are progressively transformed across network blocks. Experiments on compositional alignment, text rendering, and human preference show that our method consistently improves Standard OPD methods. In particular, it increases the GenEval score of DiffusionOPD from 0.927 to 0.961, while also improving OCR and all preference-based metrics. The resulting unified student surpasses the corresponding single-task teachers across all three capability groups, showing that output extrapolation enables beyond-teacher learning. And representation change alignment provides complementary guidance for the student's internal transformations.

Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth $Ω(N)$ in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.

Functional flow matching is posed on distributions of functions but implemented from finitely many coefficients or point values. Under scattered or adaptive refinement, the resulting conditioning sigma-algebras need not be nested, so martingale convergence does not justify the sensor limit. We prove strong $L^2$ convergence of finite conditional velocity targets for every strongly consistent sequence of finite-rank reconstructions, with quantitative bounds for orthogonal projections and a point-sensor extension through a regularity space. For learned flows, coupling directly to a population superposition path yields an end-to-end Wasserstein bound without assuming uniqueness of the population finite-dimensional ODE. We verify sensor-independent constants for a normalized quadrature neural operator, including globally Lipschitz activations through an explicit magnitude recurrence. A noncommuting trace-class Gaussian example gives boundary multiplier $0$ under projected restriction and $0.72$ under exact conditioning. A spatial regularity--cubature certificate closes the operator-realization term, a Bernstein argument gives a $\widetilde{O}(n^{-1})$ excess-risk term for fixed model dimension and envelopes, and an exactly realizable clipped Gaussian scaling specialization yields an explicit end-to-end rate.

We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure. Latent diffusion models (LDMs) address the high dimensionality by learning a latent space, but they typically impose a Euclidean structure, failing to capture the underlying manifold geometry, especially problematic in data-sparse regimes. ILDM addresses these limitations by interpreting the latent space as a chart of an unknown Riemannian manifold, with geometry and uncertainty quantified through a probabilistic decoder. The forward process is a hybrid diffusion that switches between Riemannian and Euclidean dynamics based on local uncertainty, where the Riemannian component is governed by a probabilistic metric tensor derived from the decoder. To learn the generative dynamics, we introduce an approximate denoising score matching method tailored to the hybrid diffusion setting, enabling a backward process defined by hybrid Langevin dynamics. Experiments on COIL-100, MNIST, and cardiac MRI datasets demonstrate that ILDM significantly improves generation quality, achieving lower FID and LPIPS scores compared to standard diffusion and latent diffusion models.

Part-level affordance grounding has advanced the localization of functional object regions associated with elemental actions. Extending this capability to complex tasks calls for connecting the semantic roles of participating objects with task-state-aligned visual observations and multi-step planning. We introduce EgoAfford, a benchmark designed to connect these three aspects. Given an egocentric observation and a high-level tabletop task, a model must generate the remaining plan and segment the functional regions of up to three components of the next action: the direct object, instrument, and destination. EgoAfford comprises approximately 15.5k human-verified images from 2,000 generated multi-step scenes, organized as semantically aligned, task-complete image series, together with EgoAfford-Real, 102 manually captured images spanning 26 tasks. We further present EgoLens, a 3B multimodal large language model with role-specific mask decoders, as an in-domain reference model for this joint task. Evaluations of recent referring-segmentation MLLMs, commercial-VLM--SAM2 pipelines, and EgoLens highlight the complementary challenges of next-step inference and action-role-conditioned part grounding. EgoLens establishes strong reference performance on both generated and manually captured observations. Together, EgoAfford and EgoLens provide a foundation for jointly studying perception and planning in multi-step tabletop tasks. Our project page is available at: https://egoafford.github.io

Agentic systems have emerged as a promising paradigm for solving complex tasks by coordinating specialized LLM-based agents. However, most existing systems primarily optimize task success while giving limited consideration to execution efficiency under practical constraints such as executor capability and computational cost. Existing router-based methods have limited ability to reason over rich, evolving task contexts, multi-step dependencies, and intermediate execution feedback, and often generalize poorly to unseen executors. We propose EASy, a trainable agentic framework that jointly optimizes task performance and computational efficiency through reinforcement learning. EASy equips an LLM-based orchestrator with explicit knowledge of the capability and cost profiles of heterogeneous executors, enabling context-sensitive coordination beyond performance-only routing. It further introduces a milestone-plan-act workflow that decomposes complex tasks into manageable milestones, constructs dependency-aware execution graphs, assigns suitable executors, and parallelizes independent steps while adapting subsequent decisions to intermediate outcomes. To train the orchestrator, we develop a tree-structured rollout procedure that explores alternative milestone decompositions and execution plans, together with multi-component rewards that capture task correctness, execution efficiency, and trajectory completeness. Extensive experiments on mathematical reasoning, embodied decision-making, and deep research benchmarks show that EASy consistently achieves stronger performance-efficiency trade-offs than strong agentic baselines.