Multi-stage neural operator learning with application for convolutions

Convolution integrals widely exist in applications, and to enable fast and accurate computations, this paper introduces two general multi-stage neural operator learning frameworks. The first, Deep Collocation Neural Operator (DCNO), is a supervised approach that iteratively refines the operator approximation by learning residuals from input-output data pairs. The second, Deep Galerkin Neural Operator (DGNO), is an unsupervised framework applicable when the target operator can be represented by a PDE, leveraging the weak form of the PDE residual for training. Both methods progressively construct basis operators through multiple training stages to enrich the approximation space, leading to significantly improved accuracy over standard one-shot operator learning. We provide theoretical analysis for their approximation capabilities and implement them for learning convolutions. Extensive numerical experiments demonstrate that both DCNO and DGNO achieve high accuracy, approaching machine precision under single float for convolution problems, and offer substantial efficiency gains for numerous queries or parametric variations compared to traditional solvers. We also extend these frameworks to handle multi-input operator learning scenarios involving variations in both the density and kernel of a convolution.

OPSD-V: On-Policy Self-Distillation for Post-Training Few-Step Autoregressive Video Generators

We propose OPSD-V, an on-policy self-distillation paradigm for post-training few-step autoregressive (AR) video diffusion models. Existing few-step AR video generators can produce long videos with low latency, but still suffer from error accumulation and weakened motion dynamics during long autoregressive rollout. OPSD-V reduces long-horizon degradation while preserving the original few-step inference path. The key idea is to introduce real long-video data as temporal context during training and use it to provide dense trajectory-level supervision. Specifically, the student follows the exact inference-time rollout, generating each chunk conditioned on its own previously generated KV cache. In parallel, the teacher is evaluated at the same student-visited denoising states, but uses a cleaner AR-consistent temporal cache in which older history can be replaced by real-video context. This provides dense denoising-level corrective targets under on-policy AR cache dynamics, without changing the sampler, number of denoising steps, or inference-time cache mechanism. We apply OPSD-V to representative few-step AR video models, including Self-Forcing and LongLive. Experiments show consistent improvements in visual quality, motion dynamics, and VBenchLong scores. A user study with 10 participants comparing 20 video pairs shows that OPSD-V is preferred over the base models in 66.0% of overall-preference judgments (82.5% excluding ties).

LongCat-Video-Avatar 1.5 Technical Report

Despite advances in audio-driven video generation, achieving commercial-grade stability remains challenging. We present LongCat-Video-Avatar 1.5, an upgraded open-source framework prioritizing systematic engineering and production-readiness over architectural novelty. By upgrading the audio encoder to Whisper Large and meticulously scaling our training recipes, v1.5 achieves accurate lip-synchronization, full-body temporal stability, and robust long-video generation with strict identity consistency. Through rigorous data curation and RLHF Training, the model readily generalizes to stylized domains such as anime and animals, and natively handles complex real-world conditions, such as multi-person interactions and object handling. Furthermore, addressing the practical demands of industrial deployment, we employ advanced step distillation to accelerate inference to an optimal 8 NFE, achieving a favorable trade-off between serving efficiency and visual fidelity. The superiority of our approach is validated through extensive quantitative metrics and a rigorous human evaluation conducted on a comprehensive benchmark of over 500 diverse test cases. Results show that v1.5 achieves competitive or superior performance compared to leading closed-source systems (e.g., HeyGen, OmniHuman 1.5, Kling Avatar 2.0) across human-likeness ratings and expert-level quality assessments on our benchmark. With its open-source release, LongCat-Video-Avatar 1.5 narrows the gap between academic research prototypes and commercial-grade deployment.

Minimum Description Length based Granular-Ball Tree Regularization for Spectral Clustering

Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.

GeoFunFlow-3D: A Physics-Guided Generative Flow Matching Framework for High-Fidelity 3D Aerodynamic Inference over Complex Geometries

Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the governing equations. To address these issues, we propose GeoFunFlow-3D, a physics-guided generative flow matching framework. Temporally, we utilize optimal transport theory to build the generation path, ensuring stable training dynamics. Spectrally, we introduce a high-order discrete engine without automatic differentiation (No-AD) to reduce gradient stiffness. Spatially, a topology-aware super-resolution module (SATO) is employed to rigorously enforce physical laws in localized regions such as shock waves. We evaluated our framework on complex industrial datasets. On the BlendedNet dataset, the model successfully avoids mode collapse even under sparse data conditions. For the NASA Rotor37 test, it accurately captures 3D detached shock structures. Compared to conventional operators, GeoFunFlow-3D significantly improves accuracy, reducing the pressure field error (RRMSE) to 0.0215 while maintaining competitive inference efficiency. Ultimately, this work provides a reliable, geometry-driven approach for generating high-dimensional fluid fields.

TurboTalk: Progressive Distillation for One-Step Audio-Driven Talking Avatar Generation

Existing audio-driven video digital human generation models rely on multi-step denoising, resulting in substantial computational overhead that severely limits their deployment in real-world settings. While one-step distillation approaches can significantly accelerate inference, they often suffer from training instability. To address this challenge, we propose TurboTalk, a two-stage progressive distillation framework that effectively compresses a multi-step audio-driven video diffusion model into a single-step generator. We first adopt Distribution Matching Distillation to obtain a strong and stable 4-step student, and then progressively reduce the denoising steps from 4 to 1 through adversarial distillation. To ensure stable training under extreme step reduction, we introduce a progressive timestep sampling strategy and a self-compare adversarial objective that provides an intermediate adversarial reference that stabilizes progressive distillation. Our method achieve single-step generation of video talking avatar, boosting inference speed by 120 times while maintaining high generation quality.

TAMISeg: Text-Aligned Multi-scale Medical Image Segmentation with Semantic Encoder Distillation

Medical image segmentation remains challenging due to limited fine-grained annotations, complex anatomical structures, and image degradation from noise, low contrast, or illumination variation. We propose TAMISeg, a text-guided segmentation framework that incorporates clinical language prompts and semantic distillation as auxiliary semantic cues to enhance visual understanding and reduce reliance on pixel-level fine-grained annotations. TAMISeg integrates three core components: a consistency-aware encoder pretrained with strong perturbations for robust feature extraction, a semantic encoder distillation module with supervision from a frozen DINOv3 teacher to enhance semantic discriminability, and a scale-adaptive decoder that segments anatomical structures across different spatial scales. Experiments on the Kvasir-SEG, MosMedData+, and QaTa-COV19 datasets demonstrate that TAMISeg consistently outperforms existing uni-modal and multi-modal methods in both qualitative and quantitative evaluations. Code will be made publicly available at https://github.com/qczggaoqiang/TAMISeg.

Hybrid Energy-Aware Reward Shaping: A Unified Lightweight Physics-Guided Methodology for Policy Optimization

Deep reinforcement learning excels in continuous control but often requires extensive exploration, while physics-based models demand complete equations and suffer cubic complexity. This study proposes Hybrid Energy-Aware Reward Shaping (H-EARS), unifying potential-based reward shaping with energy-aware action regularization. H-EARS constrains action magnitude while balancing task-specific and energy-based potentials via functional decomposition, achieving linear complexity O(n) by capturing dominant energy components without full dynamics. We establish a theoretical foundation including: (1) functional independence for separate task/energy optimization; (2) energy-based convergence acceleration; (3) convergence guarantees under function approximation; and (4) approximate potential error bounds. Lyapunov stability connections are analyzed as heuristic guides. Experiments across baselines show improved convergence, stability, and energy efficiency. Vehicle simulations validate applicability in safety-critical domains under extreme conditions. Results confirm that integrating lightweight physics priors enhances model-free RL without complete system models, enabling transfer from lab research to industrial applications.

WildActor: Unconstrained Identity-Preserving Video Generation

Production-ready human video generation requires digital actors to maintain strictly consistent full-body identities across dynamic shots, viewpoints and motions, a setting that remains challenging for existing methods. Prior methods often suffer from face-centric behavior that neglects body-level consistency, or produce copy-paste artifacts where subjects appear rigid due to pose locking. We present Actor-18M, a large-scale human video dataset designed to capture identity consistency under unconstrained viewpoints and environments. Actor-18M comprises 1.6M videos with 18M corresponding human images, covering both arbitrary views and canonical three-view representations. Leveraging Actor-18M, we propose WildActor, a framework for any-view conditioned human video generation. We introduce an Asymmetric Identity-Preserving Attention mechanism coupled with a Viewpoint-Adaptive Monte Carlo Sampling strategy that iteratively re-weights reference conditions by marginal utility for balanced manifold coverage. Evaluated on the proposed Actor-Bench, WildActor consistently preserves body identity under diverse shot compositions, large viewpoint transitions, and substantial motions, surpassing existing methods in these challenging settings.

U-Mind: A Unified Framework for Real-Time Multimodal Interaction with Audiovisual Generation

Full-stack multimodal interaction in real-time is a central goal in building intelligent embodied agents capable of natural, dynamic communication. However, existing systems are either limited to unimodal generation or suffer from degraded reasoning and poor cross-modal alignment, preventing coherent and perceptually grounded interactions. In this work, we introduce U-Mind, the first unified system for high-intelligence multimodal dialogue that supports real-time generation and jointly models language, speech, motion, and video synthesis within a single interactive loop. At its core, U-Mind implements a Unified Alignment and Reasoning Framework that addresses two key challenges: enhancing cross-modal synchronization via a segment-wise alignment strategy, and preserving reasoning abilities through Rehearsal-Driven Learning. During inference, U-Mind adopts a text-first decoding pipeline that performs internal chain-of-thought planning followed by temporally synchronized generation across modalities. To close the loop, we implement a real-time video rendering framework conditioned on pose and speech, enabling expressive and synchronized visual feedback. Extensive experiments demonstrate that U-Mind achieves state-of-the-art performance on a range of multimodal interaction tasks, including question answering, instruction following, and motion generation, paving the way toward intelligent, immersive conversational agents.