Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization

We study approximation by shallow ReLU$^s$ networks, $σ_s(t)=\max{0,t}^s$, and the generalization behavior of such networks under $\ell_1$ path-norm control. For the $L^p$-type integral spaces $\widetilde{\mathcal{F}}_{p,τ_d,s}$, $1\le p\le2$, we establish approximation bounds for shallow networks using spherical harmonic analysis. In particular, when the parameter measure is the uniform measure $τ_d$ and $p<p^*=(2d+2)/(d+3)$, we obtain the rate $O(m^{-1/2-d(2-p)/(2d(2-p)+2p(2s+d+1))}\log^{3/2}m)$, which improves the corresponding random-feature rate. We also derive approximation rates for Sobolev spaces $W^{α,p}$ in the range $1\le p<2$ by embedding them into spectral Barron spaces. Finally, for nonparametric regression with sub-Gaussian noise, we prove minimax-optimal generalization bounds for path-norm-regularized shallow ReLU$^s$ networks over Barron and Sobolev spaces, with matching lower bounds up to logarithmic factors.

Lens: Rethinking Training Efficiency for Foundational Text-to-Image Models

We introduce Lens, a 3.8B-parameter T2I model that achieves performance competitive with, and in several cases surpassing, state-of-the-art models with more than 6B parameters across various benchmarks, while requiring significantly less training compute. For example, Lens requires only about 19.3% of the training compute used by Z-Image. The training efficiency of Lens stems from two key strategies beyond its compact model size. First, we maximize data information density per training batch by (i) training on Lens-800M, a dataset of 800M densely captioned image-text pairs whose captions are generated by GPT-4.1 and contain approximately 109 words on average, providing richer semantic supervision than conventional short captions, and (ii) constructing each batch from images with multiple resolutions and diverse aspect ratios, thereby enlarging the effective visual coverage of each optimization step. Second, we improve convergence speed through careful architectural choices, including adopting a semantic VAE that provides better latent representations and employing a strong language encoder that accelerates optimization while enabling multilingual generalization from English-only training data. After pre-training, we apply RL with taxonomy-driven prompts (Lens-RL-8K) and structured reward rubrics to suppress artifacts and improve visual quality, a reasoner module with training-free system prompt search to better align user requests with the model, and distillation-based acceleration for 4-step inference. Through efficient training and systematic optimization, Lens generalizes to arbitrary aspect ratios from 1:2 to 2:1 and resolutions up to 1440^2, and supports prompts in several commonly used languages. Thanks to its compact size, Lens generates a 1024^2 image in 3.15 seconds on a single NVIDIA H100 GPU, while its distilled turbo version performs 4-step generation in 0.84 seconds.

InsightTok: Improving Text and Face Fidelity in Discrete Tokenization for Autoregressive Image Generation

Text and faces are among the most perceptually salient and practically important patterns in visual generation, yet they remain challenging for autoregressive generators built on discrete tokenization. A central bottleneck is the tokenizer: aggressive downsampling and quantization often discard the fine-grained structures needed to preserve readable glyphs and distinctive facial features. We attribute this gap to standard discrete-tokenizer objectives being weakly aligned with text legibility and facial fidelity, as these objectives typically optimize generic reconstruction while compressing diverse content uniformly. To address this, we propose InsightTok, a simple yet effective discrete visual tokenization framework that enhances text and face fidelity through localized, content-aware perceptual losses. With a compact 16k codebook and a 16x downsampling rate, InsightTok significantly outperforms prior tokenizers in text and face reconstruction without compromising general reconstruction quality. These gains consistently transfer to autoregressive image generation in InsightAR, producing images with clearer text and more faithful facial details. Overall, our results highlight the potential of specialized supervision in tokenizer training for advancing discrete image generation.

Image-Based Whole-Heart Cardiac Flow Simulations in Health and Congenital Heart Disease

Intracardiac flow patterns are shaped by the coupled motion of the cardiac chambers and heart valves and provide important information about cardiac function. However, clinical flow imaging remains limited by exam times, noise, resolution, and incomplete details of the three-dimensional flow. Computational fluid dynamics (CFD) can potentially provide detailed flow quantification and predictive insight into treatment outcomes, but clinical translation requires frameworks that reproduce patient-specific measurements while balancing physiological realism, computational cost, and modeling effort. Herein, we present an image-based, patient-specific computational framework for simulating whole-heart intracardiac hemodynamics that balances physiological fidelity with computational efficiency. The framework first employs machine learning-based segmentation and mesh propagation to reconstruct moving cardiac anatomies from time-resolved images. CFD simulations are then performed to resolve blood flow in deforming domains, while resistive immersed surfaces (RIS) are used to model all four cardiac valves with physiologically realistic opening and closing dynamics. The framework was applied to model hemodynamics in a healthy adult and a pediatric patient with complex congenital heart disease (CHD). In the healthy case, the simulations reproduced physiologic pressure-volume behavior, valve timing, and ventricular vortex formation. In the CHD case, simulated chamber and vessel pressures showed agreement with cardiac catheterization measurements. Simulated flow fields were qualitatively consistent with 4D-Flow MRI, while providing higher-resolution visualization of flow structures that were partially obscured by imaging artifacts. Comparison between the healthy and CHD cases further revealed altered diastolic flow organization and elevated normalized viscous dissipation in the CHD heart.

Information Coordination as a Bridge: A Neuro-Symbolic Architecture for Reliable Autonomous Driving Scene Understanding

Reliable autonomous driving requires scene understanding that is semantically consistent across heterogeneous sensors and verifiable at the reasoning stage. However, many recent LLM-driven driving systems attach the language model as a post-processor and force it to reason over redundant or conflicting perception outputs, which can amplify hallucinated entities and unsafe conclusions. This paper proposes InfoCoordiBridge, a BEV-centric neuro-symbolic architecture that inserts an explicit coordination bridge between perception and language reasoning. InfoCoordiBridge comprises (i) a unified multi-agent perception layer that outputs typed structured facts together with modality-focused synopses, (ii) an ICA module that aligns and fuses multi-source outputs into a single SceneSummary, and (iii) an SSRE module that performs SceneSummary-grounded reasoning with verification. Experiments on nuScenes and Waymo show that ICA preserves competitive 3D detection accuracy while substantially improving fusion consistency, reducing redundancy to below 1% and achieving about 98% attribute agreement. On NuScenes-QA and a template-aligned Waymo-QA benchmark, SSRE improves factual grounding and reduces hallucinated entity mentions compared with representative VLM and agentic baselines. Overall, by coordinating multi-sensor outputs into a single conflict-aware SceneSummary before prompting, InfoCoordiBridge prevents redundant and cross-modally inconsistent perception evidence from propagating into high-level reasoning.

Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

This paper develops convolutional neural network (CNN) methods for simultaneous approximation and elliptic boundary value problems on compact Riemannian manifolds. We establish simultaneous Sobolev approximation results for single- and multichannel CNNs, showing that manifold functions and their derivatives can be approximated with rates governed by the intrinsic dimension and the smoothness gap, rather than by the ambient dimension, thereby mitigating the curse of dimensionality. Building on this approximation theory, we propose a physics-informed CNN (PICNN) framework specially designed for boundary value problems. The main numerical issue is a boundary-norm mismatch: standard PINNs usually impose boundary data through low-order, often L2-type, penalties, whereas elliptic stability requires Sobolev trace control. We address this by introducing a spectral boundary loss based on the boundary Laplace-Beltrami operator, which represents trace errors as weighted frequency energies and relates truncation error to boundary eigenvalue decay. This avoids smooth auxiliary constructions required by exact boundary enforcement and singular double integrals arising in Sobolev-Slobodeckij penalties, while enabling implementations based on Fast Fourier Transforms (FFTs) or precomputed spectral bases on structured boundaries. Numerical experiments demonstrate improved accuracy, convergence, and stability over standard PINNs.

Seedance 2.0: Advancing Video Generation for World Complexity

Seedance 2.0 is a new native multi-modal audio-video generation model, officially released in China in early February 2026. Compared with its predecessors, Seedance 1.0 and 1.5 Pro, Seedance 2.0 adopts a unified, highly efficient, and large-scale architecture for multi-modal audio-video joint generation. This allows it to support four input modalities: text, image, audio, and video, by integrating one of the most comprehensive suites of multi-modal content reference and editing capabilities available in the industry to date. It delivers substantial, well-rounded improvements across all key sub-dimensions of video and audio generation. In both expert evaluations and public user tests, the model has demonstrated performance on par with the leading levels in the field. Seedance 2.0 supports direct generation of audio-video content with durations ranging from 4 to 15 seconds, with native output resolutions of 480p and 720p. For multi-modal inputs as reference, its current open platform supports up to 3 video clips, 9 images, and 3 audio clips. In addition, we provide Seedance 2.0 Fast version, an accelerated variant of Seedance 2.0 designed to boost generation speed for low-latency scenarios. Seedance 2.0 has delivered significant improvements to its foundational generation capabilities and multi-modal generation performance, bringing an enhanced creative experience for end users.

Enhanced Polarization Locking in VCSELs

While optical injection locking (OIL) of vertical-cavity surface-emitting lasers (VCSELs) has been widely studied in the past, the polarization dynamics of OIL have received far less attention. Recent studies suggest that polarization locking via OIL could enable novel computational applications such as polarization-encoded Ising computers. However, the inherent polarization preference and limited polarization switchability of VCSELs hinder their use for such purposes. To address these challenges, we fabricate VCSELs with tailored oxide aperture designs and combine these with bias current tuning to study the overall impact on polarization locking. Experimental results demonstrate that this approach reduces the required injection power (to as low as 3.6 μW) and expands the locking range. To investigate the impact of the approach, the spin-flip model (SFM) is used to analyze the effects of amplitude anisotropy and bias current on polarization locking, demonstrating strong coherence with experimental results.

Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation

This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the density ratio is either uniformly bounded or unbounded but known exactly. These conditions are often violated in practice, creating a gap between theoretical guarantees and real-world applicability. In contrast, this work directly addresses unbounded density ratios and integrates them into importance weighting for effective covariate shift adaptation. We propose a three-step estimation method that leverages unlabeled data from both the source and target distributions: (1) estimating a relative density ratio; (2) applying a truncation operation to control its unboundedness; and (3) transforming the truncated estimate back into the standard density ratio. The estimated density ratio is then employed as importance weights for regression under covariate shift. We establish rigorous, non-asymptotic convergence guarantees for both the proposed density ratio estimator and the resulting regression function estimator, demonstrating optimal or near-optimal convergence rates. Our findings offer new theoretical insights into density ratio estimation and learning under covariate shift, extending classical learning theory to more practical and challenging scenarios.

VistaGEN: Consistent Driving Video Generation with Fine-Grained Control Using Multiview Visual-Language Reasoning

Driving video generation has achieved much progress in controllability, video resolution, and length, but fails to support fine-grained object-level controllability for diverse driving videos, while preserving the spatiotemporal consistency, especially in long video generation. In this paper, we present a new driving video generation technique, called VistaGEN, which enables fine-grained control of specific entities, including 3D objects, images, and text descriptions, while maintaining spatiotemporal consistency in long video sequences. Our key innovation is the incorporation of multiview visual-language reasoning into the long driving video generation. To this end, we inject visual-language features into a multiview video generator to enable fine-grained controllability. More importantly, we propose a multiview vision-language evaluator (MV-VLM) to intelligently and automatically evaluate spatiotemporal consistency of the generated content, thus formulating a novel generation-evaluation-regeneration closed-loop generation mechanism. This mechanism ensures high-quality, coherent outputs, facilitating the creation of complex and reliable driving scenarios. Besides, within the closed-loop generation, we introduce an object-level refinement module to refine the unsatisfied results evaluated from the MV-VLM and then feed them back to the video generator for regeneration. Extensive evaluation shows that our VistaGEN achieves diverse driving video generation results with fine-grained controllability, especially for long-tail objects, and much better spatiotemporal consistency than previous approaches.