Daily Papers

Designing sparse attention for diffusion transformers requires reconciling two-dimensional spatial locality with GPU efficiency, a trade-off that current methods struggle to achieve. Existing approaches enforce two-dimensional spatial locality but often incur uncoalesced memory access. We present HilbertA, a 2D-aware and GPU-efficient sparse attention mechanism. HilbertA reorders image tokens along Hilbert curves to achieve a contiguous memory layout while preserving spatial neighborhoods, and employs a sliding schedule across layers to enable long-range information propagation without repeated or uncoalesced memory access. To further enhance cross-tile communication and positional awareness, HilbertA introduces a small central shared region. Implemented in Triton, HilbertA delivers comparable image quality with significant acceleration over prior methods on Flux.1-dev, demonstrating the feasibility of hardware-aligned two-dimensional sparse attention for high-resolution image generation. HilbertA delivers attention speedups of 2.3times when generating 1024times 1024 images, and up to 4.17times at 2048times 2048, while achieving image quality comparable to or surpassing baselines.

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel grids or range images. While such intermediate representations solve the problem of permutation invariance, they can result in significant loss of information. Approaches that do learn on raw point clouds either have trouble in resolving neighborhood relationships between points or are too complicated in their formulation. In this paper, we propose a novel approach to representing point clouds as a locality preserving 1D ordering induced by the Hilbert space-filling curve. We also introduce Point2Point, a neural architecture that can effectively learn on Hilbert-sorted point clouds. We show that Point2Point shows competitive performance on point cloud segmentation and generation tasks. Finally, we show the performance of Point2Point on Spatio-temporal Occupancy prediction from Point clouds.

Object compositing offers significant promise for augmented reality (AR) and embodied intelligence applications. Existing approaches predominantly focus on single-image scenarios or intrinsic decomposition techniques, facing challenges with multi-view consistency, complex scenes, and diverse lighting conditions. Recent inverse rendering advancements, such as 3D Gaussian and diffusion-based methods, have enhanced consistency but are limited by scalability, heavy data requirements, or prolonged reconstruction time per scene. To broaden its applicability, we introduce MV-CoLight, a two-stage framework for illumination-consistent object compositing in both 2D images and 3D scenes. Our novel feed-forward architecture models lighting and shadows directly, avoiding the iterative biases of diffusion-based methods. We employ a Hilbert curve-based mapping to align 2D image inputs with 3D Gaussian scene representations seamlessly. To facilitate training and evaluation, we further introduce a large-scale 3D compositing dataset. Experiments demonstrate state-of-the-art harmonized results across standard benchmarks and our dataset, as well as casually captured real-world scenes demonstrate the framework's robustness and wide generalization.

Enabling Large Language Models (LLMs) to understand the 3D physical world is an emerging yet challenging research direction. Current strategies for processing point clouds typically downsample the scene or divide it into smaller parts for separate analysis. However, both approaches risk losing key local details or global contextual information. In this paper, we introduce PerLA, a 3D language assistant designed to be more perceptive to both details and context, making visual representations more informative for the LLM. PerLA captures high-resolution (local) details in parallel from different point cloud areas and integrates them with (global) context obtained from a lower-resolution whole point cloud. We present a novel algorithm that preserves point cloud locality through the Hilbert curve and effectively aggregates local-to-global information via cross-attention and a graph neural network. Lastly, we introduce a novel loss for local representation consensus to promote training stability. PerLA outperforms state-of-the-art 3D language assistants, with gains of up to +1.34 CiDEr on ScanQA for question answering, and +4.22 on ScanRefer and +3.88 on Nr3D for dense captioning.https://gfmei.github.io/PerLA/

Ultra-high-resolution text-to-image generation demands both fine-grained texture synthesis and globally coherent structure, yet current diffusion models remain constrained to sub-1K times 1K resolutions due to the prohibitive quadratic complexity of attention and the scarcity of native 4K training data. We present Scale-DiT, a new diffusion framework that introduces hierarchical local attention with low-resolution global guidance, enabling efficient, scalable, and semantically coherent image synthesis at ultra-high resolutions. Specifically, high-resolution latents are divided into fixed-size local windows to reduce attention complexity from quadratic to near-linear, while a low-resolution latent equipped with scaled positional anchors injects global semantics. A lightweight LoRA adaptation bridges global and local pathways during denoising, ensuring consistency across structure and detail. To maximize inference efficiency, we repermute token sequence in Hilbert curve order and implement a fused-kernel for skipping masked operations, resulting in a GPU-friendly design. Extensive experiments demonstrate that Scale-DiT achieves more than 2times faster inference and lower memory usage compared to dense attention baselines, while reliably scaling to 4K times 4K resolution without requiring additional high-resolution training data. On both quantitative benchmarks (FID, IS, CLIP Score) and qualitative comparisons, Scale-DiT delivers superior global coherence and sharper local detail, matching or outperforming state-of-the-art methods that rely on native 4K training. Taken together, these results highlight hierarchical local attention with guided low-resolution anchors as a promising and effective approach for advancing ultra-high-resolution image generation.

Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is permutation-equivariant, modern long-sequence transformers increasingly rely on architectural approximations that break this invariance and introduce sensitivity to patch ordering. We show that patch order significantly affects model performance in such settings, with simple alternatives like column-major or Hilbert curves yielding notable accuracy shifts. Motivated by this, we propose REOrder, a two-stage framework for discovering task-optimal patch orderings. First, we derive an information-theoretic prior by evaluating the compressibility of various patch sequences. Then, we learn a policy over permutations by optimizing a Plackett-Luce policy using REINFORCE. This approach enables efficient learning in a combinatorial permutation space. REOrder improves top-1 accuracy over row-major ordering on ImageNet-1K by up to 3.01% and Functional Map of the World by 13.35%.

We present Neural Space-filling Curves (SFCs), a data-driven approach to infer a context-based scan order for a set of images. Linear ordering of pixels forms the basis for many applications such as video scrambling, compression, and auto-regressive models that are used in generative modeling for images. Existing algorithms resort to a fixed scanning algorithm such as Raster scan or Hilbert scan. Instead, our work learns a spatially coherent linear ordering of pixels from the dataset of images using a graph-based neural network. The resulting Neural SFC is optimized for an objective suitable for the downstream task when the image is traversed along with the scan line order. We show the advantage of using Neural SFCs in downstream applications such as image compression. Code and additional results will be made available at https://hywang66.github.io/publication/neuralsfc.

Using Hilbert schemes of points, we establish a number of results for a smooth projective variety X in a sufficiently ample embedding. If X is a curve or a surface, we show that the ideals of higher secant varieties are determinantally presented, and we prove the same for the first secant variety if X has arbitrary dimension. This completely settles a conjecture of Eisenbud-Koh-Stillman for curves and partially resolves a conjecture of Sidman-Smith in higher dimensions. If X is a curve or a surface we also prove that the corresponding embedding of the Hilbert scheme of points X^{[d]} into the Grassmannian is projectively normal. Finally, if X is an arbitrary projective scheme in a sufficiently ample embedding, then we demonstrate that its homogeneous ideal is generated by quadrics of rank three, confirming a conjecture of Han-Lee-Moon-Park. Along the way, we check that the Hilbert scheme of three points on a smooth variety is the blow-up of the symmetric product along the big diagonal.

The Kramers-Kronig relations are a pivotal foundation of linear optics and atomic physics, embedding a physical connection between the real and imaginary components of any causal response function. A mathematically equivalent, but simpler, approach instead utilises the Hilbert transform. In a previous study, the Hilbert transform was applied to absorption spectra in order to infer the sole refractive index of an atomic medium in the absence of an external magnetic field. The presence of a magnetic field causes the medium to become birefringent and dichroic, and therefore it is instead characterised by two refractive indices. In this study, we apply the same Hilbert transform technique to independently measure both refractive indices of a birefringent atomic medium, leading to an indirect measurement of atomic magneto-optical rotation. Key to this measurement is the insight that inputting specific light polarisations into an atomic medium induces absorption associated with only one of the refractive indices. We show this is true in two configurations, commonly referred to in literature as the Faraday and Voigt geometries, which differ by the magnetic field orientation with respect to the light wavevector. For both cases, we measure the two refractive indices independently for a Rb thermal vapour in a 0.6 T magnetic field, finding excellent agreement with theory. This study further emphasises the application of the Hilbert transform to the field of quantum and atomic optics in the linear regime.

Core collapse supernovae are among the most energetic astrophysical events in the Universe. Despite huge efforts on understanding the main ingredients triggering such explosions, we still lack of compelling evidences for the precise mechanism driving those phenomena. They are expected to produce gravitational waves due to asymmetric mass motions in the collapsing core, and emit in the meanwhile neutrinos as a result of the interactions in their high-density environment. The combination of these two cosmic messengers can provide a unique probe to study the inner engine of these processes and unveil the explosion mechanism. Among the possible detectable signature, standing accretion shock instabilities (SASI) are particularly relevant in this context as they establish a direct connection between gravitational wave emission and the outcoming neutrino flux. In this work, Hilbert-Huang transform is applied to a selected sample of 3D numerical simulations, with the aim of identifying SASI contribution and extract its instantaneous frequency. The performance of the method is evaluated in the context of Einstein Telescope.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

In this article, we continue the development of the Riemann-Hilbert formalism for studying the asymptotics of Toeplitz+Hankel determinants with non-identical symbols, which we initiated in GI. In GI, we showed that the Riemann-Hilbert problem we formulated admits the Deift-Zhou nonlinear steepest descent analysis, but with a special restriction on the winding numbers of the associated symbols. In particular, the most natural case, namely zero winding numbers, is not allowed. A principal goal of this paper is to develop a framework that extends the asymptotic analysis of Toeplitz+Hankel determinants to a broader range of winding-number configurations. As an application, we consider the case in which the winding numbers of the Szego-type Toeplitz and Hankel symbols are zero and one, respectively, and compute the asymptotics of the norms of the corresponding system of orthogonal polynomials.