Daily Papers

Decoder-only large language models (LLMs) are increasingly replacing BERT-style architectures as the backbone for dense retrieval, achieving substantial performance gains and broad adoption. However, the robustness of these LLM-based retrievers remains underexplored. In this paper, we present the first systematic study of the robustness of state-of-the-art open-source LLM-based dense retrievers from two complementary perspectives: generalizability and stability. For generalizability, we evaluate retrieval effectiveness across four benchmarks spanning 30 datasets, using linear mixed-effects models to estimate marginal mean performance and disentangle intrinsic model capability from dataset heterogeneity. Our analysis reveals that while instruction-tuned models generally excel, those optimized for complex reasoning often suffer a ``specialization tax,'' exhibiting limited generalizability in broader contexts. For stability, we assess model resilience against both unintentional query variations~(e.g., paraphrasing, typos) and malicious adversarial attacks~(e.g., corpus poisoning). We find that LLM-based retrievers show improved robustness against typos and corpus poisoning compared to encoder-only baselines, yet remain vulnerable to semantic perturbations like synonymizing. Further analysis shows that embedding geometry (e.g., angular uniformity) provides predictive signals for lexical stability and suggests that scaling model size generally improves robustness. These findings inform future robustness-aware retriever design and principled benchmarking. Our code is publicly available at https://github.com/liyongkang123/Robust_LLM_Retriever_Eval.

Code retrieval is a crucial component in modern software development, particularly in large-scale projects. However, existing approaches relying on sequence-based models often fail to fully exploit the structural dependencies inherent in code, leading to suboptimal retrieval performance, particularly with structurally complex code fragments. In this paper, we introduce GNN-Coder, a novel framework based on Graph Neural Network (GNN) to utilize Abstract Syntax Tree (AST). We make the first attempt to study how GNN-integrated Transformer can promote the development of semantic retrieval tasks by capturing the structural and semantic features of code. We further propose an innovative graph pooling method tailored for AST, utilizing the number of child nodes as a key feature to highlight the intrinsic topological relationships within the AST. This design effectively integrates both sequential and hierarchical representations, enhancing the model's ability to capture code structure and semantics. Additionally, we introduce the Mean Angular Margin (MAM), a novel metric for quantifying the uniformity of code embedding distributions, providing a standardized measure of feature separability. The proposed method achieves a lower MAM, indicating a more discriminative feature representation. This underscores GNN-Coder's superior ability to distinguish between code snippets, thereby enhancing retrieval accuracy. Experimental results show that GNN-Coder significantly boosts retrieval performance, with a 1\%-10\% improvement in MRR on the CSN dataset, and a notable 20\% gain in zero-shot performance on the CosQA dataset.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

Uniformity plays a crucial role in the assessment of learned representations, contributing to a deeper comprehension of self-supervised learning. The seminal work by Wang2020UnderstandingCR introduced a uniformity metric that quantitatively measures the collapse degree of learned representations. Directly optimizing this metric together with alignment proves to be effective in preventing constant collapse. However, we present both theoretical and empirical evidence revealing that this metric lacks sensitivity to dimensional collapse, highlighting its limitations. To address this limitation and design a more effective uniformity metric, this paper identifies five fundamental properties, some of which the existing uniformity metric fails to meet. We subsequently introduce a novel uniformity metric that satisfies all of these desiderata and exhibits sensitivity to dimensional collapse. When applied as an auxiliary loss in various established self-supervised methods, our proposed uniformity metric consistently enhances their performance in downstream tasks.Our code was released at https://github.com/sunset-clouds/WassersteinUniformityMetric.

Alignment and uniformity are fundamental principles within the domain of contrastive learning. In recommender systems, prior work has established that optimizing the Bayesian Personalized Ranking (BPR) loss contributes to the objectives of alignment and uniformity. Specifically, alignment aims to draw together the representations of interacting users and items, while uniformity mandates a uniform distribution of user and item embeddings across a unit hypersphere. This study revisits the alignment and uniformity properties within the context of multimodal recommender systems, revealing a proclivity among extant models to prioritize uniformity to the detriment of alignment. Our hypothesis challenges the conventional assumption of equitable item treatment through a uniformity loss, proposing a more nuanced approach wherein items with similar multimodal attributes converge toward proximal representations within the hyperspheric manifold. Specifically, we leverage the inherent similarity between items' multimodal data to calibrate their uniformity distribution, thereby inducing a more pronounced repulsive force between dissimilar entities within the embedding space. A theoretical analysis elucidates the relationship between this calibrated uniformity loss and the conventional uniformity function. Moreover, to enhance the fusion of multimodal features, we introduce a Spherical B\'ezier method designed to integrate an arbitrary number of modalities while ensuring that the resulting fused features are constrained to the same hyperspherical manifold. Empirical evaluations conducted on five real-world datasets substantiate the superiority of our approach over competing baselines. We also shown that the proposed methods can achieve up to a 5.4% increase in NDCG@20 performance via the integration of MLLM-extracted features. Source code is available at: https://github.com/enoche/CM3.

In this work we introduce a physically motivated method of performing disc/spheroid decomposition of simulated galaxies, which we apply to the Eagle sample. We make use of the HEALPix package to create Mollweide projections of the angular momentum map of each galaxy's stellar particles. A number of features arise on the angular momentum space which allows us to decompose galaxies and classify them into different morphological types. We assign stellar particles with angular separation of less/greater than 30 degrees from the densest grid cell on the angular momentum sphere to the disc/spheroid components, respectively. We analyse the spatial distribution for a subsample of galaxies and show that the surface density profiles of the disc and spheroid closely follow an exponential and a Sersic profile, respectively. In addition discs rotate faster, have smaller velocity dispersions, are younger and are more metal rich than spheroids. Thus our morphological classification reproduces the observed properties of such systems. Finally, we demonstrate that our method is able to identify a significant population of galaxies with counter-rotating discs and provide a more realistic classification of such systems compared to previous methods.

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.

Contours or closed planar curves are common in many domains. For example, they appear as object boundaries in computer vision, isolines in meteorology, and the orbits of rotating machinery. In many cases when learning from contour data, planar rotations of the input will result in correspondingly rotated outputs. It is therefore desirable that deep learning models be rotationally equivariant. In addition, contours are typically represented as an ordered sequence of edge points, where the choice of starting point is arbitrary. It is therefore also desirable for deep learning methods to be equivariant under cyclic shifts. We present RotaTouille, a deep learning framework for learning from contour data that achieves both rotation and cyclic shift equivariance through complex-valued circular convolution. We further introduce and characterize equivariant non-linearities, coarsening layers, and global pooling layers to obtain invariant representations for downstream tasks. Finally, we demonstrate the effectiveness of RotaTouille through experiments in shape classification, reconstruction, and contour regression.

With the rapidly increasing demand for oriented object detection, e.g. in autonomous driving and remote sensing, the recently proposed paradigm involving weakly-supervised detector H2RBox for learning rotated box (RBox) from the more readily-available horizontal box (HBox) has shown promise. This paper presents H2RBox-v2, to further bridge the gap between HBox-supervised and RBox-supervised oriented object detection. Specifically, we propose to leverage the reflection symmetry via flip and rotate consistencies, using a weakly-supervised network branch similar to H2RBox, together with a novel self-supervised branch that learns orientations from the symmetry inherent in visual objects. The detector is further stabilized and enhanced by practical techniques to cope with peripheral issues e.g. angular periodicity. To our best knowledge, H2RBox-v2 is the first symmetry-aware self-supervised paradigm for oriented object detection. In particular, our method shows less susceptibility to low-quality annotation and insufficient training data compared to H2RBox. Specifically, H2RBox-v2 achieves very close performance to a rotation annotation trained counterpart -- Rotated FCOS: 1) DOTA-v1.0/1.5/2.0: 72.31%/64.76%/50.33% vs. 72.44%/64.53%/51.77%; 2) HRSC: 89.66% vs. 88.99%; 3) FAIR1M: 42.27% vs. 41.25%.

Small and cluttered objects are common in real-world which are challenging for detection. The difficulty is further pronounced when the objects are rotated, as traditional detectors often routinely locate the objects in horizontal bounding box such that the region of interest is contaminated with background or nearby interleaved objects. In this paper, we first innovatively introduce the idea of denoising to object detection. Instance-level denoising on the feature map is performed to enhance the detection to small and cluttered objects. To handle the rotation variation, we also add a novel IoU constant factor to the smooth L1 loss to address the long standing boundary problem, which to our analysis, is mainly caused by the periodicity of angular (PoA) and exchangeability of edges (EoE). By combing these two features, our proposed detector is termed as SCRDet++. Extensive experiments are performed on large aerial images public datasets DOTA, DIOR, UCAS-AOD as well as natural image dataset COCO, scene text dataset ICDAR2015, small traffic light dataset BSTLD and our released S^2TLD by this paper. The results show the effectiveness of our approach. The released dataset S2TLD is made public available, which contains 5,786 images with 14,130 traffic light instances across five categories.

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.

The angular power spectrum is a gauge-independent observable that is in principle the natural tool for analysing galaxy number counts. In practice, the problem is that the computational requirements for next-generation spectroscopic surveys such as Euclid and the Square Kilometre Array are currently unfeasible. We propose a new method to save computational time for spectroscopic angular power spectra. This hybrid method is modelled on the Fourier power spectrum approach of treating relatively thick redshift bins (redshift width ~0.1) as separate surveys. In the hybrid method, each thick bin is further subdivided into thin bins (redshift width ~0.01); all the correlations within each thick bin are computed, while cross-bin correlations beyond the thick bins are neglected. Constraints on cosmological parameters from the hybrid method are comparable to those from the standard galaxy power spectrum analysis - but they have the advantage that cosmic evolution, wide-angle and lensing effects are naturally included, while no Alcock-Paczynski correction is needed. The hybrid method delivers much tighter constraints than a 2D tomographic approach that is typical for photometric surveys, which considers only thick bins and the correlations between them. Furthermore, for standard cosmological parameters our method is not biased by neglecting the effects of lensing on number counts, while the tomographic method is strongly biased.

We analyse the observational signatures of galactic magnetic fields that are self-consistently generated in magnetohydrodynamic simulations of the interstellar medium through turbulence driven by supernova (SN) explosions and differential rotation. In particular, we study the time evolution of the Faraday rotation measure (RM), synchrotron radiation, and Stokes parameters by characterising the typical structures formed in the plane of observation. We do this by defining two distinct models for both thermal and cosmic ray (CR) electron distributions. Our results indicate that the maps of RM have structures which are sheared and rendered anisotropically by differential rotation and that they depend on the choice of thermal electrons model as well as the SN rate. Synchrotron maps are qualitatively similar to the maps of the mean magnetic field along the line of sight and structures are only marginally affected by the CR model. Stokes parameters and related quantities, such as the degree of linear polarisation, are highly dependent on both frequency and resolution of the observation.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

The polarization of an X-ray beam that produces electrons with velocity components perpendicular to the beam generates an azimuthal distribution of the ejected electrons. We present methods for simulating and for analyzing the angular dependence of electron detections which enable us to derive simple analytical expressions for useful statistical properties of observable data. The derivations are verified by simulations. While we confirm the results of previous work on this topic, we provide an extension needed for analytical treatment of the full range of possible polarization amplitudes.

We present the requirements, design and evaluation of the cryogenic continuously rotating half-wave plate (CHWP) for the Simons Observatory (SO). SO is a cosmic microwave background (CMB) polarization experiment at Parque Astron\'{o}mico Atacama in northern Chile that covers a wide range of angular scales using both small (0.42 m) and large (6 m) aperture telescopes. In particular, the small aperture telescopes (SATs) focus on large angular scales for primordial B-mode polarization. To this end, the SATs employ a CHWP to modulate the polarization of the incident light at 8 Hz, suppressing atmospheric 1/f noise and mitigating systematic uncertainties that would otherwise arise due to the differential response of detectors sensitive to orthogonal polarizations. The CHWP consists of a 505 mm diameter achromatic sapphire HWP and a cryogenic rotation mechanism, both of which are cooled down to sim50 K to reduce detector thermal loading. Under normal operation the HWP is suspended by a superconducting magnetic bearing and rotates with a constant 2 Hz frequency, controlled by an electromagnetic synchronous motor. We find that the number of superconductors and magnets that make up the superconducting magnetic bearing are important design parameters, especially for the rotation mechanism's vibration performance. The rotation angle is detected through an angular encoder with a noise level of 0.07 muradmathrm{s}. During a cooldown, the rotor is held in place by a grip-and-release mechanism that serves as both an alignment device and a thermal path. In this paper we provide an overview of the SO SAT CHWP: its requirements, hardware design, and laboratory performance.

The planned space-based gravitational wave detector, LISA, will provide a fundamentally new means of studying the orbital alignment of close white dwarf binaries. However, due to the inherent symmetry of their gravitational wave signals, a fourfold degeneracy arises in the transverse projections of their angular momentum vectors. In this paper, we demonstrate that by incorporating timing information from electromagnetic observations, such as radial velocity modulations and light curves, this degeneracy can be reduced to twofold.

A stochastic gravitational wave background causes the apparent positions of distant sources to fluctuate, with angular deflections of order the characteristic strain amplitude of the gravitational waves. These fluctuations may be detectable with high precision astrometry, as first suggested by Braginsky et al. in 1990. Several researchers have made order of magnitude estimates of the upper limits obtainable on the gravitational wave spectrum \Omega_gw(f), at frequencies of order f ~ 1 yr^-1, both for the future space-based optical interferometry missions GAIA and SIM, and for VLBI interferometry in radio wavelengths with the SKA. For GAIA, tracking N ~ 10^6 quasars over a time of T ~ 1 yr with an angular accuracy of \Delta \theta ~ 10 \mu as would yield a sensitivity level of \Omega_gw ~ (\Delta \theta)^2/(N T^2 H_0^2) ~ 10^-6, which would be comparable with pulsar timing. In this paper we take a first step toward firming up these estimates by computing in detail the statistical properties of the angular deflections caused by a stochastic background. We compute analytically the two point correlation function of the deflections on the sphere, and the spectrum as a function of frequency and angular scale. The fluctuations are concentrated at low frequencies (for a scale invariant stochastic background), and at large angular scales, starting with the quadrupole. The magnetic-type and electric-type pieces of the fluctuations have equal amounts of power.

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles theta_1, dots, theta_nin[0, 2pi) from m noisy measurements of their offsets theta_i-theta_j ;mod ; 2pi. Applications include, for example, sensor network localization, phase retrieval, and distributed clock synchronization. An extension of the problem to the heterogeneous setting (dubbed k-synchronization) is to estimate k groups of angles simultaneously, given noisy observations (with unknown group assignment) from each group. Existing methods for angular synchronization usually perform poorly in high-noise regimes, which are common in applications. In this paper, we leverage neural networks for the angular synchronization problem, and its heterogeneous extension, by proposing GNNSync, a theoretically-grounded end-to-end trainable framework using directed graph neural networks. In addition, new loss functions are devised to encode synchronization objectives. Experimental results on extensive data sets demonstrate that GNNSync attains competitive, and often superior, performance against a comprehensive set of baselines for the angular synchronization problem and its extension, validating the robustness of GNNSync even at high noise levels.

This work presents the first quantitative study of alignment errors between small uncrewed aerial systems (sUAS) geospatial imagery and a priori building polygons and finds that alignment errors are non-uniform and irregular. The work also introduces a publicly available dataset of imagery, building polygons, and human-generated and curated adjustments that can be used to evaluate existing strategies for aligning building polygons with sUAS imagery. There are no efforts that have aligned pre-existing spatial data with sUAS imagery, and thus, there is no clear state of practice. However, this effort and analysis show that the translational alignment errors present in this type of data, averaging 82px and an intersection over the union of 0.65, which would induce further errors and biases in downstream machine learning systems unless addressed. This study identifies and analyzes the translational alignment errors of 21,619 building polygons in fifty-one orthomosaic images, covering 16787.2 Acres (26.23 square miles), constructed from sUAS raw imagery from nine wide-area disasters (Hurricane Ian, Hurricane Harvey, Hurricane Michael, Hurricane Ida, Hurricane Idalia, Hurricane Laura, the Mayfield Tornado, the Musset Bayou Fire, and the Kilauea Eruption). The analysis finds no uniformity among the angle and distance metrics of the building polygon alignments as they present an average degree variance of 0.4 and an average pixel distance variance of 0.45. This work alerts the sUAS community to the problem of spatial alignment and that a simple linear transform, often used to align satellite imagery, will not be sufficient to align spatial data in sUAS orthomosaic imagery.

Illuminating the surface of a convex body with parallel beams of light in a given direction generates a shadow region. We prove sharp regularity results for the boundary of this shadow in every direction of illumination. Moreover, techniques are developed for investigating the regularity of the region generated by orthogonally projecting a convex set onto another. As an application we study the geometry and Hausdorff dimension of the singular set corresponding to a Monge-Ampere equation.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

Phenomenological characteristics of the sample of the Algol-type stars are revised using a recently developed NAV ("New Algol Variable") algorithm (2012Ap.....55..536A, 2012arXiv 1212.6707A) and compared to that obtained using common methods of Trigonometric Polynomial Fit (TP) or local Algebraic Polynomial (A) fit of a fixed or (alternately) statistically optimal degree (1994OAP.....7...49A, 2003ASPC..292..391A). The computer program NAV is introduced, which allows to determine the best fit with 7 "linear" and 5 "non-linear" parameters and their error estimates. The number of parameters is much smaller than for the TP fit (typically 20-40, depending on the width of the eclipse, and is much smaller (5-20) for the W UMa and beta Lyrae - type stars. This causes more smooth approximation taking into account the reflection and ellipsoidal effects (TP2) and generally different shapes of the primary and secondary eclipses. An application of the method to two-color CCD photometry to the recently discovered eclipsing variable 2MASS J18024395 + 4003309 = VSX J180243.9 +400331 (2015JASS...32..101A) allowed to make estimates of the physical parameters of the binary system based on the phenomenological parameters of the light curve. The phenomenological parameters of the light curves were determined for the sample of newly discovered EA and EW - type stars (VSX J223429.3+552903, VSX J223421.4+553013, VSX J223416.2+553424, US-NO-B1.0 1347-0483658, UCAC3-191-085589, VSX J180755.6+074711= UCAC3 196-166827). Despite we have used original observations published by the discoverers, the accuracy estimates of the period using the NAV method are typically better than the original ones.

Recent progress in panoramic image generation has underscored two critical limitations in existing approaches. First, most methods are built upon diffusion models, which are inherently ill-suited for equirectangular projection (ERP) panoramas due to the violation of the identically and independently distributed (i.i.d.) Gaussian noise assumption caused by their spherical mapping. Second, these methods often treat text-conditioned generation (text-to-panorama) and image-conditioned generation (panorama outpainting) as separate tasks, relying on distinct architectures and task-specific data. In this work, we propose a unified framework, Panoramic AutoRegressive model (PAR), which leverages masked autoregressive modeling to address these challenges. PAR avoids the i.i.d. assumption constraint and integrates text and image conditioning into a cohesive architecture, enabling seamless generation across tasks. To address the inherent discontinuity in existing generative models, we introduce circular padding to enhance spatial coherence and propose a consistency alignment strategy to improve generation quality. Extensive experiments demonstrate competitive performance in text-to-image generation and panorama outpainting tasks while showcasing promising scalability and generalization capabilities.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view-conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.

We present a method for 3D reconstruction only using calibrated multi-view surface azimuth maps. Our method, multi-view azimuth stereo, is effective for textureless or specular surfaces, which are difficult for conventional multi-view stereo methods. We introduce the concept of tangent space consistency: Multi-view azimuth observations of a surface point should be lifted to the same tangent space. Leveraging this consistency, we recover the shape by optimizing a neural implicit surface representation. Our method harnesses the robust azimuth estimation capabilities of photometric stereo methods or polarization imaging while bypassing potentially complex zenith angle estimation. Experiments using azimuth maps from various sources validate the accurate shape recovery with our method, even without zenith angles.

Processing information on 3D objects requires methods stable to rigid-body transformations, in particular rotations, of the input data. In image processing tasks, convolutional neural networks achieve this property using rotation-equivariant operations. However, contrary to images, graphs generally have irregular topology. This makes it challenging to define a rotation-equivariant convolution operation on these structures. In this work, we propose Spherical Graph Convolutional Network (S-GCN) that processes 3D models of proteins represented as molecular graphs. In a protein molecule, individual amino acids have common topological elements. This allows us to unambiguously associate each amino acid with a local coordinate system and construct rotation-equivariant spherical filters that operate on angular information between graph nodes. Within the framework of the protein model quality assessment problem, we demonstrate that the proposed spherical convolution method significantly improves the quality of model assessment compared to the standard message-passing approach. It is also comparable to state-of-the-art methods, as we demonstrate on Critical Assessment of Structure Prediction (CASP) benchmarks. The proposed technique operates only on geometric features of protein 3D models. This makes it universal and applicable to any other geometric-learning task where the graph structure allows constructing local coordinate systems.

Recent studies illustrate the correlation between the angular momenta of cosmic structures and their Lagrangian properties. However, only baryons are observable and it is unclear whether they reliably trace the cosmic angular momenta. We study the Lagrangian mass distribution, spin correlation, and predictability of dark matter, gas, and stellar components of galaxy-halo systems using IllustrisTNG, and show that the primordial segregations between components are typically small. Their protoshapes are also similar in terms of the statistics of moment of inertia tensors. Under the common gravitational potential they are expected to exert the same tidal torque and the strong spin correlations are not destroyed by the nonlinear evolution and complicated baryonic effects, as confirmed by the high-resolution hydrodynamic simulations. We further show that their late-time angular momenta traced by total gas, stars, or the central galaxies, can be reliably reconstructed by the initial perturbations. These results suggest that baryonic angular momenta can potentially be used in reconstructing the parameters and models related to the initial perturbations.

We consider the convergence of the ESD for non-Hermitian random band matrices with independent entries to the circular law, which is the uniform measure on the unit disk in the center of the complex plane. We assume that the bandwidth of the matrix scales like n^γ for some γin(0,1], where n is the matrix size, and the variance profile of the matrix is only assumed to be doubly stochastic with no additional assumption on its specific mixing properties. We prove that the circular law limit holds either (1) when γ>5{6} and the entries are independent Gaussians, (2) or when γ>8{9} and the entries are independent subgaussian random variables. This new threshold improves the previous threshold γ>32{33} which was only proven for block band matrices and periodic band matrices. After the initial version of this paper, the author further extended the range of circular law for much smaller values of γ in 2508.18143 and 2511.01744 when the variance profile has specific mixing properties, but not for an arbitrary doubly stochastic variance profile. Thus the main contribution of this paper is the circular law for a genuine power law bandwidth for any doubly stochastic variance profile. We also prove an extended form of product circular law with a growing number of matrices. Weak delocalization estimates on eigenvectors are also derived. The new technical input is new polynomial lower bounds on some intermediate small singular values, and this estimate does not depend on the specific structure of the variance profile beyond the fact that it is doubly stochastic.

A precise and user-friendly manipulation of image content while preserving image fidelity has always been crucial to the field of image editing. Thanks to the power of generative models, recent point-based image editing methods allow users to interactively change the image content with high generalizability by clicking several control points. But the above mentioned editing process is usually based on the assumption that features stay constant in the motion supervision step from initial to target points. In this work, we conduct a comprehensive investigation in the feature space of diffusion models, and find that features change acutely under in-plane rotation. Based on this, we propose a novel approach named RotationDrag, which significantly improves point-based image editing performance when users intend to in-plane rotate the image content. Our method tracks handle points more precisely by utilizing the feature map of the rotated images, thus ensuring precise optimization and high image fidelity. Furthermore, we build a in-plane rotation focused benchmark called RotateBench, the first benchmark to evaluate the performance of point-based image editing method under in-plane rotation scenario on both real images and generated images. A thorough user study demonstrates the superior capability in accomplishing in-plane rotation that users intend to achieve, comparing the DragDiffusion baseline and other existing diffusion-based methods. See the project page https://github.com/Tony-Lowe/RotationDrag for code and experiment results.

Many colour maps provided by vendors have highly uneven perceptual contrast over their range. It is not uncommon for colour maps to have perceptual flat spots that can hide a feature as large as one tenth of the total data range. Colour maps may also have perceptual discontinuities that induce the appearance of false features. Previous work in the design of perceptually uniform colour maps has mostly failed to recognise that CIELAB space is only designed to be perceptually uniform at very low spatial frequencies. The most important factor in designing a colour map is to ensure that the magnitude of the incremental change in perceptual lightness of the colours is uniform. The specific requirements for linear, diverging, rainbow and cyclic colour maps are developed in detail. To support this work two test images for evaluating colour maps are presented. The use of colour maps in combination with relief shading is considered and the conditions under which colour can enhance or disrupt relief shading are identified. Finally, a set of new basis colours for the construction of ternary images are presented. Unlike the RGB primaries these basis colours produce images whereby the salience of structures are consistent irrespective of the assignment of basis colours to data channels.

Automatic 3D content creation has gained increasing attention recently, due to its potential in various applications such as video games, film industry, and AR/VR. Recent advancements in diffusion models and multimodal models have notably improved the quality and efficiency of 3D object generation given a single RGB image. However, 3D objects generated even by state-of-the-art methods are still unsatisfactory compared to human-created assets. Considering only textures instead of materials makes these methods encounter challenges in photo-realistic rendering, relighting, and flexible appearance editing. And they also suffer from severe misalignment between geometry and high-frequency texture details. In this work, we propose a novel approach to boost the quality of generated 3D objects from the perspective of Physics-Based Rendering (PBR) materials. By analyzing the components of PBR materials, we choose to consider albedo, roughness, metalness, and bump maps. For albedo and bump maps, we leverage Stable Diffusion fine-tuned on synthetic data to extract these values, with novel usages of these fine-tuned models to obtain 3D consistent albedo UV and bump UV for generated objects. In terms of roughness and metalness maps, we adopt a semi-automatic process to provide room for interactive adjustment, which we believe is more practical. Extensive experiments demonstrate that our model is generally beneficial for various state-of-the-art generation methods, significantly boosting the quality and realism of their generated 3D objects, with natural relighting effects and substantially improved geometry.

We complement the recent paper of Zheng and Wu [Uniform recurrence properties for beta-transformation, Nonlinearity 33 (2020), 4590--4612], where the authors study, from the metrical point of view, the uniform recurrence properties of the orbit of a point under the β-transformation to the point itself.

We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for G^1 smoothness are given, which, up to a certain degenerate case, are also necessary. Further, we investigate curvature integrability and present examples

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

We present synthetic light curves and spectra from three-dimensional (3D) Monte Carlo radiative transfer simulations based on a 3D core-collapse supernova explosion model of an ultra-stripped 3.5,M_{odot} progenitor. Our calculations predict a fast and faint transient with Delta m_{15} sim 1- 2,mag and peak bolometric luminosity between -15.3,mag and -16.4,mag. Due to a large-scale unipolar asymmetry in the distribution of ^{56}Ni, there is a pronounced viewing-angle dependence with about 1,mag difference between the directions of highest and lowest luminosity. The predicted spectra for this rare class of explosions do not yet match any observed counterpart. They are dominated by prominent Mg~II lines, but features from O, C, Si, and Ca are also found. In particular, the O~I line at 7{774} appears as a blended feature together with Mg~II emission. Our model is not only faster and fainter than the observed Ib/c supernova population, but also shows a correlation between higher peak luminosity and larger Delta m_{15} that is not present in observational samples. A possible explanation is that the unusually small ejecta mass of our model accentuates the viewing-angle dependence of the photometry. We suggest that the viewing-angle dependence of the photometry may be used to constrain asymmetries in explosion models of more typical stripped-envelope supernova progenitors in future.

Automatic image rotation estimation is a key preprocessing step in many vision pipelines. This task is challenging because angles have circular topology, creating boundary discontinuities that hinder standard regression methods. We present a comprehensive study of five circular-aware methods for global orientation estimation: direct angle regression with circular loss, classification via angular binning, unit-vector regression, phase-shifting coder, and circular Gaussian distribution. Using transfer learning from ImageNet-pretrained models, we systematically evaluate these methods across sixteen modern architectures by adapting their output heads for rotation-specific predictions. Our results show that probabilistic methods, particularly the circular Gaussian distribution, are the most robust across architectures, while classification achieves the best accuracy on well-matched backbones but suffers training instabilities on others. The best configuration (classification with EfficientViT-B3) achieves a mean absolute error (MAE) of 1.23° (mean across five independent runs) on the DRC-D dataset, while the circular Gaussian distribution with MambaOut Base achieves a virtually identical 1.24° with greater robustness across backbones. Training and evaluating our top-performing method-architecture combinations on COCO 2014, the best configuration reaches 3.71° MAE, improving substantially over prior work, with further improvement to 2.84° on the larger COCO 2017 dataset.

We present new radio images of the supernova remnant (SNR) CTA 1 at 1420 and 408 MHz, and in the 21 cm line of H I observed with the Dominion Radio Astrophysical Observatory Synthesis Telescope and at 1420 MHz observed with the Effelsberg 100 m telescope. We confirm previously described continuum features and elaborate further on filamentary features identified using the high-resolution (1') maps from these new observations. We investigate the abrupt change in sign of rotation measure (RM) across the SNR, using the linear polarization observations in the four bands around 1420 MHz. Following X. H. Sun et al.'s (2011) investigation, we both confirm that the distribution of signs of the RMs for extragalactic sources in the area appears to match that of the shell, as well as combine the data from the four bands to estimate the relative depolarization and the intrinsic rotation measure of the SNR. We do not conclusively reject X. H. Sun et al.'s (2011) claim of a Faraday screen in the foreground causing the distribution of RMs that we observe; however, we do suggest an alternative explanation of a swept-up stellar wind from the progenitor star with a toroidal magnetic field. Finally, we expand on the analysis of the H I observations by applying the Rolling Hough Transform to isolate filamentary structure and better identify H I emission with the SNR. Further constraining the H I velocity channels associated with CTA 1, we use more recent Galactic rotation curves to calculate an updated kinematic distance of 1.09 +/- 0.2 kpc.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

This is a technical report on the 360-degree panoramic image generation task based on diffusion models. Unlike ordinary 2D images, 360-degree panoramic images capture the entire 360^circtimes 180^circ field of view. So the rightmost and the leftmost sides of the 360 panoramic image should be continued, which is the main challenge in this field. However, the current diffusion pipeline is not appropriate for generating such a seamless 360-degree panoramic image. To this end, we propose a circular blending strategy on both the denoising and VAE decoding stages to maintain the geometry continuity. Based on this, we present two models for Text-to-360-panoramas and Single-Image-to-360-panoramas tasks. The code has been released as an open-source project at https://github.com/ArcherFMY/SD-T2I-360PanoImage{https://github.com/ArcherFMY/SD-T2I-360PanoImage} and https://www.modelscope.cn/models/damo/cv_diffusion_text-to-360panorama-image_generation/summary{ModelScope}

Real-world data often exhibits long tail distributions with heavy class imbalance, where the majority classes can dominate the training process and alter the decision boundaries of the minority classes. Recently, researchers have investigated the potential of supervised contrastive learning for long-tailed recognition, and demonstrated that it provides a strong performance gain. In this paper, we show that while supervised contrastive learning can help improve performance, past baselines suffer from poor uniformity brought in by imbalanced data distribution. This poor uniformity manifests in samples from the minority class having poor separability in the feature space. To address this problem, we propose targeted supervised contrastive learning (TSC), which improves the uniformity of the feature distribution on the hypersphere. TSC first generates a set of targets uniformly distributed on a hypersphere. It then makes the features of different classes converge to these distinct and uniformly distributed targets during training. This forces all classes, including minority classes, to maintain a uniform distribution in the feature space, improves class boundaries, and provides better generalization even in the presence of long-tail data. Experiments on multiple datasets show that TSC achieves state-of-the-art performance on long-tailed recognition tasks.

Novel-view synthesis of specular objects like shiny metals or glossy paints remains a significant challenge. Not only the glossy appearance but also global illumination effects, including reflections of other objects in the environment, are critical components to faithfully reproduce a scene. In this paper, we present Neural Directional Encoding (NDE), a view-dependent appearance encoding of neural radiance fields (NeRF) for rendering specular objects. NDE transfers the concept of feature-grid-based spatial encoding to the angular domain, significantly improving the ability to model high-frequency angular signals. In contrast to previous methods that use encoding functions with only angular input, we additionally cone-trace spatial features to obtain a spatially varying directional encoding, which addresses the challenging interreflection effects. Extensive experiments on both synthetic and real datasets show that a NeRF model with NDE (1) outperforms the state of the art on view synthesis of specular objects, and (2) works with small networks to allow fast (real-time) inference. The project webpage and source code are available at: https://lwwu2.github.io/nde/.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

Traditional deep learning models rely on methods such as softmax cross-entropy and ArcFace loss for tasks like classification and face recognition. These methods mainly explore angular features in a hyperspherical space, often resulting in entangled inter-class features due to dense angular data across many classes. In this paper, a new field of feature exploration is proposed known as HyperSpaceX which enhances class discrimination by exploring both angular and radial dimensions in multi-hyperspherical spaces, facilitated by a novel DistArc loss. The proposed DistArc loss encompasses three feature arrangement components: two angular and one radial, enforcing intra-class binding and inter-class separation in multi-radial arrangement, improving feature discriminability. Evaluation of HyperSpaceX framework for the novel representation utilizes a proposed predictive measure that accounts for both angular and radial elements, providing a more comprehensive assessment of model accuracy beyond standard metrics. Experiments across seven object classification and six face recognition datasets demonstrate state-of-the-art (SoTA) results obtained from HyperSpaceX, achieving up to a 20% performance improvement on large-scale object datasets in lower dimensions and up to 6% gain in higher dimensions.

While the temporal variations of the spectro-polarimetric nature of pulsars remains unexplored, this investigation offers significant potential for uncovering key insights into pulsar emission mechanisms, magnetic field geometry, and propagation effects within the magnetosphere. We developed a package for investigating time-varying spectral behavior for full Stokes parameters and demonstrate it on a millisecond pulsar (MSP) J2144-5237 in a binary system (orbital period ~10 days) using the Parkes UWL receiver. In this study we report rotation measure (RM) variation with orbital phase. We find that the temporal variations in the spectra of Stokes I, Q, and V are generally correlated throughout the orbit, while Stokes U exhibits intervals of both correlation and anticorrelation with Stokes I, depending on the orbital phase. We also provide a Poincare sphere representation of the polarization properties of J2144-5237, demonstrating a systematic temporal change of Poincare sphere location for the main component with orbital phase. To our knowledge, this is the first investigation of time-varying properties of the spectro-polarimetric nature of any pulsars or MSPs. Extending this study to probe the spectro-temporal nature of full Stokes data on a larger sample of MSPs or pulsars has the potential to provide vital information on emission mechanisms inside the magnetosphere, interstellar propagation effects, and binary interactions.

We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and symbolic/numerical elimination. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram. We illustrate with a number of examples that this algebraic formalism allows to compute many components of the Landau singular locus. We adapt the GKZ framework by carefully specializing Euler integrals to Feynman integrals. For instance, ultraviolet and infrared singularities are detected as irreducible components of an incidence variety, which project dominantly to the kinematic space. We compute principal Landau determinants for the infinite families of one-loop and banana diagrams with different mass configurations, and for a range of cutting-edge Standard Model processes. Our algorithms build on the Julia package Landau.jl and are implemented in the new open-source package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales.

Light emission from galaxies exhibit diverse brightness profiles, influenced by factors such as galaxy type, structural features and interactions with other galaxies. Elliptical galaxies feature more uniform light distributions, while spiral and irregular galaxies have complex, varied light profiles due to their structural heterogeneity and star-forming activity. In addition, galaxies with an active galactic nucleus (AGN) feature intense, concentrated emission from gas accretion around supermassive black holes, superimposed on regular galactic light, while quasi-stellar objects (QSO) are the extreme case of the AGN emission dominating the galaxy. The challenge of identifying AGN and QSO has been discussed many times in the literature, often requiring multi-wavelength observations. This paper introduces a novel approach to identify AGN and QSO from a single image. Diffusion models have been recently developed in the machine-learning literature to generate realistic-looking images of everyday objects. Utilising the spatial resolving power of the Euclid VIS images, we created a diffusion model trained on one million sources, without using any source pre-selection or labels. The model learns to reconstruct light distributions of normal galaxies, since the population is dominated by them. We condition the prediction of the central light distribution by masking the central few pixels of each source and reconstruct the light according to the diffusion model. We further use this prediction to identify sources that deviate from this profile by examining the reconstruction error of the few central pixels regenerated in each source's core. Our approach, solely using VIS imaging, features high completeness compared to traditional methods of AGN and QSO selection, including optical, near-infrared, mid-infrared, and X-rays.

The Jovian atmosphere contains a wide diversity of vortices, which have a large range of sizes, colors and forms in different dynamical regimes. The formation processes for these vortices is poorly understood, and aside from a few known, long-lived ovals, such as the Great Red Spot, and Oval BA, vortex stability and their temporal evolution are currently largely unknown. In this study, we use JunoCam data and a citizen-science project on Zooniverse to derive a catalog of vortices, some with repeated observations, through May 2018 to Sep 2021, and analyze their associated properties, such as size, location and color. We find that different colored vortices (binned as white, red, brown and dark), follow vastly different distributions in terms of their sizes and where they are found on the planet. We employ a simplified stability criterion using these vortices as a proxy, to derive a minimum Rossby deformation length for the planet of sim1800 km. We find that this value of L_d is largely constant throughout the atmosphere, and does not have an appreciable meridional gradient.

Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed for surface normal estimation and propose to (1) utilize the per-pixel ray direction and (2) encode the relationship between neighboring surface normals by learning their relative rotation. The proposed method can generate crisp - yet, piecewise smooth - predictions for challenging in-the-wild images of arbitrary resolution and aspect ratio. Compared to a recent ViT-based state-of-the-art model, our method shows a stronger generalization ability, despite being trained on an orders of magnitude smaller dataset. The code is available at https://github.com/baegwangbin/DSINE.

Personalized text-to-image (T2I) synthesis based on diffusion models has attracted significant attention in recent research. However, existing methods primarily concentrate on customizing subjects or styles, neglecting the exploration of global geometry. In this study, we propose an approach that focuses on the customization of 360-degree panoramas, which inherently possess global geometric properties, using a T2I diffusion model. To achieve this, we curate a paired image-text dataset specifically designed for the task and subsequently employ it to fine-tune a pre-trained T2I diffusion model with LoRA. Nevertheless, the fine-tuned model alone does not ensure the continuity between the leftmost and rightmost sides of the synthesized images, a crucial characteristic of 360-degree panoramas. To address this issue, we propose a method called StitchDiffusion. Specifically, we perform pre-denoising operations twice at each time step of the denoising process on the stitch block consisting of the leftmost and rightmost image regions. Furthermore, a global cropping is adopted to synthesize seamless 360-degree panoramas. Experimental results demonstrate the effectiveness of our customized model combined with the proposed StitchDiffusion in generating high-quality 360-degree panoramic images. Moreover, our customized model exhibits exceptional generalization ability in producing scenes unseen in the fine-tuning dataset. Code is available at https://github.com/littlewhitesea/StitchDiffusion.