Daily Papers

A new class of solutions describing the composition of compact stars has been proposed, assuming that the fluid distribution inside the star is anisotropic. This is achieved by assuming the appropriate metric potential and then solving Einstein's field equations using Karmarkar conditions [Karmarkar K. R., Proc. Indian Acad. Sci. 27 (1948) 56] to derive the expressions for star density, the radial and tangential pressures in terms of the constants A, B, a paramter `a' and the curvature parameter R. The equations thus obtained have been passed through rigorous conditional analysis. It is further shown that the model is physically viable and mathematically well-behaved, fulfilling the requisite conditions viz., regularity condition, strong energy condition, causality condition, etc. Observed star candidates including EXO 1785-248, SMC X-1, SAXJ1808.43658(SS2), HER X-1, 4U 1538-52, Cen X-3 and LMC X-4 were found to conform to a good approximation through the outcome of this model for a=0.5.

We develop a multiexposure image fusion method based on texture features, which exploits the edge preserving and intraregion smoothing property of nonlinear diffusion filters based on partial differential equations (PDE). With the captured multiexposure image series, we first decompose images into base layers and detail layers to extract sharp details and fine details, respectively. The magnitude of the gradient of the image intensity is utilized to encourage smoothness at homogeneous regions in preference to inhomogeneous regions. Then, we have considered texture features of the base layer to generate a mask (i.e., decision mask) that guides the fusion of base layers in multiresolution fashion. Finally, well-exposed fused image is obtained that combines fused base layer and the detail layers at each scale across all the input exposures. Proposed algorithm skipping complex High Dynamic Range Image (HDRI) generation and tone mapping steps to produce detail preserving image for display on standard dynamic range display devices. Moreover, our technique is effective for blending flash/no-flash image pair and multifocus images, that is, images focused on different targets.

Among a huge variety of known two-dimensional materials, some of them have anisotropic crystal structures; examples include so different systems as a few-layer black phoshphorus (phosphorene), beryllium nitride BeN_4, van der Waals magnet CrSBr, rhenium dichalgogenides ReX_2. As a consequence, their optical and electronic properties turn out to be highly anisotropic as well. In some cases, the anisotropy results not just in a smooth renormalization of observable properties in comparison with the isotropic case but in the appearance of dramatically new physics. The examples are hyperbolic plasmons and excitons, strongly anisotropic ordering of adatoms at the surface of two-dimensional or van der Waals materials, essential change of transport and superconducting properties. Here, we present a systematic review of electronic structure, transport and optical properties of several representative groups of anisotropic two-dimensional materials including semiconductors, anisotropic Dirac and semi-Dirac materials, as well as superconductors.

Hyperelastic models have been widely used to model polymers and soft tissues. However, most hyperelastic models are phenomenological material models. Based on statistical mechanics and molecular chain configuration, 8 chain model or Arruda-Boyce model is a physical model which can be used to understand how microstructures of chains affect macroscopic mechanical properties of polymers and soft tissues. Mechanical properties of many polymers and soft tissues are directional dependent. Polymer matrix can be reinforced by fibers. For soft tissues, ligaments and tendons will lead to anisotropic properties. Since matrix and reinforcements are composed of similar microstructural molecular chains, they can be modeled by using the same mathematical model. In this paper, a series of 8 chain models is used to understand composite properties. That is, an isotropic 8 chain model will be used to model matrix and anisotropic 8 chain models will be used to model fibers. Replacing I_1 in isotropic 8 chain model with I_4 in anisotropic 8 chain model is physically corresponding to changing representative 8 chain cubic cell to 8 chain slender cell. This treatment not only simplifies exist anisotropic mathematical structures but also keeps microscopic physics of 8 chain model unchanged.

Training multimodal large language models has long been limited by the scarcity of high-quality paired multimodal data. Recent studies show that the shared representation space of pretrained multimodal contrastive models can serve as a bridge, enabling models to perform multimodal training with unimodal data. However, the key premise of this paradigm remains insufficiently understood: can representations from different modalities be reliably interchanged? The core obstacle lies in the persistent Modality Gap in the shared space. In this work, we revisit the geometric nature of the modality gap. We find that modality representations already share compatible dominant semantic geometry. What truly hinders modality interchangeability is not a simple global shift, but an anisotropic residual structure concentrated along a small number of dominant directions. Based on this finding, we further propose the principle of anisotropic modality gap alignment: effective modality alignment should align with the target-modality distribution while preserving the semantic structure of the source modality. Guided by this principle, we propose an anisotropic geometric correction framework, AnisoAlign, for unpaired modality alignment. This framework leverages the internal geometric prior of the target modality and performs bounded correction on source-modality representations, thereby constructing substitute representations in the target modality. Experiments confirm its benefits in both geometric diagnostics and text-only MLLM training. Overall, this work recasts the modality gap from an empirical observation into a correctable, structured geometric phenomenon and provides a new representation alignment perspective for training multimodal models with unimodal data.

Latent world models learn action-conditioned dynamics in representation space and often score candidate actions by Euclidean distance to a goal representation. Joint training typically regularizes the representation to prevent collapse, but the resulting representation geometry also determines how terminal errors are weighted during planning. We show that accurate prediction and noncollapsed representations do not guarantee a task-aligned latent planning cost: isotropic Gaussian regularization can induce a geometry that ranks feasible outcomes differently from the task cost. To address this mismatch, we introduce AnisoWM with ΛReg, which replaces the fixed isotropic Gaussian target with a learnable diagonal covariance under fixed-trace and anisotropy constraints. The prediction objective, predictor architecture, and Euclidean planner remain unchanged; the target is used only during training. Our analysis characterizes the prediction-driven allocation of target variance, its dependence on the training distribution, and the conditions under which the induced metric reduces planning regret. Across four visual control environments, AnisoWM improves planning success over LeWorldModel in all four. Its latent planning cost also shows better agreement with task outcomes. Project website: https://rkdrn79.github.io/AnisoWM-page/

Given the success of Large Language Models (LLMs), there has been considerable interest in studying the properties of model activations. The literature overwhelmingly agrees that LLM representations are dominated by a few ``outlier dimensions'' with exceedingly high variance and magnitude. Several studies in Natural Language Processing (NLP) have sought to mitigate the impact of such outlier dimensions and force LLMs to be isotropic (i.e., have uniform variance across all dimensions in embedding space). Isotropy is thought to be a desirable property for LLMs that improves model performance and more closely aligns textual representations with human intuition. However, many of the claims regarding isotropy in NLP have been based on the average cosine similarity of embeddings, which has recently been shown to be a flawed measure of isotropy. In this paper, we propose I-STAR: IsoScore*-based STable Anisotropic Regularization, a novel regularization method that can be used to increase or decrease levels of isotropy in embedding space during training. I-STAR uses IsoScore*, the first accurate measure of isotropy that is both differentiable and stable on mini-batch computations. In contrast to several previous works, we find that decreasing isotropy in contextualized embeddings improves performance on the majority of tasks and models considered in this paper.

We confirm for the first time the existence of distinctive halo bias associated with the quadrupolar type of statistical anisotropy (SA) of the linear matter density field using cosmological N-body simulations. We find that the coefficient of the SA-induced bias for cluster-sized halos takes negative values and exhibits a decreasing trend with increasing halo mass. This results in the quadrupole halo power spectra in a statistically anisotropic universe being less amplified compared to the monopole spectra. The anisotropic feature in halo bias that we found presents a promising new tool for testing the hypothesis of a statistically anisotropic universe, with significant implications for the precise verification of anisotropic inflation scenarios and vector dark matter and dark energy models.

Speculative decoding accelerates large language model inference by drafting multiple candidate tokens and verifying them in a single forward pass. Candidates are organized as a tree: deeper trees accept more tokens per step, but adding depth requires sacrificing breadth (fallback options) under a fixed verification budget. Existing training-free methods draft from a single token source and shape their trees without distinguishing candidate quality across origins. We observe that two common training-free token sources - n-gram matches copied from the input context, and statistical predictions from prior forward passes - differ dramatically in acceptance rate (~6x median gap, range 2-18x across five models and five benchmarks). We prove that when such a quality gap exists, the optimal tree is anisotropic (asymmetric): reliable tokens should form a deep chain while unreliable tokens spread as wide branches, breaking through the depth limit of balanced trees. We realize this structure in GOOSE, a training-free framework that builds an adaptive spine tree - a deep chain of high-acceptance context-matched tokens with wide branches of low-acceptance alternatives at each node. We prove that the number of tokens accepted per step is at least as large as that of either source used alone. On five LLMs (7B-33B) and five benchmarks, GOOSE achieves 1.9-4.3x lossless speedup, outperforming balanced-tree baselines by 12-33% under the same budget.

We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted distance score, and we compute pixel colors as a softmax blend over a small per-pixel top-K subset of sites. We induce a soft anisotropic additively weighted Voronoi partition (i.e., an Apollonius diagram) with learnable per-site temperatures, preserving informative gradients while allowing clear, content-aligned boundaries and explicit ownership. Such a formulation enables efficient rendering by maintaining a per-query top-K map that approximates nearest neighbors under the same shading score, allowing GPU-friendly, fixed-size local computation. We update this list using our top-K propagation scheme inspired by jump flooding, augmented with stochastic injection to provide probabilistic global coverage. Training follows a GPU-first pipeline with gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. Across standard benchmarks, SAD consistently outperforms Image-GS and Instant-NGP at matched bitrate. On Kodak, SAD reaches 46.0 dB PSNR with 2.2 s encoding time (vs. 28 s for Image-GS), and delivers 4-19 times end-to-end training speedups over state-of-the-art baselines. We demonstrate the effectiveness of SAD by showcasing the seamless integration with differentiable pipelines for forward and inverse problems, efficiency of fast random access, and compact storage.

Dense self-attention treats all token pairs as equally plausible before learning, an interaction-isotropic prior that can be mismatched to structured signals. For structured, low signal-to-noise ratio (SNR) signals such as EEG, dependencies are organized along the electrode and time axes, and this uniform prior exposes each token to many irrelevant interactions. We introduce Adaptive Anisotropic Attention (AAA), which splits attention into two paths: a temporal path, where each token attends to the tokens of its own electrode across time, and a spatial path, where it attends to the tokens of the other electrodes at the same time step. A small gate predicts, for every token, a convex combination of the two path outputs: two non-negative weights that sum to one. On six EEG downstream tasks, the resulting model, AXON (AXis-factorized Operator Network), improves mean balanced accuracy over a dense baseline under both linear probing and full fine-tuning. We show that both paths (temporal and spatial) are necessary and that the weighted sum beats a hard choice of one path; most of the benefit comes from the gate learning a different temporal/spatial balance at each layer of the network. Controlled audio spectrogram experiments show that axis factorization transfers beyond EEG. These results suggest that aligning attention with the natural axes of structured signals provides a useful inductive bias.

The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its exceptional rendering quality and performance on standard datasets, 3D-GS frequently encounters difficulties in accurately modeling specular and anisotropic components. This issue stems from the limited ability of spherical harmonics (SH) to represent high-frequency information. To overcome this challenge, we introduce Spec-Gaussian, an approach that utilizes an anisotropic spherical Gaussian (ASG) appearance field instead of SH for modeling the view-dependent appearance of each 3D Gaussian. Additionally, we have developed a coarse-to-fine training strategy to improve learning efficiency and eliminate floaters caused by overfitting in real-world scenes. Our experimental results demonstrate that our method surpasses existing approaches in terms of rendering quality. Thanks to ASG, we have significantly improved the ability of 3D-GS to model scenes with specular and anisotropic components without increasing the number of 3D Gaussians. This improvement extends the applicability of 3D GS to handle intricate scenarios with specular and anisotropic surfaces.

We continue our analysis on conductivity in the anisotropic background by employing the D-brane probe technique, where the D-branes play the role of charge carriers. The DC and AC conductivity for massless charge carriers are obtained analytically, while interesting curves for the AC conductivity are also plotted. For massive charge carriers, we calculate the DC and AC conductivities in the dilute limit and we fix the parameters in the Einstein-Maxwell-dilaton theory so that the background exhibits the same scaling behaviors as those for real-world strange metals. The DC conductivity at finite density is also computed.

We present the results of simulated injections testing the first Bayesian search-pipeline capable of investigating the angular-structure of a gravitational-wave (GW) background influencing pulsar signals. A stochastic background of GWs from the incoherent superposition of many inspiraling supermassive black hole binaries at nHz frequencies is likely to be the dominant GW signal detectable by pulsar timing arrays (PTAs). Even though one might expect a background composed of a high-redshift cosmological population of sources to be fairly isotropic, deviations from isotropy may be indicative of local GW hotspots or some form of continuous anisotropy in the angular-distribution of GW-power. A GWB induces time-of-arrival deviations in pulsar signals which are correlated between separated pulsars. In an isotropic background this cross-correlation follows a distinctive relationship, known as the Hellings and Downs curve, that depends only on the angular separation of the pulsars. If the background is anisotropic, the cross-correlation is different, but predictable, and also depends on the absolute position of the pulsars. By simulating datasets containing GWBs with various anisotropic configurations, we have explored the prospects for constraining anisotropy using near future data. We find that at moderate to high signal to noise ratio the assumption of isotropy is no longer an appropriate description of the simulated background. Furthermore, we can recover the nature of the injected anisotropy in a Bayesian parameter-estimation search, and propose a prior on the anisotropy search-space motivated by the physicality of the implied distribution of sources.

Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce isotropic refinement in regions of interest, which can be especially inefficient for problems that are intrinsically anisotropic--much resolution is spent where little information is gained. This paper presents omnitrees as an anisotropic generalization of octrees and related data structures. Omnitrees allow to refine only the locally most important dimensions, providing tree structures that are less deep than bintrees and less wide than octrees. As a result, the convergence of the AMR schemes can be increased by up to a factor of the dimensionality d for very anisotropic problems, quickly offsetting their modest increase in storage overhead. We validate this finding on the problem of binary shape representation across 4,166 three-dimensional objects: Omnitrees increase the mean convergence rate by 1.5x, require less storage to achieve equivalent error bounds, and maximize the information density of the stored function faster than octrees. These advantages are projected to be even stronger for higher-dimensional problems. We provide a first validation by introducing a time-dependent rotation to create four-dimensional representations, and discuss the properties of their 4-d octree and omnitree approximations. Overall, omnitree discretizations can make existing AMR approaches more efficient, and open up new possibilities for high-dimensional applications.

Accurate and rapid estimation of hemodynamic metrics, such as pressure and wall shear stress (WSS), is important for assessing the severity of Coronary Artery Disease (CAD). Existing approaches, including invasive Fractional Flow Reserve (FFR) measurements and computationally expensive Computational Fluid Dynamics (CFD) simulations, face challenges in invasiveness, cost, and speed. We present a framework for fast, non-invasive coronary hemodynamics prediction. The model encodes 1D vessel centerlines together with inlet flow rate using a transformer-based encoder, and predicts continuous wall-based fields via an anisotropic Radial Basis Function (RBF) decoder aligned with vessel morphology. To support training and evaluation, we introduce two datasets with paired steady-state OpenFOAM simulations: (i) a synthetic benchmark of 4,200 single-vessel geometries with controlled anatomical variations, and (ii) a multi-vessel dataset derived from ImageCAS including 4,800 cases spanning both right and left coronary arteries, generated by randomly introducing stenoses and varying physiologically plausible flow rates. Across both datasets, our method achieves lower pressure and WSS errors than strong neural-operator baselines (GNOT, Transolver, and ONO) at a fraction of the computational cost of CFD. On the multi-vessel dataset, using 1,024 anisotropic RBF centers our model reduces the mean relative L2 error by 52% compared to the best neural-operator baseline, while at 128 centers it requires 13.8x fewer FLOPs than GNOT and still outperforms all baselines. The single-vessel dataset is publicly available at https://huggingface.co/datasets/angioinsight/single-vessel-flow.

Most modern optimizers form their momentum as an exponential moving average (EMA) of past gradients, forgetting every direction at one fixed rate. However, the inputs a deep network sees during training can be highly anisotropic, with a few directions queried frequently while most are seen rarely. Preconditioning methods address this anisotropy by wrapping extra processing around this buffer and leave the momentum update itself unchanged. We propose Activation-Keyed Momentum (AK-Momentum), which builds direction-awareness into the momentum update rule. The gradient of a linear layer splits into an input activation that acts as a key and an output-side error that acts as a value. Keying on that activation, AK-Momentum updates the momentum buffer by the canonical delta rule, so each direction is forgotten at a rate set by how often it appears. We prove that it is a valid momentum, that it applies the input-side curvature correction without matrix inversion, and that it clears stale directions faster than EMA under both a fixed and a drifting optimum. It is a drop-in replacement for the momentum buffer of any optimizer, its coefficient transfers across widths under μP, and its extra compute stays between 22.2% and 25.0% of a gated-MLP block's linear cost with no persistent memory. In FineWeb-Edu pretraining, AdamW with AK-Momentum (AK-AdamW) reaches AdamW's validation loss in up to 46.39 pm 4.32% fewer steps at 67M and 22.12 pm 0.80% at 370M over three seeds, and the gain persists at 1B on a Chinchilla-optimal budget. A Muon baseline tuned under the same protocol sits above AK-AdamW at both language-model scales, and the gain holds for SGD, ResNet-18, and ViT-Tiny on CIFAR-10. Training-time diagnostics confirm the predicted mechanism, better gradient tracking and healthier input directions.

We propose PRISM, an optimizer that enhances first-order spectral descent methods like Muon with partial second-order information. It constructs an efficient, low-rank quasi-second-order preconditioner via innovation-augmented polar decomposition. This mechanism enables PRISM to perform anisotropic spectral shaping, which adaptively suppresses updates in high-variance subspaces while preserving update strength in signal-dominated directions. Crucially, this is achieved with minimal computational overhead and zero additional memory compared to first-order baselines. PRISM demonstrates a practical strategy for integrating curvature-adaptive properties into the spectral optimization paradigm.

Westerlund 1 (Wd1) is one of the Milky Way's most massive young clusters, in which heavy extinction and field contamination have historically hampered its kinematic characterization. We aim to assess Wd1's internal kinematics, dynamical state, and formation scenario. Using a robust 5D clustering approach, we identified 559 bona fide members. We modeled their proper motions via a 2D first-order Taylor expansion to derive the velocity gradient tensor, mapping expansion, rotation, and shear. Restricting the kinematic analysis to 524 stars with proper motion uncertainties <0.5~mas,yr^{-1}, we find at least 103 gravitationally unbound members, including 14 walkaway stars. The 2D analysis reveals a statistically significant divergence (>4σ) highlighting preferred expansion along the Galactic latitude (position angle 164^circpm10.1^circ). A detected cross-gradient (partial v_b / partial l = -0.41 pm 0.08 km s^{-1} pc^{-1}) provides a clear signature of shear on the plane of the sky. Wd1 does not behave as a single cohesive population, but comprises two decoupled subsystems: a stable, bound core in dynamical equilibrium and an escaping, unbound envelope. This prominent anisotropic expansion perpendicular to the Galactic plane has a kinematic timescale (Δt_{kin} = 2.08 pm 0.44 Myr) matching the independent orbital mid-plane crossing time (Δt_{orbit} = 2.10 pm 0.05 Myr). This temporal alignment indicates the expansion onset coincided with Wd1's Galactic disk passage, triggered either by internal dynamics (e.g., early supernova feedback) or external tidal perturbations. Finally, the robust unbound population demonstrates that active cluster dissolution is underway, driven by discrete dynamical ejection events rather than long-term stellar evaporation.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

Statistics that capture the directional dependence of the baryon distribution in the cosmic web enable unique tests of cosmology and astrophysical feedback. We use constrained oriented stacking of thermal Sunyaev-Zel'dovich (tSZ) maps to measure the anisotropic distribution of hot gas 2.5-40 Mpc away from galaxy clusters embedded in massive filaments and superclusters. The cluster selection and orientation (at a scale of sim15 Mpc) use Dark Energy Survey (DES) Year 3 data, while expanded tSZ maps from the Atacama Cosmology Telescope Data Release 6 enable a sim3times more significant measurement of the extended gas compared to the technique's proof-of-concept. Decomposing stacks into cosine multipoles of order m, we detect a dipole (m=1) and quadrupole (m=2) at 8-10sigma, as well as evidence for m=4 signal at up to 6sigma, indicating sensitivity to late-time non-Gaussianity. We compare to the Cardinal simulations with spherical gas models pasted onto dark matter halos. The fiducial tSZ data can discriminate between two models that deplete pressure differently in low-mass halos (mimicking astrophysical feedback), preferring higher average pressure in extended structures. However, uncertainty in the amount of cosmic infrared background contamination reduces the constraining power. Additionally, we apply the technique to DES galaxy density and weak lensing to study for the first time their oriented relationships with tSZ. In the tSZ-to-lensing relation, averaged on 7.5 Mpc (transverse) scales, we observe dependence on redshift but not shape or radial distance. Thus, on large scales, the superclustering of gas pressure, galaxies, and total matter is coherent in shape and extent.

Following Dibenedetto's intrinsic scaling method, we prove local H\"older continuity of weak solutions to obstacle problems related to some anisotropic parabolic equations under the condition for which only H\"older's continuity of the obstacle is known.

Heavy-ball momentum with decaying learning rates is widely used with SGD for optimizing deep learning models. In contrast to its empirical popularity, the understanding of its theoretical property is still quite limited, especially under the standard anisotropic gradient noise condition for quadratic regression problems. Although it is widely conjectured that heavy-ball momentum method can provide accelerated convergence and should work well in large batch settings, there is no rigorous theoretical analysis. In this paper, we fill this theoretical gap by establishing a non-asymptotic convergence bound for stochastic heavy-ball methods with step decay scheduler on quadratic objectives, under the anisotropic gradient noise condition. As a direct implication, we show that heavy-ball momentum can provide mathcal{O}(kappa) accelerated convergence of the bias term of SGD while still achieving near-optimal convergence rate with respect to the stochastic variance term. The combined effect implies an overall convergence rate within log factors from the statistical minimax rate. This means SGD with heavy-ball momentum is useful in the large-batch settings such as distributed machine learning or federated learning, where a smaller number of iterations can significantly reduce the number of communication rounds, leading to acceleration in practice.

In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with anisotropic materials and are prone to instability caused by zero energy modes. Our novel model extend the linear bond based peridynamics framework by incorporating the elastic tensor into the micrmodulus function, thereby ensuring stability for anisotropic materials without the need for additional corrections. For isotropic materials. the model mantains compatibility with conventional bond based peridynamics, assuming Possion's rations of 1/4 in 3D and 1/3 in 2D.Numerical experiments confirm the model's stability and accuracy across various scenarios. Additionally, we introduce a damage model for isotropic materials. validating its performance in predicting crack propagation paths in a 2D plate. The results show superior alignment with experimental date compared to traditional model.

Using K giants from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI) Milky Way (MW) Survey, we measure the shape, orientation, radial profile, and density anisotropies of the MW stellar halo over 8 kpc<r_GC<200 kpc. We identify a triaxial stellar halo (axes ratio 10:8:7), 43 degrees tilted from the disk, showing two break radii at sim16 kpc and sim76 kpc, likely associated with Gaia-Sausage/Enceladus (GSE) and Large Magellanic Cloud (LMC), respectively. The inner stellar halo (<30 kpc) is oblate and aligned with the disk, whereas the outer stellar halo becomes prolate and perpendicular to the disk, consistent with the Vast Polar Structure of MW satellites. The twisted halo may arise from the disk-halo angular momentum shift triggered by the infall of a massive satellite. The anisotropic density distribution of the stellar halo is also measured, with successful re-identification of the Hercules-Aquila Cloud South/North (HAC-N/-S) and Virgo overdensities (VOD). Break radii are found at 15/30 kpc for VOD/HAC-N(-S). We identify the LMC transient density wake with a break radius at 60 kpc in the Pisces overdensity region. We also find new observational evidence of the LMC collective density wake, by showing a break radius at sim100 kpc in the northern Galactic cap with a clear density peak at 90 kpc. In the end, we found that more metal-poor halo stars are more radially extended. Our results provide important clues to the assembly and evolution of the MW stellar halo under the standard cosmic structure formation framework.

The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing either pure triangular meshes or pure quadrilateral meshes with isotropic densities. In this paper, we present QuadLink, a unified framework consisting of three stages for quad-dominant mesh generation by linking points into structured faces. QuadLink formulates polygonal mesh generation as a hybrid centroid-conditioned vertex linking model: it first predicts a unified set of anchors (vertices and face centroids), then learns centroid-conditioned links that associate vertices with face centroids, and finally assembles polygonal faces with a quad-first strategy guided by robust geometric verification strategies. This link-based formulation enables efficient generation of sparse and anisotropic quad-dominant meshes with coherent edge flow and meanwhile supporting hybrid polygonal topology. To construct training data for this model, we further introduce a Tri-to-Quad Operator that converts artistic triangle meshes into quad-dominant training data via global merge selection. Extensive experiments show that QuadLink produces production-ready quad-dominant meshes from point clouds and achieves improved geometric fidelity and topological quality compared to prior baselines. Our method natively supports hybrid polygonal topology, generalizing to arbitrary n-gon meshes without architectural changes.

Recursive models can continue updating their latent states beyond their nominal inference budget, so an incorrect output at that budget does not show whether computation is unfinished or has entered a persistently unsuccessful regime. We study the dynamics of completion in attention- and MLP-based Tiny Recursive Models (TRMs) on 1,000 hard Sudoku puzzles. Extending recurrence from the nominal 16 steps to 512 steps increases cumulative exact-solve accuracy from 59.2% to 87.5% for the attention model and from 74.4% to 91.9% for the MLP model, solving more than two-thirds of the puzzles unsolved in the nominal budget. Across both architectures, latent-state motion drops sharply after the first exact solution. Completed states are typically locally contractive along the trajectory direction, even though the same local Jacobian retains strongly expanding directions. We characterize this phenomenon as trajectory-conditioned anisotropic stability. Perturbation experiments confirm this directional stability across both models. The multi-step fate of the maximally expanding direction differs: it is absorbed within 16 steps in the attention model but persists longer in the MLP model. The anisotropic-stability pattern also holds for a second attention checkpoint. Together, these results distinguish nominal-budget failure from completed computation and identify a common dynamical signature of completion across two recurrent architectures.

Precise shaping of surface acoustic waves (SAWs) on anisotropic piezoelectric substrates is complicated by elastic anisotropy and electromechanical coupling. Here we introduce a continuous diffractive acoustic lens (CDAL), in which weak phase-velocity perturbations produced by subwavelength metallization, together with diffraction, drive lateral field redistribution. An anisotropic thin-element propagation model enables efficient inverse design of the CDAL contour. Laser Doppler vibrometry verifies prescribed lateral field profiles and multichannel beam splitting with unequal widths. By combining continuous diffractive modulation with discrete source-phase encoding, we further shape the lateral field into a Bessel profile, demonstrating joint amplitude-and-phase control. This work provides a high-precision and fabrication-compatible mechanism for on-chip SAW field modulation.

Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic for statisticians and practitioners. The low-rank scalar-on-tensor regression model, in particular, has received widespread attention and has been re-formulated as a tensor Gaussian Process (Tensor-GP) model with multi-linear kernel in Yu et al. (2018). In this paper, we extend the Tensor-GP model by integrating a dimensionality reduction technique, called tensor contraction, with a Tensor-GP for a scalar-on-tensor regression task with multi-channel imaging data. This is motivated by the solar flare forecasting problem with high dimensional multi-channel imaging data. We first estimate a latent, reduced-size tensor for each data tensor and then apply a multi-linear Tensor-GP on the latent tensor data for prediction. We introduce an anisotropic total-variation regularization when conducting the tensor contraction to obtain a sparse and smooth latent tensor. We then propose an alternating proximal gradient descent algorithm for estimation. We validate our approach via extensive simulation studies and applying it to the solar flare forecasting problem.

In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the d-dimensional advection-diffusion equation, our proposal is a two-level algorithm that merges the solutions obtained from the discretization of the equation over highly anisotropic submeshes to compute an initial approximation of the fine solution. The algorithm then iteratively refines the initial guess by leveraging the structure of the residual. Performing costly calculations on anisotropic submeshes enable us to reduce the dimensionality of the problem by one, and the merging process, which involves the computation of solutions over disjoint domains, allows for parallel implementation.

Generating text with autoregressive language models (LMs) is of great importance to many natural language processing (NLP) applications. Previous solutions for this task often produce text that contains degenerative expressions or lacks semantic consistency. Recently, Su et al. introduced a new decoding method, contrastive search, based on the isotropic representation space of the language model and obtained new state of the art on various benchmarks. Additionally, Su et al. argued that the representations of autoregressive LMs (e.g. GPT-2) are intrinsically anisotropic which is also shared by previous studies. Therefore, to ensure the language model follows an isotropic distribution, Su et al. proposed a contrastive learning scheme, SimCTG, which calibrates the language model's representations through additional training. In this study, we first answer the question: "Are autoregressive LMs really anisotropic?". To this end, we extensively evaluate the isotropy of LMs across 16 major languages. Surprisingly, we find that the anisotropic problem only exists in the two specific English GPT-2-small/medium models. On the other hand, all other evaluated LMs are naturally isotropic which is in contrast to the conclusion drawn by previous studies. Based on our findings, we further assess the contrastive search decoding method using off-the-shelf LMs on four generation tasks across 16 languages. Our experimental results demonstrate that contrastive search significantly outperforms previous decoding methods without any additional training. More notably, on 12 out of the 16 evaluated languages, contrastive search performs comparably with human-level performances as judged by human evaluations. Our code and other related resources are publicly available at https://github.com/yxuansu/Contrastive_Search_Is_What_You_Need.

Every second greater than 10^{25} antineutrinos radiate to space from Earth, shining like a faint antineutrino star. Underground antineutrino detectors have revealed the rapidly decaying fission products inside nuclear reactors, verified the long-lived radioactivity inside our planet, and informed sensitive experiments for probing fundamental physics. Mapping the anisotropic antineutrino flux and energy spectrum advance geoscience by defining the amount and distribution of radioactive power within Earth while critically evaluating competing compositional models of the planet. We present the Antineutrino Global Map 2015 (AGM2015), an experimentally informed model of Earth's surface antineutrino flux over the 0 to 11 MeV energy spectrum, along with an assessment of systematic errors. The open source AGM2015 provides fundamental predictions for experiments, assists in strategic detector placement to determine neutrino mass hierarchy, and aids in identifying undeclared nuclear reactors. We use cosmochemically and seismologically informed models of the radiogenic lithosphere/mantle combined with the estimated antineutrino flux, as measured by KamLAND and Borexino, to determine the Earth's total antineutrino luminosity at 3.4^{+2.3}_{-2.2} times 10^{25} nu_e. We find a dominant flux of geo-neutrinos, predict sub-equal crust and mantle contributions, with sim1% of the total flux from man-made nuclear reactors.

We build slowly rotating anisotropic neutron stars using the Hartle-Thorne formalism, employing three distinct anisotropy models--Horvat, Bowers-Liang, and a covariant model--to characterize the relationship between radial and tangential pressure. We analyze how anisotropy influences stellar properties such as the mass-radius relation, angular momentum, moment of inertia, and binding energy. Our findings reveal that the maximum stable mass of non-rotating stars depends strongly on the anisotropy model, with some configurations supporting up to 60% more mass than their isotropic counterparts with the same central density. This mass increase is most pronounced in the models where the anisotropy grows toward the star's surface, as seen in the covariant model. Furthermore, slowly rotating anisotropic stars adhere to universal relations for the moment of inertia and binding energy, regardless of the chosen anisotropy model or equation of state.

Holistic 3D scene understanding, which jointly models geometry, appearance, and semantics, is crucial for applications like augmented reality and robotic interaction. Existing feed-forward 3D scene understanding methods (e.g., LSM) are limited to extracting language-based semantics from scenes, failing to achieve holistic scene comprehension. Additionally, they suffer from low-quality geometry reconstruction and noisy artifacts. In contrast, per-scene optimization methods rely on dense input views, which reduces practicality and increases complexity during deployment. In this paper, we propose SemanticSplat, a feed-forward semantic-aware 3D reconstruction method, which unifies 3D Gaussians with latent semantic attributes for joint geometry-appearance-semantics modeling. To predict the semantic anisotropic Gaussians, SemanticSplat fuses diverse feature fields (e.g., LSeg, SAM) with a cost volume representation that stores cross-view feature similarities, enhancing coherent and accurate scene comprehension. Leveraging a two-stage distillation framework, SemanticSplat reconstructs a holistic multi-modal semantic feature field from sparse-view images. Experiments demonstrate the effectiveness of our method for 3D scene understanding tasks like promptable and open-vocabulary segmentation. Video results are available at https://semanticsplat.github.io.

This work identifies anisotropic parameter distributions as a fundamental barrier to training large language models (LLMs) with low-bit quantization: a few dominant singular values create wide numerical ranges that conflict with the inherent bias of block-wise quantization. This bias disproportionately preserves high-magnitude values while discarding smaller ones, causing training instability and low model performance. This work introduces Metis, a training framework that combines (i) spectral decomposition with random embedding to efficiently disentangle dominant from long-tail components, compressing broad distributions into quantization-friendly narrow ranges; (ii) adaptive learning rates in the spectral domain to amplify underrepresented directions and better capture diverse features critical for performance; and (iii) a dual-range regularizer that jointly constrains numerical precision and parameter range distribution, ensuring stable, unbiased low-bit training. With Metis, FP8 training surpasses FP32 baselines, and FP4 training achieves accuracy comparable to FP32, paving the way for robust and scalable LLM training under advanced low-bit quantization. The code implementation for Metis is available at: https://github.com/typename-yyf/Metis-quantization.

Detecting a stochastic gravitational wave background, particularly radiation from individually unresolvable super-massive black hole binary systems, is one of the primary targets for Pulsar Timing Arrays. Increasingly more stringent upper limits are being set on these signals under the assumption that the background radiation is isotropic. However, some level of anisotropy may be present and the characterisation of the power at different angular scales carries important information. We show that the standard analysis for isotropic backgrounds can be generalised in a conceptually straightforward way to the case of generic anisotropic background radiation by decomposing the angular distribution of the gravitational wave power on the sky into multipole moments. We introduce the concept of generalised overlap reduction functions which characterise the effect of the anisotropy multipoles on the correlation of the timing residuals from the pulsars timed by a Pulsar Timing Array. In a search for a signal characterised by a generic anisotropy, the generalised overlap reduction functions play the role of the so-called Hellings and Downs curve used for isotropic radiation. We compute the generalised overlap reduction functions for a generic level of anisotropy and Pulsar Timing Array configuration. We also provide an order of magnitude estimate of the level of anisotropy that can be expected in the background generated by super-massive black hole binary systems.

Constructing vivid 3D head avatars for given subjects and realizing a series of animations on them is valuable yet challenging. This paper presents GaussianHead, which models the actional human head with anisotropic 3D Gaussians. In our framework, a motion deformation field and multi-resolution tri-plane are constructed respectively to deal with the head's dynamic geometry and complex texture. Notably, we impose an exclusive derivation scheme on each Gaussian, which generates its multiple doppelgangers through a set of learnable parameters for position transformation. With this design, we can compactly and accurately encode the appearance information of Gaussians, even those fitting the head's particular components with sophisticated structures. In addition, an inherited derivation strategy for newly added Gaussians is adopted to facilitate training acceleration. Extensive experiments show that our method can produce high-fidelity renderings, outperforming state-of-the-art approaches in reconstruction, cross-identity reenactment, and novel view synthesis tasks. Our code is available at: https://github.com/chiehwangs/gaussian-head.

Machine-learned coarse-grained (CG) models often suffer from noisy training data, limiting their accuracy and transferability. We propose a method to generate low-noise training data based on the potential of mean force by constraining CG beads during atomistic simulations and accumulating time-averaged forces. Implemented within the neuroevolution potential (NEP) framework, our approach achieves training accuracy comparable to atomistic models trained on density functional theory data. For liquid water, the NEP-CG model accurately reproduces densities from 1 bar to 1 GPa, successfully extrapolating beyond the 0.5 GPa training limit, with a virial correction essential for the correct equation of state. For an anisotropic C_{60} monolayer, distinguishing crystallographically distinct bead types reduces stress errors by an order of magnitude and captures directional thermal conductivity. We further introduce a multiscale NEP-AACG model integrating all-atom (AA) and CG degrees of freedom, demonstrated for gold nanowire fracture at an experimentally relevant strain rate. Computational speeds for NEP-CG models reach hundreds to thousands of ns/day using a single consumer-grade GPU. This work provides a robust framework for constructing accurate, transferable, and efficient CG models across diverse systems.

In this work, we leverage CMB data from the Atacama Cosmology Telescope (ACT) and LSS data from the imaging survey conducted by the Dark Energy Spectroscopic Instrument (DESI) to study the distribution of gas around galaxy groups at low redshift, z approx 0.3, via the kinematic Sunyaev-Zel'dovich (kSZ) effect. In particular, we perform velocity-weighted stacking on the photometric Bright Galaxy Sample (BGS) to isolate the monopole and quadrupole of the kSZ signal, orienting the stacked images along 2D filaments identified using the Hessian of the projected gravitational potential. We find a 7.2σ detection in the monopole of the signal (i.e., the gas density profile) and a 4σ detection in the quadrupole (m = 2), constituting the first measurement of the alignment between gas distribution and the cosmic web through the kSZ effect. As it is a linear probe of the local gas density, the kSZ has heightened sensitivity to the warm-hot intergalactic medium (WHIM), which is believed to house the majority of the ``missing baryons.'' Mapping out the gas density at low redshifts, as enabled by our measurements, is crucial for weak lensing surveys, for which the impact of baryons on small scales is a major impediment. We compare the anisotropic signal against two hydrodynamical simulations, TNG300-1 and Illustris, which have very different baryonic feedback prescriptions. We find that the anisotropic signal measured in the data is comparable but slightly larger and more extended compared with the simulations. This suggests that there is excess accretion and feedback taking place through the filaments, hinting at the possible presence of spin-filament alignment of the BGS objects.

The structural stability and phonon properties of SnSe/SnS superlattices at finite temperatures have been studied using machine learning force field molecular dynamics and the anharmonic phonon approach. The vertical SnSe/SnS superlattice undergoes a phase transition from the Pnma phase to a novel P4/nmm phase at finite temperatures, which is different from the high-temperature Cmcm phase of the SnSe and SnS systems. The stability of P4/nmm phase is determined by molecular dynamics trajectories and anharmonic phonon dispersion relations. The imaginary modes of TO modes at the q=M(1/2,1/2,0) point of the P4/nmm phase in harmonic approximation become rigid at elevated temperatures. An analysis of phonon power spectra upon temperature also confirms the dynamic stabilization. The P4/nmm phase has higher symmetry than the Pnma phase, and the phase transition between them is accompanied by competition between the Jahn-Teller effect and phonon anharmonicity. Unlike the anisotropic distribution of Sn-Se/S bonds in the Pnma phase, the P4/nmm phase forms chemical bonds with similar bond lengths both in-plane and interlayer, and their resonance effect can significantly enhance phonon scattering. The calculated phonon density of states and lifetime is strongly temperature dependent, demonstrating the heavy anharmonicity in the SnSe/SnS system. The P4/nmm phase has an extremely low lattice thermal conductivity, close to the experimental values of SnSe and SnS. Moreover, with the reduction of band gap and the enhancement of band degeneracy near the Fermi level, the P4/nmm phase exhibits superior electronic transport properties and significantly enhanced response to infrared and visible light. This makes it show great potential in thermoelectric and photovoltaic applications.

We report the anomalous and topological Hall effect of the ferromagnetic Weyl semimetal Mn_5Ge_3. We observe a significant anisotropic anomalous Hall effect (AHE) due to nonzero Berry curvature in the momentum space, such that the anomalous Hall conductivity (AHC) is 965 S/cm for the xy-plane and 233 S/cm for the zx-plane of the single crystal. The band structure calculations predict several Weyl and nodal points span across the momentum space, gapped out under the spin-orbit coupling effect, leading to significant k-space Berry curvature and large AHC. Experimentally, we also demonstrate a sizeable topological Hall effect that is originated by the non-coplanar chiral spin structure due to the competition between the out-of-plane uniaxial magnetocrystalline anisotropy and the dipole-dipole interaction between two Mn sublattices. This study hints at the importance of dipole-dipole interactions in producing the skyrmion lattice in Mn_5Ge_3.

Many materials show anisotropic light scattering patterns due to the shape and local alignment of their underlying micro structures: surfaces with small elements such as fibers, or the ridges of a brushed metal, are very sparse and require a high spatial resolution to be properly represented as a volume. The acquisition of voxel data from such objects is a time and memory-intensive task, and most rendering approaches require an additional Level-of-Detail (LoD) data structure to aggregate the visual appearance, as observed from multiple distances, in order to reduce the number of samples computed per pixel (E.g.: MIP mapping). In this work we introduce first, an efficient parallel voxelization method designed to facilitate fast data aggregation at multiple resolution levels, and second, a novel representation based on hierarchical SGGX clustering that provides better accuracy than baseline methods. We validate our approach with a CUDA-based implementation of the voxelizer, tested both on triangle meshes and volumetric fabrics modeled with explicit fibers. Finally, we show the results generated with a path tracer based on the proposed LoD rendering model.

LoRA-based continual learning methods mitigate catastrophic forgetting through various mechanisms, yet nearly all complement these with small learning rates as a heuristic to restrict gradient scaling magnitude. Such fixed heuristics lack theoretical guidance on how the strength of this restriction should evolve as tasks accumulate. We reveal that even under directional constraints such as nullspace projection, finite-precision updates inevitably leak into the subspace of accumulated prior knowledge along multiple directions. While small learning rates attenuate such leakage, they cannot prevent the accumulated forgetting from intensifying as the effective rank of historical knowledge grows. We show that the optimal magnitude restriction should adaptively increase with this effective rank to balance stability and plasticity, i.e., preservation of previous knowledge and acquisition of new task information. Under an anisotropic leakage model, we derive a pacing law s^*=R/c that characterizes the optimal scaling of gradient steps, i.e., the magnitude restriction itself, where R is the effective rank of past updates. Based on this insight, we propose PaLoRA, which compresses historical knowledge via adaptive SVD truncation, projects gradients onto the nullspace of prior tasks, and applies rank-aware adaptive pacing. Experiments demonstrate consistent improvements over prior methods, with particularly strong performance in long-horizon settings, achieving substantial gains of 4% accuracy on challenging 50-task ImageNet-A and ImageNet-R benchmarks.

Recent advances in diffusion and flow models have substantially improved text-driven human motion generation. Yet most methods generate in low-dimensional, temporally downsampled latent spaces learned primarily for reconstruction, a bottleneck that can limit generation quality and preclude direct manipulation of individual frames and joints. We introduce MotionSpaceFlow (MSFlow), a representation-aware flow-matching framework that predicts clean motion directly in continuous motion space without a learned encoder or decoder. To account for the anisotropic structure of direct motion representations, we propose representation-aware noise scaling and show how the initial Gaussian source scale governs the covariance of intermediate probability-path marginals. We further introduce a Representation-Aware Multimodal Diffusion Transformer (RA-MMDiT), which jointly updates token-level language and full-resolution motion features through joint attention while adapting temporal information flow to the motion representation: causal attention for incremental features defined by frame-to-frame changes, and bidirectional attention for global features such as absolute joint coordinates. Across different datasets and motion representations, MSFlow achieves state-of-the-art text-to-motion performance. Its global representation variant additionally enables zero-shot, inference-time control over any joint or frame through projection sampling without control-conditioned training, delivering leading motion quality with exact constraint satisfaction.

Classical CUSUM relies on the log-likelihood ratio of the underlying distributions, which cannot generally be computed from finite pre- and post-change samples alone. We propose diffusion-integrated score CUSUM (DI-SCUSUM), a training-free detector. We add Gaussian noise to the samples to form two smooth density estimates and calculate their Hyvärinen scores exactly, without training a score network. For each incoming observation, we sample a diffusion time, perturb the observation, and use the importance-weighted score difference as an increment in the DI-SCUSUM recursion. Under the assumption that observations follow the fixed empirical distributions, the post-change mean increment is proportional to the Kullback-Leibler (KL) divergence from the smoothed post-change to the smoothed pre-change empirical distribution. We establish exponential false-alarm scaling and a first-order delay bound that, for a fixed threshold and increment scaling, is inversely proportional to the KL divergence. In the calibrated anisotropic Gaussian simulation, DI-SCUSUM nearly matches likelihood-ratio CUSUM and reduces the measured detection delay by about 91% relative to score-based CUSUM. On MNIST and Oxford-IIIT Pet, DI-SCUSUM also has lower empirical conditional detection delay than SCUSUM at comparable false-alarm levels.

We present a complete system for real-time rendering of scenes with complex appearance previously reserved for offline use. This is achieved with a combination of algorithmic and system level innovations. Our appearance model utilizes learned hierarchical textures that are interpreted using neural decoders, which produce reflectance values and importance-sampled directions. To best utilize the modeling capacity of the decoders, we equip the decoders with two graphics priors. The first prior -- transformation of directions into learned shading frames -- facilitates accurate reconstruction of mesoscale effects. The second prior -- a microfacet sampling distribution -- allows the neural decoder to perform importance sampling efficiently. The resulting appearance model supports anisotropic sampling and level-of-detail rendering, and allows baking deeply layered material graphs into a compact unified neural representation. By exposing hardware accelerated tensor operations to ray tracing shaders, we show that it is possible to inline and execute the neural decoders efficiently inside a real-time path tracer. We analyze scalability with increasing number of neural materials and propose to improve performance using code optimized for coherent and divergent execution. Our neural material shaders can be over an order of magnitude faster than non-neural layered materials. This opens up the door for using film-quality visuals in real-time applications such as games and live previews.

Three-dimensional microscopy is often limited by anisotropic spatial resolution, resulting in lower axial resolution than lateral resolution. Current State-of-The-Art (SoTA) isotropic reconstruction methods utilizing deep neural networks can achieve impressive super-resolution performance in fixed imaging settings. However, their generality in practical use is limited by degraded performance caused by artifacts and blurring when facing unseen anisotropic factors. To address these issues, we propose DiffuseIR, an unsupervised method for isotropic reconstruction based on diffusion models. First, we pre-train a diffusion model to learn the structural distribution of biological tissue from lateral microscopic images, resulting in generating naturally high-resolution images. Then we use low-axial-resolution microscopy images to condition the generation process of the diffusion model and generate high-axial-resolution reconstruction results. Since the diffusion model learns the universal structural distribution of biological tissues, which is independent of the axial resolution, DiffuseIR can reconstruct authentic images with unseen low-axial resolutions into a high-axial resolution without requiring re-training. The proposed DiffuseIR achieves SoTA performance in experiments on EM data and can even compete with supervised methods.

Despite their remarkable capabilities, LLMs learn word representations that exhibit the undesirable yet poorly understood feature of anisotropy. In this paper, we argue that the second moment in Adam is a cause of anisotropic embeddings, and suggest a modified optimizer called Coupled Adam to mitigate the problem. Our experiments demonstrate that Coupled Adam significantly improves the quality of embeddings, while also leading to better upstream and downstream performance on large enough datasets.

The dynamical realisation of the equation of state p +rho =0 is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid paradigm. It is shown that an anisotropic stress must be always present. The Hamiltonian of the system in isolation resembles the one of a Pais-Uhlenbeck oscillator and linear stability requires that it cannot be positive definite. The dynamics of linear cosmological perturbations in a DCC dominated Universe is studied in detail showing that when DCC is minimally coupled to gravity no dramatic instability is present. In contrast to what happens in a cosmological constant dominated Universe, the non-relativistic matter contrast is no longer constant and exhibits an oscillator behaviour at small scales while it grows weakly at large scales. In the gravitational waves sector, at small scales, the amplitude is still suppressed as the inverse power of the scale factor while it grows logarithmically at large scales. Also the vector modes propagate, though no growing mode is found.

The magnetic phase diagram at zero external field of an ensemble of dipoles with uniaxial anisotropy on a FCC lattice is investigated from tempered Monte Carlo simulations. The uniaxial anisotropy is characterized by a random distribution of easy axes and its magnitude lambda_u is the driving force of disorder and consequently frustration. The phase diagram, separating the paramagnetic, ferromagnetic, quasi long range ordered ferromagnetic and spin-glass regions is thus considered in the temperature, lambda_u plane. This system is aimed at modeling the magnetic phase diagram of supracrystals of magnetic nanoparticles.

The NMR measurements performed on a single orthorhombic crystal of superconducting ferromagnet UCoGe (Y.Ihara et al, Phys. Rev. Lett. v.105, 206403 (2010)) demonstrate strongly anisotropic magnetic properties of this material. The presented calculations allow to establish the dependence of longitudinal spin-lattice relaxation rate from temperature and magnetic field. The value 1/T_1T in field perpendicular to spontaneous magnetisation directed along c-axis has maximum in vicinity of Curie temperature whereas it does not reveal similar behaviour in field parallel to the direction of spontaneous magnetisation. Also there was shown that the longitudinal spin-lattice relaxation rate is strongly field dependent when the field directed in b-crystallographic direction but field independent if magnetic field is oriented along a-axis.

Gradient signals in LLM training are highly anisotropic: recurrent linguistic structure concentrates energy into a small set of dominant spectral directions, while context specific information resides in a long tail. We show that this spike tail separation persists throughout training, with the spike occupying only about 1.5% of directions yet dominating optimizer statistics. This dominance suppresses tail learning by contracting tail updates through second moment normalization and tightening the globally stable learning rate bound. Motivated by this analysis, we propose Spectra, a spike aware optimizer that suppresses the dominant low rank spike subspace without amplifying the noise sensitive spectral tail. Spectra tracks the spike subspace via cached, warm started power iteration and applies low rank spectral shaping with negligible overhead and substantially reduced optimizer state memory. On LLaMA3 8B trained on 50B tokens, Spectra reaches the same target loss 30% faster than AdamW, reduces per step end to end overhead by 0.7%, cuts optimizer state memory by 49.25%, and improves average downstream accuracy by 1.62%. Compared to Muon, Spectra is 5.1x faster in optimizer processing time, achieves a lower final loss, and improves average accuracy by 0.66%.

In a previous study, structure of silica gels prepared in a high magnetic field was investigated. While a direct application of such anisotropic silica gels is for an optical anisotropic medium possessing chemical resistance, we show here their possibility of medium in materials processing. In this direction, for example, silica hydrogels have so far been used as media of crystal growth. In this paper, as opposed to the soft-wet state, dried silica gels have been investigated. We have found that lead (II) nanocrystallites were formed induced by electron irradiation to lead (II)-doped dried silica gels prepared in a high magnetic field such as B = 10 T. Hydrogels made from a sodium metasilicate solution doped with lead (II) acetate were prepared. The dried specimens were irradiated by electrons in a transmission electron microscope environment. Electron diffraction patterns indicated the crystallinity of lead (II) nanocrystallites depending on B. An advantage of this processing technique is that the crystallinity can be controlled through the strength of magnetic field B applied during gel preparation. Specific skills are not required to control the strength of magnetic field.

Cross-entropy pretraining and preference alignment update the same transformer weights, but leave geometrically distinct traces. We characterise this asymmetry with a relative-subspace-fraction probe that tracks how weight deltas align with residual-stream activation subspaces and with the prediction subspace defined by the unembedding. Alignment deltas concentrate in the read pathway (W_Q, W_K), along principal directions of attention-input activations, while remaining near-isotropic in the write pathway (W_O, W_2) relative to the prediction subspace. We explain this pattern through anisotropic gradient accumulation: updates to a matrix W are sums of outer products δ_t a_t^top, and inherit directional structure from whichever side has concentrated covariance. For read-pathway matrices, this side is the input activation a_t, whose covariance is spiked in trained transformers and therefore produces objective-agnostic concentration. For write-pathway matrices, the relevant side is the upstream gradient δ_t, whose anisotropy depends on the loss. Cross-entropy supplies the canonical sharp per-sample signal, inducing write-pathway prediction geometry during pretraining; alignment objectives typically add little further write-side concentration. We support this explanation with a within-checkpoint trajectory, a graded contrastive-objective control, and a closed-form rank-1 intervention with matched direction controls, providing causal evidence for the proposed weight-space geometry.

Vision-language pre-trained models (VLPs) are widely used in real-world applications. However, they remain vulnerable to adversarial attacks. Although adversarial detection methods have demonstrated success in single-modality settings (either vision or language), their effectiveness and reliability in multimodal models such as VLPs remain largely unexplored. In this work, we study the geometry of VLP embedding spaces and observe structured anisotropy that differs from unimodal vision models. Our theoretical analysis shows that under this anisotropic structure, adversarial attacks increase the expected geometric separation between clean and adversarial examples (AEs). Specifically, we demonstrate that AEs consistently exhibit greater expected distances to randomly sampled points than their clean counterparts, indicating that AEs tend to push representations out of manifold regions. Building on these insights, we propose GeoDetect, which leverages these off-manifold deviations via geometric scores to identify AEs. Through comprehensive evaluations, we show that our approach reliably detects AEs across diverse VLP architectures and threat settings, covering unimodal and multimodal attacks as well as adaptive attacks, thereby providing a robust and practical approach to improving the safety and reliability of these models.

The second part of Hilbert's 16th problem is one of the most fundamental open problems in the qualitative theory of ordinary differential equations and dynamical systems. A central unresolved question is whether the Hilbert number H(d) is finite for arbitrary polynomial degree d. (A very recent manuscript from OpenAI asserts the finiteness of H(d); see the remark at the end of this paper.) In the absence of a general upper bound theory, most existing work constructs explicit perturbed polynomial systems to obtain improved lower bounds for H(d), while rigorous upper bound estimates remain largely unavailable. This paper focuses on improving the quantitative lower bound for polynomial systems through a systematic Hierarchical Melnikov Realization framework. We construct perturbed dynamics based on an anisotropic Chebyshev Hamiltonian, where hierarchically selected perturbation coefficients generate simple zeros of the first-order Melnikov function simultaneously across multiple disjoint period annuli. Two distinct 3-adic filtrations supply the necessary logarithmic correction factors, and a Borel--Gauss analysis establishes the required local rank condition under sufficiently strong anisotropy. As the main result of this work, we prove that H(d)=Ωbigl(d^2ln^2 dbigr), which improves the previously known lower bound by a factor of ln d. The full construction of limit cycles and the resulting dynamical bounds are formally certified using Lean 4 formal verification.

The global topology of the Universe is a longstanding open question. In this work, we examine the statistical signatures of a positively curved universe with a Friedmann--Lemaitre--Robertson--Walker metric and the topology of a lens space L(p,q). Since these manifolds are generally statistically anisotropic and inhomogeneous, their cosmic microwave background (CMB) covariance matrices contain non-zero off-diagonal entries that depend on observer location. We compute these full harmonic-space covariance matrices for scalar perturbations for arbitrary lens spaces and observer position. Using the Kullback--Leibler divergence, we assess the distinguishability of these spaces from a simply connected three-sphere with the same curvature. The results show that topological signatures can still be significant in a cosmic-variance-limited regime even when the length, d_{rm NC}, of the shortest loop around the Universe through the observer exceeds the diameter, d_{rm LSS}, of the last-scattering surface by up to 10%. This distinguishability depends on the curvature, the lens space and the observer position mainly through the ratio d_{rm NC}/d_{rm LSS}, which is set not only by the curvature radius but also by p, q and the observer location. Therefore, for any value of the spatial curvature, however small, there are lens spaces and observer positions for which 0.985,d_{rm LSS}<d_{rm NC}<1.1,d_{rm LSS}. Such observers would find no matched circles in the CMB large enough to have been detected to date, yet the topology would remain potentially discoverable through its statistical signatures.

We investigate gravitational-wave echoes in a horizonless compact object model, a non-perturbative solution of the semi-classical Einstein equation that reproduces the entropy-area law from the bulk structure. By employing a model of anisotropic fluids in classical general relativity (GR), we show that odd-parity gravitational waves are not reflected at the object's surface but are trapped inside due to the exponentially strong redshift, and that the echo-delay time extremely exceeds the age of the Universe. Consequently, the echo signals are effectively unobservable, which is consistent with current null results from echo searches. We finally discuss how this quantum black hole and the conventional classical black hole could be distinguished observationally.

We allow the Higgs field Phi to interact with a dilaton field chi of the background spacetime via the coupling chi^2,Phi^daggerPhi. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to chi. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on chi, we present an textit alternative mechanism: the Higgs VEV will be used to construct Planck's constant hbar and speed of light c. Specifically, each open set vicinity of a given point x^* on the spacetime manifold is equipped with a replica of the Glashow-Weinberg-Salam action operating with its own effective values of hbar_* and c_* per hbar_*proptochi^{-1/2}(x^*) and c_*proptochi^{1/2}(x^*), causing these ``fundamental constants'' to vary alongside the dynamical field chi. Moreover, in each open set around x^*, the prevailing value chi(x^*) determines the length and time scales for physical processes occurring in this region as lproptochi^{-1}(x^*) and tauproptochi^{-3/2}(x^*). This leads to an textit anisotropic relation tau^{-1}propto l^{-3/2} between the rate of clocks and the length of rods, resulting in a distinct set of novel physical phenomena. For late-time cosmology, the variation of c along the trajectory of light waves from distant supernovae towards the Earth-based observer necessitates modifications to the Lema\^itre redshift relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa through a declining speed of light in an expanding Einstein--de Sitter universe, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the H_0 tension without requiring a dynamical dark energy component.

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation ability of Transformers as sequence-to-sequence functions with infinite dimensional inputs. Although inputs and outputs are both infinite dimensional, we show that when the target function has anisotropic smoothness, Transformers can avoid the curse of dimensionality due to their feature extraction ability and parameter sharing property. In addition, we show that even if the smoothness changes depending on each input, Transformers can estimate the importance of features for each input and extract important features dynamically. Then, we proved that Transformers achieve similar convergence rate as in the case of the fixed smoothness. Our theoretical results support the practical success of Transformers for high dimensional data.

In the realm of text-to-3D generation, utilizing 2D diffusion models through score distillation sampling (SDS) frequently leads to issues such as blurred appearances and multi-faced geometry, primarily due to the intrinsically noisy nature of the SDS loss. Our analysis identifies the core of these challenges as the interaction among noise levels in the 2D diffusion process, the architecture of the diffusion network, and the 3D model representation. To overcome these limitations, we present StableDreamer, a methodology incorporating three advances. First, inspired by InstructNeRF2NeRF, we formalize the equivalence of the SDS generative prior and a simple supervised L2 reconstruction loss. This finding provides a novel tool to debug SDS, which we use to show the impact of time-annealing noise levels on reducing multi-faced geometries. Second, our analysis shows that while image-space diffusion contributes to geometric precision, latent-space diffusion is crucial for vivid color rendition. Based on this observation, StableDreamer introduces a two-stage training strategy that effectively combines these aspects, resulting in high-fidelity 3D models. Third, we adopt an anisotropic 3D Gaussians representation, replacing Neural Radiance Fields (NeRFs), to enhance the overall quality, reduce memory usage during training, and accelerate rendering speeds, and better capture semi-transparent objects. StableDreamer reduces multi-face geometries, generates fine details, and converges stably.

Reconstructing and understanding 3D structures from a limited number of images is a well-established problem in computer vision. Traditional methods usually break this task into multiple subtasks, each requiring complex transformations between different data representations. For instance, dense reconstruction through Structure-from-Motion (SfM) involves converting images into key points, optimizing camera parameters, and estimating structures. Afterward, accurate sparse reconstructions are required for further dense modeling, which is subsequently fed into task-specific neural networks. This multi-step process results in considerable processing time and increased engineering complexity. In this work, we present the Large Spatial Model (LSM), which processes unposed RGB images directly into semantic radiance fields. LSM simultaneously estimates geometry, appearance, and semantics in a single feed-forward operation, and it can generate versatile label maps by interacting with language at novel viewpoints. Leveraging a Transformer-based architecture, LSM integrates global geometry through pixel-aligned point maps. To enhance spatial attribute regression, we incorporate local context aggregation with multi-scale fusion, improving the accuracy of fine local details. To tackle the scarcity of labeled 3D semantic data and enable natural language-driven scene manipulation, we incorporate a pre-trained 2D language-based segmentation model into a 3D-consistent semantic feature field. An efficient decoder then parameterizes a set of semantic anisotropic Gaussians, facilitating supervised end-to-end learning. Extensive experiments across various tasks show that LSM unifies multiple 3D vision tasks directly from unposed images, achieving real-time semantic 3D reconstruction for the first time.

Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.

In this study, we utilize the minimal geometric deformation technique of gravitational decoupling to extend the regular Bardeen black hole, leading to the derivation of new black hole solutions within the framework of Rastall theory. By decoupling the field equations associated with an extended matter source into two subsystems, we address the first subsystem using the metric components of the regular Bardeen black hole. The second subsystem, incorporating the effects of the additional source, is solved through a constraint imposed by a linear equation of state. By linearly combining the solutions of these subsystems, we obtain two extended models. We then explore the distinct physical properties of these models for specific values of the Rastall and decoupling parameters. Our investigations encompass effective thermodynamic variables such as density and anisotropic pressure, asymptotic flatness, energy conditions, and thermodynamic properties including Hawking temperature, entropy, and specific heat. The results reveal that both models violate asymptotic flatness of the resulting spacetimes. The violation of energy conditions indicate the presence of exotic matter, for both models. Nonetheless, the energy density, radial pressure, as well as the Hawking temperature exhibit acceptable behavior, while the specific heat and Hessian matrix suggest thermodynamic stability.

Transcranial focused ultrasound (tFUS) is an emerging modality for non-invasive brain stimulation and therapeutic intervention, offering millimeter-scale spatial precision and the ability to target deep brain structures. However, the heterogeneous and anisotropic nature of the human skull introduces significant distortions to the propagating ultrasound wavefront, which require time-consuming patient-specific planning and corrections using numerical solvers for accurate targeting. To enable data-driven approaches in this domain, we introduce TFUScapes, the first large-scale, high-resolution dataset of tFUS simulations through anatomically realistic human skulls derived from T1-weighted MRI images. We have developed a scalable simulation engine pipeline using the k-Wave pseudo-spectral solver, where each simulation returns a steady-state pressure field generated by a focused ultrasound transducer placed at realistic scalp locations. In addition to the dataset, we present DeepTFUS, a deep learning model that estimates normalized pressure fields directly from input 3D CT volumes and transducer position. The model extends a U-Net backbone with transducer-aware conditioning, incorporating Fourier-encoded position embeddings and MLP layers to create global transducer embeddings. These embeddings are fused with U-Net encoder features via feature-wise modulation, dynamic convolutions, and cross-attention mechanisms. The model is trained using a combination of spatially weighted and gradient-sensitive loss functions, enabling it to approximate high-fidelity wavefields. The TFUScapes dataset is publicly released to accelerate research at the intersection of computational acoustics, neurotechnology, and deep learning. The project page is available at https://github.com/CAMMA-public/TFUScapes.

Semantic search is an important task which objective is to find the relevant index from a database for query. It requires a retrieval model that can properly learn the semantics of sentences. Transformer-based models are widely used as retrieval models due to their excellent ability to learn semantic representations. in the meantime, many regularization methods suitable for them have also been proposed. In this paper, we propose a new regularization method: Regularized Contrastive Learning, which can help transformer-based models to learn a better representation of sentences. It firstly augments several different semantic representations for every sentence, then take them into the contrastive objective as regulators. These contrastive regulators can overcome overfitting issues and alleviate the anisotropic problem. We firstly evaluate our approach on 7 semantic search benchmarks with the outperforming pre-trained model SRoBERTA. The results show that our method is more effective for learning a superior sentence representation. Then we evaluate our approach on 2 challenging FAQ datasets, Cough and Faqir, which have long query and index. The results of our experiments demonstrate that our method outperforms baseline methods.

Microbial swarming on mucosal surfaces reshapes microbial communities and influences mucosal healing and antibiotic tolerance. Yet even with time-lapse microscopy and deep learning, analyses of swarming colonies remain descriptive and cannot forecast how their fronts reorganize in time. This limitation is significant because the advancing edge determines access to nutrients, host tissue and competing microbes. We recast the expansion of Enterobacter sp. SM3 swarms as a problem of morphological forecasting, and assemble SwarmEvo, a time-lapse dataset represented as boundary-resolved segmentations. TexPol--Net, a texture- and geometry-aware segmentation model, sharpens diffuse edges and preserves fingered fronts, creating a stable substrate for dynamics. On this representation, we develop Morpher, an autoregressive forecasting network with a ``Morphon'' memory that links local curvature to long-range temporal dependencies. Morpher outperforms leading video-prediction models in maintaining front localization and anisotropic branching, and modest segmentation improvements yield noticeably more stable forecasts. Ablations across sequence models, inference strategies and observation ratios show that attention-based architectures with structural memory best preserve dense-finger propagation. By uniting geometry-aware segmentation with morphology-level forecasting, this framework turns swarming expansion into a predictive dynamical system, enabling quantitative interrogation and potential control of microbial collectives during mucosal repair and gut ecosystem engineering.

Diffusion-based image generative models produce high-fidelity images through iterative denoising but remain vulnerable to memorization, where they unintentionally reproduce exact copies or parts of training images. Recent memorization detection methods are primarily based on the norm of score difference as indicators of memorization. We prove that such norm-based metrics are mainly effective under the assumption of isotropic log-probability distributions, which generally holds at high or medium noise levels. In contrast, analyzing the anisotropic regime reveals that memorized samples exhibit strong angular alignment between the guidance vector and unconditional scores in the low-noise setting. Through these insights, we develop a memorization detection metric by integrating isotropic norm and anisotropic alignment. Our detection metric can be computed directly on pure noise inputs via two conditional and unconditional forward passes, eliminating the need for costly denoising steps. Detection experiments on Stable Diffusion v1.4 and v2 show that our metric outperforms existing denoising-free detection methods while being at least approximately 5x faster than the previous best approach. Finally, we demonstrate the effectiveness of our approach by utilizing a mitigation strategy that adapts memorized prompts based on our developed metric. The code is available at https://github.com/rohanasthana/memorization-anisotropy .

Adapting pre-trained image models to video modality has proven to be an effective strategy for robust few-shot action recognition. In this work, we explore the potential of adapter tuning in image-to-video model adaptation and propose a novel video adapter tuning framework, called Disentangled-and-Deformable Spatio-Temporal Adapter (D^2ST-Adapter). It features a lightweight design, low adaptation overhead and powerful spatio-temporal feature adaptation capabilities. D^2ST-Adapter is structured with an internal dual-pathway architecture that enables built-in disentangled encoding of spatial and temporal features within the adapter, seamlessly integrating into the single-stream feature learning framework of pre-trained image models. In particular, we develop an efficient yet effective implementation of the D^2ST-Adapter, incorporating the specially devised anisotropic Deformable Spatio-Temporal Attention as its pivotal operation. This mechanism can be individually tailored for two pathways with anisotropic sampling densities along the spatial and temporal domains in 3D spatio-temporal space, enabling disentangled encoding of spatial and temporal features while maintaining a lightweight design. Extensive experiments by instantiating our method on both pre-trained ResNet and ViT demonstrate the superiority of our method over state-of-the-art methods. Our method is particularly well-suited to challenging scenarios where temporal dynamics are critical for action recognition. Code is available at https://github.com/qizhongtan/D2ST-Adapter.

The Laplace-Beltrami operator (LBO) emerges from studying manifolds equipped with a Riemannian metric. It is often called the Swiss army knife of geometry processing as it allows to capture intrinsic shape information and gives rise to heat diffusion, geodesic distances, and a multitude of shape descriptors. It also plays a central role in geometric deep learning. In this work, we explore Finsler manifolds as a generalization of Riemannian manifolds. We revisit the Finsler heat equation and derive a Finsler heat kernel and a Finsler-Laplace-Beltrami Operator (FLBO): a novel theoretically justified anisotropic Laplace-Beltrami operator (ALBO). In experimental evaluations we demonstrate that the proposed FLBO is a valuable alternative to the traditional Riemannian-based LBO and ALBOs for spatial filtering and shape correspondence estimation. We hope that the proposed Finsler heat kernel and the FLBO will inspire further exploration of Finsler geometry in the computer vision community.

Hyperparameter Optimization (HPO) is essential for building high-performing ML/DL models, yet conventional optimizers often struggle in high-dimensional spaces where evaluations are costly and progress is diluted across many low-impact variables. We propose Greedy Importance First (GIF), an importance-aware scheduling strategy that uses a small-sample warm start to estimate hyperparameter importance, forms importance-based groups, allocates trials proportionally, and retains a full-space fallback. We evaluate GIF under fixed evaluation budgets on five anisotropic analytic functions, Bayesmark, and NAS-Bench-301. On the higher-dimensional benchmarks, GIF reaches better incumbents with faster convergence than TPE, BOHB, Random Search, and Sequential Grouping. On Bayesmark, where the effective dimensionality is smaller, GIF remains competitive but the margins are smaller. Ablation studies show that importance estimation, proportional allocation, and the fallback step all contribute to the gains. We also verify that the HIA component recovers the intended anisotropy on the analytic benchmarks. These results suggest that GIF is a simple and plug-compatible way to improve sample efficiency in high-dimensional HPO.

Energy Dispersive X-ray (EDX) tomography in Scanning Transmission Electron Microscopy (STEM) enables 3D compositional and elemental mapping at the nanoscale, but its use is limited by restricted tilt ranges and low-dose conditions required to avoid beam damage. Limited-angle acquisition introduces missing-wedge artefacts such as elongation and anisotropic resolution, while noisy low-dose data further degrade reconstruction quality and quantitative reliability. Here, we introduce an unsupervised deep learning framework based on Deep Image Prior with total variation regularization (DIP-TV) for limited-angle STEM-EDX tomography. We extend it to a multi-channel formulation (DIPm-TV) that jointly reconstructs multiple elemental maps by exploiting spatial correlations. Using a synthetic 3-channel phantom, we show that the method compensates for severe missing-wedge artefacts corresponding to approximately 100^circ of missing angular range under moderate noise, outperforming simultaneous iterative reconstruction technique and compressed sensing approaches. We apply the method to 3D chemical analysis of Ge-Sb-Te (GST) memory devices in virgin (as-fabricated) and SET (crystalline) operational states. Samples were prepared as cross-sectional focused ion beam lamellae and acquired under a limited-angle tilt range from -40^circ to +40^circ with 5^circ steps and a dose of 2.0times10^5 e^-/Ang^2. The multi-channel approach enables voxel-by-voxel elemental reconstruction using only EDX signals without external structural priors such as high-angle annular dark-field imaging. The reconstructed volumes show near-isotropic spatial resolution and reveal compositional heterogeneities associated with device operation. This approach enables 3D chemical characterization in experimentally accessible sample geometries where conventional methods fail due to severe angular limitations.

Magnetic Resonance Imaging (MRI) is often acquired with anisotropic resolution to reduce scan time, producing stair-step artifacts along the through-plane direction. In through-plane MRI super-resolution, an efficiency-fidelity trade-off arises: feed-forward regressors are fast but oversmooth at large slice-thicknesses, while sampling-based methods improve fidelity at high inference cost. We propose DRIFT, a two-stage thickness-conditioned rectified flow framework for through-plane MRI super-resolution with continuous input slice-thickness. Stage 1 employs an Anatomical Projection Network (APN) to map low-resolution patches to a coarse high-resolution manifold, providing a deterministic anatomical initialization that shortens the residual transport of Stage 2 and stabilizes slice-wise refinement. Stage 2 refines details via rectified flow and introduces a Physics-Aware Difficulty (PAD) metric derived from slice-thickness induced through-plane bandwidth deficit to guide an Adaptive Integration Scheduler (AIS), allocating ODE steps by thickness. A Consistent Endpoint Trajectory Alignment (CETA) loss enforces thickness-consistent reconstructions. Experiments show that DRIFT outperforms super-resolution baselines while reducing inference cost. Code, models, and interactive demos are available at https://yoonseokchoi-ai.github.io/drift-eccv2026/.

One might think that learning the identity function with a deep linear residual network is trivial - the path along residual connections already implements the identity, and so the network need only drive its weights to zero. However, this zero-weight solution is just one point on an entire manifold of population-loss minimizers, each corresponding to a different decomposition of the identity across the network's layers. Although the population loss does not distinguish among these solutions, stochastic gradient descent (SGD) reproducibly favors particular ones. For instance, under anisotropic label noise, the learned layers exhibit a noise-dependent spectrum; even with weight decay, SGD does not generally recover the zero-weight solution. Changing only the parametrization, while leaving the set of realizable functions unchanged, yields different behavior: factoring each weight matrix as a product of two matrices causes the weights to collapse to zero, even without explicit weight decay. While perhaps mysterious and unintuitive at first, these phenomena can be understood through the lens of entropic loss, which augments the population loss with a term proportional to the expected squared norm of the minibatch gradient (Ziyin et al., 2025). On the identity manifold, the population loss is constant, while the entropic term distinguishes among these decompositions. We characterize its minimizers analytically and use them to derive predictions for the structure of solutions favored by SGD. Networks trained with SGD closely match these predictions. Overall, the identity learning task studied here serves as a clean and simple case study of how the lens of entropic loss can clarify why SGD favors particular decompositions of the same input-output function.

Image-based Virtual Try-ON aims to transfer an in-shop garment onto a specific person. Existing methods employ a global warping module to model the anisotropic deformation for different garment parts, which fails to preserve the semantic information of different parts when receiving challenging inputs (e.g, intricate human poses, difficult garments). Moreover, most of them directly warp the input garment to align with the boundary of the preserved region, which usually requires texture squeezing to meet the boundary shape constraint and thus leads to texture distortion. The above inferior performance hinders existing methods from real-world applications. To address these problems and take a step towards real-world virtual try-on, we propose a General-Purpose Virtual Try-ON framework, named GP-VTON, by developing an innovative Local-Flow Global-Parsing (LFGP) warping module and a Dynamic Gradient Truncation (DGT) training strategy. Specifically, compared with the previous global warping mechanism, LFGP employs local flows to warp garments parts individually, and assembles the local warped results via the global garment parsing, resulting in reasonable warped parts and a semantic-correct intact garment even with challenging inputs.On the other hand, our DGT training strategy dynamically truncates the gradient in the overlap area and the warped garment is no more required to meet the boundary constraint, which effectively avoids the texture squeezing problem. Furthermore, our GP-VTON can be easily extended to multi-category scenario and jointly trained by using data from different garment categories. Extensive experiments on two high-resolution benchmarks demonstrate our superiority over the existing state-of-the-art methods.

Categorising invoices into the correct General Ledger (GL) code underpins financial reporting and tax compliance. This is a skilled accounting judgement rather than a routine task: the correct category depends subtly on the nature of the purchasing business, the vendor and the invoice text. Whilst AI is increasingly being adopted across industries to automate tasks, including invoice categorisation, implementations built on in-house small language models (SLMs) can simultaneously reduce cost and improve data security, confidentiality, and interpretability. We investigate this approach by first analysing the pre-trained embedding geometry of a small sentence transformer (SBERT) and classic SLM (DeBERTa). The sentence-embedding space of this financial corpus is globally anisotropic but composed of locally isotropic clusters, extending prior token-level findings to sentence embeddings in a financial setting, and these clusters are strongly correlated with the vendor identity. SBERT fine-tuned on a single GPU reaches 0.96 accuracy on invoice classification, above both a zero-shot LLM and a vendor identity baseline, increasing performance for smaller, challenging categories and new clients. For this important generalisation problem, SBERT reaches 0.9 F1 with roughly 100 client-specific invoices, showing that an in-house SLM implementation is promising. Combining these results with geometric analysis shows that pre-trained embedding geometry is associated with classification performance and reveals a counterintuitive finding that a structured input that would help a human reader does not improve the SLM performance.

Arbitrary slice super-resolution reconstructs isotropic volumes from anisotropic clinical acquisitions by synthesizing intermediate slices at arbitrary scales. However, treating this ill-posed inverse problem as unconstrained residual-based regression risks hallucinating anatomically implausible structures or altering the originally observed data. To address both concerns, this paper presents the Dual-Prior Null-space Learning (DP-NSL) framework, which reformulates the task as a constrained recovery process guided by two complementary priors. A Measurement-Consistent Projection (MCP) enforces a Deterministic Observation Prior: the reconstruction undergoes an exact orthogonal projection that reproduces every acquired slice with zero error, confining all learned details to the unobservable null space. Within this null space, a Mixture-of-Splines (MoS) module imposes a Geometric Continuity Prior by dynamically mixing B-spline experts of different analytic orders, allowing each anatomical region to be modeled with a content-aware level of continuity. To promote spatial coherence, a Local Spatial Consistency Decoder (LSCD) further injects local inductive bias. Experiments on three CT and one MRI benchmark show that DP-NSL outperforms existing approaches while strictly preserving measurement consistency. Code is available at https://github.com/DeepMed-Lab-ECNU/Medical-Image-Reconstruction.

Previous work has shown that the representations output by contextual language models are more anisotropic than static type embeddings, and typically display outlier dimensions. This seems to be true for both monolingual and multilingual models, although much less work has been done on the multilingual context. Why these outliers occur and how they affect the representations is still an active area of research. We investigate outlier dimensions and their relationship to anisotropy in multiple pre-trained multilingual language models. We focus on cross-lingual semantic similarity tasks, as these are natural tasks for evaluating multilingual representations. Specifically, we examine sentence representations. Sentence transformers which are fine-tuned on parallel resources (that are not always available) perform better on this task, and we show that their representations are more isotropic. However, we aim to improve multilingual representations in general. We investigate how much of the performance difference can be made up by only transforming the embedding space without fine-tuning, and visualise the resulting spaces. We test different operations: Removing individual outlier dimensions, cluster-based isotropy enhancement, and ZCA whitening. We publish our code for reproducibility.

We have investigated the effects of strain on two-dimensional square lattices and examined the methods for inducing pseudo-magnetic fields. In both the columnar and staggered pi-flux square lattices, we have found that strain only modulates Fermi velocities rather than inducing pseudo-magnetic fields. However, spatially non-uniform on-site potentials (anisotropic hoppings) can create pseudo-magnetic fields in columnar (staggered) pi-flux square lattices. On the other hand, we demonstrate that strain does induce pseudo-magnetic fields in staggered zero-flux square lattices. By breaking a quarter of the bonds, we clarify that a staggered zero-flux square lattice is topologically equivalent to a honeycomb lattice and displays pseudo-vector potentials and pseudo-Landau levels at the Dirac points.

We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the corresponding (d+1)-dimensional gravity duals, engineered with a variety of matter Lagrangians, and their finite temperature generalizations. The thermodynamic properties of the finite temperature backgrounds are precisely those expected for anisotropic, scale invariant field theories. The brane and string theory realizations of such backgrounds are briefly discussed, along with their holographic interpretation in terms of marginal but non Lorentz invariant deformations of conformal field theories. We initiate discussion of holographic renormalization in these backgrounds, and note that such systematic renormalization is necessary to obtain the correct behavior of correlation functions.

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (α-ReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d ll |V|). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.

We present Upsample Anything, a lightweight test-time optimization (TTO) framework that restores low-resolution features to high-resolution, pixel-wise outputs without any training. Although Vision Foundation Models demonstrate strong generalization across diverse downstream tasks, their representations are typically downsampled by 14x/16x (e.g., ViT), which limits their direct use in pixel-level applications. Existing feature upsampling approaches depend on dataset-specific retraining or heavy implicit optimization, restricting scalability and generalization. Upsample Anything addresses these issues through a simple per-image optimization that learns an anisotropic Gaussian kernel combining spatial and range cues, effectively bridging Gaussian Splatting and Joint Bilateral Upsampling. The learned kernel acts as a universal, edge-aware operator that transfers seamlessly across architectures and modalities, enabling precise high-resolution reconstruction of features, depth, or probability maps. It runs in only approx0.419 s per 224x224 image and achieves state-of-the-art performance on semantic segmentation, depth estimation, and both depth and probability map upsampling. Project page: https://seominseok0429.github.io/Upsample-Anything/{https://seominseok0429.github.io/Upsample-Anything/}

We develop a differential-geometric framework for variational quantum circuits in which noisy single- and multi-qubit parameter spaces are modeled by weighted projective lines (WPLs). Starting from the pure-state Bloch sphere CP1, we show that realistic hardware noise induces anisotropic contractions of the Bloch ball that can be represented by a pair of physically interpretable parameters (lambda_perp, lambda_parallel). These parameters determine a unique WPL metric g_WPL(a_over_b, b) whose scalar curvature is R = 2 / b^2, yielding a compact and channel-resolved geometric surrogate for the intrinsic information structure of noisy quantum circuits. We develop a tomography-to-geometry pipeline that extracts (lambda_perp, lambda_parallel) from hardware data and maps them to the WPL parameters (a_over_b, b, R). Experiments on IBM Quantum backends show that the resulting WPL geometries accurately capture anisotropic curvature deformation across calibration periods. Finally, we demonstrate that WPL-informed quantum natural gradients (WPL-QNG) provide stable optimization dynamics for noisy variational quantum eigensolvers and enable curvature-aware mitigation of barren plateaus.

We present Gaussian Pixel Codec Avatars (GPiCA), photorealistic head avatars that can be generated from multi-view images and efficiently rendered on mobile devices. GPiCA utilizes a unique hybrid representation that combines a triangle mesh and anisotropic 3D Gaussians. This combination maximizes memory and rendering efficiency while maintaining a photorealistic appearance. The triangle mesh is highly efficient in representing surface areas like facial skin, while the 3D Gaussians effectively handle non-surface areas such as hair and beard. To this end, we develop a unified differentiable rendering pipeline that treats the mesh as a semi-transparent layer within the volumetric rendering paradigm of 3D Gaussian Splatting. We train neural networks to decode a facial expression code into three components: a 3D face mesh, an RGBA texture, and a set of 3D Gaussians. These components are rendered simultaneously in a unified rendering engine. The networks are trained using multi-view image supervision. Our results demonstrate that GPiCA achieves the realism of purely Gaussian-based avatars while matching the rendering performance of mesh-based avatars.

Industrial quality inspection plays a critical role in modern manufacturing by identifying defective products during production. While single-modality approaches using either 3D point clouds or 2D RGB images suffer from information incompleteness, multimodal anomaly detection offers promise through the complementary fusion of crossmodal data. However, existing methods face challenges in effectively integrating unimodal results and improving discriminative power. To address these limitations, we first reinterpret memory bank-based anomaly scores in single modalities as isotropic Euclidean distances in local feature spaces. Dynamically evolving from Euclidean metrics, we propose a novel Geometry-Guided Score Fusion (G^{2}SF) framework that progressively learns an anisotropic local distance metric as a unified score for the fusion task. Through a geometric encoding operator, a novel Local Scale Prediction Network (LSPN) is proposed to predict direction-aware scaling factors that characterize first-order local feature distributions, thereby enhancing discrimination between normal and anomalous patterns. Additionally, we develop specialized loss functions and score aggregation strategy from geometric priors to ensure both metric generalization and efficacy. Comprehensive evaluations on the MVTec-3D AD and Eyecandies datasets demonstrate the state-of-the-art detection performance of our method, and detailed ablation analysis validates each component's contribution. Our code is available at https://github.com/ctaoaa/G2SF.

Can reinforcement learning with hard, verifiable rewards teach a compact language model to reason about physics, or does it primarily learn to pattern-match toward correct answers? We study this question by training a 1.5B-parameter reasoning model on beam statics, a classic engineering problem, using parameter-efficient RLVR with binary correctness rewards from symbolic solvers, without teacher-generated reasoning traces. The best BeamPERL checkpoint achieves a 66.7% improvement in Pass@1 over the base model. However, the learned competence is anisotropic: the model generalizes compositionally (more loads) but fails under topological shifts (moved supports) that require the same equilibrium equations. Intermediate checkpoints yield the strongest reasoning, while continued optimization degrades robustness while maintaining reward. These findings reveal a key limitation of outcome-level alignment: reinforcement learning with exact physics rewards induces procedural solution templates rather than internalization of governing equations. The precision of the reward signal - even when analytically exact - does not by itself guarantee transferable physical reasoning. Our results suggest that verifiable rewards may need to be paired with structured reasoning scaffolding to move beyond template matching toward robust scientific reasoning.

Parameter-efficient fine-tuning (PEFT) is a standard way to adapt multimodal large language models, yet extremely low-rank settings -- especially rank-1 LoRA -- are often unstable. We show that this instability is not solely due to limited capacity: in the rank-1 regime, optimization is highly sensitive to the update direction. Concretely, pretrained vision and text features form mismatched anisotropic regions, yielding a dominant "gap" direction that acts like a translation component and disproportionately steers early gradients under rank-1 constraints. Analyzing pretrained representations, we identify a modality-gap axis that dominates early gradient flow, while a random rank-1 initialization is unlikely to align with it, leading to weak gradients and training collapse. We propose Gap-Init, a geometry-aware initialization that aligns the rank-1 LoRA direction with an estimated modality-gap vector from a small calibration set, while keeping the initial LoRA update zero. Across multiple vision-language tasks and backbones, Gap-Init consistently stabilizes rank-1 training and can match or outperform strong rank-8 baselines. Our results suggest that at the extreme low-rank limit, initial alignment can matter as much as rank itself.

Appearance-based gaze estimation (AGE) has achieved remarkable performance in constrained settings, yet we reveal a significant generalization gap where existing AGE models often fail in practical, unconstrained scenarios, particularly those involving facial wearables and poor lighting conditions. We attribute this failure to two core factors: limited image diversity and inconsistent label fidelity across different datasets, especially along the pitch axis. To address these, we propose a robust AGE framework that enhances generalization without requiring additional human-annotated data. First, we expand the image manifold via an ensemble of augmentation techniques, including synthesis of eyeglasses, masks, and varied lighting. Second, to mitigate the impact of anisotropic inter-dataset label deviation, we reformulate gaze regression as a multi-task learning problem, incorporating multi-view supervised contrastive (SupCon) learning, discretized label classification, and eye-region segmentation as auxiliary objectives. To rigorously validate our approach, we curate new benchmark datasets designed to evaluate gaze robustness under challenging conditions, a dimension largely overlooked by existing evaluation protocols. Our MobileNet-based lightweight model achieves generalization performance competitive with the state-of-the-art (SOTA) UniGaze-H, while utilizing less than 1\% of its parameters, enabling high-fidelity, real-time gaze tracking on mobile devices.

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the L_2 regularization as an upper bound of the 2-Wasserstein distance (W_2), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the L_2 (or upper bound of W_2) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.

Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of vertices and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibility of this formulation. Perhaps surprisingly, comparison with previous work suggests that anisotropic filters might be an unnecessary price to pay. Our code is available at https://github.com/deepsphere

Generating a 3D dental volume from a single panoramic radiograph (PXR) could provide a low-radiation alternative to Cone-Beam Computed Tomography (CBCT), but the problem is highly underdetermined: panoramic acquisition integrates 3D attenuation along curved X-ray paths into a 2D image, leaving depth-resolved anatomy unobserved. Existing implicit and generative approaches often produce oversmoothed geometry or anatomically inconsistent hallucinations, lacking geometry-driven supervision and relying on smooth representations unable to precisely localize sharp anatomical boundaries. We propose X-Splat, the first Gaussian Splatting framework for generating CBCT-like 3D dental volumes from a single PXR. X-Splat uses the known panoramic acquisition geometry as a generation scaffold: learnable anisotropic Gaussian primitives are initialized along the X-ray paths that formed the input image and adjusted in a single feed-forward pass, constrained by Beer-Lambert reprojection and multi-view radiographic training supervision. A lightweight residual refiner adds dataset-level anatomical priors without overriding the geometry already resolved by the Gaussians. We train on synthetic PXR-CBCT pairs, enabling direct volumetric supervision without paired real scans. We further introduce segmentation-based geometry-aware metrics, providing the first evaluation of PXR-based generation over maxillofacial anatomy. X-Splat outperforms NeRF- and GAN-based baselines, recovering individual teeth, cortical boundaries, and alveolar structure, including the mandibular canal which prior methods fail to reconstruct. Code will be available at https://github.com/tomek1911/X-Splat

The current version of the Fermi Large Area Telescope data (P8R2) has been publicly available since June 2015, with the caveat that the residual background of all event classes, except ULTRACLEANVETO, was not fully isotropic: it was enhanced by a factor ~2 at 1-3 GeV within ~20 deg of the Ecliptic compared to the poles. By investigating the residual background using data only, we were able to find two sources of residual background: one due to non-interacting heavy ions and one due to cosmic-ray electrons leaking through the ribbons of the Anti-Coincidence Detector, the latter source being responsible for the background anisotropy. A set of simple cuts allows us to reject these events while losing less than 1% of the SOURCE class acceptance. This new selection has been used to produce a new version of the LAT data (P8R3).

Fast-spinning, nonaxisymmetrically deformed neutron stars (NSs) are promising targets for continuous gravitational-wave (CGW) searches with current and next-generation ground-based detectors. Ultraluminous X-ray pulsars (ULXPs), characterized by super-Eddington accretion and strong magnetic fields, provide extreme environments in which substantial nonaxisymmetric deformations may develop. In this Letter, we investigate thermo-elastic mountains generated by magnetically induced temperature asymmetries in the accreted crusts of ULXPs. We connect the crustal thermal structure to an accretion-column model and solve the full anisotropic heat-transport equation, extending previous perturbative treatments into the nonlinear, strongly magnetized regime. We find that the weak-field approximation begins to break down near B_{rm ref}sim10^{13},{rm G}, beyond which nonlinear anisotropic heat transport significantly modifies the quadrupolar thermal response. The resulting thermal asymmetries generate substantial thermo-elastic mass quadrupoles at higher field strengths. Although the currently known ULXPs are unfavorable CGW targets because of their relatively slow spins and, in most cases, large distances, our illustrative spin-evolution calculations show that a NS can enter the super-Eddington accretor phase with a spin period of order 20,{rm ms}. Such rapidly rotating Galactic ULXPs could lie within the projected sensitivities of next-generation detectors such as the Einstein Telescope and Cosmic Explorer. These results extend thermal-mountain physics into the strongly magnetized regime relevant to ULXPs and connect super-Eddington accretion with prospective CGW observations.

Synthetic data are increasingly used as an alternative to sharing sensitive records. However, synthetic data generation does not guarantee privacy, as diffusion models trained or adapted on sensitive data remain susceptible to reconstruction attacks. Moreover, while approaches that use differential privacy (DP), such as DP-SGD, achieve provably private diffusion model training, the repeated gradient clipping and noise injection they require result in significant utility loss. An important limitation of DP-based privacy is that, although it has a provable relationship to reconstruction privacy (RP), that relationship is indirect. RP is defined in terms of limiting how much an adversary's posterior distribution over sensitive data differs from the prior, whereas DP provides guarantees by bounding the sensitivity of outputs to changes in individual records. This indirection is an important source of the utility loss. To address this, we propose a PAC-private diffusion model adaptation to achieve reconstruction privacy. Since PAC-privacy is defined directly with respect to posterior advantage over the prior, it directly implicates RP. To obtain scalable PAC privatization in high dimensions, we first learn a compact data-dependent diffusion model component using LoRA or Textual Inversion, and then calibrate anisotropic Gaussian noise from the covariance of repeated mechanism outputs. Unlike DP-SGD, our method perturbs the learned component only once after optimization, thereby avoiding privacy composition across gradient updates. We evaluate the framework on few-shot concept personalization and full-dataset image synthesis, and show that the proposed approach better preserves subject identity, generation quality, and downstream classification accuracy than DP while achieving the same reconstruction privacy.

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.

Text generation is of great importance to many natural language processing applications. However, maximization-based decoding methods (e.g. beam search) of neural language models often lead to degenerate solutions -- the generated text is unnatural and contains undesirable repetitions. Existing approaches introduce stochasticity via sampling or modify training objectives to decrease probabilities of certain tokens (e.g., unlikelihood training). However, they often lead to solutions that lack coherence. In this work, we show that an underlying reason for model degeneration is the anisotropic distribution of token representations. We present a contrastive solution: (i) SimCTG, a contrastive training objective to calibrate the model's representation space, and (ii) a decoding method -- contrastive search -- to encourage diversity while maintaining coherence in the generated text. Extensive experiments and analyses on three benchmarks from two languages demonstrate that our proposed approach significantly outperforms current state-of-the-art text generation methods as evaluated by both human and automatic metrics.

This paper presents SimCSE, a simple contrastive learning framework that greatly advances state-of-the-art sentence embeddings. We first describe an unsupervised approach, which takes an input sentence and predicts itself in a contrastive objective, with only standard dropout used as noise. This simple method works surprisingly well, performing on par with previous supervised counterparts. We find that dropout acts as minimal data augmentation, and removing it leads to a representation collapse. Then, we propose a supervised approach, which incorporates annotated pairs from natural language inference datasets into our contrastive learning framework by using "entailment" pairs as positives and "contradiction" pairs as hard negatives. We evaluate SimCSE on standard semantic textual similarity (STS) tasks, and our unsupervised and supervised models using BERT base achieve an average of 76.3% and 81.6% Spearman's correlation respectively, a 4.2% and 2.2% improvement compared to the previous best results. We also show -- both theoretically and empirically -- that the contrastive learning objective regularizes pre-trained embeddings' anisotropic space to be more uniform, and it better aligns positive pairs when supervised signals are available.

It is widely acknowledged that single image super-resolution (SISR) methods would not perform well if the assumed degradation model deviates from those in real images. Although several degradation models take additional factors into consideration, such as blur, they are still not effective enough to cover the diverse degradations of real images. To address this issue, this paper proposes to design a more complex but practical degradation model that consists of randomly shuffled blur, downsampling and noise degradations. Specifically, the blur is approximated by two convolutions with isotropic and anisotropic Gaussian kernels; the downsampling is randomly chosen from nearest, bilinear and bicubic interpolations; the noise is synthesized by adding Gaussian noise with different noise levels, adopting JPEG compression with different quality factors, and generating processed camera sensor noise via reverse-forward camera image signal processing (ISP) pipeline model and RAW image noise model. To verify the effectiveness of the new degradation model, we have trained a deep blind ESRGAN super-resolver and then applied it to super-resolve both synthetic and real images with diverse degradations. The experimental results demonstrate that the new degradation model can help to significantly improve the practicability of deep super-resolvers, thus providing a powerful alternative solution for real SISR applications.

Pixel-based language models process text rendered as images, which allows them to handle any script, making them a promising approach to open vocabulary language modelling. However, recent approaches use text renderers that produce a large set of almost-equivalent input patches, which may prove sub-optimal for downstream tasks, due to redundancy in the input representations. In this paper, we investigate four approaches to rendering text in the PIXEL model (Rust et al., 2023), and find that simple character bigram rendering brings improved performance on sentence-level tasks without compromising performance on token-level or multilingual tasks. This new rendering strategy also makes it possible to train a more compact model with only 22M parameters that performs on par with the original 86M parameter model. Our analyses show that character bigram rendering leads to a consistently better model but with an anisotropic patch embedding space, driven by a patch frequency bias, highlighting the connections between image patch- and tokenization-based language models.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

Reconstructing dynamic 3D scenes from 2D images and generating diverse views over time is challenging due to scene complexity and temporal dynamics. Despite advancements in neural implicit models, limitations persist: (i) Inadequate Scene Structure: Existing methods struggle to reveal the spatial and temporal structure of dynamic scenes from directly learning the complex 6D plenoptic function. (ii) Scaling Deformation Modeling: Explicitly modeling scene element deformation becomes impractical for complex dynamics. To address these issues, we consider the spacetime as an entirety and propose to approximate the underlying spatio-temporal 4D volume of a dynamic scene by optimizing a collection of 4D primitives, with explicit geometry and appearance modeling. Learning to optimize the 4D primitives enables us to synthesize novel views at any desired time with our tailored rendering routine. Our model is conceptually simple, consisting of a 4D Gaussian parameterized by anisotropic ellipses that can rotate arbitrarily in space and time, as well as view-dependent and time-evolved appearance represented by the coefficient of 4D spherindrical harmonics. This approach offers simplicity, flexibility for variable-length video and end-to-end training, and efficient real-time rendering, making it suitable for capturing complex dynamic scene motions. Experiments across various benchmarks, including monocular and multi-view scenarios, demonstrate our 4DGS model's superior visual quality and efficiency.

Recent studies have determined that the learned token embeddings of large-scale neural language models are degenerated to be anisotropic with a narrow-cone shape. This phenomenon, called the representation degeneration problem, facilitates an increase in the overall similarity between token embeddings that negatively affect the performance of the models. Although the existing methods that address the degeneration problem based on observations of the phenomenon triggered by the problem improves the performance of the text generation, the training dynamics of token embeddings behind the degeneration problem are still not explored. In this study, we analyze the training dynamics of the token embeddings focusing on rare token embedding. We demonstrate that the specific part of the gradient for rare token embeddings is the key cause of the degeneration problem for all tokens during training stage. Based on the analysis, we propose a novel method called, adaptive gradient gating (AGG). AGG addresses the degeneration problem by gating the specific part of the gradient for rare token embeddings. Experimental results from language modeling, word similarity, and machine translation tasks quantitatively and qualitatively verify the effectiveness of AGG.

Learned image compression (LIC) has gained traction as an effective solution for image storage and transmission in recent years. However, existing LIC methods are redundant in latent representation due to limitations in capturing anisotropic frequency components and preserving directional details. To overcome these challenges, we propose a novel frequency-aware transformer (FAT) block that for the first time achieves multiscale directional ananlysis for LIC. The FAT block comprises frequency-decomposition window attention (FDWA) modules to capture multiscale and directional frequency components of natural images. Additionally, we introduce frequency-modulation feed-forward network (FMFFN) to adaptively modulate different frequency components, improving rate-distortion performance. Furthermore, we present a transformer-based channel-wise autoregressive (T-CA) model that effectively exploits channel dependencies. Experiments show that our method achieves state-of-the-art rate-distortion performance compared to existing LIC methods, and evidently outperforms latest standardized codec VTM-12.1 by 14.5%, 15.1%, 13.0% in BD-rate on the Kodak, Tecnick, and CLIC datasets.

In the present work, we study the dynamical evolution of an homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to an homogeneous and isotropic NC Friedmann-Robertson-Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor a(t) and the two parameters beta_pm (t), which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model where the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe.

This paper presents a significant improvement on the previous conference paper known as DefSent. The prior study seeks to improve sentence embeddings of language models by projecting definition sentences into the vector space of dictionary entries. We discover that this approach is not fully explored due to the methodological limitation of using word embeddings of language models to represent dictionary entries. This leads to two hindrances. First, dictionary entries are constrained by the single-word vocabulary, and thus cannot be fully exploited. Second, semantic representations of language models are known to be anisotropic, but pre-processing word embeddings for DefSent is not allowed because its weight is frozen during training and tied to the prediction layer. In this paper, we propose a novel method to progressively build entry embeddings not subject to the limitations. As a result, definition sentences can be projected into a quasi-isotropic or isotropic vector space of unlimited dictionary entries, so that sentence embeddings of noticeably better quality are attainable. We abbreviate our approach as DefSent+ (a plus version of DefSent), involving the following strengths: 1) the task performance on measuring sentence similarities is significantly improved compared to DefSent; 2) when DefSent+ is used to further train data-augmented models like SIMCSE, SNCSE, and SynCSE, state-of-the-art performance on measuring sentence similarities can be achieved among the approaches without using manually labeled datasets; 3) DefSent+ is also competitive in feature-based transfer for NLP downstream tasks.

Digitally reconstructed radiographs (DRRs) are simulated 2D X-ray images generated from 3D CT volumes, widely used in preoperative settings but limited in intraoperative applications due to computational bottlenecks, especially for accurate but heavy physics-based Monte Carlo methods. While analytical DRR renderers offer greater efficiency, they overlook anisotropic X-ray image formation phenomena, such as Compton scattering. We present a novel approach that marries realistic physics-inspired X-ray simulation with efficient, differentiable DRR generation using 3D Gaussian splatting (3DGS). Our direction-disentangled 3DGS (DDGS) method separates the radiosity contribution into isotropic and direction-dependent components, approximating complex anisotropic interactions without intricate runtime simulations. Additionally, we adapt the 3DGS initialization to account for tomography data properties, enhancing accuracy and efficiency. Our method outperforms state-of-the-art techniques in image accuracy. Furthermore, our DDGS shows promise for intraoperative applications and inverse problems such as pose registration, delivering superior registration accuracy and runtime performance compared to analytical DRR methods.

In diffraction-based crystal structure analysis, thermal ellipsoids, quantified via Anisotropic Displacement Parameters (ADPs), are critical yet challenging to determine. ADPs capture atomic vibrations, reflecting thermal and structural properties, but traditional computation is often expensive. This paper introduces CartNet, a novel graph neural network (GNN) for efficiently predicting crystal properties by encoding atomic geometry into Cartesian coordinates alongside the crystal temperature. CartNet integrates a neighbour equalization technique to emphasize covalent and contact interactions, and a Cholesky-based head to ensure valid ADP predictions. We also propose a rotational SO(3) data augmentation strategy during training to handle unseen orientations. An ADP dataset with over 200,000 experimental crystal structures from the Cambridge Structural Database (CSD) was curated to validate the approach. CartNet significantly reduces computational costs and outperforms existing methods in ADP prediction by 10.87%, while delivering a 34.77% improvement over theoretical approaches. We further evaluated CartNet on other datasets covering formation energy, band gap, total energy, energy above the convex hull, bulk moduli, and shear moduli, achieving 7.71% better results on the Jarvis Dataset and 13.16% on the Materials Project Dataset. These gains establish CartNet as a state-of-the-art solution for diverse crystal property predictions. Project website and online demo: https://www.ee.ub.edu/cartnet

Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D Gaussians lack proficiency in defining accurate 3D geometric structures despite their explicit primitive representations. This is due to the fact that Gaussian's attributes are primarily tailored and fine-tuned for rendering diverse 2D images by their anisotropic nature. To pave the way for efficient 3D reconstruction, we present Spherical Gaussians, a simple and effective representation for 3D geometric boundaries, from which we can directly reconstruct 3D feature curves from a set of calibrated multi-view images. Spherical Gaussians is optimized from grid initialization with a view-based rendering loss, where a 2D edge map is rendered at a specific view and then compared to the ground-truth edge map extracted from the corresponding image, without the need for any 3D guidance or supervision. Given Spherical Gaussians serve as intermedia for the robust edge representation, we further introduce a novel optimization-based algorithm called SGCR to directly extract accurate parametric curves from aligned Spherical Gaussians. We demonstrate that SGCR outperforms existing state-of-the-art methods in 3D edge reconstruction while enjoying great efficiency.

We extend our previous work on applying CMB techniques to the mapping of gravitational-wave backgrounds to backgrounds which have non-GR polarisations. Our analysis and results are presented in the context of pulsar-timing array observations, but the overarching methods are general, and can be easily applied to LIGO or eLISA observations using appropriately modified response functions. Analytic expressions for the pulsar-timing response to gravitational waves with non-GR polarisation are given for each mode of a spin-weighted spherical-harmonic decomposition of the background, which permit the signal to be mapped across the sky to any desired resolution. We also derive the pulsar-timing overlap reduction functions for the various non-GR polarisations, finding analytic forms for anisotropic backgrounds with scalar-transverse ("breathing") and vector-longitudinal polarisations, and a semi-analytic form for scalar-longitudinal backgrounds. Our results indicate that pulsar-timing observations will be completely insensitive to scalar-transverse mode anisotropies in the polarisation amplitude beyond dipole, and anisotropies in the power beyond quadrupole. Analogously to our previous findings that pulsar-timing observations lack sensitivity to tensor-curl modes for a transverse-traceless tensor background, we also find insensitivity to vector-curl modes for a vector-longitudinal background.

We present AudioGen-Omni - a unified approach based on multimodal diffusion transformers (MMDit), capable of generating high-fidelity audio, speech, and song coherently synchronized with the input video. AudioGen-Omni introduces a novel joint training paradigm that seamlessly integrates large-scale video-text-audio corpora, enabling a model capable of generating semantically rich, acoustically diverse audio conditioned on multimodal inputs and adaptable to a wide range of audio generation tasks. AudioGen-Omni employs a unified lyrics-transcription encoder that encodes graphemes and phonemes from both song and spoken inputs into dense frame-level representations. Dense frame-level representations are fused using an AdaLN-based joint attention mechanism enhanced with phase-aligned anisotropic positional infusion (PAAPI), wherein RoPE is selectively applied to temporally structured modalities to ensure precise and robust cross-modal alignment. By unfreezing all modalities and masking missing inputs, AudioGen-Omni mitigates the semantic constraints of text-frozen paradigms, enabling effective cross-modal conditioning. This joint training approach enhances audio quality, semantic alignment, and lip-sync accuracy, while also achieving state-of-the-art results on Text-to-Audio/Speech/Song tasks. With an inference time of 1.91 seconds for 8 seconds of audio, it offers substantial improvements in both efficiency and generality.

A bilayer formed by stacking two distinct materials creates a moiré lattice, which can serve as a platform for novel electronic phases. In this work we study a unique example of such a system: the graphene-black phosphorus heterostructure (G/BP), which has been suggested to have an intricate band structure. Most notably, the valence band hosts a quasi-one-dimensional region in the Brillouin zone of high density of states, suggesting that various many-body electronic phases are likely to emerge. We derive an effective tight-binding model that reproduces this band structure, and explore the emergent broken-symmetry phases when interactions are introduced. Employing a mean-field analysis, we find that the favored ground-state exhibits a striped spin density wave (SDW) order, characterized by either one of two-fold degenerate wave-vectors that are tunable by gating. Further exploring the phase-diagram controlled by gate voltage and the interaction strength, we find that the SDW-ordered state undergoes a metal to insulator transition via an intermediate metallic phase which supports striped SDW correlations. Possible experimental signatures are discussed, in particular a highly anisotropic dispersion of the collective excitations which should be manifested in electric and thermal transport.

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in 100,000 effective dimensions in 12 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Training large-scale neural networks requires solving nonconvex optimization where the choice of optimizer fundamentally determines both convergence behavior and computational efficiency. While adaptive methods like Adam have long dominated practice, the recently proposed Muon optimizer achieves superior performance through orthogonalized momentum updates that enforce isotropic geometry with uniform singular values. However, this strict isotropy discards potentially valuable curvature information encoded in gradient spectra, motivating optimization methods that balance geometric structure with adaptivity. We introduce FISMO (Fisher-Structured Momentum-Orthogonalized) optimizer, which generalizes isotropic updates to incorporate anisotropic curvature information through Fisher information geometry. By reformulating the optimizer update as a trust-region problem constrained by a Kronecker-factored Fisher metric, FISMO achieves structured preconditioning that adapts to local loss landscape geometry while maintaining computational tractability. We establish convergence guarantees for FISMO in stochastic nonconvex settings, proving an O(1/T) rate for the expected squared gradient norm with explicit characterization of variance reduction through mini-batching. Empirical evaluation on image classification and language modeling benchmarks demonstrates that FISMO achieves superior training efficiency and final performance compared to established baselines.

Vision-Language Models like CLIP are extensively used for inter-modal tasks which involve both visual and text modalities. However, when the individual modality encoders are applied to inherently intra-modal tasks like image-to-image retrieval, their performance suffers from the intra-modal misalignment. In this paper we study intra-modal misalignment in CLIP with a focus on the role of the projectors that map pre-projection image and text embeddings into the shared embedding space. By analyzing the form of the cosine similarity applied to projected features, and its interaction with the contrastive CLIP loss, we show that there is an inter-modal operator responsible for aligning the two modalities during training, and a second, intra-modal operator that only enforces intra-modal normalization but does nothing to promote intra-modal alignment. Via spectral analysis of the inter-modal operator, we identify an approximately isotropic subspace in which the two modalities are well-aligned, as well as anisotropic directions specific to each modality. We demonstrate that this aligned subspace can be directly obtained from the projector weights and that removing the anisotropic directions improves intra-modal alignment. Our experiments on intra-modal retrieval and classification benchmarks show that our training-free method reduces intra-modal misalignment, greatly lowers latency, and outperforms existing approaches across multiple pre-trained CLIP-like models. The code is publicly available at: https://github.com/simomagi/IsoCLIP.

Vision-Language models (VLMs), such as CLIP, achieve powerful zero-shot classification. However, their predictions remain sensitive to spurious correlations, where contextual cues dominate over semantic content. Earlier solutions typically rely on fine-tuning or prompt engineering, which either undermine the advantages of pre-trained models or are prone to hallucination. In this work, we propose Density-Aware Translation (DAT) that refines image-text similarity scores using a local geometric density term derived from group reference sets. Our approach is motivated by the phenomenon that CLIP embeddings exhibit a modality gap and lie on an anisotropic shell in the feature space: common patterns cluster near the mean, while rare patterns are pushed outward. This geometry creates uneven alignment, where spurious correlations are amplified while semantically meaningful but rare cues are marginalised. To address this, we employ a relative measure to rescale similarities based on embedding density, suppressing overconfident scores in diffuse regions while preserving dense, semantically consistent matches. Experimental results on benchmark datasets demonstrate consistent improvements in worst-group and average accuracy, highlighting density-aware translation as a simple and effective calibration mechanism for reliable zero-shot classification using multimodal models.

Backdoor and data poisoning attacks can achieve high attack success while evading existing spectral and optimisation based defences. We show that this behaviour is not incidental, but arises from a fundamental geometric mechanism in input space. Using kernel ridge regression as an exact model of wide neural networks, we prove that clustered dirty label poisons induce a rank one spike in the input Hessian whose magnitude scales quadratically with attack efficacy. Crucially, for nonlinear kernels we identify a near clone regime in which poison efficacy remains order one while the induced input curvature vanishes, making the attack provably spectrally undetectable. We further show that input gradient regularisation contracts poison aligned Fisher and Hessian eigenmodes under gradient flow, yielding an explicit and unavoidable safety efficacy trade off by reducing data fitting capacity. For exponential kernels, this defence admits a precise interpretation as an anisotropic high pass filter that increases the effective length scale and suppresses near clone poisons. Extensive experiments on linear models and deep convolutional networks across MNIST and CIFAR 10 and CIFAR 100 validate the theory, demonstrating consistent lags between attack success and spectral visibility, and showing that regularisation and data augmentation jointly suppress poisoning. Our results establish when backdoors are inherently invisible, and provide the first end to end characterisation of poisoning, detectability, and defence through input space curvature.

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100\% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

Reconstructing transparent surfaces is essential for tasks such as robotic manipulation in labs, yet it poses a significant challenge for 3D reconstruction techniques like 3D Gaussian Splatting (3DGS). These methods often encounter a transparency-depth dilemma, where the pursuit of photorealistic rendering through standard α-blending undermines geometric precision, resulting in considerable depth estimation errors for transparent materials. To address this issue, we introduce Transparent Surface Gaussian Splatting (TSGS), a new framework that separates geometry learning from appearance refinement. In the geometry learning stage, TSGS focuses on geometry by using specular-suppressed inputs to accurately represent surfaces. In the second stage, TSGS improves visual fidelity through anisotropic specular modeling, crucially maintaining the established opacity to ensure geometric accuracy. To enhance depth inference, TSGS employs a first-surface depth extraction method. This technique uses a sliding window over α-blending weights to pinpoint the most likely surface location and calculates a robust weighted average depth. To evaluate the transparent surface reconstruction task under realistic conditions, we collect a TransLab dataset that includes complex transparent laboratory glassware. Extensive experiments on TransLab show that TSGS achieves accurate geometric reconstruction and realistic rendering of transparent objects simultaneously within the efficient 3DGS framework. Specifically, TSGS significantly surpasses current leading methods, achieving a 37.3% reduction in chamfer distance and an 8.0% improvement in F1 score compared to the top baseline. The code and dataset are available at https://longxiang-ai.github.io/TSGS/.

Post-training quantization (PTQ) is essential for deploying LLMs under memory and bandwidth constraints. However, extreme low-bit quantization remains highly sensitive to activation outliers and anisotropic weight curvature. Existing incoherence-based PTQ methods mitigate this issue with fixed randomized Hadamard transforms (RHTs), which improve quantization robustness but cannot adapt the rotated basis to the layer, calibration distribution, or quantizer. We introduce HARP (Hadamard-preconditioned Adaptive Rotation Processor), a learnable structured two-sided orthogonal processor that replaces fixed Hadamard mixing while preserving exact full-precision equivalence. HARP represents each rotation as a product of sparse butterfly-like block-orthogonal stages, supports non-power-of-two dimensions via Mixed-Radix schedules, and initializes to the RHT processor up to a fixed permutation. Fitted only on calibration data, HARP adapts the quantization basis to each layer and backend. Across 2-4 bit settings on models ranging from 1B to 70B parameters, HARP improves perplexity and zero-shot accuracy over fixed RHT. Importantly, HARP preserves deployment efficiency, reaching 128 tok/s versus 61 tok/s for FP16.

Analytic Continual Learning (ACL) offers a computationally efficient alternative to gradient-based approaches. Recent ACL methods are based on Recursive Least Squares (RLS) and have achieved the state-of-the-art results compared to other alternatives. However, they falter significantly in Class-Incremental Learning scenarios characterized by Long-Tailed distributions. While the ill-conditioning of the autocorrelation (Gram) matrix is a known limitation of RLS, we demonstrate that class imbalance exacerbates this issue into a distinct spectral pathology: "tail" classes suffer from severe spectral collapse, rendering their subspaces numerically indistinguishable from noise. Standard Ridge Regression (L_2) fails to address this effectively as it applies isotropic regularization - a uniform penalty that is insufficient to stabilize the tail without over-shrinking the head. To address this, we propose Geometry-Spectral Rectification (GSR), a theoretically grounded framework that treats long-tailed learning as a spectral regularization problem. Unlike standard isotropic regularization (Ridge) which uniformly penalizes all eigenvalues, GSR acts as an anisotropic spectral filter, selectively inflating the collapsed eigenvalues of tail classes. We construct a structured, data-dependent spectral perturbation matrix Δ that selectively inflates collapsed tail eigen-directions of the Gram matrix. Theoretical analysis proves that GSR guarantees an improved stable rank for the Gram matrix, ensuring numerical stability. Extensive experiments show that GSR establishes a new state-of-the-art for analytic CIL, offering a superior trade-off between computational efficiency and robust generalization in long-tailed settings.