Daily Papers

3D Gaussian Splatting (3D-GS) enables real-time rendering but struggles with fast motion due to low temporal resolution of RGB cameras. To address this, we introduce the first approach combining event cameras, which capture high-temporal-resolution, continuous motion data, with deformable 3D-GS for fast dynamic scene reconstruction. We observe that threshold modeling for events plays a crucial role in achieving high-quality reconstruction. Therefore, we propose a GS-Threshold Joint Modeling (GTJM) strategy, creating a mutually reinforcing process that greatly improves both 3D reconstruction and threshold modeling. Moreover, we introduce a Dynamic-Static Decomposition (DSD) strategy that first identifies dynamic areas by exploiting the inability of static Gaussians to represent motions, then applies a buffer-based soft decomposition to separate dynamic and static areas. This strategy accelerates rendering by avoiding unnecessary deformation in static areas, and focuses on dynamic areas to enhance fidelity. Our approach achieves high-fidelity dynamic reconstruction at 156 FPS with a 400times400 resolution on an RTX 3090 GPU.

We propose GS-LRM, a scalable large reconstruction model that can predict high-quality 3D Gaussian primitives from 2-4 posed sparse images in 0.23 seconds on single A100 GPU. Our model features a very simple transformer-based architecture; we patchify input posed images, pass the concatenated multi-view image tokens through a sequence of transformer blocks, and decode final per-pixel Gaussian parameters directly from these tokens for differentiable rendering. In contrast to previous LRMs that can only reconstruct objects, by predicting per-pixel Gaussians, GS-LRM naturally handles scenes with large variations in scale and complexity. We show that our model can work on both object and scene captures by training it on Objaverse and RealEstate10K respectively. In both scenarios, the models outperform state-of-the-art baselines by a wide margin. We also demonstrate applications of our model in downstream 3D generation tasks. Our project webpage is available at: https://sai-bi.github.io/project/gs-lrm/ .

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

The top-down and bottom-up methods are two mainstreams of referring segmentation, while both methods have their own intrinsic weaknesses. Top-down methods are chiefly disturbed by Polar Negative (PN) errors owing to the lack of fine-grained cross-modal alignment. Bottom-up methods are mainly perturbed by Inferior Positive (IP) errors due to the lack of prior object information. Nevertheless, we discover that two types of methods are highly complementary for restraining respective weaknesses but the direct average combination leads to harmful interference. In this context, we build Win-win Cooperation (WiCo) to exploit complementary nature of two types of methods on both interaction and integration aspects for achieving a win-win improvement. For the interaction aspect, Complementary Feature Interaction (CFI) provides fine-grained information to top-down branch and introduces prior object information to bottom-up branch for complementary feature enhancement. For the integration aspect, Gaussian Scoring Integration (GSI) models the gaussian performance distributions of two branches and weightedly integrates results by sampling confident scores from the distributions. With our WiCo, several prominent top-down and bottom-up combinations achieve remarkable improvements on three common datasets with reasonable extra costs, which justifies effectiveness and generality of our method.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

2D-to-3D human pose lifting is fundamental for 3D human pose estimation (HPE), for which graph convolutional networks (GCNs) have proven inherently suitable for modeling the human skeletal topology. However, the current GCN-based 3D HPE methods update the node features by aggregating their neighbors' information without considering the interaction of joints in different joint synergies. Although some studies have proposed importing limb information to learn the movement patterns, the latent synergies among joints, such as maintaining balance are seldom investigated. We propose the Hop-wise GraphFormer with Intragroup Joint Refinement (HopFIR) architecture to tackle the 3D HPE problem. HopFIR mainly consists of a novel hop-wise GraphFormer (HGF) module and an intragroup joint refinement (IJR) module. The HGF module groups the joints by k-hop neighbors and applies a hopwise transformer-like attention mechanism to these groups to discover latent joint synergies. The IJR module leverages the prior limb information for peripheral joint refinement. Extensive experimental results show that HopFIR outperforms the SOTA methods by a large margin, with a mean per-joint position error (MPJPE) on the Human3.6M dataset of 32.67 mm. We also demonstrate that the state-of-the-art GCN-based methods can benefit from the proposed hop-wise attention mechanism with a significant improvement in performance: SemGCN and MGCN are improved by 8.9% and 4.5%, respectively.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

Lung diseases represent a significant global health challenge, with Chest X-Ray (CXR) being a key diagnostic tool due to their accessibility and affordability. Nonetheless, the detection of pulmonary lesions is often hindered by overlapping bone structures in CXR images, leading to potential misdiagnoses. To address this issue, we developed an end-to-end framework called BS-LDM, designed to effectively suppress bone in high-resolution CXR images. This framework is based on conditional latent diffusion models and incorporates a multi-level hybrid loss-constrained vector-quantized generative adversarial network which is crafted for perceptual compression, ensuring the preservation of details. To further enhance the framework's performance, we introduce offset noise and a temporal adaptive thresholding strategy. These additions help minimize discrepancies in generating low-frequency information, thereby improving the clarity of the generated soft tissue images. Additionally, we have compiled a high-quality bone suppression dataset named SZCH-X-Rays. This dataset includes 818 pairs of high-resolution CXR and dual-energy subtraction soft tissue images collected from a partner hospital. Moreover, we processed 241 data pairs from the JSRT dataset into negative images, which are more commonly used in clinical practice. Our comprehensive experimental and clinical evaluations reveal that BS-LDM excels in bone suppression, underscoring its significant clinical value.

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

Multi-turn-to-single-turn (M2S) compresses iterative red-teaming into one structured prompt, but prior work relied on a handful of manually written templates. We present X-Teaming Evolutionary M2S, an automated framework that discovers and optimizes M2S templates through language-model-guided evolution. The system pairs smart sampling from 12 sources with an LLM-as-judge inspired by StrongREJECT and records fully auditable logs. Maintaining selection pressure by setting the success threshold to theta = 0.70, we obtain five evolutionary generations, two new template families, and 44.8% overall success (103/230) on GPT-4.1. A balanced cross-model panel of 2,500 trials (judge fixed) shows that structural gains transfer but vary by target; two models score zero at the same threshold. We also find a positive coupling between prompt length and score, motivating length-aware judging. Our results demonstrate that structure-level search is a reproducible route to stronger single-turn probes and underscore the importance of threshold calibration and cross-model evaluation. Code, configurations, and artifacts are available at https://github.com/hyunjun1121/M2S-x-teaming.

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the ell_0-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screening

Multi-modal three-dimensional (3D) medical imaging data, derived from ultrasound, magnetic resonance imaging (MRI), and potentially computed tomography (CT), provide a widely adopted approach for non-invasive anatomical visualization. Accurate modeling, registration, and visualization in this setting depend on surface reconstruction and frame-to-frame interpolation. Traditional methods often face limitations due to image noise and incomplete information between frames. To address these challenges, we present MedGS, a semi-supervised neural implicit surface reconstruction framework that employs a Gaussian Splatting (GS)-based interpolation mechanism. In this framework, medical imaging data are represented as consecutive two-dimensional (2D) frames embedded in 3D space and modeled using Gaussian-based distributions. This representation enables robust frame interpolation and high-fidelity surface reconstruction across imaging modalities. As a result, MedGS offers more efficient training than traditional neural implicit methods. Its explicit GS-based representation enhances noise robustness, allows flexible editing, and supports precise modeling of complex anatomical structures with fewer artifacts. These features make MedGS highly suitable for scalable and practical applications in medical imaging.

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness. Probabilistic models with more parameters, such as the Gaussian mixture models, can fit the distribution of latent variables more precisely, but the corresponding complexity will also be higher. To balance between compression performance and complexity, we extend the Gaussian model to the generalized Gaussian model for more flexible latent distribution modeling, introducing only one additional shape parameter, beta, than the Gaussian model. To enhance the performance of the generalized Gaussian model by alleviating the train-test mismatch, we propose improved training methods, including beta-dependent lower bounds for scale parameters and gradient rectification. Our proposed generalized Gaussian model, coupled with the improved training methods, is demonstrated to outperform the Gaussian and Gaussian mixture models on a variety of learned image compression methods.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of these systems typically assumes fixed working points based on pre-defined rejection thresholds, methodological progress requires benchmarking the general performance of systems akin to the AUROC in standard classification. In this work, we define 5 requirements for multi-threshold metrics in selective classification regarding task alignment, interpretability, and flexibility, and show how current approaches fail to meet them. We propose the Area under the Generalized Risk Coverage curve (AUGRC), which meets all requirements and can be directly interpreted as the average risk of undetected failures. We empirically demonstrate the relevance of AUGRC on a comprehensive benchmark spanning 6 data sets and 13 confidence scoring functions. We find that the proposed metric substantially changes metric rankings on 5 out of the 6 data sets.

Graphical User Interface (GUI) grounding maps natural language instructions to precise interface locations for autonomous interaction. Current reinforcement learning approaches use binary rewards that treat elements as hit-or-miss targets, creating sparse signals that ignore the continuous nature of spatial interactions. Motivated by human clicking behavior that naturally forms Gaussian distributions centered on target elements, we introduce GUI Gaussian Grounding Rewards (GUI-G^2), a principled reward framework that models GUI elements as continuous Gaussian distributions across the interface plane. GUI-G^2 incorporates two synergistic mechanisms: Gaussian point rewards model precise localization through exponentially decaying distributions centered on element centroids, while coverage rewards assess spatial alignment by measuring the overlap between predicted Gaussian distributions and target regions. To handle diverse element scales, we develop an adaptive variance mechanism that calibrates reward distributions based on element dimensions. This framework transforms GUI grounding from sparse binary classification to dense continuous optimization, where Gaussian distributions generate rich gradient signals that guide models toward optimal interaction positions. Extensive experiments across ScreenSpot, ScreenSpot-v2, and ScreenSpot-Pro benchmarks demonstrate that GUI-G^2, substantially outperforms state-of-the-art method UI-TARS-72B, with the most significant improvement of 24.7% on ScreenSpot-Pro. Our analysis reveals that continuous modeling provides superior robustness to interface variations and enhanced generalization to unseen layouts, establishing a new paradigm for spatial reasoning in GUI interaction tasks.

We present GSD, a diffusion model approach based on Gaussian Splatting (GS) representation for 3D object reconstruction from a single view. Prior works suffer from inconsistent 3D geometry or mediocre rendering quality due to improper representations. We take a step towards resolving these shortcomings by utilizing the recent state-of-the-art 3D explicit representation, Gaussian Splatting, and an unconditional diffusion model. This model learns to generate 3D objects represented by sets of GS ellipsoids. With these strong generative 3D priors, though learning unconditionally, the diffusion model is ready for view-guided reconstruction without further model fine-tuning. This is achieved by propagating fine-grained 2D features through the efficient yet flexible splatting function and the guided denoising sampling process. In addition, a 2D diffusion model is further employed to enhance rendering fidelity, and improve reconstructed GS quality by polishing and re-using the rendered images. The final reconstructed objects explicitly come with high-quality 3D structure and texture, and can be efficiently rendered in arbitrary views. Experiments on the challenging real-world CO3D dataset demonstrate the superiority of our approach. Project page: https://yxmu.foo/GSD/{this https URL}

Semi-supervised text classification (SSTC) has gained increasing attention due to its ability to leverage unlabeled data. However, existing approaches based on pseudo-labeling suffer from the issues of pseudo-label bias and error accumulation. In this paper, we propose JointMatch, a holistic approach for SSTC that addresses these challenges by unifying ideas from recent semi-supervised learning and the task of learning with noise. JointMatch adaptively adjusts classwise thresholds based on the learning status of different classes to mitigate model bias towards current easy classes. Additionally, JointMatch alleviates error accumulation by utilizing two differently initialized networks to teach each other in a cross-labeling manner. To maintain divergence between the two networks for mutual learning, we introduce a strategy that weighs more disagreement data while also allowing the utilization of high-quality agreement data for training. Experimental results on benchmark datasets demonstrate the superior performance of JointMatch, achieving a significant 5.13% improvement on average. Notably, JointMatch delivers impressive results even in the extremely-scarce-label setting, obtaining 86% accuracy on AG News with only 5 labels per class. We make our code available at https://github.com/HenryPengZou/JointMatch.

This paper proposes a new method for accurate and robust 6D pose estimation of novel objects, named GS2Pose. By introducing 3D Gaussian splatting, GS2Pose can utilize the reconstruction results without requiring a high-quality CAD model, which means it only requires segmented RGBD images as input. Specifically, GS2Pose employs a two-stage structure consisting of coarse estimation followed by refined estimation. In the coarse stage, a lightweight U-Net network with a polarization attention mechanism, called Pose-Net, is designed. By using the 3DGS model for supervised training, Pose-Net can generate NOCS images to compute a coarse pose. In the refinement stage, GS2Pose formulates a pose regression algorithm following the idea of reprojection or Bundle Adjustment (BA), referred to as GS-Refiner. By leveraging Lie algebra to extend 3DGS, GS-Refiner obtains a pose-differentiable rendering pipeline that refines the coarse pose by comparing the input images with the rendered images. GS-Refiner also selectively updates parameters in the 3DGS model to achieve environmental adaptation, thereby enhancing the algorithm's robustness and flexibility to illuminative variation, occlusion, and other challenging disruptive factors. GS2Pose was evaluated through experiments conducted on the LineMod dataset, where it was compared with similar algorithms, yielding highly competitive results. The code for GS2Pose will soon be released on GitHub.

Model merging integrates the weights of multiple task-specific models into a single multi-task model. Despite recent interest in the problem, a significant performance gap between the combined and single-task models remains. In this paper, we investigate the key characteristics of task matrices -- weight update matrices applied to a pre-trained model -- that enable effective merging. We show that alignment between singular components of task-specific and merged matrices strongly correlates with performance improvement over the pre-trained model. Based on this, we propose an isotropic merging framework that flattens the singular value spectrum of task matrices, enhances alignment, and reduces the performance gap. Additionally, we incorporate both common and task-specific subspaces to further improve alignment and performance. Our proposed approach achieves state-of-the-art performance across multiple scenarios, including various sets of tasks and model scales. This work advances the understanding of model merging dynamics, offering an effective methodology to merge models without requiring additional training. Code is available at https://github.com/danielm1405/iso-merging .

The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and intuitions: joint Shapley values measure a set of features' average contribution to a model's prediction. We prove the uniqueness of joint Shapley values, for any order of explanation. Results for games show that joint Shapley values present different insights from existing interaction indices, which assess the effect of a feature within a set of features. The joint Shapley values provide intuitive results in ML attribution problems. With binary features, we present a presence-adjusted global value that is more consistent with local intuitions than the usual approach.

3D Gaussian Splatting (3DGS) has revolutionized neural rendering with its efficiency and quality, but like many novel view synthesis methods, it heavily depends on accurate camera poses from Structure-from-Motion (SfM) systems. Although recent SfM pipelines have made impressive progress, questions remain about how to further improve both their robust performance in challenging conditions (e.g., textureless scenes) and the precision of camera parameter estimation simultaneously. We present 3R-GS, a 3D Gaussian Splatting framework that bridges this gap by jointly optimizing 3D Gaussians and camera parameters from large reconstruction priors MASt3R-SfM. We note that naively performing joint 3D Gaussian and camera optimization faces two challenges: the sensitivity to the quality of SfM initialization, and its limited capacity for global optimization, leading to suboptimal reconstruction results. Our 3R-GS, overcomes these issues by incorporating optimized practices, enabling robust scene reconstruction even with imperfect camera registration. Extensive experiments demonstrate that 3R-GS delivers high-quality novel view synthesis and precise camera pose estimation while remaining computationally efficient. Project page: https://zsh523.github.io/3R-GS/

We present JointDiT, a diffusion transformer that models the joint distribution of RGB and depth. By leveraging the architectural benefit and outstanding image prior of the state-of-the-art diffusion transformer, JointDiT not only generates high-fidelity images but also produces geometrically plausible and accurate depth maps. This solid joint distribution modeling is achieved through two simple yet effective techniques that we propose, namely, adaptive scheduling weights, which depend on the noise levels of each modality, and the unbalanced timestep sampling strategy. With these techniques, we train our model across all noise levels for each modality, enabling JointDiT to naturally handle various combinatorial generation tasks, including joint generation, depth estimation, and depth-conditioned image generation by simply controlling the timesteps of each branch. JointDiT demonstrates outstanding joint generation performance. Furthermore, it achieves comparable results in depth estimation and depth-conditioned image generation, suggesting that joint distribution modeling can serve as a viable alternative to conditional generation. The project page is available at https://byungki-k.github.io/JointDiT/.

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for novel view synthesis. However, existing methods struggle to adaptively optimize the distribution of Gaussian primitives based on scene characteristics, making it challenging to balance reconstruction quality and efficiency. Inspired by human perception, we propose scene-adaptive perceptual densification for Gaussian Splatting (Perceptual-GS), a novel framework that integrates perceptual sensitivity into the 3DGS training process to address this challenge. We first introduce a perception-aware representation that models human visual sensitivity while constraining the number of Gaussian primitives. Building on this foundation, we develop a perceptual sensitivity-adaptive distribution to allocate finer Gaussian granularity to visually critical regions, enhancing reconstruction quality and robustness. Extensive evaluations on multiple datasets, including BungeeNeRF for large-scale scenes, demonstrate that Perceptual-GS achieves state-of-the-art performance in reconstruction quality, efficiency, and robustness. The code is publicly available at: https://github.com/eezkni/Perceptual-GS

Reconstructing realistic 3D human models from monocular images has significant applications in creative industries, human-computer interfaces, and healthcare. We base our work on 3D Gaussian Splatting (3DGS), a scene representation composed of a mixture of Gaussians. Predicting such mixtures for a human from a single input image is challenging, as it is a non-uniform density (with a many-to-one relationship with input pixels) with strict physical constraints. At the same time, it needs to be flexible to accommodate a variety of clothes and poses. Our key observation is that the vertices of standardized human meshes (such as SMPL) can provide an adequate density and approximate initial position for Gaussians. We can then train a transformer model to jointly predict comparatively small adjustments to these positions, as well as the other Gaussians' attributes and the SMPL parameters. We show empirically that this combination (using only multi-view supervision) can achieve fast inference of 3D human models from a single image without test-time optimization, expensive diffusion models, or 3D points supervision. We also show that it can improve 3D pose estimation by better fitting human models that account for clothes and other variations. The code is available on the project website https://abdullahamdi.com/gst/ .

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.

Simultaneously achieving robust classification and high-fidelity generative modeling within a single framework presents a significant challenge. Hybrid approaches, such as Joint Energy-Based Models (JEM), interpret classifiers as EBMs but are often limited by the instability and poor sample quality inherent in SGLD-based training. We address these limitations by proposing a novel training framework that integrates adversarial training (AT) principles for both discriminative robustness and stable generative learning. The proposed method introduces three key innovations: (1) the replacement of SGLD-based JEM learning with a stable, AT-based approach that optimizes the energy function by discriminating between real data and PGD-generated contrastive samples using the BCE loss; (2) synergistic adversarial training for the discriminative component that enhances classification robustness while eliminating the need for explicit gradient penalties; and (3) a two-stage training procedure to resolve the incompatibility between batch normalization and EBM training. Experiments on CIFAR-10, CIFAR-100, and ImageNet demonstrate that our method substantially improves adversarial robustness over existing hybrid models while maintaining competitive generative performance. On ImageNet, when optimized for generative modeling, our model's generative fidelity surpasses that of BigGAN and approaches diffusion models, representing the first MCMC-based EBM approach to achieve high-quality generation on complex, high-resolution datasets. Our approach addresses key stability issues that have limited JEM scaling and demonstrates that adversarial training can serve as an effective foundation for unified frameworks capable of generating and robustly classifying visual data.

We introduce GS2E (Gaussian Splatting to Event), a large-scale synthetic event dataset for high-fidelity event vision tasks, captured from real-world sparse multi-view RGB images. Existing event datasets are often synthesized from dense RGB videos, which typically lack viewpoint diversity and geometric consistency, or depend on expensive, difficult-to-scale hardware setups. GS2E overcomes these limitations by first reconstructing photorealistic static scenes using 3D Gaussian Splatting, and subsequently employing a novel, physically-informed event simulation pipeline. This pipeline generally integrates adaptive trajectory interpolation with physically-consistent event contrast threshold modeling. Such an approach yields temporally dense and geometrically consistent event streams under diverse motion and lighting conditions, while ensuring strong alignment with underlying scene structures. Experimental results on event-based 3D reconstruction demonstrate GS2E's superior generalization capabilities and its practical value as a benchmark for advancing event vision research.

Recent advancements in Large Multi-modal Models (LMMs) underscore the importance of scaling by increasing image-text paired data, achieving impressive performance on general tasks. Despite their effectiveness in broad applications, generalist models are primarily trained on web-scale datasets dominated by natural images, resulting in the sacrifice of specialized capabilities for domain-specific tasks that require extensive domain prior knowledge. Moreover, directly integrating expert models tailored for specific domains is challenging due to the representational gap and imbalanced optimization between the generalist model and experts. To address these challenges, we introduce Chimera, a scalable and low-cost multi-modal pipeline designed to boost the ability of existing LMMs with domain-specific experts. Specifically, we design a progressive training strategy to integrate features from expert models into the input of a generalist LMM. To address the imbalanced optimization caused by the well-aligned general visual encoder, we introduce a novel Generalist-Specialist Collaboration Masking (GSCM) mechanism. This results in a versatile model that excels across the chart, table, math, and document domains, achieving state-of-the-art performance on multi-modal reasoning and visual content extraction tasks, both of which are challenging tasks for assessing existing LMMs.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a varphi-divergence to an empirical distribution. However, the use of varphi-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

Sexual dimorphism is a critical factor in many biological and medical research fields. In biomechanics and bioengineering, understanding sex differences is crucial for studying musculoskeletal conditions such as temporomandibular disorder (TMD). This paper focuses on the association between the craniofacial skeletal morphology and temporomandibular joint (TMJ) related masticatory muscle attachments to discern sex differences. Data were collected from 10 male and 11 female cadaver heads to investigate sex-specific relationships between the skull and muscles. We propose a conditional cross-covariance reduction (CCR) model, designed to examine the dynamic association between two sets of random variables conditioned on a third binary variable (e.g., sex), highlighting the most distinctive sex-related relationships between skull and muscle attachments in the human cadaver data. Under the CCR model, we employ a sparse singular value decomposition algorithm and introduce a sequential permutation for selecting sparsity (SPSS) method to select important variables and to determine the optimal number of selected variables.

Vision tokenizers have gained a lot of attraction due to their scalability and compactness; previous works depend on old-school GAN-based hyperparameters, biased comparisons, and a lack of comprehensive analysis of the scaling behaviours. To tackle those issues, we introduce Grouped Spherical Quantization (GSQ), featuring spherical codebook initialization and lookup regularization to constrain codebook latent to a spherical surface. Our empirical analysis of image tokenizer training strategies demonstrates that GSQ-GAN achieves superior reconstruction quality over state-of-the-art methods with fewer training iterations, providing a solid foundation for scaling studies. Building on this, we systematically examine the scaling behaviours of GSQ, specifically in latent dimensionality, codebook size, and compression ratios, and their impact on model performance. Our findings reveal distinct behaviours at high and low spatial compression levels, underscoring challenges in representing high-dimensional latent spaces. We show that GSQ can restructure high-dimensional latent into compact, low-dimensional spaces, thus enabling efficient scaling with improved quality. As a result, GSQ-GAN achieves a 16x down-sampling with a reconstruction FID (rFID) of 0.50.

This paper presents the first application of spiking neural networks (SNNs) for the classification of chronic lower back pain (CLBP) using the EmoPain dataset. Our work has two main contributions. We introduce Spike Threshold Adaptive Learning (STAL), a trainable encoder that effectively converts continuous biosignals into spike trains. Additionally, we propose an ensemble of Spiking Recurrent Neural Network (SRNN) classifiers for the multi-stream processing of sEMG and IMU data. To tackle the challenges of small sample size and class imbalance, we implement minority over-sampling with weighted sample replacement during batch creation. Our method achieves outstanding performance with an accuracy of 80.43%, AUC of 67.90%, F1 score of 52.60%, and Matthews Correlation Coefficient (MCC) of 0.437, surpassing traditional rate-based and latency-based encoding methods. The STAL encoder shows superior performance in preserving temporal dynamics and adapting to signal characteristics. Importantly, our approach (STAL-SRNN) outperforms the best deep learning method in terms of MCC, indicating better balanced class prediction. This research contributes to the development of neuromorphic computing for biosignal analysis. It holds promise for energy-efficient, wearable solutions in chronic pain management.

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input value before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

Recent advancements in 3D Gaussian Splatting (3DGS) and Neural Radiance Fields (NeRF) have achieved impressive results in real-time 3D reconstruction and novel view synthesis. However, these methods struggle in large-scale, unconstrained environments where sparse and uneven input coverage, transient occlusions, appearance variability, and inconsistent camera settings lead to degraded quality. We propose GS-Diff, a novel 3DGS framework guided by a multi-view diffusion model to address these limitations. By generating pseudo-observations conditioned on multi-view inputs, our method transforms under-constrained 3D reconstruction problems into well-posed ones, enabling robust optimization even with sparse data. GS-Diff further integrates several enhancements, including appearance embedding, monocular depth priors, dynamic object modeling, anisotropy regularization, and advanced rasterization techniques, to tackle geometric and photometric challenges in real-world settings. Experiments on four benchmarks demonstrate that GS-Diff consistently outperforms state-of-the-art baselines by significant margins.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyper-parameters. The newly proposed grid spectral mixture product (GSMP) kernel is tailored for multi-dimensional data, effectively reducing the number of hyper-parameters while maintaining good approximation capability. We further demonstrate that the associated hyper-parameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity of the solutions, we introduce the Sparse LInear Multiple Kernel Learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMM) scheme for collaborative learning among multiple agents, where the local optimization problem is solved using a distributed successive convex approximation (DSCA) algorithm. SLIM-KL effectively manages large-scale hyper-parameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. Theoretical analysis establishes convergence guarantees for the learning framework, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our proposed methods.

3D Gaussian Splatting (3DGS) has demonstrated remarkable effectiveness in novel view synthesis (NVS). However, 3DGS tends to overfit when trained with sparse views, limiting its generalization to novel viewpoints. In this paper, we address this overfitting issue by introducing Self-Ensembling Gaussian Splatting (SE-GS). We achieve self-ensembling by incorporating an uncertainty-aware perturbation strategy during training. A Delta-model and a Sigma-model are jointly trained on the available images. The Delta-model is dynamically perturbed based on rendering uncertainty across training steps, generating diverse perturbed models with negligible computational overhead. Discrepancies between the Sigma-model and these perturbed models are minimized throughout training, forming a robust ensemble of 3DGS models. This ensemble, represented by the Sigma-model, is then used to generate novel-view images during inference. Experimental results on the LLFF, Mip-NeRF360, DTU, and MVImgNet datasets demonstrate that our approach enhances NVS quality under few-shot training conditions, outperforming existing state-of-the-art methods. The code is released at: https://sailor-z.github.io/projects/SEGS.html.

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://github.com/GSL-Benchmark/GSLB.

Scene graph generation (SGG) in satellite imagery (SAI) benefits promoting understanding of geospatial scenarios from perception to cognition. In SAI, objects exhibit great variations in scales and aspect ratios, and there exist rich relationships between objects (even between spatially disjoint objects), which makes it attractive to holistically conduct SGG in large-size very-high-resolution (VHR) SAI. However, there lack such SGG datasets. Due to the complexity of large-size SAI, mining triplets <subject, relationship, object> heavily relies on long-range contextual reasoning. Consequently, SGG models designed for small-size natural imagery are not directly applicable to large-size SAI. This paper constructs a large-scale dataset for SGG in large-size VHR SAI with image sizes ranging from 512 x 768 to 27,860 x 31,096 pixels, named STAR (Scene graph generaTion in lArge-size satellite imageRy), encompassing over 210K objects and over 400K triplets. To realize SGG in large-size SAI, we propose a context-aware cascade cognition (CAC) framework to understand SAI regarding object detection (OBD), pair pruning and relationship prediction for SGG. We also release a SAI-oriented SGG toolkit with about 30 OBD and 10 SGG methods which need further adaptation by our devised modules on our challenging STAR dataset. The dataset and toolkit are available at: https://linlin-dev.github.io/project/STAR.

Reconstructing 3D scenes using 3D Gaussian Splatting (3DGS) from sparse views is an ill-posed problem due to insufficient information, often resulting in noticeable artifacts. While recent approaches have sought to leverage generative priors to complete information for under-constrained regions, they struggle to generate content that remains consistent with input observations. To address this challenge, we propose GSFixer, a novel framework designed to improve the quality of 3DGS representations reconstructed from sparse inputs. The core of our approach is the reference-guided video restoration model, built upon a DiT-based video diffusion model trained on paired artifact 3DGS renders and clean frames with additional reference-based conditions. Considering the input sparse views as references, our model integrates both 2D semantic features and 3D geometric features of reference views extracted from the visual geometry foundation model, enhancing the semantic coherence and 3D consistency when fixing artifact novel views. Furthermore, considering the lack of suitable benchmarks for 3DGS artifact restoration evaluation, we present DL3DV-Res which contains artifact frames rendered using low-quality 3DGS. Extensive experiments demonstrate our GSFixer outperforms current state-of-the-art methods in 3DGS artifact restoration and sparse-view 3D reconstruction. Project page: https://github.com/GVCLab/GSFixer.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

With the proliferation of domain-specific models, model merging has emerged as a set of techniques that combine the capabilities of multiple models into one that can multitask without the cost of additional training. In this paper, we propose a new model merging technique, Drop and rEscaLe via sampLing with mAgnitude (DELLA-Merging), that employs a novel pruning technique, MAGPRUNE, which shows significant advantages over DARE and TIES. MAGPRUNE first ranks the parameters in order of their magnitude and assigns higher dropout probabilities (p) to parameters with lower ranks corresponding to lower magnitudes. To approximate the original embeddings, MAGPRUNE employs a rescaling operation on the parameters that survive the random dropping by 1/(1 - p). On three different expert models considered for merging (LM, Math, Code) and corresponding benchmark datasets (AlpacaEval, GSM8K, MBPP), DELLA shows an average improvement of 2.4 points over baseline methods employing delta parameter pruning (an improvement of 3.6 points over TIES, 1.2 points over DARE), and 11.1 points over the no-pruning baseline (TA). We release the source code at: https://github.com/declare-lab/della.

The unsupervised task of Joint Alignment (JA) of images is beset by challenges such as high complexity, geometric distortions, and convergence to poor local or even global optima. Although Vision Transformers (ViT) have recently provided valuable features for JA, they fall short of fully addressing these issues. Consequently, researchers frequently depend on expensive models and numerous regularization terms, resulting in long training times and challenging hyperparameter tuning. We introduce the Spatial Joint Alignment Model (SpaceJAM), a novel approach that addresses the JA task with efficiency and simplicity. SpaceJAM leverages a compact architecture with only 16K trainable parameters and uniquely operates without the need for regularization or atlas maintenance. Evaluations on SPair-71K and CUB datasets demonstrate that SpaceJAM matches the alignment capabilities of existing methods while significantly reducing computational demands and achieving at least a 10x speedup. SpaceJAM sets a new standard for rapid and effective image alignment, making the process more accessible and efficient. Our code is available at: https://bgu-cs-vil.github.io/SpaceJAM/.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 13%, with several families of models (e.g., Phi and Mistral) showing evidence of systematic overfitting across almost all model sizes. At the same time, many models, especially those on the frontier, (e.g., Gemini/GPT/Claude) show minimal signs of overfitting. Further analysis suggests a positive relationship (Spearman's r^2=0.32) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that many models may have partially memorized GSM8k.

With the growing prominence of the Mixture of Experts (MoE) architecture in developing large-scale foundation models, we investigate the Hierarchical Mixture of Experts (HMoE), a specialized variant of MoE that excels in handling complex inputs and improving performance on targeted tasks. Our analysis highlights the advantages of using the Laplace gating function over the traditional Softmax gating within the HMoE frameworks. We theoretically demonstrate that applying the Laplace gating function at both levels of the HMoE model helps eliminate undesirable parameter interactions caused by the Softmax gating and, therefore, accelerates the expert convergence as well as enhances the expert specialization. Empirical validation across diverse scenarios supports these theoretical claims. This includes large-scale multimodal tasks, image classification, and latent domain discovery and prediction tasks, where our modified HMoE models show great performance improvements compared to the conventional HMoE models.

As large language models (LLMs) continue to evolve, efficient evaluation metrics are vital for assessing their ability to compress information and reduce redundancy. While traditional metrics like Matrix Entropy offer valuable insights, they are computationally intensive for large-scale models due to their \( O(n^3) \) time complexity with Singular Value Decomposition (SVD). To mitigate this issue, we introduce the Matrix Nuclear-Norm, which not only serves as a metric to quantify the data compression proficiency of LLM but also provides a convex approximation of matrix rank to capture both predictive discriminability and diversity. By employing the \( L_{1,2}-norm \) to further approximate the nuclear norm, we can effectively assess the model's information compression capabilities. This approach reduces the time complexity to \( O(n^2) \) and eliminates the need for SVD computation. Consequently, the Matrix Nuclear-Norm achieves speeds 8 to 24 times faster than Matrix Entropy for the CEREBRAS-GPT model as sizes increase from 111M to 6.7B. This performance gap becomes more pronounced with larger models, as validated in tests with other models like Pythia. Additionally, evaluations on benchmarks and model responses confirm that our proposed Matrix Nuclear-Norm is a reliable, scalable, and efficient tool for assessing LLMs' performance, striking a balance between accuracy and computational efficiency. The code is available at https://github.com/MLGroupJLU/MatrixNuclearNorm.

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages the redundancies across problems to obtain significant computational improvements relative to solving the problems sequentially by a conventional algorithm. We demonstrate our fast simultaneous training of generalized linear models (FaSTGLZ) algorithm on a number of real-world datasets, and we run otherwise computationally intensive bootstrapping and permutation test analyses that are typically necessary for obtaining statistically rigorous classification results and meaningful interpretation. Code is freely available at http://liinc.bme.columbia.edu/fastglz.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Denoising diffusion probabilistic models that were initially proposed for realistic image generation have recently shown success in various perception tasks (e.g., object detection and image segmentation) and are increasingly gaining attention in computer vision. However, extending such models to multi-frame human pose estimation is non-trivial due to the presence of the additional temporal dimension in videos. More importantly, learning representations that focus on keypoint regions is crucial for accurate localization of human joints. Nevertheless, the adaptation of the diffusion-based methods remains unclear on how to achieve such objective. In this paper, we present DiffPose, a novel diffusion architecture that formulates video-based human pose estimation as a conditional heatmap generation problem. First, to better leverage temporal information, we propose SpatioTemporal Representation Learner which aggregates visual evidences across frames and uses the resulting features in each denoising step as a condition. In addition, we present a mechanism called Lookup-based MultiScale Feature Interaction that determines the correlations between local joints and global contexts across multiple scales. This mechanism generates delicate representations that focus on keypoint regions. Altogether, by extending diffusion models, we show two unique characteristics from DiffPose on pose estimation task: (i) the ability to combine multiple sets of pose estimates to improve prediction accuracy, particularly for challenging joints, and (ii) the ability to adjust the number of iterative steps for feature refinement without retraining the model. DiffPose sets new state-of-the-art results on three benchmarks: PoseTrack2017, PoseTrack2018, and PoseTrack21.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-DeltaUQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-DeltaUQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

Neural rendering methods have significantly advanced photo-realistic 3D scene rendering in various academic and industrial applications. The recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed combining the benefits of both primitive-based representations and volumetric representations. However, it often leads to heavily redundant Gaussians that try to fit every training view, neglecting the underlying scene geometry. Consequently, the resulting model becomes less robust to significant view changes, texture-less area and lighting effects. We introduce Scaffold-GS, which uses anchor points to distribute local 3D Gaussians, and predicts their attributes on-the-fly based on viewing direction and distance within the view frustum. Anchor growing and pruning strategies are developed based on the importance of neural Gaussians to reliably improve the scene coverage. We show that our method effectively reduces redundant Gaussians while delivering high-quality rendering. We also demonstrates an enhanced capability to accommodate scenes with varying levels-of-detail and view-dependent observations, without sacrificing the rendering speed.

3D Gaussian Splatting (3D-GS) has recently attracted great attention with real-time and photo-realistic renderings. This technique typically takes perspective images as input and optimizes a set of 3D elliptical Gaussians by splatting them onto the image planes, resulting in 2D Gaussians. However, applying 3D-GS to panoramic inputs presents challenges in effectively modeling the projection onto the spherical surface of {360^circ} images using 2D Gaussians. In practical applications, input panoramas are often sparse, leading to unreliable initialization of 3D Gaussians and subsequent degradation of 3D-GS quality. In addition, due to the under-constrained geometry of texture-less planes (e.g., walls and floors), 3D-GS struggles to model these flat regions with elliptical Gaussians, resulting in significant floaters in novel views. To address these issues, we propose 360-GS, a novel 360^{circ} Gaussian splatting for a limited set of panoramic inputs. Instead of splatting 3D Gaussians directly onto the spherical surface, 360-GS projects them onto the tangent plane of the unit sphere and then maps them to the spherical projections. This adaptation enables the representation of the projection using Gaussians. We guide the optimization of 360-GS by exploiting layout priors within panoramas, which are simple to obtain and contain strong structural information about the indoor scene. Our experimental results demonstrate that 360-GS allows panoramic rendering and outperforms state-of-the-art methods with fewer artifacts in novel view synthesis, thus providing immersive roaming in indoor scenarios.

Mixture of Experts (MoE) LLMs face significant obstacles due to their massive parameter scale, which imposes memory, storage, and deployment challenges. Although recent expert merging methods promise greater efficiency by consolidating multiple experts, they are fundamentally hindered by parameter conflicts arising from expert specialization. In this paper, we present Sub-MoE, a novel MoE compression framework via Subspace Expert Merging. Our key insight is to perform joint Singular Value Decomposition (SVD) on concatenated expert weights, reducing conflicting parameters by extracting shared U-matrices while enabling effective merging of the expert-specific V components. Specifically, Sub-MoE consists of two innovative phases: (1) Adaptive Expert Clustering, which groups functionally coherent experts via K-means clustering based on cosine similarity of expert outputs; and (2) Subspace Expert Merging, which first enforces Experts Union Decomposition to derive the shared U-matrix across experts in the same group, then pursues frequency-based merging for individual V-matrices, and finalizes expert reconstruction using the merged V-matrix. In this way, we align and fuse experts in a shared subspace, and can be extended with intra-expert compression for further inference optimization. Extensive experiments on Mixtral, DeepSeek, and Qwen-1.5|3 MoE LLMs demonstrate that our Sub-MoE significantly outperforms existing expert pruning and merging methods. Notably, our Sub-MoE maintains 96\%|86\% of original performance with 25\%|50\% expert reduction on Mixtral-8x7B in zero-shot benchmarks. Code will be released at https://github.com/lliai/MoERazor.

Machine learning models often have uneven performance among subpopulations (a.k.a., groups) in the data distributions. This poses a significant challenge for the models to generalize when the proportions of the groups shift during deployment. To improve robustness to such shifts, existing approaches have developed strategies that train models or perform hyperparameter tuning using the group-labeled data to minimize the worst-case loss over groups. However, a non-trivial amount of high-quality labels is often required to obtain noticeable improvements. Given the costliness of the labels, we propose to adopt a different paradigm to enhance group label efficiency: utilizing the group-labeled data as a target set to optimize the weights of other group-unlabeled data. We introduce Group-robust Sample Reweighting (GSR), a two-stage approach that first learns the representations from group-unlabeled data, and then tinkers the model by iteratively retraining its last layer on the reweighted data using influence functions. Our GSR is theoretically sound, practically lightweight, and effective in improving the robustness to subpopulation shifts. In particular, GSR outperforms the previous state-of-the-art approaches that require the same amount or even more group labels.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

3D Gaussian Splatting (3D GS) has gained popularity due to its faster rendering speed and high-quality novel view synthesis. Some researchers have explored using 3D GS for reconstructing driving scenes. However, these methods often rely on various data types, such as depth maps, 3D boxes, and trajectories of moving objects. Additionally, the lack of annotations for synthesized images limits their direct application in downstream tasks. To address these issues, we propose EGSRAL, a 3D GS-based method that relies solely on training images without extra annotations. EGSRAL enhances 3D GS's capability to model both dynamic objects and static backgrounds and introduces a novel adaptor for auto labeling, generating corresponding annotations based on existing annotations. We also propose a grouping strategy for vanilla 3D GS to address perspective issues in rendering large-scale, complex scenes. Our method achieves state-of-the-art performance on multiple datasets without any extra annotation. For example, the PSNR metric reaches 29.04 on the nuScenes dataset. Moreover, our automated labeling can significantly improve the performance of 2D/3D detection tasks. Code is available at https://github.com/jiangxb98/EGSRAL.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

Unsupervised feature extraction algorithms form one of the most important building blocks in machine learning systems. These algorithms are often adapted to the event-based domain to perform online learning in neuromorphic hardware. However, not designed for the purpose, such algorithms typically require significant simplification during implementation to meet hardware constraints, creating trade offs with performance. Furthermore, conventional feature extraction algorithms are not designed to generate useful intermediary signals which are valuable only in the context of neuromorphic hardware limitations. In this work a novel event-based feature extraction method is proposed that focuses on these issues. The algorithm operates via simple adaptive selection thresholds which allow a simpler implementation of network homeostasis than previous works by trading off a small amount of information loss in the form of missed events that fall outside the selection thresholds. The behavior of the selection thresholds and the output of the network as a whole are shown to provide uniquely useful signals indicating network weight convergence without the need to access network weights. A novel heuristic method for network size selection is proposed which makes use of noise events and their feature representations. The use of selection thresholds is shown to produce network activation patterns that predict classification accuracy allowing rapid evaluation and optimization of system parameters without the need to run back-end classifiers. The feature extraction method is tested on both the N-MNIST benchmarking dataset and a dataset of airplanes passing through the field of view. Multiple configurations with different classifiers are tested with the results quantifying the resultant performance gains at each processing stage.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Precise localization of GUI elements is crucial for the development of GUI agents. Traditional methods rely on bounding box or center-point regression, neglecting spatial interaction uncertainty and visual-semantic hierarchies. Recent methods incorporate attention mechanisms but still face two key issues: (1) ignoring processing background regions causes attention drift from the desired area, and (2) uniform labeling fails to distinguish between center and edges of the target UI element, leading to click imprecision. Inspired by how humans visually process and interact with GUI elements, we propose the Valley-to-Peak (V2P) method to address these issues. To mitigate background distractions, V2P introduces a suppression attention mechanism that minimizes the model's focus on irrelevant regions to highlight the intended region. For the issue of center-edge distinction, V2P applies a Fitts' Law-inspired approach by modeling GUI interactions as 2D Gaussian heatmaps where the weight gradually decreases from the center towards the edges. The weight distribution follows a Gaussian function, with the variance determined by the target's size. Consequently, V2P effectively isolates the target area and teaches the model to concentrate on the most essential point of the UI element. The model trained by V2P achieves the performance with 92.3% and 50.5% on two benchmarks ScreenSpot-v2 and ScreenSpot-Pro. Ablations further confirm each component's contribution, highlighting V2P's generalizability for precise GUI grounding tasks.

Separating a stochastic gravitational wave background (SGWB) from noise is a challenging statistical task. One approach to establishing a detection criterion for the SGWB is using Bayesian evidence. If the evidence ratio (Bayes factor) between models with and without the signal exceeds a certain threshold, the signal is considered detected. We present a formalism to compute the averaged Bayes factor, incorporating instrumental-noise and SGWB uncertainties. As an example, we consider the case of power-law-shaped SGWB in LISA and generate the corresponding bayesian sensitivity curve. Unlike existing methods in the literature, which typically neglect uncertainties in both the signal and noise, our approach provides a reliable and realistic alternative. This flexible framework opens avenues for more robust stochastic gravitational wave background detection across gravitational-wave experiments.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

Recently, a range of neural network-based methods for image rendering have been introduced. One such widely-researched neural radiance field (NeRF) relies on a neural network to represent 3D scenes, allowing for realistic view synthesis from a small number of 2D images. However, most NeRF models are constrained by long training and inference times. In comparison, Gaussian Splatting (GS) is a novel, state-of-the-art technique for rendering points in a 3D scene by approximating their contribution to image pixels through Gaussian distributions, warranting fast training and swift, real-time rendering. A drawback of GS is the absence of a well-defined approach for its conditioning due to the necessity to condition several hundred thousand Gaussian components. To solve this, we introduce the Gaussian Mesh Splatting (GaMeS) model, which allows modification of Gaussian components in a similar way as meshes. We parameterize each Gaussian component by the vertices of the mesh face. Furthermore, our model needs mesh initialization on input or estimated mesh during training. We also define Gaussian splats solely based on their location on the mesh, allowing for automatic adjustments in position, scale, and rotation during animation. As a result, we obtain a real-time rendering of editable GS.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

In this paper, we propose to create animatable avatars for interacting hands with 3D Gaussian Splatting (GS) and single-image inputs. Existing GS-based methods designed for single subjects often yield unsatisfactory results due to limited input views, various hand poses, and occlusions. To address these challenges, we introduce a novel two-stage interaction-aware GS framework that exploits cross-subject hand priors and refines 3D Gaussians in interacting areas. Particularly, to handle hand variations, we disentangle the 3D presentation of hands into optimization-based identity maps and learning-based latent geometric features and neural texture maps. Learning-based features are captured by trained networks to provide reliable priors for poses, shapes, and textures, while optimization-based identity maps enable efficient one-shot fitting of out-of-distribution hands. Furthermore, we devise an interaction-aware attention module and a self-adaptive Gaussian refinement module. These modules enhance image rendering quality in areas with intra- and inter-hand interactions, overcoming the limitations of existing GS-based methods. Our proposed method is validated via extensive experiments on the large-scale InterHand2.6M dataset, and it significantly improves the state-of-the-art performance in image quality. Project Page: https://github.com/XuanHuang0/GuassianHand.

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where eta:=M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X,Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to R\'{e}nyi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of gamma-H\"{o}lder smooth functions, the estimator achieves the MSE rate of O(N^{-2gamma/(gamma+d)}). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.

Despite rapid advancements in the research and deployment of large language models (LLMs), the statistical distribution of model parameters, as well as their influence on initialization, training dynamics, and downstream efficiency, has received surprisingly little attention. A recent work introduced BackSlash, a training-time compression algorithm. It first demonstrated that pre-trained LLM parameters follow generalized Gaussian distributions (GGDs) better. By optimizing GG priors during training, BackSlash can reduce parameters by up to 90\% with minimal performance loss. Building on this foundational insight, we propose a unified, end-to-end framework for LLM optimization based on the GG model. Our contributions are threefold: (1) GG-based initialization scheme that aligns with the statistical structure of trained models, resulting in faster convergence and improved accuracy; (2) DeepShape, a post-training regularization method that reshapes weight distributions to match a GG profile, improving compressibility with minimized degradation in performance; and (3) RF8, a compact and hardware-efficient 8-bit floating-point format designed for GG-distributed-initialized BackSlash training, enabling low-cost inference without compromising accuracy. Experiments across diverse model architectures show that our framework consistently yields smaller and faster models that match or outperform standard training baselines. By grounding LLM development in principled statistical modeling, this work forges a new path toward efficient, scalable, and hardware-aware AI systems. The code is available on our project page: https://huggingface.co/spaces/shifeng3711/gg_prior.

Large Language and Vision-Language Models (LLMs/VLMs) are increasingly used in safety-critical applications, yet their opaque decision-making complicates risk assessment and reliability. Uncertainty quantification (UQ) helps assess prediction confidence and enables abstention when uncertainty is high. Conformal prediction (CP), a leading UQ method, provides statistical guarantees but relies on static thresholds, which fail to adapt to task complexity and evolving data distributions, leading to suboptimal trade-offs in accuracy, coverage, and informativeness. To address this, we propose learnable conformal abstention, integrating reinforcement learning (RL) with CP to optimize abstention thresholds dynamically. By treating CP thresholds as adaptive actions, our approach balances multiple objectives, minimizing prediction set size while maintaining reliable coverage. Extensive evaluations across diverse LLM/VLM benchmarks show our method outperforms Least Ambiguous Classifiers (LAC) and Adaptive Prediction Sets (APS), improving accuracy by up to 3.2%, boosting AUROC for hallucination detection by 22.19%, enhancing uncertainty-guided selective generation (AUARC) by 21.17%, and reducing calibration error by 70%-85%. These improvements hold across multiple models and datasets while consistently meeting the 90% coverage target, establishing our approach as a more effective and flexible solution for reliable decision-making in safety-critical applications. The code is available at: {https://github.com/sinatayebati/vlm-uncertainty}.

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and train it end-to-end to predict MI values. Training is performed on a large meta-dataset of 625,000 synthetic joint distributions with known ground-truth MI. To handle variable sample sizes and dimensions, we employ a two-dimensional attention scheme ensuring permutation invariance across input samples. To quantify uncertainty, we optimize a quantile regression loss, enabling the estimator to approximate the sampling distribution of MI rather than return a single point estimate. This research program departs from prior work by taking a fully empirical route, trading universal theoretical guarantees for flexibility and efficiency. Empirically, the learned estimators largely outperform classical baselines across sample sizes and dimensions, including on joint distributions unseen during training. The resulting quantile-based intervals are well-calibrated and more reliable than bootstrap-based confidence intervals, while inference is orders of magnitude faster than existing neural baselines. Beyond immediate empirical gains, this framework yields trainable, fully differentiable estimators that can be embedded into larger learning pipelines. Moreover, exploiting MI's invariance to invertible transformations, meta-datasets can be adapted to arbitrary data modalities via normalizing flows, enabling flexible training for diverse target meta-distributions.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

3D Gaussian Splatting (3DGS) has emerged as a promising framework for novel view synthesis, boasting rapid rendering speed with high fidelity. However, the substantial Gaussians and their associated attributes necessitate effective compression techniques. Nevertheless, the sparse and unorganized nature of the point cloud of Gaussians (or anchors in our paper) presents challenges for compression. To achieve a compact size, we propose HAC++, which leverages the relationships between unorganized anchors and a structured hash grid, utilizing their mutual information for context modeling. Additionally, HAC++ captures intra-anchor contextual relationships to further enhance compression performance. To facilitate entropy coding, we utilize Gaussian distributions to precisely estimate the probability of each quantized attribute, where an adaptive quantization module is proposed to enable high-precision quantization of these attributes for improved fidelity restoration. Moreover, we incorporate an adaptive masking strategy to eliminate invalid Gaussians and anchors. Overall, HAC++ achieves a remarkable size reduction of over 100X compared to vanilla 3DGS when averaged on all datasets, while simultaneously improving fidelity. It also delivers more than 20X size reduction compared to Scaffold-GS. Our code is available at https://github.com/YihangChen-ee/HAC-plus.

Many skeletal action recognition models use GCNs to represent the human body by 3D body joints connected body parts. GCNs aggregate one- or few-hop graph neighbourhoods, and ignore the dependency between not linked body joints. We propose to form hypergraph to model hyper-edges between graph nodes (e.g., third- and fourth-order hyper-edges capture three and four nodes) which help capture higher-order motion patterns of groups of body joints. We split action sequences into temporal blocks, Higher-order Transformer (HoT) produces embeddings of each temporal block based on (i) the body joints, (ii) pairwise links of body joints and (iii) higher-order hyper-edges of skeleton body joints. We combine such HoT embeddings of hyper-edges of orders 1, ..., r by a novel Multi-order Multi-mode Transformer (3Mformer) with two modules whose order can be exchanged to achieve coupled-mode attention on coupled-mode tokens based on 'channel-temporal block', 'order-channel-body joint', 'channel-hyper-edge (any order)' and 'channel-only' pairs. The first module, called Multi-order Pooling (MP), additionally learns weighted aggregation along the hyper-edge mode, whereas the second module, Temporal block Pooling (TP), aggregates along the temporal block mode. Our end-to-end trainable network yields state-of-the-art results compared to GCN-, transformer- and hypergraph-based counterparts.

Sparse Mixture-of-Experts (SMoE) models represent a significant advancement in large language model (LLM) development through their efficient parameter utilization. These models achieve substantial performance improvements at reduced inference costs. However, the deployment of SMoE models faces constraints from extensive memory requirements of expert components in resource-limited environments. To address these limitations, this paper introduces Hierarchical Clustering for Sparsely activated Mixture of Experts (HC-SMoE), a task-agnostic expert merging framework for parameter reduction without retraining. HC-SMoE introduces a novel hierarchical clustering approach based on expert outputs to ensure merging robustness independent of routing decisions. The proposed output-based clustering method enables effective capture of functional relationships between experts for large-scale architectures. We provide theoretical analysis and comprehensive evaluations across multiple zero-shot language tasks to demonstrate HC-SMoE's effectiveness in state-of-the-art models including Qwen and Mixtral. The experimental results validate HC-SMoE's superior performance and practical applicability for real-world deployments.

Universal medical image segmentation models have emerged as a promising paradigm due to their strong generalizability across diverse tasks, showing great potential for a wide range of clinical applications. This potential has been partly driven by the success of general-purpose vision models such as the Segment Anything Model (SAM), which has inspired the development of various fine-tuned variants for medical segmentation tasks. However, fine-tuned variants like MedSAM are trained on comparatively limited medical imaging data that often suffers from heterogeneity, scarce annotations, and distributional shifts. These challenges limit their ability to generalize across a wide range of medical segmentation tasks. In this regard, we propose MedSAMix, a training-free model merging method that integrates the strengths of both generalist models (e.g., SAM) and specialist models (e.g., MedSAM) for medical image segmentation. In contrast to traditional model merging approaches that rely on manual configuration and often result in suboptimal outcomes, we propose a zero-order optimization method to automatically discover optimal layer-wise merging solutions. Furthermore, for clinical applications, we develop two regimes to meet the demand of domain-specificity and generalizability in different scenarios by single-task optimization and multi-objective optimization respectively. Extensive evaluations on 25 medical segmentation tasks demonstrate that MedSAMix effectively mitigates model bias and consistently improves performance in both domain-specific accuracy and generalization, achieving improvements of 6.67% on specialized tasks and 4.37% on multi-task evaluations.

The Mixtures-of-Experts (MoE) model is a widespread distributed and integrated learning method for large language models (LLM), which is favored due to its ability to sparsify and expand models efficiently. However, the performance of MoE is limited by load imbalance and high latency of All-To-All communication, along with relatively redundant computation owing to large expert capacity. Load imbalance may result from existing routing policies that consistently tend to select certain experts. The frequent inter-node communication in the All-To-All procedure also significantly prolongs the training time. To alleviate the above performance problems, we propose a novel routing strategy that combines load balance and locality by converting partial inter-node communication to that of intra-node. Notably, we elucidate that there is a minimum threshold for expert capacity, calculated through the maximal angular deviation between the gating weights of the experts and the assigned tokens. We port these modifications on the PanGu-Sigma model based on the MindSpore framework with multi-level routing and conduct experiments on Ascend clusters. The experiment results demonstrate that the proposed LocMoE reduces training time per epoch by 12.68% to 22.24% compared to classical routers, such as hash router and switch router, without impacting the model accuracy.

Model compression has emerged as a mainstream solution to reduce memory usage and computational overhead. This paper presents Group Quantization and Sparse Acceleration (GQSA), a novel compression technique tailored for LLMs. Traditional methods typically focus exclusively on either quantization or sparsification, but relying on a single strategy often results in significant performance loss at high compression rates. In contrast, GQSA integrates quantization and sparsification in a tightly coupled manner, leveraging GPU-friendly structured group sparsity and quantization for efficient acceleration. Building upon system-algorithm co-design principles, we propose a two-stage sparse optimization strategy that ensures the performance superiority of the compressed model. On the engine side, we introduce a "task-centric" parallel strategy, which, to the best of our knowledge, is the first application in the domain of sparse computing. Compared to the traditional 2:4 sparse method, the GQSA offers a more flexible and adjustable sparsity rate, as well as a higher weight compression rate, and is efficiently compatible with weight-only quantization methods. Experimental results demonstrate that, under the GQSA W4S50% compression setting, the model's accuracy surpasses that of both 2:4 pruning and W2 quantization. Furthermore, at the inference level, GQSA outperforms W2 by 1.26times and 2:4 pruning by 2.35times in terms of speed.

3D Gaussian Splatting (3DGS) integrates the strengths of primitive-based representations and volumetric rendering techniques, enabling real-time, high-quality rendering. However, 3DGS models typically overfit to single-scene training and are highly sensitive to the initialization of Gaussian ellipsoids, heuristically derived from Structure from Motion (SfM) point clouds, which limits both generalization and practicality. To address these limitations, we propose GS-Net, a generalizable, plug-and-play 3DGS module that densifies Gaussian ellipsoids from sparse SfM point clouds, enhancing geometric structure representation. To the best of our knowledge, GS-Net is the first plug-and-play 3DGS module with cross-scene generalization capabilities. Additionally, we introduce the CARLA-NVS dataset, which incorporates additional camera viewpoints to thoroughly evaluate reconstruction and rendering quality. Extensive experiments demonstrate that applying GS-Net to 3DGS yields a PSNR improvement of 2.08 dB for conventional viewpoints and 1.86 dB for novel viewpoints, confirming the method's effectiveness and robustness.

Mixture of Experts (MoE) architectures have significantly increased computational efficiency in both research and real-world applications of large-scale machine learning models. However, their scalability and efficiency under memory constraints remain relatively underexplored. In this work, we present joint scaling laws for dense and MoE models, incorporating key factors such as the number of active parameters, dataset size, and the number of experts. Our findings provide a principled framework for selecting the optimal MoE configuration under fixed memory and compute budgets. Surprisingly, we show that MoE models can be more memory-efficient than dense models, contradicting conventional wisdom. To derive and validate the theoretical predictions of our scaling laws, we conduct over 280 experiments with up to 2.7B active parameters and up to 5B total parameters. These results offer actionable insights for designing and deploying MoE models in practical large-scale training scenarios.

Modeling, understanding, and reconstructing the real world are crucial in XR/VR. Recently, 3D Gaussian Splatting (3D-GS) methods have shown remarkable success in modeling and understanding 3D scenes. Similarly, various 4D representations have demonstrated the ability to capture the dynamics of the 4D world. However, there is a dearth of research focusing on segmentation within 4D representations. In this paper, we propose Segment Any 4D Gaussians (SA4D), one of the first frameworks to segment anything in the 4D digital world based on 4D Gaussians. In SA4D, an efficient temporal identity feature field is introduced to handle Gaussian drifting, with the potential to learn precise identity features from noisy and sparse input. Additionally, a 4D segmentation refinement process is proposed to remove artifacts. Our SA4D achieves precise, high-quality segmentation within seconds in 4D Gaussians and shows the ability to remove, recolor, compose, and render high-quality anything masks. More demos are available at: https://jsxzs.github.io/sa4d/.

Neural Radiance Fields (NeRF) and Gaussian Splatting (GS) have recently transformed 3D scene representation and rendering. NeRF achieves high-fidelity novel view synthesis by learning volumetric representations through neural networks, but its implicit encoding makes editing and physical interaction challenging. In contrast, GS represents scenes as explicit collections of Gaussian primitives, enabling real-time rendering, faster training, and more intuitive manipulation. This explicit structure has made GS particularly well-suited for interactive editing and integration with physics-based simulation. In this paper, we introduce GENIE (Gaussian Encoding for Neural Radiance Fields Interactive Editing), a hybrid model that combines the photorealistic rendering quality of NeRF with the editable and structured representation of GS. Instead of using spherical harmonics for appearance modeling, we assign each Gaussian a trainable feature embedding. These embeddings are used to condition a NeRF network based on the k nearest Gaussians to each query point. To make this conditioning efficient, we introduce Ray-Traced Gaussian Proximity Search (RT-GPS), a fast nearest Gaussian search based on a modified ray-tracing pipeline. We also integrate a multi-resolution hash grid to initialize and update Gaussian features. Together, these components enable real-time, locality-aware editing: as Gaussian primitives are repositioned or modified, their interpolated influence is immediately reflected in the rendered output. By combining the strengths of implicit and explicit representations, GENIE supports intuitive scene manipulation, dynamic interaction, and compatibility with physical simulation, bridging the gap between geometry-based editing and neural rendering. The code can be found under (https://github.com/MikolajZielinski/genie)

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty lambda and the limiting subsample aspect ratio phi_s (the ratio of the feature size to the subsample size), we characterize contours in the (lambda, phi_s)-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

Anchor-based 3D Gaussian splatting (3D-GS) exploits anchor features in 3D Gaussian prediction, which has achieved impressive 3D rendering quality with reduced Gaussian redundancy. On the other hand, it often encounters the dilemma among anchor features, model size, and rendering quality - large anchor features lead to large 3D models and high-quality rendering whereas reducing anchor features degrades Gaussian attribute prediction which leads to clear artifacts in the rendered textures and geometries. We design SOGS, an anchor-based 3D-GS technique that introduces second-order anchors to achieve superior rendering quality and reduced anchor features and model size simultaneously. Specifically, SOGS incorporates covariance-based second-order statistics and correlation across feature dimensions to augment features within each anchor, compensating for the reduced feature size and improving rendering quality effectively. In addition, it introduces a selective gradient loss to enhance the optimization of scene textures and scene geometries, leading to high-quality rendering with small anchor features. Extensive experiments over multiple widely adopted benchmarks show that SOGS achieves superior rendering quality in novel view synthesis with clearly reduced model size.

Medical imaging analysis plays a critical role in the diagnosis and treatment of various medical conditions. This paper focuses on chest X-ray images and their corresponding radiological reports. It presents a new model that learns a joint X-ray image & report representation. The model is based on a novel alignment scheme between the visual data and the text, which takes into account both local and global information. Furthermore, the model integrates domain-specific information of two types -- lateral images and the consistent visual structure of chest images. Our representation is shown to benefit three types of retrieval tasks: text-image retrieval, class-based retrieval, and phrase-grounding.

The problems of detecting and recovering planted structures/subgraphs in Erdős-Rényi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques. However, prior work has largely focused on specific ad hoc planted structures and inferential settings, while a general theory has remained elusive. In this paper, we bridge this gap by investigating the detection of an arbitrary planted subgraph Γ= Γ_n in an Erdős-Rényi random graph G(n, q_n), where the edge probability within Γ is p_n. We examine both the statistical and computational aspects of this problem and establish the following results. In the dense regime, where the edge probabilities p_n and q_n are fixed, we tightly characterize the information-theoretic and computational thresholds for detecting Γ, and provide conditions under which a computational-statistical gap arises. Most notably, these thresholds depend on Γ only through its number of edges, maximum degree, and maximum subgraph density. Our lower and upper bounds are general and apply to any value of p_n and q_n as functions of n. Accordingly, we also analyze the sparse regime where q_n = Θ(n^{-α}) and p_n-q_n =Θ(q_n), with αin[0,2], as well as the critical regime where p_n=1-o(1) and q_n = Θ(n^{-α}), both of which have been widely studied, for specific choices of Γ. For these regimes, we show that our bounds are tight for all planted subgraphs investigated in the literature thus farand many more. Finally, we identify conditions under which detection undergoes sharp phase transition, where the boundaries at which algorithms succeed or fail shift abruptly as a function of q_n.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

We present GS-ProCams, the first Gaussian Splatting-based framework for projector-camera systems (ProCams). GS-ProCams is not only view-agnostic but also significantly enhances the efficiency of projection mapping (PM) that requires establishing geometric and radiometric mappings between the projector and the camera. Previous CNN-based ProCams are constrained to a specific viewpoint, limiting their applicability to novel perspectives. In contrast, NeRF-based ProCams support view-agnostic projection mapping, however, they require an additional co-located light source and demand significant computational and memory resources. To address this issue, we propose GS-ProCams that employs 2D Gaussian for scene representations, and enables efficient view-agnostic ProCams applications. In particular, we explicitly model the complex geometric and photometric mappings of ProCams using projector responses, the projection surface's geometry and materials represented by Gaussians, and the global illumination component. Then, we employ differentiable physically-based rendering to jointly estimate them from captured multi-view projections. Compared to state-of-the-art NeRF-based methods, our GS-ProCams eliminates the need for additional devices, achieving superior ProCams simulation quality. It also uses only 1/10 of the GPU memory for training and is 900 times faster in inference speed. Please refer to our project page for the code and dataset: https://realqingyue.github.io/GS-ProCams/.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Traditionally, monocular 3D human pose estimation employs a machine learning model to predict the most likely 3D pose for a given input image. However, a single image can be highly ambiguous and induces multiple plausible solutions for the 2D-3D lifting step which results in overly confident 3D pose predictors. To this end, we propose DiffPose, a conditional diffusion model, that predicts multiple hypotheses for a given input image. In comparison to similar approaches, our diffusion model is straightforward and avoids intensive hyperparameter tuning, complex network structures, mode collapse, and unstable training. Moreover, we tackle a problem of the common two-step approach that first estimates a distribution of 2D joint locations via joint-wise heatmaps and consecutively approximates them based on first- or second-moment statistics. Since such a simplification of the heatmaps removes valid information about possibly correct, though labeled unlikely, joint locations, we propose to represent the heatmaps as a set of 2D joint candidate samples. To extract information about the original distribution from these samples we introduce our embedding transformer that conditions the diffusion model. Experimentally, we show that DiffPose slightly improves upon the state of the art for multi-hypothesis pose estimation for simple poses and outperforms it by a large margin for highly ambiguous poses.

Multi-subject fMRI studies are challenging due to the high variability of both brain anatomy and functional brain topographies across participants. An effective way of aggregating multi-subject fMRI data is to extract a shared representation that filters out unwanted variability among subjects. Some recent work has implemented probabilistic models to extract a shared representation in task fMRI. In the present work, we improve upon these models by incorporating temporal information in the common latent structures. We introduce a new model, Shared Gaussian Process Factor Analysis (S-GPFA), that discovers shared latent trajectories and subject-specific functional topographies, while modelling temporal correlation in fMRI data. We demonstrate the efficacy of our model in revealing ground truth latent structures using simulated data, and replicate experimental performance of time-segment matching and inter-subject similarity on the publicly available Raider and Sherlock datasets. We further test the utility of our model by analyzing its learned model parameters in the large multi-site SPINS dataset, on a social cognition task from participants with and without schizophrenia.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

Sparse models, including sparse Mixture-of-Experts (MoE) models, have emerged as an effective approach for scaling Transformer models. However, they often suffer from computational inefficiency since a significant number of parameters are unnecessarily involved in computations via multiplying values by zero or low activation values. To address this issue, we present \tool, a novel MoE designed to enhance both the efficacy and efficiency of sparse MoE models. \tool leverages small experts and a threshold-based router to enable tokens to selectively engage only essential parameters. Our extensive experiments on language modeling and machine translation tasks demonstrate that \tool can enhance model performance while decreasing the computation load at MoE layers by over 50\% without sacrificing performance. Furthermore, we present the versatility of \tool by applying it to dense models, enabling sparse computation during inference. We provide a comprehensive analysis and make our code available at https://anonymous.4open.science/r/XMoE.

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

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO_{2} emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from O(k^2 p^2) to O(p^2), significantly improving scalability.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

3D Gaussian Splatting (3DGS) has garnered significant attention in robotics for its explicit, high fidelity dense scene representation, demonstrating strong potential for robotic applications. However, 3DGS-based methods in robotics primarily focus on static scenes, with limited attention to the dynamic scene changes essential for long-term service robots. These robots demand sustained task execution and efficient scene updates-challenges current approaches fail to meet. To address these limitations, we propose GS-LTS (Gaussian Splatting for Long-Term Service), a 3DGS-based system enabling indoor robots to manage diverse tasks in dynamic environments over time. GS-LTS detects scene changes (e.g., object addition or removal) via single-image change detection, employs a rule-based policy to autonomously collect multi-view observations, and efficiently updates the scene representation through Gaussian editing. Additionally, we propose a simulation-based benchmark that automatically generates scene change data as compact configuration scripts, providing a standardized, user-friendly evaluation benchmark. Experimental results demonstrate GS-LTS's advantages in reconstruction, navigation, and superior scene updates-faster and higher quality than the image training baseline-advancing 3DGS for long-term robotic operations. Code and benchmark are available at: https://vipl-vsu.github.io/3DGS-LTS.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

In applications such as elderly care, dementia anti-wandering and pandemic control, it is important to ensure that people are within a predefined area for their safety and well-being. We propose GEM, a practical, semi-supervised Geofencing system with network EMbedding, which is based only on ambient radio frequency (RF) signals. GEM models measured RF signal records as a weighted bipartite graph. With access points on one side and signal records on the other, it is able to precisely capture the relationships between signal records. GEM then learns node embeddings from the graph via a novel bipartite network embedding algorithm called BiSAGE, based on a Bipartite graph neural network with a novel bi-level SAmple and aggreGatE mechanism and non-uniform neighborhood sampling. Using the learned embeddings, GEM finally builds a one-class classification model via an enhanced histogram-based algorithm for in-out detection, i.e., to detect whether the user is inside the area or not. This model also keeps on improving with newly collected signal records. We demonstrate through extensive experiments in diverse environments that GEM shows state-of-the-art performance with up to 34% improvement in F-score. BiSAGE in GEM leads to a 54% improvement in F-score, as compared to the one without BiSAGE.

We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e., decision-boundary)-awareness of the softmax function. The resulting SDM activation function provides strong signals of the relative epistemic (reducible) predictive uncertainty. We use this novel behavior to further address the complementary HCI problem of mapping the output to human-interpretable summary statistics over relevant partitions of a held-out calibration set. Estimates of prediction-conditional uncertainty are obtained via a parsimonious learned transform over the class-conditional empirical CDFs of the output of a final-layer SDM activation function. For decision-making and as an intrinsic model check, estimates of class-conditional accuracy are obtained by further partitioning the high-probability regions of this calibrated output into class-conditional, region-specific CDFs. The uncertainty estimates from SDM calibration are remarkably robust to test-time distribution shifts and out-of-distribution inputs; incorporate awareness of the effective sample size; provide estimates of uncertainty from the learning and data splitting processes; and are well-suited for selective classification and conditional branching for additional test-time compute based on the predictive uncertainty, as for selective LLM generation, routing, and composition over multiple models and retrieval. Finally, we construct SDM networks, LLMs with uncertainty-aware verification and interpretability-by-exemplar as intrinsic properties. We provide open-source software implementing these results.

For privacy and security concerns, the need to erase unwanted information from pre-trained vision models is becoming evident nowadays. In real-world scenarios, erasure requests originate at any time from both users and model owners. These requests usually form a sequence. Therefore, under such a setting, selective information is expected to be continuously removed from a pre-trained model while maintaining the rest. We define this problem as continual forgetting and identify two key challenges. (i) For unwanted knowledge, efficient and effective deleting is crucial. (ii) For remaining knowledge, the impact brought by the forgetting procedure should be minimal. To address them, we propose Group Sparse LoRA (GS-LoRA). Specifically, towards (i), we use LoRA modules to fine-tune the FFN layers in Transformer blocks for each forgetting task independently, and towards (ii), a simple group sparse regularization is adopted, enabling automatic selection of specific LoRA groups and zeroing out the others. GS-LoRA is effective, parameter-efficient, data-efficient, and easy to implement. We conduct extensive experiments on face recognition, object detection and image classification and demonstrate that GS-LoRA manages to forget specific classes with minimal impact on other classes. Codes will be released on https://github.com/bjzhb666/GS-LoRA.

Implicit Neural Representation (INR) has been successfully employed for Arbitrary-scale Super-Resolution (ASR). However, INR-based models need to query the multi-layer perceptron module numerous times and render a pixel in each query, resulting in insufficient representation capability and computational efficiency. Recently, Gaussian Splatting (GS) has shown its advantages over INR in both visual quality and rendering speed in 3D tasks, which motivates us to explore whether GS can be employed for the ASR task. However, directly applying GS to ASR is exceptionally challenging because the original GS is an optimization-based method through overfitting each single scene, while in ASR we aim to learn a single model that can generalize to different images and scaling factors. We overcome these challenges by developing two novel techniques. Firstly, to generalize GS for ASR, we elaborately design an architecture to predict the corresponding image-conditioned Gaussians of the input low-resolution image in a feed-forward manner. Each Gaussian can fit the shape and direction of an area of complex textures, showing powerful representation capability. Secondly, we implement an efficient differentiable 2D GPU/CUDA-based scale-aware rasterization to render super-resolved images by sampling discrete RGB values from the predicted continuous Gaussians. Via end-to-end training, our optimized network, namely GSASR, can perform ASR for any image and unseen scaling factors. Extensive experiments validate the effectiveness of our proposed method.

As consumer Virtual Reality (VR) and Mixed Reality (MR) technologies gain momentum, there's a growing focus on the development of engagements with 3D virtual content. Unfortunately, traditional techniques for content creation, editing, and interaction within these virtual spaces are fraught with difficulties. They tend to be not only engineering-intensive but also require extensive expertise, which adds to the frustration and inefficiency in virtual object manipulation. Our proposed VR-GS system represents a leap forward in human-centered 3D content interaction, offering a seamless and intuitive user experience. By developing a physical dynamics-aware interactive Gaussian Splatting in a Virtual Reality setting, and constructing a highly efficient two-level embedding strategy alongside deformable body simulations, VR-GS ensures real-time execution with highly realistic dynamic responses. The components of our Virtual Reality system are designed for high efficiency and effectiveness, starting from detailed scene reconstruction and object segmentation, advancing through multi-view image in-painting, and extending to interactive physics-based editing. The system also incorporates real-time deformation embedding and dynamic shadow casting, ensuring a comprehensive and engaging virtual experience.Our project page is available at: https://yingjiang96.github.io/VR-GS/.

As large language models (LLMs) scale, the question is not only how large they become, but how much of their capacity is effectively utilized. Existing scaling laws relate model size to loss, yet overlook how components exploit their latent space. We study feed-forward networks (FFNs) and recast width selection as a spectral utilization problem. Using a lightweight diagnostic suite -- Hard Rank (participation ratio), Soft Rank (Shannon rank), Spectral Concentration, and the composite Spectral Utilization Index (SUI) -- we quantify how many latent directions are meaningfully activated across LLaMA, GPT-2, and nGPT families. Our key finding is an asymmetric spectral scaling law: soft rank follows an almost perfect power law with FFN width, while hard rank grows only sublinearly and with high variance. This asymmetry suggests that widening FFNs mostly adds low-energy tail directions, while dominant-mode subspaces saturate early. Moreover, at larger widths, variance further collapses into a narrow subspace, leaving much of the latent space under-utilized. These results recast FFN width selection as a principled trade-off between tail capacity and dominant-mode capacity, offering concrete guidance for inference-efficient LLM design.

Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to accurately resemble almost all characteristics inherited in multilevel data, including the marginal distributions, dependence structures, regression links, random intercepts and random slopes. In a particular case where the multilevel data is hierarchical, we further show that a nested version of the MMoE universally approximates a broad range of dependence structures of the random effects among different factor levels.

Recently, 3D Gaussian splatting (3D-GS) has gained popularity in novel-view scene synthesis. It addresses the challenges of lengthy training times and slow rendering speeds associated with Neural Radiance Fields (NeRFs). Through rapid, differentiable rasterization of 3D Gaussians, 3D-GS achieves real-time rendering and accelerated training. They, however, demand substantial memory resources for both training and storage, as they require millions of Gaussians in their point cloud representation for each scene. We present a technique utilizing quantized embeddings to significantly reduce memory storage requirements and a coarse-to-fine training strategy for a faster and more stable optimization of the Gaussian point clouds. Our approach results in scene representations with fewer Gaussians and quantized representations, leading to faster training times and rendering speeds for real-time rendering of high resolution scenes. We reduce memory by more than an order of magnitude all while maintaining the reconstruction quality. We validate the effectiveness of our approach on a variety of datasets and scenes preserving the visual quality while consuming 10-20x less memory and faster training/inference speed. Project page and code is available https://efficientgaussian.github.io

In sports analytics, accurately capturing both the 3D locations and rotations of body joints is essential for understanding an athlete's biomechanics. While Human Mesh Recovery (HMR) models can estimate joint rotations, they often exhibit lower accuracy in joint localization compared to 3D Human Pose Estimation (HPE) models. Recent work addressed this limitation by combining a 3D HPE model with inverse kinematics (IK) to estimate both joint locations and rotations. However, IK is computationally expensive. To overcome this, we propose a novel 2D-to-3D uplifting model that directly estimates 3D human poses, including joint rotations, in a single forward pass. We investigate multiple rotation representations, loss functions, and training strategies - both with and without access to ground truth rotations. Our models achieve state-of-the-art accuracy in rotation estimation, are 150 times faster than the IK-based approach, and surpass HMR models in joint localization precision.