Daily Papers

We update predictions for observables in the "delicate" D3/anti-D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the zeta power spectrum often cannot be modelled as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction fNL ~ -(5/12)(ns-1) if nt << 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNLeq| ~ 75 at kt/3 = 0.002/Mpc. It has been suggested that the quasi-single field inflation ("QSFI") mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of "shape" running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.

Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA(p,d,q) models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes N in {100, 200, 500, 1000} and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with N=500, relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and χ^2(3) innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry (|γ_3| geq 0.5) and N geq 200, with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typical of financial markets, macroeconomic indicators, and industrial measurements. Future extensions include seasonal SARIMA models, GARCH integration, and automatic order selection.

A major goal of ongoing and future cosmological surveys of the large-scale structure is to measure local type primordial non-Gaussianity in the galaxy power spectrum through the scale-dependent bias. General relativistic effects have been shown to be degenerate with this measurement, therefore requiring a non-Newtonian approach. In this work, we develop a consistent framework to compute integrated effects, including lensing convergence, time delay, and integrated Sachs--Wolfe, along with the local relativistic projection and wide-separation corrections in the multipoles of the power spectrum. We show that, for a Euclid-like Hα-line galaxy survey and a MegaMapper-like Lyman-break galaxy survey, ignoring these effects leads to a bias on the best fit measurement of the amplitude of primordial non-Gaussianity, f_{rm NL}, of around 3,σ and 20 , σ respectively. When we include these corrections, the uncertainty in our knowledge of the luminosity function leads to further uncertainty in our measurement of f_{rm NL}. In this work, we show that this degeneracy can be partly mitigated by using a bright-faint multi-tracer analysis, where the observed galaxy sample is subdivided into two separate populations based on luminosity, which provides a 15--20% improvement on the forecasted constraints of local type f_{rm NL}. In addition, we present a novel calculation of the full multi-tracer covariance with the inclusion of wide-separation corrections~-- all of these results are implemented in the Python code CosmoWAP.

Recorrupted-to-Recorrupted (R2R) has emerged as a methodology for training deep networks for image restoration in a self-supervised manner from noisy measurement data alone, demonstrating equivalence in expectation to the supervised squared loss in the case of Gaussian noise. However, its effectiveness with non-Gaussian noise remains unexplored. In this paper, we propose Generalized R2R (GR2R), extending the R2R framework to handle a broader class of noise distribution as additive noise like log-Rayleigh and address the natural exponential family including Poisson and Gamma noise distributions, which play a key role in many applications including low-photon imaging and synthetic aperture radar. We show that the GR2R loss is an unbiased estimator of the supervised loss and that the popular Stein's unbiased risk estimator can be seen as a special case. A series of experiments with Gaussian, Poisson, and Gamma noise validate GR2R's performance, showing its effectiveness compared to other self-supervised methods.

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduce Flow Annealing Posterior Sampling (FAPS), to our knowledge the first function-space posterior sampling framework that unifies stochastic-process regression and PDE inverse problems. Built on pretrained function-space flow-matching priors, FAPS enables likelihood-guided posterior inference from sparse and noisy observations, supports variable query discretizations, and avoids explicit prior-density evaluation. Its Langevin correction uses a low-rank covariance preconditioner to exploit dominant function-space correlations across discretizations. Across Gaussian and non-Gaussian stochastic-process regression benchmarks and diverse PDE inverse problems, FAPS produces coherent posterior samples with accurate uncertainty quantification, significantly outperforming existing functional regression baselines and achieving competitive or better PDE noisy inverse performance than diffusion-based posterior samplers while reducing test-time sampling cost.

Non-linear interactions during inflation generate non-Gaussianities in the distribution of primordial curvature. In many theories, the physics is scale-invariant, such that the induced three-point function depends solely on a dimensionless shape function S(x,y)sim k^6B_ζ(kx,ky,k). To confront such models with observations, one typically builds specialized estimators for each shape, then applies them to cosmic microwave background datasets at significant computational expense. In this Letter, we take a different approach, directly reconstructing S(x,y) from observations using an efficient logarithmically-binned estimator in primordial-space (motivated by the modal program). Applying this to temperature and polarization maps from Planck, we obtain high-resolution shape measurements across the full (x,y)-plane, including squeezed limits. Our approach is close-to-optimal, highly interpretable, and preserves the information content on (optimally-analyzed) standard templates within approx 10%; moreover, we can use it to assess the scale-dependence of our constraints, finding that Planck is sensitive to approx 6 e-folds of non-Gaussian evolution with a peak sensitivity around 0.1h,Mpc^{-1}. Since we work directly in shape-space, data and theory can be compared in milliseconds. As an example, we perform a search for massive particle exchange using a suite of over 20,000 theoretical templates computed with exact bootstrap methods (for the first time) across a wide range of masses, spins, and sound-speeds; the spin-two analysis yields a maximum significance of 2.6σ. Our approach can be used to probe a wide range of scale-invariant models in orders-of-magnitude less time than with direct estimators, allowing the inflationary paradigm to be explored in new ways.

This study introduces a novel and interpretable model, DiffVox, for matching vocal effects in music production. DiffVox, short for ``Differentiable Vocal Fx", integrates parametric equalisation, dynamic range control, delay, and reverb with efficient differentiable implementations to enable gradient-based optimisation for parameter estimation. Vocal presets are retrieved from two datasets, comprising 70 tracks from MedleyDB and 365 tracks from a private collection. Analysis of parameter correlations highlights strong relationships between effects and parameters, such as the high-pass and low-shelf filters often behaving together to shape the low end, and the delay time correlates with the intensity of the delayed signals. Principal component analysis reveals connections to McAdams' timbre dimensions, where the most crucial component modulates the perceived spaciousness while the secondary components influence spectral brightness. Statistical testing confirms the non-Gaussian nature of the parameter distribution, highlighting the complexity of the vocal effects space. These initial findings on the parameter distributions set the foundation for future research in vocal effects modelling and automatic mixing. Our source code and datasets are accessible at https://github.com/SonyResearch/diffvox.

PGD adversarial training, the standard robustness method, can reduce Jacobian Frobenius norm yet worsen clean-input geometry (e.g., TDI 1.336 vs. ERM 1.093). We show this is not an implementation artifact but a theorem-level consequence of supervised learning. We prove that any encoder minimizing supervised loss must retain non-zero sensitivity along directions correlated with training labels, including directions that are nuisance at test time. This holds across proper scoring rules, architectures, and dataset sizes. We call this the geometric blind spot of supervised learning. This theorem unifies four empirical phenomena often treated separately: non-robust features, texture bias, corruption fragility, and the robustness-accuracy tradeoff. It also explains why suppressing sensitivity in one adversarial direction can redistribute sensitivity elsewhere. We introduce Trajectory Deviation Index (TDI), a diagnostic of geometric isotropy. Unlike CKA, intrinsic dimension, or Jacobian Frobenius norm alone, TDI captures the failure mode above. In our experiments, PGD attains low Frobenius norm but high TDI, while PMH attains the lowest TDI with one additional training term and no architectural changes. Across seven tasks, BERT/SST-2, and ImageNet ViT-B/16 (backbone family underlying CLIP/DINO/SAM), the blind spot is measurable and repairable. It appears at foundation-model scale, worsens with model scale and task-specific fine-tuning, and is substantially reduced by PMH. PMH also leads on non-Gaussian corruption types (blur/brightness/contrast) without corruption-specific training.

The surging demand for cloud computing resources, driven by the rapid growth of sophisticated large-scale models and data centers, underscores the critical importance of efficient and adaptive resource allocation. As major tech enterprises deploy massive infrastructures with thousands of GPUs, existing cloud platforms still struggle with low resource utilization due to key challenges: capturing hierarchical indicator structures, modeling non-Gaussian distributions, and decision-making under uncertainty. To address these challenges, we propose HRAMONY, an adaptive Hierarchical Attention-based Resource Modeling and Decision-Making System. HARMONY combines hierarchical multi-indicator distribution forecasting and uncertainty-aware Bayesian decision-making. It introduces a novel hierarchical attention mechanism that comprehensively models complex inter-indicator dependencies, enabling accurate predictions that can adapt to evolving environment states. By transforming Gaussian projections into adaptive non-Gaussian distributions via Normalizing Flows. Crucially, HARMONY leverages the full predictive distributions in an adaptive Bayesian process, proactively incorporating uncertainties to optimize resource allocation while robustly meeting SLA constraints under varying conditions. Extensive evaluations across four large-scale cloud datasets demonstrate HARMONY's state-of-the-art performance, significantly outperforming nine established methods. A month-long real-world deployment validated HARMONY's substantial practical impact, realizing over 35,000 GPU hours in savings and translating to $100K+ in cost reduction, showcasing its remarkable economic value through adaptive, uncertainty-aware scaling. Our code is available at https://github.com/Floating-LY/HARMONY1.

Recent Pulsar Timing Array datasets provide compelling evidence for a nano-Hertz gravitational-wave background, but robust detection requires characterizing statistical fluctuations of the Hellings-Downs (HD) correlation expected from a finite population of discrete sources. Building on the variance calculation of Allen (2023), we derive the third central moment (skewness) of the HD correlation for a single unpolarized point source and an ensemble of many interfering point sources in the confusion-noise regime. To isolate the intrinsic non-Gaussianity of the background, we extend the pulsar-averaging formalism to third order by introducing a three-point averaged correlation function, which allows us to define the cosmic skewness. We find that the skewness remains non-zero in the large-source-number limit and is controlled by a new geometric three-point function. These results suggest that incorporating higher-order moments could provide additional information on source discreteness beyond standard Gaussian analyses.

Large nonlinear recurrent neural networks with random couplings generate high-dimensional, potentially chaotic activity whose structure is of interest in neuroscience and other fields. A fundamental object encoding the collective structure of this activity is the N times N covariance matrix. Prior analytical work on the covariance matrix has been limited to low-dimensional summary statistics. Recent work proposed an ansatz in which, at large N, the covariance matrix for a typical quenched realization takes the same form as that of a linear network with the same couplings, driven by independent noise, with DMFT order parameters setting the transfer function and the noise spectrum. Here, we derive this ansatz using the two-site cavity method, providing two derivations with complementary perspectives. The first decomposes each unit's activity into a linear response to its local field and a nonlinear residual, and shows that cross-covariances between residuals at distinct sites are strongly suppressed, so the residuals act as independent noise driving a linear network. The second derives a self-consistent matrix equation for the covariance matrix. A naive Gaussian closure for the joint statistics of local fields at distinct sites misses cross terms that, in a linear network, would be generated by an external drive. The cavity method recovers these terms from non-Gaussian contributions, revealing an emergent external drive. Higher-order cross-site moments follow a Wick-like decomposition into products of pairwise covariances at leading order, reducing them to the linear-equivalent form. We verify the predictions in simulations. These results extend linear equivalence from feedforward high-dimensional nonlinear systems, where the activations are independent of the weights, to recurrent networks, where the activations are correlated with the couplings that generate them.

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.

In this paper, we introduce DiQP; a novel Transformer-Diffusion model for restoring 8K video quality degraded by codec compression. To the best of our knowledge, our model is the first to consider restoring the artifacts introduced by various codecs (AV1, HEVC) by Denoising Diffusion without considering additional noise. This approach allows us to model the complex, non-Gaussian nature of compression artifacts, effectively learning to reverse the degradation. Our architecture combines the power of Transformers to capture long-range dependencies with an enhanced windowed mechanism that preserves spatiotemporal context within groups of pixels across frames. To further enhance restoration, the model incorporates auxiliary "Look Ahead" and "Look Around" modules, providing both future and surrounding frame information to aid in reconstructing fine details and enhancing overall visual quality. Extensive experiments on different datasets demonstrate that our model outperforms state-of-the-art methods, particularly for high-resolution videos such as 4K and 8K, showcasing its effectiveness in restoring perceptually pleasing videos from highly compressed sources.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation spacex2014an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtiltsx2014known as glitchesx2014from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide several illustrative examples. We find that VQOL provides a a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.

Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for Gaussian and mildly non-Gaussian fields. In this paper we extend the formulae to composite fields which are sums of two fields and explicitly derive the expressions for the sum of uncorrelated mildly non-Gaussian and Gaussian fields. These formulae are applicable to observed data which is usually a sum of the true signal and one or more secondary fields that can be either noise, or some residual contaminating signal. Our formulae provide explicit quantification of the effect of the secondary field on the morphology and statistical nature of the true signal. As examples, we apply the formulae to determine how the presence of Gaussian noise can bias the morphological properties and statistical nature of Gaussian and non-Gaussian CMB temperature maps.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for K classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (k leq 10), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37\% sharper prediction intervals at 90\% coverage, and uniquely produces adaptive intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Finding interpretable directions in language-model representations is critical for understanding and controlling model behavior. Sparse autoencoders (SAEs) have become the standard tool for this purpose, but using them as the default first lens often requires training, storing, and evaluating large overcomplete dictionaries. This bottleneck limits rapid exploration and raises a fundamental question: how much interpretable structure is already visible from activation geometry before training another neural dictionary? Our intuition is simple: many interpretable directions are selective on tokens, and these directions should look less Gaussian than random directions. We therefore revisit independent component analysis (ICA), a classical method for finding non-Gaussian directions, as a compact lens for language-model interpretability. We find that ICA has been underestimated for LLM interpretability, because prior uses often relied on off-the-shelf ICA implementations that are brittle on LLM activations and lacked systematic tools for inspecting and evaluating the recovered directions. To bridge these gaps, we introduce ICALens, the first practical workflow for stable, efficient, and auditable ICA analysis of LLM representations. It combines an optimized GPU-parallel FastICA pipeline with LLM-specific stability recipes and better fitting diagnostics, enabling efficient and reliable layer-wise analysis. Across GPT-2 Small, Gemma 2 2B, and Qwen 3.5 2B Base, ICALens efficiently recovers compact, human-interpretable directions without per-layer gradient-based dictionary training. On SAEBench, ICA is competitive with public SAEs in sparse probing and outperforms them in targeted probe perturbation under small-to-medium budgets. These results suggest that ICA should not be viewed as a weak baseline, but as an efficient and complementary first lens for exploring language-model representations.

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Neural HMMs are a type of neural transducer recently proposed for sequence-to-sequence modelling in text-to-speech. They combine the best features of classic statistical speech synthesis and modern neural TTS, requiring less data and fewer training updates, and are less prone to gibberish output caused by neural attention failures. In this paper, we combine neural HMM TTS with normalising flows for describing the highly non-Gaussian distribution of speech acoustics. The result is a powerful, fully probabilistic model of durations and acoustics that can be trained using exact maximum likelihood. Compared to dominant flow-based acoustic models, our approach integrates autoregression for improved modelling of long-range dependences such as utterance-level prosody. Experiments show that a system based on our proposal gives more accurate pronunciations and better subjective speech quality than comparable methods, whilst retaining the original advantages of neural HMMs. Audio examples and code are available at https://shivammehta25.github.io/OverFlow/

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

A representation that scrambles the true degrees of freedom of the world cannot support reliable planning or compositional generalization. We prove that LeJEPA (alignment plus Gaussian regularization) linearly recovers the world's latent variables from nonlinear observations, a property known as linear identifiability, in a broad class of worlds where latents evolve under stationary, additive-noise transitions. Our main result is that among all such worlds, the Gaussian is the unique latent distribution for which this guarantee holds. The forward direction rests on a spectral decomposition in which each degree of nonlinearity is strictly penalized by alignment, making the linear map the optimum; the converse rules out every non-Gaussian alternative. We further prove an approximate identifiability result where the guarantee degrades gracefully, and show that linear, orthogonal identifiability enables optimal latent-space planning. We validate the theory with experiments ranging from 2D examples to 1024-dimensional latents, including distributional ablations and pixel-based robotic control. Our theory turns an empirically successful recipe into a mathematical guarantee, providing the foundation for building World Models that provably recover the structure of the world.

Expressive generative policies such as diffusion and flow models are appealing for MaxEnt online reinforcement learning because of their ability to model multimodal and highly non-Gaussian action distributions. However, training effective soft generative policies faces two obstacles that often arise together. First, marginal action densities are often unavailable, so existing methods typically rely on entropy bounds, heuristic proxies or approximations. Second, iterative shared-parameter samplers raise inference cost and require backpropagation through time over repeated network evaluations, increasing memory cost and destabilizing policy optimization. These obstacles motivate us to seek a generative policy that exposes a tractable MaxEnt objective while requiring only a single sampled actor forward pass for action generation. To this end, we propose soft generative actor-critic (SoftGAC), whose actor defines a stochastic bridge from a fixed base latent to a terminal action latent in pre-tanh space. This structured bridge allows us to lift the MaxEnt objective as an analytically tractable path-wise relative-entropy objective against a high-entropy reference process. In practical finite-step implementation, this relative entropy reduces exactly to sampled transition control energy and thus provides principled soft regularization. Moreover, we keep the single-pass actor lightweight by using small step-specific bridge transitions, each evaluated only once per sampled action, while maintaining a parameter budget comparable to strong actor baselines. Extensive experiments on challenging continuous-control benchmarks show that SoftGAC attains higher or competitive returns than strong generative policy baselines, including diffusion and flow-matching policies, while staying in the low-latency regime of one-pass actors and showing considerable improvements in the compute-return tradeoff.

We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models, (2) smooth the resulting estimates along the bivariate functional domain, and (3) compute confidence bands using either an analytic approach for Gaussian data or a cluster bootstrap for Gaussian or non-Gaussian data. Simulation studies demonstrate that the proposed method achieves accurate estimation and valid inference, while substantially reducing computational burden compared to existing approaches. Methods are motivated by a physical activity intervention trial in older adults where high-dimensional wearable data were collected longitudinally across multiple visits. Our applications reveal significant increases in physical activity in the morning using interpersonal intervention strategies, but not intrapersonal strategies. The proposed methods are implemented in an R package.

The redshifted 21-cm signal is a unique probe of the early universe, particularly the Epoch of Reionization (EoR). While the 21-cm power spectrum has been the primary statistic for parameter inference, it fails to capture the non-Gaussian information in the signal, motivating the use of higher-order statistics such as the bispectrum. We perform a rigorous cross-simulation validation to infer the mean neutral hydrogen fraction (x_{HI}) by training a Bayesian neural network on 21cmFAST simulations and applying it to mock observations generated by ReionYuga code. Our analysis spans six redshifts and includes realistic SKA system noise and cosmic variance, calculated from 50 statistically independent realizations. We find that the bispectrum adds useful information, but the improvement is moderate, with constraints tightened by sim 1.4times the power-spectrum only case. The cross-simulation analysis also identifies a persistent systematic discrepancy between inferred and true values that often exceeds the statistical uncertainties, implying that modeling uncertainty remains the dominant limitation. Our results, therefore, indicate that the highly stringent constraints obtained in same-code validation studies may be overly optimistic, and mitigating cross-model systematics is crucial for robust parameter inference in the SKA era.

Channel state information (CSI) prediction is a promising strategy for ensuring reliable and efficient operation of massive multiple-input multiple-output (mMIMO) systems by providing timely downlink (DL) CSI. While deep learning-based methods have advanced beyond conventional model-driven and statistical approaches, they remain limited in robustness to practical non-Gaussian noise, generalization across diverse channel conditions, and computational efficiency. This paper introduces CSI-4CAST, a hybrid deep learning architecture that integrates 4 key components, i.e., Convolutional neural network residuals, Adaptive correction layers, ShuffleNet blocks, and Transformers, to efficiently capture both local and long-range dependencies in CSI prediction. To enable rigorous evaluation, this work further presents a comprehensive benchmark, CSI-RRG for Regular, Robustness and Generalization testing, which includes more than 300,000 samples across 3,060 realistic scenarios for both TDD and FDD systems. The dataset spans multiple channel models, a wide range of delay spreads and user velocities, and diverse noise types and intensity degrees. Experimental results show that CSI-4CAST achieves superior prediction accuracy with substantially lower computational cost, outperforming baselines in 88.9% of TDD scenarios and 43.8% of FDD scenario, the best performance among all evaluated models, while reducing FLOPs by 5x and 3x compared to LLM4CP, the strongest baseline. In addition, evaluation over CSI-RRG provides valuable insights into how different channel factors affect the performance and generalization capability of deep learning models. Both the dataset (https://huggingface.co/CSI-4CAST) and evaluation protocols (https://github.com/AI4OPT/CSI-4CAST) are publicly released to establish a standardized benchmark and to encourage further research on robust and efficient CSI prediction.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative modelling, we propose Neural Diffusion Processes (NDPs), a novel approach that learns to sample from a rich distribution over functions through its finite marginals. By introducing a custom attention block we are able to incorporate properties of stochastic processes, such as exchangeability, directly into the NDP's architecture. We empirically show that NDPs can capture functional distributions close to the true Bayesian posterior, demonstrating that they can successfully emulate the behaviour of Gaussian processes and surpass the performance of neural processes. NDPs enable a variety of downstream tasks, including regression, implicit hyperparameter marginalisation, non-Gaussian posterior prediction and global optimisation.

In a recent paper Juodis and Reese (2022) (JR) show that the application of the CD test proposed by Pesaran (2004) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This paper considers the same problem but from a different perspective, and shows that the standard CD test remains valid if the latent factors are weak in the sense the strength is less than half. In the case where latent factors are strong, we propose a bias-corrected version, CD*, which is shown to be asymptotically standard normal under the null of error cross-sectional independence and have power against network type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD* test are investigated by Monte Carlo experiments and are shown to have the correct size for strong and weak factors as well as for Gaussian and non-Gaussian errors. In contrast, it is found that JR's test tends to over-reject in the case of panels with non-Gaussian errors, and has low power against spatial network alternatives. In an empirical application, using the CD* test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the U.S., even after the effects of latent factors are filtered out.

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

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k_2=2k_1=0.2 h/Mpc by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

We introduce GaussianAvatar-Editor, an innovative framework for text-driven editing of animatable Gaussian head avatars that can be fully controlled in expression, pose, and viewpoint. Unlike static 3D Gaussian editing, editing animatable 4D Gaussian avatars presents challenges related to motion occlusion and spatial-temporal inconsistency. To address these issues, we propose the Weighted Alpha Blending Equation (WABE). This function enhances the blending weight of visible Gaussians while suppressing the influence on non-visible Gaussians, effectively handling motion occlusion during editing. Furthermore, to improve editing quality and ensure 4D consistency, we incorporate conditional adversarial learning into the editing process. This strategy helps to refine the edited results and maintain consistency throughout the animation. By integrating these methods, our GaussianAvatar-Editor achieves photorealistic and consistent results in animatable 4D Gaussian editing. We conduct comprehensive experiments across various subjects to validate the effectiveness of our proposed techniques, which demonstrates the superiority of our approach over existing methods. More results and code are available at: [Project Link](https://xiangyueliu.github.io/GaussianAvatar-Editor/).

Reconstructing deformable tissues from endoscopic videos is essential in many downstream surgical applications. However, existing methods suffer from slow rendering speed, greatly limiting their practical use. In this paper, we introduce EndoGaussian, a real-time endoscopic scene reconstruction framework built on 3D Gaussian Splatting (3DGS). By integrating the efficient Gaussian representation and highly-optimized rendering engine, our framework significantly boosts the rendering speed to a real-time level. To adapt 3DGS for endoscopic scenes, we propose two strategies, Holistic Gaussian Initialization (HGI) and Spatio-temporal Gaussian Tracking (SGT), to handle the non-trivial Gaussian initialization and tissue deformation problems, respectively. In HGI, we leverage recent depth estimation models to predict depth maps of input binocular/monocular image sequences, based on which pixels are re-projected and combined for holistic initialization. In SPT, we propose to model surface dynamics using a deformation field, which is composed of an efficient encoding voxel and a lightweight deformation decoder, allowing for Gaussian tracking with minor training and rendering burden. Experiments on public datasets demonstrate our efficacy against prior SOTAs in many aspects, including better rendering speed (195 FPS real-time, 100times gain), better rendering quality (37.848 PSNR), and less training overhead (within 2 min/scene), showing significant promise for intraoperative surgery applications. Code is available at: https://yifliu3.github.io/EndoGaussian/.

Real-world single image denoising is crucial and practical in computer vision. Bayesian inversions combined with score priors now have proven effective for single image denoising but are limited to white Gaussian noise. Moreover, applying existing score-based methods for real-world denoising requires not only the explicit train of score priors on the target domain but also the careful design of sampling procedures for posterior inference, which is complicated and impractical. To address these limitations, we propose a score priors-guided deep variational inference, namely ScoreDVI, for practical real-world denoising. By considering the deep variational image posterior with a Gaussian form, score priors are extracted based on easily accessible minimum MSE Non-i.i.d Gaussian denoisers and variational samples, which in turn facilitate optimizing the variational image posterior. Such a procedure adaptively applies cheap score priors to denoising. Additionally, we exploit a Non-i.i.d Gaussian mixture model and variational noise posterior to model the real-world noise. This scheme also enables the pixel-wise fusion of multiple image priors and variational image posteriors. Besides, we develop a noise-aware prior assignment strategy that dynamically adjusts the weight of image priors in the optimization. Our method outperforms other single image-based real-world denoising methods and achieves comparable performance to dataset-based unsupervised methods.

In-context learning (ICL) in large language models (LLMs) is a striking phenomenon, yet its underlying mechanisms remain only partially understood. Previous work connects linear self-attention (LSA) to gradient descent (GD), this connection has primarily been established under simplified conditions with zero-mean Gaussian priors and zero initialization for GD. However, subsequent studies have challenged this simplified view by highlighting its overly restrictive assumptions, demonstrating instead that under conditions such as multi-layer or nonlinear attention, self-attention performs optimization-like inference, akin to but distinct from GD. We investigate how multi-head LSA approximates GD under more realistic conditions specifically when incorporating non-zero Gaussian prior means in linear regression formulations of ICL. We first extend multi-head LSA embedding matrix by introducing an initial estimation of the query, referred to as the initial guess. We prove an upper bound on the number of heads needed for ICL linear regression setup. Our experiments confirm this result and further observe that a performance gap between one-step GD and multi-head LSA persists. To address this gap, we introduce yq-LSA, a simple generalization of single-head LSA with a trainable initial guess yq. We theoretically establish the capabilities of yq-LSA and provide experimental validation on linear regression tasks, thereby extending the theory that bridges ICL and GD. Finally, inspired by our findings in the case of linear regression, we consider widespread LLMs augmented with initial guess capabilities, and show that their performance is improved on a semantic similarity task.

We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered. Notably, we allow the unlabeled samples to deviate slightly (in total variation sense) from the in-domain distribution. The core idea behind our framework is to combine Distributionally Robust Optimization (DRO) with self-supervised training. As a result, we also leverage efficient polynomial-time algorithms for the training stage. From a theoretical standpoint, we apply our framework on the classification problem of a mixture of two Gaussians in R^d, where in addition to the m independent and labeled samples from the true distribution, a set of n (usually with ngg m) out of domain and unlabeled samples are given as well. Using only the labeled data, it is known that the generalization error can be bounded by proptoleft(d/mright)^{1/2}. However, using our method on both isotropic and non-isotropic Gaussian mixture models, one can derive a new set of analytically explicit and non-asymptotic bounds which show substantial improvement on the generalization error compared to ERM. Our results underscore two significant insights: 1) out-of-domain samples, even when unlabeled, can be harnessed to narrow the generalization gap, provided that the true data distribution adheres to a form of the ``cluster assumption", and 2) the semi-supervised learning paradigm can be regarded as a special case of our framework when there are no distributional shifts. We validate our claims through experiments conducted on a variety of synthetic and real-world datasets.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of pre-conditioned GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of nonlinear functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

Accurate 3D tracking in highly deformable scenes with occlusions and shadows can facilitate new applications in robotics, augmented reality, and generative AI. However, tracking under these conditions is extremely challenging due to the ambiguity that arises with large deformations, shadows, and occlusions. We introduce MD-Splatting, an approach for simultaneous 3D tracking and novel view synthesis, using video captures of a dynamic scene from various camera poses. MD-Splatting builds on recent advances in Gaussian splatting, a method that learns the properties of a large number of Gaussians for state-of-the-art and fast novel view synthesis. MD-Splatting learns a deformation function to project a set of Gaussians with non-metric, thus canonical, properties into metric space. The deformation function uses a neural-voxel encoding and a multilayer perceptron (MLP) to infer Gaussian position, rotation, and a shadow scalar. We enforce physics-inspired regularization terms based on local rigidity, conservation of momentum, and isometry, which leads to trajectories with smaller trajectory errors. MD-Splatting achieves high-quality 3D tracking on highly deformable scenes with shadows and occlusions. Compared to state-of-the-art, we improve 3D tracking by an average of 23.9 %, while simultaneously achieving high-quality novel view synthesis. With sufficient texture such as in scene 6, MD-Splatting achieves a median tracking error of 3.39 mm on a cloth of 1 x 1 meters in size. Project website: https://md-splatting.github.io/.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.

Reconstructing dynamic objects from monocular videos is a severely underconstrained and challenging problem, and recent work has approached it in various directions. However, owing to the ill-posed nature of this problem, there has been no solution that can provide consistent, high-quality novel views from camera positions that are significantly different from the training views. In this work, we introduce Neural Parametric Gaussians (NPGs) to take on this challenge by imposing a two-stage approach: first, we fit a low-rank neural deformation model, which then is used as regularization for non-rigid reconstruction in the second stage. The first stage learns the object's deformations such that it preserves consistency in novel views. The second stage obtains high reconstruction quality by optimizing 3D Gaussians that are driven by the coarse model. To this end, we introduce a local 3D Gaussian representation, where temporally shared Gaussians are anchored in and deformed by local oriented volumes. The resulting combined model can be rendered as radiance fields, resulting in high-quality photo-realistic reconstructions of the non-rigidly deforming objects, maintaining 3D consistency across novel views. We demonstrate that NPGs achieve superior results compared to previous works, especially in challenging scenarios with few multi-view cues.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

We propose the first 4D tracking and mapping method that jointly performs camera localization and non-rigid surface reconstruction via differentiable rendering. Our approach captures 4D scenes from an online stream of color images with depth measurements or predictions by jointly optimizing scene geometry, appearance, dynamics, and camera ego-motion. Although natural environments exhibit complex non-rigid motions, 4D-SLAM remains relatively underexplored due to its inherent challenges; even with 2.5D signals, the problem is ill-posed because of the high dimensionality of the optimization space. To overcome these challenges, we first introduce a SLAM method based on Gaussian surface primitives that leverages depth signals more effectively than 3D Gaussians, thereby achieving accurate surface reconstruction. To further model non-rigid deformations, we employ a warp-field represented by a multi-layer perceptron (MLP) and introduce a novel camera pose estimation technique along with surface regularization terms that facilitate spatio-temporal reconstruction. In addition to these algorithmic challenges, a significant hurdle in 4D SLAM research is the lack of reliable ground truth and evaluation protocols, primarily due to the difficulty of 4D capture using commodity sensors. To address this, we present a novel open synthetic dataset of everyday objects with diverse motions, leveraging large-scale object models and animation modeling. In summary, we open up the modern 4D-SLAM research by introducing a novel method and evaluation protocols grounded in modern vision and rendering techniques.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

This paper presents Non-Attentive Tacotron based on the Tacotron 2 text-to-speech model, replacing the attention mechanism with an explicit duration predictor. This improves robustness significantly as measured by unaligned duration ratio and word deletion rate, two metrics introduced in this paper for large-scale robustness evaluation using a pre-trained speech recognition model. With the use of Gaussian upsampling, Non-Attentive Tacotron achieves a 5-scale mean opinion score for naturalness of 4.41, slightly outperforming Tacotron 2. The duration predictor enables both utterance-wide and per-phoneme control of duration at inference time. When accurate target durations are scarce or unavailable in the training data, we propose a method using a fine-grained variational auto-encoder to train the duration predictor in a semi-supervised or unsupervised manner, with results almost as good as supervised training.

We introduce an approach that creates animatable human avatars from monocular videos using 3D Gaussian Splatting (3DGS). Existing methods based on neural radiance fields (NeRFs) achieve high-quality novel-view/novel-pose image synthesis but often require days of training, and are extremely slow at inference time. Recently, the community has explored fast grid structures for efficient training of clothed avatars. Albeit being extremely fast at training, these methods can barely achieve an interactive rendering frame rate with around 15 FPS. In this paper, we use 3D Gaussian Splatting and learn a non-rigid deformation network to reconstruct animatable clothed human avatars that can be trained within 30 minutes and rendered at real-time frame rates (50+ FPS). Given the explicit nature of our representation, we further introduce as-isometric-as-possible regularizations on both the Gaussian mean vectors and the covariance matrices, enhancing the generalization of our model on highly articulated unseen poses. Experimental results show that our method achieves comparable and even better performance compared to state-of-the-art approaches on animatable avatar creation from a monocular input, while being 400x and 250x faster in training and inference, respectively.

Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, largescale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers the potential to overcome this limitation by embedding data into exponentially large Hilbert spaces, capturing complex correlations that remain inaccessible to classical computing approaches. In this paper, we propose a Distributed Quantum Gaussian Process (DQGP) method in a multiagent setting to enhance modeling capabilities and scalability. To address the challenging non-Euclidean optimization problem, we develop a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model. We evaluate the efficacy of our method through numerical experiments conducted on a quantum simulator in classical hardware. We use real-world, non-stationary elevation datasets of NASA's Shuttle Radar Topography Mission and synthetic datasets generated by Quantum Gaussian Processes. Beyond modeling advantages, our framework highlights potential computational speedups that quantum hardware may provide, particularly in Gaussian processes and distributed optimization.

High-quality scene reconstruction and novel view synthesis based on Gaussian Splatting (3DGS) typically require steady, high-quality photographs, often impractical to capture with handheld cameras. We present a method that adapts to camera motion and allows high-quality scene reconstruction with handheld video data suffering from motion blur and rolling shutter distortion. Our approach is based on detailed modelling of the physical image formation process and utilizes velocities estimated using visual-inertial odometry (VIO). Camera poses are considered non-static during the exposure time of a single image frame and camera poses are further optimized in the reconstruction process. We formulate a differentiable rendering pipeline that leverages screen space approximation to efficiently incorporate rolling-shutter and motion blur effects into the 3DGS framework. Our results with both synthetic and real data demonstrate superior performance in mitigating camera motion over existing methods, thereby advancing 3DGS in naturalistic settings.

We propose Relightable Full-Body Gaussian Codec Avatars, a new approach for modeling relightable full-body avatars with fine-grained details including face and hands. The unique challenge for relighting full-body avatars lies in the large deformations caused by body articulation and the resulting impact on appearance caused by light transport. Changes in body pose can dramatically change the orientation of body surfaces with respect to lights, resulting in both local appearance changes due to changes in local light transport functions, as well as non-local changes due to occlusion between body parts. To address this, we decompose the light transport into local and non-local effects. Local appearance changes are modeled using learnable zonal harmonics for diffuse radiance transfer. Unlike spherical harmonics, zonal harmonics are highly efficient to rotate under articulation. This allows us to learn diffuse radiance transfer in a local coordinate frame, which disentangles the local radiance transfer from the articulation of the body. To account for non-local appearance changes, we introduce a shadow network that predicts shadows given precomputed incoming irradiance on a base mesh. This facilitates the learning of non-local shadowing between the body parts. Finally, we use a deferred shading approach to model specular radiance transfer and better capture reflections and highlights such as eye glints. We demonstrate that our approach successfully models both the local and non-local light transport required for relightable full-body avatars, with a superior generalization ability under novel illumination conditions and unseen poses.

Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian embeddings are provably advantageous. In particular, they induce stable tracking of time-varying targets for linear readouts, achieve maximal entropy under a fixed variance budget, and encourage a balanced use of all representational dimensions--all of which enable agents to be more adaptive and stable. Building on this insight, we propose the use of Sketched Isotropic Gaussian Regularization for shaping representations toward an isotropic Gaussian distribution during training. We demonstrate empirically, over a variety of domains, that this simple and computationally inexpensive method improves performance under non-stationarity while reducing representation collapse, neuron dormancy, and training instability.

We propose the Multi-Head Gaussian Adaptive Attention Mechanism (GAAM), a novel probabilistic attention framework, and the Gaussian Adaptive Transformer (GAT), designed to enhance information aggregation across multiple modalities, including Speech, Text and Vision. GAAM integrates learnable mean and variance into its attention mechanism, implemented in a Multi-Headed framework enabling it to collectively model any Probability Distribution for dynamic recalibration of feature significance. This method demonstrates significant improvements, especially with highly non-stationary data, surpassing the state-of-the-art attention techniques in model performance (up to approximately +20% in accuracy) by identifying key elements within the feature space. GAAM's compatibility with dot-product-based attention models and relatively low number of parameters showcases its adaptability and potential to boost existing attention frameworks. Empirically, GAAM exhibits superior adaptability and efficacy across a diverse range of tasks, including emotion recognition in speech, image classification, and text classification, thereby establishing its robustness and versatility in handling multi-modal data. Furthermore, we introduce the Importance Factor (IF), a new learning-based metric that enhances the explainability of models trained with GAAM-based methods. Overall, GAAM represents an advancement towards development of better performing and more explainable attention models across multiple modalities.

Given sparse observations of buoy velocities, oceanographers are interested in reconstructing ocean currents away from the buoys and identifying divergences in a current vector field. As a first and modular step, we focus on the time-stationary case - for instance, by restricting to short time periods. Since we expect current velocity to be a continuous but highly non-linear function of spatial location, Gaussian processes (GPs) offer an attractive model. But we show that applying a GP with a standard stationary kernel directly to buoy data can struggle at both current reconstruction and divergence identification, due to some physically unrealistic prior assumptions. To better reflect known physical properties of currents, we propose to instead put a standard stationary kernel on the divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. We show that, because this decomposition relates to the original vector field just via mixed partial derivatives, we can still perform inference given the original data with only a small constant multiple of additional computational expense. We illustrate the benefits of our method with theory and experiments on synthetic and real ocean data.

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.

Mixture of experts (MoE) has a well-principled finite mixture model construction for prediction, allowing the gating network (mixture weights) to learn from the predictors (explanatory variables) together with the experts' network (mixture component densities). We investigate the estimation properties of MoEs in a high-dimensional setting, where the number of predictors is much larger than the sample size, for which the literature lacks computational and especially theoretical results. We consider the class of finite MoE models with softmax gating functions and Gaussian regression experts, and focus on the theoretical properties of their l_1-regularized estimation via the Lasso. We provide a lower bound on the regularization parameter of the Lasso penalty that ensures an l_1-oracle inequality is satisfied by the Lasso estimator according to the Kullback--Leibler loss. We further state an l_1-ball oracle inequality for the l_1-penalized maximum likelihood estimator from the model selection.

Ultrasound imaging is a cornerstone of non-invasive clinical diagnostics, yet its limited field of view poses challenges for novel view synthesis. We present UltraGS, a real-time framework that adapts Gaussian Splatting to sensorless ultrasound imaging by integrating explicit radiance fields with lightweight, physics-inspired acoustic modeling. UltraGS employs depth-aware Gaussian primitives with learnable fields of view to improve geometric consistency under unconstrained probe motion, and introduces PD Rendering, a differentiable acoustic operator that combines low-order spherical harmonics with first-order wave effects for efficient intensity synthesis. We further present a clinical ultrasound dataset acquired under real-world scanning protocols. Extensive evaluations across three datasets demonstrate that UltraGS establishes a new performance-efficiency frontier, achieving state-of-the-art results in PSNR (up to 29.55) and SSIM (up to 0.89) while achieving real-time synthesis at 64.69 fps on a single GPU. The code and dataset are open-sourced at: https://github.com/Bean-Young/UltraGS.

3D Gaussian Splatting (3D-GS) has demonstrated exceptional capabilities in 3D scene reconstruction and novel view synthesis. However, its training heavily depends on high-quality, sharp images and accurate camera poses. Fulfilling these requirements can be challenging in non-ideal real-world scenarios, where motion-blurred images are commonly encountered in high-speed moving cameras or low-light environments that require long exposure times. To address these challenges, we introduce Event Stream Assisted Gaussian Splatting (EvaGaussians), a novel approach that integrates event streams captured by an event camera to assist in reconstructing high-quality 3D-GS from blurry images. Capitalizing on the high temporal resolution and dynamic range offered by the event camera, we leverage the event streams to explicitly model the formation process of motion-blurred images and guide the deblurring reconstruction of 3D-GS. By jointly optimizing the 3D-GS parameters and recovering camera motion trajectories during the exposure time, our method can robustly facilitate the acquisition of high-fidelity novel views with intricate texture details. We comprehensively evaluated our method and compared it with previous state-of-the-art deblurring rendering methods. Both qualitative and quantitative comparisons demonstrate that our method surpasses existing techniques in restoring fine details from blurry images and producing high-fidelity novel views.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

We have recently seen tremendous progress in photo-real human modeling and rendering. Yet, efficiently rendering realistic human performance and integrating it into the rasterization pipeline remains challenging. In this paper, we present HiFi4G, an explicit and compact Gaussian-based approach for high-fidelity human performance rendering from dense footage. Our core intuition is to marry the 3D Gaussian representation with non-rigid tracking, achieving a compact and compression-friendly representation. We first propose a dual-graph mechanism to obtain motion priors, with a coarse deformation graph for effective initialization and a fine-grained Gaussian graph to enforce subsequent constraints. Then, we utilize a 4D Gaussian optimization scheme with adaptive spatial-temporal regularizers to effectively balance the non-rigid prior and Gaussian updating. We also present a companion compression scheme with residual compensation for immersive experiences on various platforms. It achieves a substantial compression rate of approximately 25 times, with less than 2MB of storage per frame. Extensive experiments demonstrate the effectiveness of our approach, which significantly outperforms existing approaches in terms of optimization speed, rendering quality, and storage overhead.

The modeling and manipulation of 3D scenes captured from the real world are pivotal in various applications, attracting growing research interest. While previous works on editing have achieved interesting results through manipulating 3D meshes, they often require accurately reconstructed meshes to perform editing, which limits their application in 3D content generation. To address this gap, we introduce a novel single-image-driven 3D scene editing approach based on 3D Gaussian Splatting, enabling intuitive manipulation via directly editing the content on a 2D image plane. Our method learns to optimize the 3D Gaussians to align with an edited version of the image rendered from a user-specified viewpoint of the original scene. To capture long-range object deformation, we introduce positional loss into the optimization process of 3D Gaussian Splatting and enable gradient propagation through reparameterization. To handle occluded 3D Gaussians when rendering from the specified viewpoint, we build an anchor-based structure and employ a coarse-to-fine optimization strategy capable of handling long-range deformation while maintaining structural stability. Furthermore, we design a novel masking strategy to adaptively identify non-rigid deformation regions for fine-scale modeling. Extensive experiments show the effectiveness of our method in handling geometric details, long-range, and non-rigid deformation, demonstrating superior editing flexibility and quality compared to previous approaches.

We present a latent diffusion model over 3D scenes, that can be trained using only 2D image data. To achieve this, we first design an autoencoder that maps multi-view images to 3D Gaussian splats, and simultaneously builds a compressed latent representation of these splats. Then, we train a multi-view diffusion model over the latent space to learn an efficient generative model. This pipeline does not require object masks nor depths, and is suitable for complex scenes with arbitrary camera positions. We conduct careful experiments on two large-scale datasets of complex real-world scenes -- MVImgNet and RealEstate10K. We show that our approach enables generating 3D scenes in as little as 0.2 seconds, either from scratch, from a single input view, or from sparse input views. It produces diverse and high-quality results while running an order of magnitude faster than non-latent diffusion models and earlier NeRF-based generative models

Effective and efficient tokenization plays an important role in image representation and generation. Conventional methods, constrained by uniform 2D/1D grid tokenization, are inflexible to represent regions with varying shapes and textures and at different locations, limiting their efficacy of feature representation. In this work, we propose GPSToken, a novel Gaussian Parameterized Spatially-adaptive Tokenization framework, to achieve non-uniform image tokenization by leveraging parametric 2D Gaussians to dynamically model the shape, position, and textures of different image regions. We first employ an entropy-driven algorithm to partition the image into texture-homogeneous regions of variable sizes. Then, we parameterize each region as a 2D Gaussian (mean for position, covariance for shape) coupled with texture features. A specialized transformer is trained to optimize the Gaussian parameters, enabling continuous adaptation of position/shape and content-aware feature extraction. During decoding, Gaussian parameterized tokens are reconstructed into 2D feature maps through a differentiable splatting-based renderer, bridging our adaptive tokenization with standard decoders for end-to-end training. GPSToken disentangles spatial layout (Gaussian parameters) from texture features to enable efficient two-stage generation: structural layout synthesis using lightweight networks, followed by structure-conditioned texture generation. Experiments demonstrate the state-of-the-art performance of GPSToken, which achieves rFID and FID scores of 0.65 and 1.50 on image reconstruction and generation tasks using 128 tokens, respectively. Codes and models of GPSToken can be found at https://github.com/xtudbxk/GPSToken{https://github.com/xtudbxk/GPSToken}.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

4D head capture aims to generate dynamic topological meshes and corresponding texture maps from videos, which is widely utilized in movies and games for its ability to simulate facial muscle movements and recover dynamic textures in pore-squeezing. The industry often adopts the method involving multi-view stereo and non-rigid alignment. However, this approach is prone to errors and heavily reliant on time-consuming manual processing by artists. To simplify this process, we propose Topo4D, a novel framework for automatic geometry and texture generation, which optimizes densely aligned 4D heads and 8K texture maps directly from calibrated multi-view time-series images. Specifically, we first represent the time-series faces as a set of dynamic 3D Gaussians with fixed topology in which the Gaussian centers are bound to the mesh vertices. Afterward, we perform alternative geometry and texture optimization frame-by-frame for high-quality geometry and texture learning while maintaining temporal topology stability. Finally, we can extract dynamic facial meshes in regular wiring arrangement and high-fidelity textures with pore-level details from the learned Gaussians. Extensive experiments show that our method achieves superior results than the current SOTA face reconstruction methods both in the quality of meshes and textures. Project page: https://xuanchenli.github.io/Topo4D/.

We present SplatFace, a novel Gaussian splatting framework designed for 3D human face reconstruction without reliance on accurate pre-determined geometry. Our method is designed to simultaneously deliver both high-quality novel view rendering and accurate 3D mesh reconstructions. We incorporate a generic 3D Morphable Model (3DMM) to provide a surface geometric structure, making it possible to reconstruct faces with a limited set of input images. We introduce a joint optimization strategy that refines both the Gaussians and the morphable surface through a synergistic non-rigid alignment process. A novel distance metric, splat-to-surface, is proposed to improve alignment by considering both the Gaussian position and covariance. The surface information is also utilized to incorporate a world-space densification process, resulting in superior reconstruction quality. Our experimental analysis demonstrates that the proposed method is competitive with both other Gaussian splatting techniques in novel view synthesis and other 3D reconstruction methods in producing 3D face meshes with high geometric precision.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

We study the problem of privately estimating the parameters of d-dimensional Gaussian Mixture Models (GMMs) with k components. For this, we develop a technique to reduce the problem to its non-private counterpart. This allows us to privatize existing non-private algorithms in a blackbox manner, while incurring only a small overhead in the sample complexity and running time. As the main application of our framework, we develop an (varepsilon, delta)-differentially private algorithm to learn GMMs using the non-private algorithm of Moitra and Valiant [MV10] as a blackbox. Consequently, this gives the first sample complexity upper bound and first polynomial time algorithm for privately learning GMMs without any boundedness assumptions on the parameters. As part of our analysis, we prove a tight (up to a constant factor) lower bound on the total variation distance of high-dimensional Gaussians which can be of independent interest.

Facial expression and hand motions are necessary to express our emotions and interact with the world. Nevertheless, most of the 3D human avatars modeled from a casually captured video only support body motions without facial expressions and hand motions.In this work, we present ExAvatar, an expressive whole-body 3D human avatar learned from a short monocular video. We design ExAvatar as a combination of the whole-body parametric mesh model (SMPL-X) and 3D Gaussian Splatting (3DGS). The main challenges are 1) a limited diversity of facial expressions and poses in the video and 2) the absence of 3D observations, such as 3D scans and RGBD images. The limited diversity in the video makes animations with novel facial expressions and poses non-trivial. In addition, the absence of 3D observations could cause significant ambiguity in human parts that are not observed in the video, which can result in noticeable artifacts under novel motions. To address them, we introduce our hybrid representation of the mesh and 3D Gaussians. Our hybrid representation treats each 3D Gaussian as a vertex on the surface with pre-defined connectivity information (i.e., triangle faces) between them following the mesh topology of SMPL-X. It makes our ExAvatar animatable with novel facial expressions by driven by the facial expression space of SMPL-X. In addition, by using connectivity-based regularizers, we significantly reduce artifacts in novel facial expressions and poses.

Vision-language models have transformed multimodal representation learning, yet dominant contrastive approaches like CLIP require large batch sizes, careful negative sampling, and extensive hyperparameter tuning. We introduce NOVA, a NOn-contrastive Vision-language Alignment framework based on joint embedding prediction with distributional regularization. NOVA aligns visual representations to a frozen, domain-specific text encoder by predicting text embeddings from augmented image views, while enforcing an isotropic Gaussian structure via Sketched Isotropic Gaussian Regularization (SIGReg). This eliminates the need for negative sampling, momentum encoders, or stop-gradients, reducing the training objective to a single hyperparameter. We evaluate NOVA on zeroshot chest X-ray classification using ClinicalBERT as the text encoder and Vision Transformers trained from scratch on MIMIC-CXR. On zero-shot classification across three benchmark datasets, NOVA outperforms multiple standard baselines while exhibiting substantially more consistent training runs. Our results demonstrate that non-contrastive vision-language pretraining offers a simpler, more stable, and more effective alternative to contrastive methods.

Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this observation, we introduce a novel PEFT method, called Gaussian noise Injected Fine Tuning of Salient Weights (GIFT-SW). Our method updates only salient columns, while injecting Gaussian noise into non-salient ones. To identify these columns, we developeda generalized sensitivity metric that extends and unifies metrics from previous studies. Experiments with LLaMA models demonstrate that GIFT-SW outperforms full fine-tuning and modern PEFT methods under the same computational budget. Moreover, GIFT-SW offers practical advantages to recover performance of models subjected to mixed-precision quantization with keeping salient weights in full precision.

Recent advancements in 3D reconstruction from single images have been driven by the evolution of generative models. Prominent among these are methods based on Score Distillation Sampling (SDS) and the adaptation of diffusion models in the 3D domain. Despite their progress, these techniques often face limitations due to slow optimization or rendering processes, leading to extensive training and optimization times. In this paper, we introduce a novel approach for single-view reconstruction that efficiently generates a 3D model from a single image via feed-forward inference. Our method utilizes two transformer-based networks, namely a point decoder and a triplane decoder, to reconstruct 3D objects using a hybrid Triplane-Gaussian intermediate representation. This hybrid representation strikes a balance, achieving a faster rendering speed compared to implicit representations while simultaneously delivering superior rendering quality than explicit representations. The point decoder is designed for generating point clouds from single images, offering an explicit representation which is then utilized by the triplane decoder to query Gaussian features for each point. This design choice addresses the challenges associated with directly regressing explicit 3D Gaussian attributes characterized by their non-structural nature. Subsequently, the 3D Gaussians are decoded by an MLP to enable rapid rendering through splatting. Both decoders are built upon a scalable, transformer-based architecture and have been efficiently trained on large-scale 3D datasets. The evaluations conducted on both synthetic datasets and real-world images demonstrate that our method not only achieves higher quality but also ensures a faster runtime in comparison to previous state-of-the-art techniques. Please see our project page at https://zouzx.github.io/TriplaneGaussian/.

4D generation has made remarkable progress in synthesizing dynamic 3D objects from input text, images, or videos. However, existing methods often represent motion as an implicit deformation field, which limits direct control and editability. To address this issue, we propose SkeletonGaussian, a novel framework for generating editable dynamic 3D Gaussians from monocular video input. Our approach introduces a hierarchical articulated representation that decomposes motion into sparse rigid motion explicitly driven by a skeleton and fine-grained non-rigid motion. Concretely, we extract a robust skeleton and drive rigid motion via linear blend skinning, followed by a hexplane-based refinement for non-rigid deformations, enhancing interpretability and editability. Experimental results demonstrate that SkeletonGaussian surpasses existing methods in generation quality while enabling intuitive motion editing, establishing a new paradigm for editable 4D generation. Project page: https://wusar.github.io/projects/skeletongaussian/

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as features, especially for neural-network-based models. Directly feeding raw Gaussian parameters into learning frameworks fails to address the non-unique and heterogeneous nature of the Gaussian parameterization, yielding highly data-dependent models. This challenge motivates us to explore a more principled approach to represent 3D Gaussian Splatting in neural networks that preserves the underlying color and geometric structure while enforcing unique mapping and channel homogeneity. In this paper, we propose an embedding representation of 3DGS based on continuous submanifold fields that encapsulate the intrinsic information of Gaussian primitives, thereby benefiting the learning of 3DGS.

Reconstructing photo-realistic animatable human avatars from monocular videos remains challenging in computer vision and graphics. Recently, methods using 3D Gaussians to represent the human body have emerged, offering faster optimization and real-time rendering. However, due to ignoring the crucial role of human body semantic information which represents the intrinsic structure and connections within the human body, they fail to achieve fine-detail reconstruction of dynamic human avatars. To address this issue, we propose SG-GS, which uses semantics-embedded 3D Gaussians, skeleton-driven rigid deformation, and non-rigid cloth dynamics deformation to create photo-realistic animatable human avatars from monocular videos. We then design a Semantic Human-Body Annotator (SHA) which utilizes SMPL's semantic prior for efficient body part semantic labeling. The generated labels are used to guide the optimization of Gaussian semantic attributes. To address the limited receptive field of point-level MLPs for local features, we also propose a 3D network that integrates geometric and semantic associations for human avatar deformation. We further implement three key strategies to enhance the semantic accuracy of 3D Gaussians and rendering quality: semantic projection with 2D regularization, semantic-guided density regularization and semantic-aware regularization with neighborhood consistency. Extensive experiments demonstrate that SG-GS achieves state-of-the-art geometry and appearance reconstruction performance.

We consider the problem of novel view synthesis (NVS) for dynamic scenes. Recent neural approaches have accomplished exceptional NVS results for static 3D scenes, but extensions to 4D time-varying scenes remain non-trivial. Prior efforts often encode dynamics by learning a canonical space plus implicit or explicit deformation fields, which struggle in challenging scenarios like sudden movements or capturing high-fidelity renderings. In this paper, we introduce 4D Gaussian Splatting (4DGS), a novel method that represents dynamic scenes with anisotropic 4D XYZT Gaussians, inspired by the success of 3D Gaussian Splatting in static scenes. We model dynamics at each timestamp by temporally slicing the 4D Gaussians, which naturally compose dynamic 3D Gaussians and can be seamlessly projected into images. As an explicit spatial-temporal representation, 4DGS demonstrates powerful capabilities for modeling complicated dynamics and fine details, especially for scenes with abrupt motions. We further implement our temporal slicing and splatting techniques in a highly optimized CUDA acceleration framework, achieving real-time inference rendering speeds of up to 277 FPS on an RTX 3090 GPU and 583 FPS on an RTX 4090 GPU. Rigorous evaluations on scenes with diverse motions showcase the superior efficiency and effectiveness of 4DGS, which consistently outperforms existing methods both quantitatively and qualitatively.

This work addresses the problem of real-time rendering of photorealistic human body avatars learned from multi-view videos. While the classical approaches to model and render virtual humans generally use a textured mesh, recent research has developed neural body representations that achieve impressive visual quality. However, these models are difficult to render in real-time and their quality degrades when the character is animated with body poses different than the training observations. We propose an animatable human model based on 3D Gaussian Splatting, that has recently emerged as a very efficient alternative to neural radiance fields. The body is represented by a set of gaussian primitives in a canonical space which is deformed with a coarse to fine approach that combines forward skinning and local non-rigid refinement. We describe how to learn our Human Gaussian Splatting (HuGS) model in an end-to-end fashion from multi-view observations, and evaluate it against the state-of-the-art approaches for novel pose synthesis of clothed body. Our method achieves 1.5 dB PSNR improvement over the state-of-the-art on THuman4 dataset while being able to render in real-time (80 fps for 512x512 resolution).

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Recent advances in Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) have made it standard practice to reconstruct 3D scenes from multi-view images. Removing objects from such 3D representations is a fundamental editing task that requires complete and seamless inpainting of occluded regions, ensuring consistency in geometry and appearance. Although existing methods have made notable progress in improving inpainting consistency, they often neglect global lighting effects, leading to physically implausible results. Moreover, these methods struggle with view-dependent non-Lambertian surfaces, where appearance varies across viewpoints, leading to unreliable inpainting. In this paper, we present 3D Gaussian Object Removal in the Intrinsic Space (GOR-IS), a novel framework for physically consistent and visually coherent 3D object removal. Our approach decomposes the scene into intrinsic components and explicitly models light transport to maintain global lighting effects consistency. Furthermore, we introduce an intrinsic-space inpainting module that operates directly in the material and lighting domains, effectively addressing the challenges posed by non-Lambertian surfaces. Extensive experiments on both synthetic and real-world datasets demonstrate that our framework substantially improves the physical consistency and visual coherence of object removal, outperforming existing methods by 13% in perceptual similarity (LPIPS) and 2dB in peak signal-to-noise ratio (PSNR). Code is publicly available at https://applezyh.github.io/GOR-IS-project-page/

The increasing demand for augmented reality and robotics is driving the need for articulated object reconstruction with high scalability. However, existing settings for reconstructing from discrete articulation states or casual monocular videos require non-trivial axis alignment or suffer from insufficient coverage, limiting their applicability. In this paper, we introduce FreeArtGS, a novel method for reconstructing articulated objects under free-moving scenario, a new setting with a simple setup and high scalability. FreeArtGS combines free-moving part segmentation with joint estimation and end-to-end optimization, taking only a monocular RGB-D video as input. By optimizing with the priors from off-the-shelf point-tracking and feature models, the free-moving part segmentation module identifies rigid parts from relative motion under unconstrained capture. The joint estimation module calibrates the unified object-to-camera poses and recovers joint type and axis robustly from part segmentation. Finally, 3DGS-based end-to-end optimization is implemented to jointly reconstruct visual textures, geometry, and joint angles of the articulated object. We conduct experiments on two benchmarks and real-world free-moving articulated objects. Experimental results demonstrate that FreeArtGS consistently excels in reconstructing free-moving articulated objects and remains highly competitive in previous reconstruction settings, proving itself a practical and effective solution for realistic asset generation. The project page is available at: https://freeartgs.github.io/

Post-training with reinforcement learning (RL) has recently shown strong promise for advancing multimodal agents beyond supervised imitation. However, RL remains limited by poor data efficiency, particularly in settings where interaction data are scarce and quickly become outdated. To address this challenge, GIPO (Gaussian Importance sampling Policy Optimization) is proposed as a policy optimization objective based on truncated importance sampling, replacing hard clipping with a log-ratio-based Gaussian trust weight to softly damp extreme importance ratios while maintaining non-zero gradients. Theoretical analysis shows that GIPO introduces an implicit, tunable constraint on the update magnitude, while concentration bounds guarantee robustness and stability under finite-sample estimation. Experimental results show that GIPO achieves state-of-the-art performance among clipping-based baselines across a wide range of replay buffer sizes, from near on-policy to highly stale data, while exhibiting superior bias--variance trade-off, high training stability and improved sample efficiency.

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.

Corner cases are crucial for training and validating autonomous driving systems, yet collecting them from the real world is often costly and hazardous. Editing objects within captured sensor data offers an effective alternative for generating diverse scenarios, commonly achieved through 3D Gaussian Splatting or image generative models. However, these approaches often suffer from limited visual fidelity or imprecise pose control. To address these issues, we propose G^2Editor, a framework designed for photorealistic and precise object editing in driving videos. Our method leverages a 3D Gaussian representation of the edited object as a dense prior, injected into the denoising process to ensure accurate pose control and spatial consistency. A scene-level 3D bounding box layout is employed to reconstruct occluded areas of non-target objects. Furthermore, to guide the appearance details of the edited object, we incorporate hierarchical fine-grained features as additional conditions during generation. Experiments on the Waymo Open Dataset demonstrate that G^2Editor effectively supports object repositioning, insertion, and deletion within a unified framework, outperforming existing methods in both pose controllability and visual quality, while also benefiting downstream data-driven tasks.

Physical adversarial attack methods expose the vulnerabilities of deep neural networks and pose a significant threat to safety-critical scenarios such as autonomous driving. Camouflage-based physical attack is a more promising approach compared to the patch-based attack, offering stronger adversarial effectiveness in complex physical environments. However, most prior work relies on mesh priors of the target object and virtual environments constructed by simulators, which are time-consuming to obtain and inevitably differ from the real world. Moreover, due to the limitations of the backgrounds in training images, previous methods often fail to produce multi-view robust adversarial camouflage and tend to fall into sub-optimal solutions. Due to these reasons, prior work lacks adversarial effectiveness and robustness across diverse viewpoints and physical environments. We propose a physical attack framework based on 3D Gaussian Splatting (3DGS), named PGA, which provides rapid and precise reconstruction with few images, along with photo-realistic rendering capabilities. Our framework further enhances cross-view robustness and adversarial effectiveness by preventing mutual and self-occlusion among Gaussians and employing a min-max optimization approach that adjusts the imaging background of each viewpoint, helping the algorithm filter out non-robust adversarial features. Extensive experiments validate the effectiveness and superiority of PGA. Our code is available at:https://github.com/TRLou/PGA.

3D Gaussian Splatting (3DGS) represents a significant advancement in the field of efficient and high-fidelity novel view synthesis. Despite recent progress, achieving accurate geometric reconstruction under sparse-view conditions remains a fundamental challenge. Existing methods often rely on non-local depth regularization, which fails to capture fine-grained structures and is highly sensitive to depth estimation noise. Furthermore, traditional smoothing methods neglect semantic boundaries and indiscriminately degrade essential edges and textures, consequently limiting the overall quality of reconstruction. In this work, we propose DET-GS, a unified depth and edge-aware regularization framework for 3D Gaussian Splatting. DET-GS introduces a hierarchical geometric depth supervision framework that adaptively enforces multi-level geometric consistency, significantly enhancing structural fidelity and robustness against depth estimation noise. To preserve scene boundaries, we design an edge-aware depth regularization guided by semantic masks derived from Canny edge detection. Furthermore, we introduce an RGB-guided edge-preserving Total Variation loss that selectively smooths homogeneous regions while rigorously retaining high-frequency details and textures. Extensive experiments demonstrate that DET-GS achieves substantial improvements in both geometric accuracy and visual fidelity, outperforming state-of-the-art (SOTA) methods on sparse-view novel view synthesis benchmarks.

Audio-Visual Question Answering (AVQA) requires not only question-based multimodal reasoning but also precise temporal grounding to capture subtle dynamics for accurate prediction. However, existing methods mainly use question information implicitly, limiting focus on question-specific details. Furthermore, most studies rely on uniform frame sampling, which can miss key question-relevant frames. Although recent Top-K frame selection methods aim to address this, their discrete nature still overlooks fine-grained temporal details. This paper proposes QA-TIGER, a novel framework that explicitly incorporates question information and models continuous temporal dynamics. Our key idea is to use Gaussian-based modeling to adaptively focus on both consecutive and non-consecutive frames based on the question, while explicitly injecting question information and applying progressive refinement. We leverage a Mixture of Experts (MoE) to flexibly implement multiple Gaussian models, activating temporal experts specifically tailored to the question. Extensive experiments on multiple AVQA benchmarks show that QA-TIGER consistently achieves state-of-the-art performance. Code is available at https://aim-skku.github.io/QA-TIGER/

In this work, we propose a novel clothed human reconstruction method called GaussianBody, based on 3D Gaussian Splatting. Compared with the costly neural radiance based models, 3D Gaussian Splatting has recently demonstrated great performance in terms of training time and rendering quality. However, applying the static 3D Gaussian Splatting model to the dynamic human reconstruction problem is non-trivial due to complicated non-rigid deformations and rich cloth details. To address these challenges, our method considers explicit pose-guided deformation to associate dynamic Gaussians across the canonical space and the observation space, introducing a physically-based prior with regularized transformations helps mitigate ambiguity between the two spaces. During the training process, we further propose a pose refinement strategy to update the pose regression for compensating the inaccurate initial estimation and a split-with-scale mechanism to enhance the density of regressed point clouds. The experiments validate that our method can achieve state-of-the-art photorealistic novel-view rendering results with high-quality details for dynamic clothed human bodies, along with explicit geometry reconstruction.

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte Carlo (MCMC) methods derived from discretizations of the overdamped Langevin diffusions, which are commonly known as Langevin Monte Carlo algorithms. Furthermore, we are also interested in two nonsmooth cases for which a large class of proximal MCMC methods have been developed: (i) a nonsmooth prior is considered with a Gaussian mixture likelihood; (ii) a Laplacian mixture distribution. Such nonsmooth and non-log-concave sampling tasks arise from a wide range of applications to Bayesian inference and imaging inverse problems such as image deconvolution. We perform numerical simulations to compare the performance of most commonly used Langevin Monte Carlo algorithms.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Gaussian Splatting demonstrates impressive results in multi-view reconstruction based on Gaussian explicit representations. However, the current Gaussian primitives only have a single view-dependent color and an opacity to represent the appearance and geometry of the scene, resulting in a non-compact representation. In this paper, we introduce a new method called SVGS (Spatially Varying Gaussian Splatting) that utilizes spatially varying colors and opacity in a single Gaussian primitive to improve its representation ability. We have implemented bilinear interpolation, movable kernels, and tiny neural networks as spatially varying functions. SVGS employs 2D Gaussian surfels as primitives, which significantly enhances novel-view synthesis while maintaining high-quality geometric reconstruction. This approach is particularly effective in practical applications, as scenes combining complex textures with relatively simple geometry occur frequently in real-world environments. Quantitative and qualitative experimental results demonstrate that all three functions outperform the baseline, with the best movable kernels achieving superior novel view synthesis performance on multiple datasets, highlighting the strong potential of spatially varying functions. Project page: https://ruixu.me/html/SuperGaussians/index.html

Novel view synthesis from unconstrained in-the-wild image collections remains a significant yet challenging task due to photometric variations and transient occluders that complicate accurate scene reconstruction. Previous methods have approached these issues by integrating per-image appearance features embeddings in Neural Radiance Fields (NeRFs). Although 3D Gaussian Splatting (3DGS) offers faster training and real-time rendering, adapting it for unconstrained image collections is non-trivial due to the substantially different architecture. In this paper, we introduce Splatfacto-W, an approach that integrates per-Gaussian neural color features and per-image appearance embeddings into the rasterization process, along with a spherical harmonics-based background model to represent varying photometric appearances and better depict backgrounds. Our key contributions include latent appearance modeling, efficient transient object handling, and precise background modeling. Splatfacto-W delivers high-quality, real-time novel view synthesis with improved scene consistency in in-the-wild scenarios. Our method improves the Peak Signal-to-Noise Ratio (PSNR) by an average of 5.3 dB compared to 3DGS, enhances training speed by 150 times compared to NeRF-based methods, and achieves a similar rendering speed to 3DGS. Additional video results and code integrated into Nerfstudio are available at https://kevinxu02.github.io/splatfactow/.

3D city generation with NeRF-based methods shows promising generation results but is computationally inefficient. Recently 3D Gaussian Splatting (3D-GS) has emerged as a highly efficient alternative for object-level 3D generation. However, adapting 3D-GS from finite-scale 3D objects and humans to infinite-scale 3D cities is non-trivial. Unbounded 3D city generation entails significant storage overhead (out-of-memory issues), arising from the need to expand points to billions, often demanding hundreds of Gigabytes of VRAM for a city scene spanning 10km^2. In this paper, we propose GaussianCity, a generative Gaussian Splatting framework dedicated to efficiently synthesizing unbounded 3D cities with a single feed-forward pass. Our key insights are two-fold: 1) Compact 3D Scene Representation: We introduce BEV-Point as a highly compact intermediate representation, ensuring that the growth in VRAM usage for unbounded scenes remains constant, thus enabling unbounded city generation. 2) Spatial-aware Gaussian Attribute Decoder: We present spatial-aware BEV-Point decoder to produce 3D Gaussian attributes, which leverages Point Serializer to integrate the structural and contextual characteristics of BEV points. Extensive experiments demonstrate that GaussianCity achieves state-of-the-art results in both drone-view and street-view 3D city generation. Notably, compared to CityDreamer, GaussianCity exhibits superior performance with a speedup of 60 times (10.72 FPS v.s. 0.18 FPS).

Recent reconstruction methods based on radiance field such as NeRF and 3DGS reproduce indoor scenes with high visual fidelity, but break down under scene editing due to baked illumination and the lack of explicit light transport. In contrast, physically based inverse rendering relies on mesh representations and path tracing, which enforce correct light transport but place strong requirements on geometric fidelity, becoming a practical bottleneck for real indoor scenes. In this work, we propose Emission-Aware Gaussians and Path Tracing (EAG-PT), aiming for physically based light transport with a unified 2D Gaussian representation. Our design is based on three cores: (1) using 2D Gaussians as a unified scene representation and transport-friendly geometry proxy that avoids reconstructed mesh, (2) explicitly separating emissive and non-emissive components during reconstruction for further scene editing, and (3) decoupling reconstruction from final rendering by using efficient single-bounce optimization and high-quality multi-bounce path tracing after scene editing. Experiments on synthetic and real indoor scenes show that EAG-PT produces more natural and physically consistent renders after editing than radiant scene reconstructions, while preserving finer geometric detail and avoiding mesh-induced artifacts compared to mesh-based inverse path tracing. These results suggest promising directions for future use in interior design, XR content creation, and embodied AI.

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

We introduce RMAvatar, a novel human avatar representation with Gaussian splatting embedded on mesh to learn clothed avatar from a monocular video. We utilize the explicit mesh geometry to represent motion and shape of a virtual human and implicit appearance rendering with Gaussian Splatting. Our method consists of two main modules: Gaussian initialization module and Gaussian rectification module. We embed Gaussians into triangular faces and control their motion through the mesh, which ensures low-frequency motion and surface deformation of the avatar. Due to the limitations of LBS formula, the human skeleton is hard to control complex non-rigid transformations. We then design a pose-related Gaussian rectification module to learn fine-detailed non-rigid deformations, further improving the realism and expressiveness of the avatar. We conduct extensive experiments on public datasets, RMAvatar shows state-of-the-art performance on both rendering quality and quantitative evaluations. Please see our project page at https://rm-avatar.github.io.

The Bird's-eye View (BeV) representation is widely used for 3D perception from multi-view camera images. It allows to merge features from different cameras into a common space, providing a unified representation of the 3D scene. The key component is the view transformer, which transforms image views into the BeV. However, actual view transformer methods based on geometry or cross-attention do not provide a sufficiently detailed representation of the scene, as they use a sub-sampling of the 3D space that is non-optimal for modeling the fine structures of the environment. In this paper, we propose GaussianBeV, a novel method for transforming image features to BeV by finely representing the scene using a set of 3D gaussians located and oriented in 3D space. This representation is then splattered to produce the BeV feature map by adapting recent advances in 3D representation rendering based on gaussian splatting. GaussianBeV is the first approach to use this 3D gaussian modeling and 3D scene rendering process online, i.e. without optimizing it on a specific scene and directly integrated into a single stage model for BeV scene understanding. Experiments show that the proposed representation is highly effective and place GaussianBeV as the new state-of-the-art on the BeV semantic segmentation task on the nuScenes dataset.

Reconstructing high-fidelity, animatable 3D head avatars from effortlessly captured monocular videos is a pivotal yet formidable challenge. Although significant progress has been made in rendering performance and manipulation capabilities, notable challenges remain, including incomplete reconstruction and inefficient Gaussian representation. To address these challenges, we introduce FATE, a novel method for reconstructing an editable full-head avatar from a single monocular video. FATE integrates a sampling-based densification strategy to ensure optimal positional distribution of points, improving rendering efficiency. A neural baking technique is introduced to convert discrete Gaussian representations into continuous attribute maps, facilitating intuitive appearance editing. Furthermore, we propose a universal completion framework to recover non-frontal appearance, culminating in a 360^circ-renderable 3D head avatar. FATE outperforms previous approaches in both qualitative and quantitative evaluations, achieving state-of-the-art performance. To the best of our knowledge, FATE is the first animatable and 360^circ full-head monocular reconstruction method for a 3D head avatar. The code will be publicly released upon publication.

We present a new approach to creating photorealistic and relightable head avatars from a phone scan with unknown illumination. The reconstructed avatars can be animated and relit in real time with the global illumination of diverse environments. Unlike existing approaches that estimate parametric reflectance parameters via inverse rendering, our approach directly models learnable radiance transfer that incorporates global light transport in an efficient manner for real-time rendering. However, learning such a complex light transport that can generalize across identities is non-trivial. A phone scan in a single environment lacks sufficient information to infer how the head would appear in general environments. To address this, we build a universal relightable avatar model represented by 3D Gaussians. We train on hundreds of high-quality multi-view human scans with controllable point lights. High-resolution geometric guidance further enhances the reconstruction accuracy and generalization. Once trained, we finetune the pretrained model on a phone scan using inverse rendering to obtain a personalized relightable avatar. Our experiments establish the efficacy of our design, outperforming existing approaches while retaining real-time rendering capability.

We introduce MIGS (Multi-Identity Gaussian Splatting), a novel method that learns a single neural representation for multiple identities, using only monocular videos. Recent 3D Gaussian Splatting (3DGS) approaches for human avatars require per-identity optimization. However, learning a multi-identity representation presents advantages in robustly animating humans under arbitrary poses. We propose to construct a high-order tensor that combines all the learnable 3DGS parameters for all the training identities. By assuming a low-rank structure and factorizing the tensor, we model the complex rigid and non-rigid deformations of multiple subjects in a unified network, significantly reducing the total number of parameters. Our proposed approach leverages information from all the training identities, enabling robust animation under challenging unseen poses, outperforming existing approaches. We also demonstrate how it can be extended to learn unseen identities.

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H_0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and ΛCDM-dependent baryon acoustic oscillation observations. The inferred H_0 values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are H_0= 66 pm 6, km,s^{-1},Mpc^{-1}, H_0= 67 pm 10, km,s^{-1},Mpc^{-1} and H_0= 69 pm 6, km,s^{-1},Mpc^{-1}, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln R=12.17pm 0.02.

Despite much progress, achieving real-time high-fidelity head avatar animation is still difficult and existing methods have to trade-off between speed and quality. 3DMM based methods often fail to model non-facial structures such as eyeglasses and hairstyles, while neural implicit models suffer from deformation inflexibility and rendering inefficiency. Although 3D Gaussian has been demonstrated to possess promising capability for geometry representation and radiance field reconstruction, applying 3D Gaussian in head avatar creation remains a major challenge since it is difficult for 3D Gaussian to model the head shape variations caused by changing poses and expressions. In this paper, we introduce PSAvatar, a novel framework for animatable head avatar creation that utilizes discrete geometric primitive to create a parametric morphable shape model and employs 3D Gaussian for fine detail representation and high fidelity rendering. The parametric morphable shape model is a Point-based Morphable Shape Model (PMSM) which uses points instead of meshes for 3D representation to achieve enhanced representation flexibility. The PMSM first converts the FLAME mesh to points by sampling on the surfaces as well as off the meshes to enable the reconstruction of not only surface-like structures but also complex geometries such as eyeglasses and hairstyles. By aligning these points with the head shape in an analysis-by-synthesis manner, the PMSM makes it possible to utilize 3D Gaussian for fine detail representation and appearance modeling, thus enabling the creation of high-fidelity avatars. We show that PSAvatar can reconstruct high-fidelity head avatars of a variety of subjects and the avatars can be animated in real-time (ge 25 fps at a resolution of 512 times 512 ).

We propose SplatArmor, a novel approach for recovering detailed and animatable human models by `armoring' a parameterized body model with 3D Gaussians. Our approach represents the human as a set of 3D Gaussians within a canonical space, whose articulation is defined by extending the skinning of the underlying SMPL geometry to arbitrary locations in the canonical space. To account for pose-dependent effects, we introduce a SE(3) field, which allows us to capture both the location and anisotropy of the Gaussians. Furthermore, we propose the use of a neural color field to provide color regularization and 3D supervision for the precise positioning of these Gaussians. We show that Gaussian splatting provides an interesting alternative to neural rendering based methods by leverging a rasterization primitive without facing any of the non-differentiability and optimization challenges typically faced in such approaches. The rasterization paradigms allows us to leverage forward skinning, and does not suffer from the ambiguities associated with inverse skinning and warping. We show compelling results on the ZJU MoCap and People Snapshot datasets, which underscore the effectiveness of our method for controllable human synthesis.

Variational inference (VI) seeks to approximate a target distribution pi by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates pi by minimizing the Kullback-Leibler (KL) divergence to pi over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when pi is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when pi is only log-smooth.

Touch and vision go hand in hand, mutually enhancing our ability to understand the world. From a research perspective, the problem of mixing touch and vision is underexplored and presents interesting challenges. To this end, we propose Tactile-Informed 3DGS, a novel approach that incorporates touch data (local depth maps) with multi-view vision data to achieve surface reconstruction and novel view synthesis. Our method optimises 3D Gaussian primitives to accurately model the object's geometry at points of contact. By creating a framework that decreases the transmittance at touch locations, we achieve a refined surface reconstruction, ensuring a uniformly smooth depth map. Touch is particularly useful when considering non-Lambertian objects (e.g. shiny or reflective surfaces) since contemporary methods tend to fail to reconstruct with fidelity specular highlights. By combining vision and tactile sensing, we achieve more accurate geometry reconstructions with fewer images than prior methods. We conduct evaluation on objects with glossy and reflective surfaces and demonstrate the effectiveness of our approach, offering significant improvements in reconstruction quality.

Recent advances in generative AI have accelerated the production of ultra-high-resolution visual content, posing significant challenges for efficient compression and real-time decoding on end-user devices. Inspired by 3D Gaussian Splatting, recent 2D Gaussian image models improve representation efficiency, yet existing methods struggle to balance compression ratio and reconstruction fidelity in ultra-high-resolution scenarios. To address this issue, we propose SmartSplat, a highly adaptive and feature-aware GS-based image compression framework that supports arbitrary image resolutions and compression ratios. SmartSplat leverages image-aware features such as gradients and color variances, introducing a Gradient-Color Guided Variational Sampling strategy together with an Exclusion-based Uniform Sampling scheme to improve the non-overlapping coverage of Gaussian primitives in pixel space. In addition, we propose a Scale-Adaptive Gaussian Color Sampling method to enhance color initialization across scales. Through joint optimization of spatial layout, scale, and color initialization, SmartSplat efficiently captures both local structures and global textures using a limited number of Gaussians, achieving high reconstruction quality under strong compression. Extensive experiments on DIV8K and a newly constructed 16K dataset demonstrate that SmartSplat consistently outperforms state-of-the-art methods at comparable compression ratios and exceeds their compression limits, showing strong scalability and practical applicability. The code is publicly available at https://github.com/lif314/SmartSplat.

Volumetric video is emerging as a key medium for digitizing the dynamic physical world, creating the virtual environments with six degrees of freedom to deliver immersive user experiences. However, robustly modeling general dynamic scenes, especially those involving topological changes while maintaining long-term tracking remains a fundamental challenge. In this paper, we present TaoGS, a novel topology-aware dynamic Gaussian representation that disentangles motion and appearance to support, both, long-range tracking and topological adaptation. We represent scene motion with a sparse set of motion Gaussians, which are continuously updated by a spatio-temporal tracker and photometric cues that detect structural variations across frames. To capture fine-grained texture, each motion Gaussian anchors and dynamically activates a set of local appearance Gaussians, which are non-rigidly warped to the current frame to provide strong initialization and significantly reduce training time. This activation mechanism enables efficient modeling of detailed textures and maintains temporal coherence, allowing high-fidelity rendering even under challenging scenarios such as changing clothes. To enable seamless integration into codec-based volumetric formats, we introduce a global Gaussian Lookup Table that records the lifespan of each Gaussian and organizes attributes into a lifespan-aware 2D layout. This structure aligns naturally with standard video codecs and supports up to 40 compression. TaoGS provides a unified, adaptive solution for scalable volumetric video under topological variation, capturing moments where "elegance in motion" and "Power in Stillness", delivering immersive experiences that harmonize with the physical world.

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence, an extension of weak convergence that compares a statistic or process to a sequence of evolving processes. Relative weak convergence retains the essential consequences of classical weak convergence and coincides with it under stationarity. Crucially, it applies in general non-stationary settings where classical weak convergence fails. We establish concrete relative CLTs for random vectors and empirical processes, along with sequential, weighted, and bootstrap variants, that parallel the state-of-the-art in stationary settings. Our framework and results offer simple, plug-in replacements for classical CLTs whenever stationarity is untenable, as illustrated by applications in nonparametric trend estimation and hypothesis testing.

Synthesizing novel views of large-scale scenes from unconstrained in-the-wild images is an important but challenging task in computer vision. Existing methods, which optimize per-image appearance and transient occlusion through implicit neural networks from dense training views (approximately 1000 images), struggle to perform effectively under sparse input conditions, resulting in noticeable artifacts. To this end, we propose SparseGS-W, a novel framework based on 3D Gaussian Splatting that enables the reconstruction of complex outdoor scenes and handles occlusions and appearance changes with as few as five training images. We leverage geometric priors and constrained diffusion priors to compensate for the lack of multi-view information from extremely sparse input. Specifically, we propose a plug-and-play Constrained Novel-View Enhancement module to iteratively improve the quality of rendered novel views during the Gaussian optimization process. Furthermore, we propose an Occlusion Handling module, which flexibly removes occlusions utilizing the inherent high-quality inpainting capability of constrained diffusion priors. Both modules are capable of extracting appearance features from any user-provided reference image, enabling flexible modeling of illumination-consistent scenes. Extensive experiments on the PhotoTourism and Tanks and Temples datasets demonstrate that SparseGS-W achieves state-of-the-art performance not only in full-reference metrics, but also in commonly used non-reference metrics such as FID, ClipIQA, and MUSIQ.

3D Gaussian Splatting (3DGS) has demonstrated superior quality in modeling 3D objects and scenes. However, generating 3DGS remains challenging due to their discrete, unstructured, and permutation-invariant nature. In this work, we present a simple yet effective method to overcome these challenges. We utilize spherical mapping to transform 3DGS into a structured 2D representation, termed UVGS. UVGS can be viewed as multi-channel images, with feature dimensions as a concatenation of Gaussian attributes such as position, scale, color, opacity, and rotation. We further find that these heterogeneous features can be compressed into a lower-dimensional (e.g., 3-channel) shared feature space using a carefully designed multi-branch network. The compressed UVGS can be treated as typical RGB images. Remarkably, we discover that typical VAEs trained with latent diffusion models can directly generalize to this new representation without additional training. Our novel representation makes it effortless to leverage foundational 2D models, such as diffusion models, to directly model 3DGS. Additionally, one can simply increase the 2D UV resolution to accommodate more Gaussians, making UVGS a scalable solution compared to typical 3D backbones. This approach immediately unlocks various novel generation applications of 3DGS by inherently utilizing the already developed superior 2D generation capabilities. In our experiments, we demonstrate various unconditional, conditional generation, and inpainting applications of 3DGS based on diffusion models, which were previously non-trivial.

We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not employ any training signal, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each subject to an unknown positive multiplicative factor (or gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable, carefully chosen initialisation point. An analysis of this algorithm allows us to show that it converges to the exact solution provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Interestingly, we show that this requirement grows linearly (up to log factors) in the number of unknowns of the problem. This sample complexity is found both in absence of prior information, as well as when subspace priors are available for both the signal and gains, allowing a further reduction of the number of observations required for our recovery guarantees to hold. Moreover, in the presence of noise we show how our descent algorithm yields a solution whose accuracy degrades gracefully with the amount of noise affecting the measurements. Finally, we present some numerical experiments in an imaging context, where our algorithm allows for a simple solution to blind calibration of the gains in a sensor array.

The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and non-linear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive biases of neural networks. However, they usually require very high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting issues. In addition, the fixed positions of the mesh parameters restrict their flexibility, making it challenging to accurately approximate complex PDEs. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/