Daily Papers

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

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.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

With the rapid growth of the low-altitude economy, UAVs have become crucial for measurement and tracking in patrol systems. However, in GNSS-denied areas, satellite-based localization methods are prone to failure. This paper presents a cross-view UAV localization framework that performs map matching via object detection, aimed at effectively addressing cross-temporal, cross-view, heterogeneous aerial image matching. In typical pipelines, UAV visual localization is formulated as an image-retrieval problem: features are extracted to build a localization map, and the pose of a query image is estimated by matching it to a reference database with known poses. Because publicly available UAV localization datasets are limited, many approaches recast localization as a classification task and rely on scene labels in these datasets to ensure accuracy. Other methods seek to reduce cross-domain differences using polar-coordinate reprojection, perspective transformations, or generative adversarial networks; however, they can suffer from misalignment, content loss, and limited realism. In contrast, we leverage modern object detection to accurately extract salient instances from UAV and satellite images, and integrate a graph neural network to reason about inter-image and intra-image node relationships. Using a fine-grained, graph-based node-similarity metric, our method achieves strong retrieval and localization performance. Extensive experiments on public and real-world datasets show that our approach handles heterogeneous appearance differences effectively and generalizes well, making it applicable to scenarios with larger modality gaps, such as infrared-visible image matching. Our dataset will be publicly available at the following URL: https://github.com/liutao23/ODGNNLoc.git.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

Cross-view geo-localization in GNSS-denied environments aims to determine an unknown location by matching drone-view images with the correct geo-tagged satellite-view images from a large gallery. Recent research shows that learning discriminative image representations under specific weather conditions can significantly enhance performance. However, the frequent occurrence of unseen extreme weather conditions hinders progress. This paper introduces MCGF, a Multi-weather Cross-view Geo-localization Framework designed to dynamically adapt to unseen weather conditions. MCGF establishes a joint optimization between image restoration and geo-localization using denoising diffusion models. For image restoration, MCGF incorporates a shared encoder and a lightweight restoration module to help the backbone eliminate weather-specific information. For geo-localization, MCGF uses EVA-02 as a backbone for feature extraction, with cross-entropy loss for training and cosine distance for testing. Extensive experiments on University160k-WX demonstrate that MCGF achieves competitive results for geo-localization in varying weather conditions.

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.

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.

Simultaneous localization and mapping (SLAM) technology now has photorealistic mapping capabilities thanks to the real-time high-fidelity rendering capability of 3D Gaussian splatting (3DGS). However, due to the static representation of scenes, current 3DGS-based SLAM encounters issues with pose drift and failure to reconstruct accurate maps in dynamic environments. To address this problem, we present D4DGS-SLAM, the first SLAM method based on 4DGS map representation for dynamic environments. By incorporating the temporal dimension into scene representation, D4DGS-SLAM enables high-quality reconstruction of dynamic scenes. Utilizing the dynamics-aware InfoModule, we can obtain the dynamics, visibility, and reliability of scene points, and filter stable static points for tracking accordingly. When optimizing Gaussian points, we apply different isotropic regularization terms to Gaussians with varying dynamic characteristics. Experimental results on real-world dynamic scene datasets demonstrate that our method outperforms state-of-the-art approaches in both camera pose tracking and map quality.

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

LiDAR-based 3D detectors need large datasets for training, yet they struggle to generalize to novel domains. Domain Generalization (DG) aims to mitigate this by training detectors that are invariant to such domain shifts. Current DG approaches exclusively rely on global geometric features (point cloud Cartesian coordinates) as input features. Over-reliance on these global geometric features can, however, cause 3D detectors to prioritize object location and absolute position, resulting in poor cross-domain performance. To mitigate this, we propose to exploit explicit local point cloud structure for DG, in particular by encoding point cloud neighborhoods with Gaussian blobs, GBlobs. Our proposed formulation is highly efficient and requires no additional parameters. Without any bells and whistles, simply by integrating GBlobs in existing detectors, we beat the current state-of-the-art in challenging single-source DG benchmarks by over 21 mAP (Waymo->KITTI), 13 mAP (KITTI->Waymo), and 12 mAP (nuScenes->KITTI), without sacrificing in-domain performance. Additionally, GBlobs demonstrate exceptional performance in multi-source DG, surpassing the current state-of-the-art by 17, 12, and 5 mAP on Waymo, KITTI, and ONCE, respectively.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

We propose to study and promote the robustness of a model as per its performance through the interpolation of training data distributions. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the geodesic connecting subpopulation distributions of different categories. (2) We regularize the model for smoother performance on the continuous geodesic path connecting subpopulation distributions. (3) Additionally, we provide a theoretical guarantee of robustness improvement and investigate how the geodesic location and the sample size contribute, respectively. Experimental validations of the proposed strategy on four datasets, including CIFAR-100 and ImageNet, establish the efficacy of our method, e.g., our method improves the baselines' certifiable robustness on CIFAR10 up to 7.7%, with 16.8% on empirical robustness on CIFAR-100. Our work provides a new perspective of model robustness through the lens of Wasserstein geodesic-based interpolation with a practical off-the-shelf strategy that can be combined with existing robust training methods.

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.

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

To support the Low Altitude Economy (LAE), precise unmanned aerial vehicles (UAVs) localization in urban areas where global positioning system (GPS) signals are unavailable. Vision-based methods offer a viable alternative but face severe bandwidth, memory and processing constraints on lightweight UAVs. Inspired by mammalian spatial cognition, we propose a task-oriented communication framework, where UAVs equipped with multi-camera systems extract compact multi-view features and offload localization tasks to edge servers. We introduce the Orthogonally-constrained Variational Information Bottleneck encoder (O-VIB), which incorporates automatic relevance determination (ARD) to prune non-informative features while enforcing orthogonality to minimize redundancy. This enables efficient and accurate localization with minimal transmission cost. Extensive evaluation on a dedicated LAE UAV dataset shows that O-VIB achieves high-precision localization under stringent bandwidth budgets. Code and dataset will be made publicly available: github.com/fangzr/TOC-Edge-Aerial.

This paper considers a joint scattering environment sensing and data recovery problem in an uplink integrated sensing and communication (ISAC) system. To facilitate joint scatterers localization and multi-user (MU) channel estimation, we introduce a three-dimensional (3D) location-domain sparse channel model to capture the joint sparsity of the MU channel (i.e., different user channels share partially overlapped scatterers). Then the joint problem is formulated as a bilinear structured sparse recovery problem with a dynamic position grid and imperfect parameters (such as time offset and user position errors). We propose an expectation maximization based turbo bilinear subspace variational Bayesian inference (EM-Turbo-BiSVBI) algorithm to solve the problem effectively, where the E-step performs Bayesian estimation of the the location-domain sparse MU channel by exploiting the joint sparsity, and the M-step refines the dynamic position grid and learns the imperfect factors via gradient update. Two methods are introduced to greatly reduce the complexity with almost no sacrifice on the performance and convergence speed: 1) a subspace constrained bilinear variational Bayesian inference (VBI) method is proposed to avoid any high-dimensional matrix inverse; 2) the multiple signal classification (MUSIC) and subspace constrained VBI methods are combined to obtain a coarse estimation result to reduce the search range. Simulations verify the advantages of the proposed scheme over baseline schemes.

Simultaneous localization and mapping is essential for position tracking and scene understanding. 3D Gaussian-based map representations enable photorealistic reconstruction and real-time rendering of scenes using multiple posed cameras. We show for the first time that using 3D Gaussians for map representation with unposed camera images and inertial measurements can enable accurate SLAM. Our method, MM3DGS, addresses the limitations of prior neural radiance field-based representations by enabling faster rendering, scale awareness, and improved trajectory tracking. Our framework enables keyframe-based mapping and tracking utilizing loss functions that incorporate relative pose transformations from pre-integrated inertial measurements, depth estimates, and measures of photometric rendering quality. We also release a multi-modal dataset, UT-MM, collected from a mobile robot equipped with a camera and an inertial measurement unit. Experimental evaluation on several scenes from the dataset shows that MM3DGS achieves 3x improvement in tracking and 5% improvement in photometric rendering quality compared to the current 3DGS SLAM state-of-the-art, while allowing real-time rendering of a high-resolution dense 3D map. Project Webpage: https://vita-group.github.io/MM3DGS-SLAM

Accurate crop yield forecasting is essential for global food security. However, current AI models systematically underperform when yields deviate from historical trends. We attribute this to the lack of rich, physically grounded datasets directly linking atmospheric states to yields. To address this, we introduce VITA (Variational Inference Transformer for Asymmetric data), a variational pretraining framework that learns representations from large satellite-based weather datasets and transfers to the ground-based limited measurements available for yield prediction. VITA is trained using detailed meteorological variables as proxy targets during pretraining and learns to predict latent atmospheric states under a seasonality-aware sinusoidal prior. This allows the model to be fine-tuned using limited weather statistics during deployment. Applied to 763 counties in the U.S. Corn Belt, VITA achieves state-of-the-art performance in predicting corn and soybean yields across all evaluation scenarios, particularly during extreme years, with statistically significant improvements (paired t-test, p < 0.0001). Importantly, VITA outperforms prior frameworks like GNN-RNN without soil data, and bigger foundational models (e.g., Chronos-Bolt) with less compute, making it practical for real-world use--especially in data-scarce regions. This work highlights how domain-aware AI design can overcome data limitations and support resilient agricultural forecasting in a changing climate.

Recent studies have introduced a new class of generative models for synthesizing implicit neural representations (INRs) that capture arbitrary continuous signals in various domains. These models opened the door for domain-agnostic generative models, but they often fail to achieve high-quality generation. We observed that the existing methods generate the weights of neural networks to parameterize INRs and evaluate the network with fixed positional embeddings (PEs). Arguably, this architecture limits the expressive power of generative models and results in low-quality INR generation. To address this limitation, we propose Domain-agnostic Latent Diffusion Model for INRs (DDMI) that generates adaptive positional embeddings instead of neural networks' weights. Specifically, we develop a Discrete-to-continuous space Variational AutoEncoder (D2C-VAE), which seamlessly connects discrete data and the continuous signal functions in the shared latent space. Additionally, we introduce a novel conditioning mechanism for evaluating INRs with the hierarchically decomposed PEs to further enhance expressive power. Extensive experiments across four modalities, e.g., 2D images, 3D shapes, Neural Radiance Fields, and videos, with seven benchmark datasets, demonstrate the versatility of DDMI and its superior performance compared to the existing INR generative models.

The next Point-of-Interest (POI) recommendation task aims to predict users' next destinations based on their historical movement data and plays a key role in location-based services and personalized applications. Accurate next POI recommendation depends on effectively modeling geographic information and POI transition relations, which are crucial for capturing spatial dependencies and user movement patterns. While Large Language Models (LLMs) exhibit strong capabilities in semantic understanding and contextual reasoning, applying them to spatial tasks like next POI recommendation remains challenging. First, the infrequent nature of specific GPS coordinates makes it difficult for LLMs to model precise spatial contexts. Second, the lack of knowledge about POI transitions limits their ability to capture potential POI-POI relationships. To address these issues, we propose GA-LLM (Geography-Aware Large Language Model), a novel framework that enhances LLMs with two specialized components. The Geographic Coordinate Injection Module (GCIM) transforms GPS coordinates into spatial representations using hierarchical and Fourier-based positional encoding, enabling the model to understand geographic features from multiple perspectives. The POI Alignment Module (PAM) incorporates POI transition relations into the LLM's semantic space, allowing it to infer global POI relationships and generalize to unseen POIs. Experiments on three real-world datasets demonstrate the state-of-the-art performance of GA-LLM.

Worldwide geolocalization aims to locate the precise location at the coordinate level of photos taken anywhere on the Earth. It is very challenging due to 1) the difficulty of capturing subtle location-aware visual semantics, and 2) the heterogeneous geographical distribution of image data. As a result, existing studies have clear limitations when scaled to a worldwide context. They may easily confuse distant images with similar visual contents, or cannot adapt to various locations worldwide with different amounts of relevant data. To resolve these limitations, we propose G3, a novel framework based on Retrieval-Augmented Generation (RAG). In particular, G3 consists of three steps, i.e., Geo-alignment, Geo-diversification, and Geo-verification to optimize both retrieval and generation phases of worldwide geolocalization. During Geo-alignment, our solution jointly learns expressive multi-modal representations for images, GPS and textual descriptions, which allows us to capture location-aware semantics for retrieving nearby images for a given query. During Geo-diversification, we leverage a prompt ensembling method that is robust to inconsistent retrieval performance for different image queries. Finally, we combine both retrieved and generated GPS candidates in Geo-verification for location prediction. Experiments on two well-established datasets IM2GPS3k and YFCC4k verify the superiority of G3 compared to other state-of-the-art methods.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Domain shifts such as sensor type changes and geographical situation variations are prevalent in Autonomous Driving (AD), which poses a challenge since AD model relying on the previous domain knowledge can be hardly directly deployed to a new domain without additional costs. In this paper, we provide a new perspective and approach of alleviating the domain shifts, by proposing a Reconstruction-Simulation-Perception (ReSimAD) scheme. Specifically, the implicit reconstruction process is based on the knowledge from the previous old domain, aiming to convert the domain-related knowledge into domain-invariant representations, e.g., 3D scene-level meshes. Besides, the point clouds simulation process of multiple new domains is conditioned on the above reconstructed 3D meshes, where the target-domain-like simulation samples can be obtained, thus reducing the cost of collecting and annotating new-domain data for the subsequent perception process. For experiments, we consider different cross-domain situations such as Waymo-to-KITTI, Waymo-to-nuScenes, Waymo-to-ONCE, etc, to verify the zero-shot target-domain perception using ReSimAD. Results demonstrate that our method is beneficial to boost the domain generalization ability, even promising for 3D pre-training.

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT), the problem of inferring the ground cost from samples drawn from a coupling that solves an eOT problem. It is a relevant problem that can be used to infer unobserved/missing links, and to obtain meaningful information about the structure of the ground cost yielding the pairing. On one side, iOT benefits from convexity, but on the other side, being ill-posed, it requires regularization to handle the sampling noise. This work presents an in-depth theoretical study of the l1 regularization to model for instance Euclidean costs with sparse interactions between features. Specifically, we derive a sufficient condition for the robust recovery of the sparsity of the ground cost that can be seen as a far reaching generalization of the Lasso's celebrated Irrepresentability Condition. To provide additional insight into this condition, we work out in detail the Gaussian case. We show that as the entropic penalty varies, the iOT problem interpolates between a graphical Lasso and a classical Lasso, thereby establishing a connection between iOT and graph estimation, an important problem in ML.

We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.

We introduce a deterministic variational formulation for training Bayesian last layer neural networks. This yields a sampling-free, single-pass model and loss that effectively improves uncertainty estimation. Our variational Bayesian last layer (VBLL) can be trained and evaluated with only quadratic complexity in last layer width, and is thus (nearly) computationally free to add to standard architectures. We experimentally investigate VBLLs, and show that they improve predictive accuracy, calibration, and out of distribution detection over baselines across both regression and classification. Finally, we investigate combining VBLL layers with variational Bayesian feature learning, yielding a lower variance collapsed variational inference method for Bayesian neural networks.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, applying different PINNs to solve the equation in each subdomain and aligning the solution at the interface of the subdomains. Hence, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of the multi-domain PINNs is sensitive to the choice of the interface conditions for solution alignment. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine the optimal interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit models. The first one applies to the entire training procedure, and online updates a Gaussian process (GP) reward surrogate that given the PDE parameters and interface conditions predicts the solution error. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP surrogate for each phase to enable different condition selections at the two stages so as to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.

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

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

In V2X collaborative perception, the domain gaps between heterogeneous nodes pose a significant challenge for effective information fusion. Pose errors arising from latency and GPS localization noise further exacerbate the issue by leading to feature misalignment. To overcome these challenges, we propose V2X-DGPE, a high-accuracy and robust V2X feature-level collaborative perception framework. V2X-DGPE employs a Knowledge Distillation Framework and a Feature Compensation Module to learn domain-invariant representations from multi-source data, effectively reducing the feature distribution gap between vehicles and roadside infrastructure. Historical information is utilized to provide the model with a more comprehensive understanding of the current scene. Furthermore, a Collaborative Fusion Module leverages a heterogeneous self-attention mechanism to extract and integrate heterogeneous representations from vehicles and infrastructure. To address pose errors, V2X-DGPE introduces a deformable attention mechanism, enabling the model to adaptively focus on critical parts of the input features by dynamically offsetting sampling points. Extensive experiments on the real-world DAIR-V2X dataset demonstrate that the proposed method outperforms existing approaches, achieving state-of-the-art detection performance. The code is available at https://github.com/wangsch10/V2X-DGPE.

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.

Learning navigation in dynamic open-world environments is an important yet challenging skill for robots. Most previous methods rely on precise localization and mapping or learn from expensive real-world demonstrations. In this paper, we propose the Navigation Diffusion Policy (NavDP), an end-to-end framework trained solely in simulation and can zero-shot transfer to different embodiments in diverse real-world environments. The key ingredient of NavDP's network is the combination of diffusion-based trajectory generation and a critic function for trajectory selection, which are conditioned on only local observation tokens encoded from a shared policy transformer. Given the privileged information of the global environment in simulation, we scale up the demonstrations of good quality to train the diffusion policy and formulate the critic value function targets with contrastive negative samples. Our demonstration generation approach achieves about 2,500 trajectories/GPU per day, 20times more efficient than real-world data collection, and results in a large-scale navigation dataset with 363.2km trajectories across 1244 scenes. Trained with this simulation dataset, NavDP achieves state-of-the-art performance and consistently outstanding generalization capability on quadruped, wheeled, and humanoid robots in diverse indoor and outdoor environments. In addition, we present a preliminary attempt at using Gaussian Splatting to make in-domain real-to-sim fine-tuning to further bridge the sim-to-real gap. Experiments show that adding such real-to-sim data can improve the success rate by 30\% without hurting its generalization capability.

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).

In crowd counting, due to the problem of laborious labelling, it is perceived intractability of collecting a new large-scale dataset which has plentiful images with large diversity in density, scene, etc. Thus, for learning a general model, training with data from multiple different datasets might be a remedy and be of great value. In this paper, we resort to the multi-domain joint learning and propose a simple but effective Domain-specific Knowledge Propagating Network (DKPNet)1 for unbiasedly learning the knowledge from multiple diverse data domains at the same time. It is mainly achieved by proposing the novel Variational Attention(VA) technique for explicitly modeling the attention distributions for different domains. And as an extension to VA, Intrinsic Variational Attention(InVA) is proposed to handle the problems of over-lapped domains and sub-domains. Extensive experiments have been conducted to validate the superiority of our DKPNet over several popular datasets, including ShanghaiTech A/B, UCF-QNRF and NWPU.

In this paper, we study the localization problem in dense urban settings. In such environments, Global Navigation Satellite Systems fail to provide good accuracy due to low likelihood of line-of-sight (LOS) links between the receiver (Rx) to be located and the satellites, due to the presence of obstacles like the buildings. Thus, one has to resort to other technologies, which can reliably operate under non-line-of-sight (NLOS) conditions. Recently, we proposed a Received Signal Strength (RSS) fingerprint and convolutional neural network-based algorithm, LocUNet, and demonstrated its state-of-the-art localization performance with respect to the widely adopted k-nearest neighbors (kNN) algorithm, and to state-of-the-art time of arrival (ToA) ranging-based methods. In the current work, we first recognize LocUNet's ability to learn the underlying prior distribution of the Rx position or Rx and transmitter (Tx) association preferences from the training data, and attribute its high performance to these. Conversely, we demonstrate that classical methods based on probabilistic approach, can greatly benefit from an appropriate incorporation of such prior information. Our studies also numerically prove LocUNet's close to optimal performance in many settings, by comparing it with the theoretically optimal formulations.

Cross-view image matching for geo-localisation is a challenging problem due to the significant visual difference between aerial and ground-level viewpoints. The method provides localisation capabilities from geo-referenced images, eliminating the need for external devices or costly equipment. This enhances the capacity of agents to autonomously determine their position, navigate, and operate effectively in GNSS-denied environments. Current research employs a variety of techniques to reduce the domain gap such as applying polar transforms to aerial images or synthesising between perspectives. However, these approaches generally rely on having a 360{\deg} field of view, limiting real-world feasibility. We propose BEV-CV, an approach introducing two key novelties with a focus on improving the real-world viability of cross-view geo-localisation. Firstly bringing ground-level images into a semantic Birds-Eye-View before matching embeddings, allowing for direct comparison with aerial image representations. Secondly, we adapt datasets into application realistic format - limited Field-of-View images aligned to vehicle direction. BEV-CV achieves state-of-the-art recall accuracies, improving Top-1 rates of 70{\deg} crops of CVUSA and CVACT by 23% and 24% respectively. Also decreasing computational requirements by reducing floating point operations to below previous works, and decreasing embedding dimensionality by 33% - together allowing for faster localisation capabilities.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

Wireless sensing has recently found widespread applications in diverse environments, including homes, offices, and public spaces. By analyzing patterns in channel state information (CSI), it is possible to infer human actions for tasks such as person identification, gesture recognition, and fall detection. However, CSI is highly sensitive to environmental changes, where even minor alterations can significantly distort the CSI patterns. This sensitivity often leads to performance degradation or outright failure when applying wireless sensing models trained in one environment to another. To address this challenge, Domain Alignment (DAL) has been widely adopted for cross-domain classification tasks, as it focuses on aligning the global distributions of the source and target domains in feature space. Despite its popularity, DAL often neglects inter-category relationships, which can lead to misalignment between categories across domains, even when global alignment is achieved. To overcome these limitations, we propose K-Nearest Neighbors Maximum Mean Discrepancy (KNN-MMD), a novel few-shot method for cross-domain wireless sensing. Our approach begins by constructing a help set using KNN from the target domain, enabling local alignment between the source and target domains within each category using MMD. Additionally, we address a key instability issue commonly observed in cross-domain methods, where model performance fluctuates sharply between epochs. Further, most existing methods struggle to determine an optimal stopping point during training due to the absence of labeled data from the target domain. Our method resolves this by excluding the support set from the target domain during training and employing it as a validation set to determine the stopping criterion.The dataset and code are publicly available at https://github.com/RS2002/KNN-MMD .

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

We present a multi-modal trajectory generation and selection algorithm for real-world mapless outdoor navigation in human-centered environments. Such environments contain rich features like crosswalks, grass, and curbs, which are easily interpretable by humans, but not by mobile robots. We aim to compute suitable trajectories that (1) satisfy the environment-specific traversability constraints and (2) generate human-like paths while navigating on crosswalks, sidewalks, etc. Our formulation uses a Conditional Variational Autoencoder (CVAE) generative model enhanced with traversability constraints to generate multiple candidate trajectories for global navigation. We develop a visual prompting approach and leverage the Visual Language Model's (VLM) zero-shot ability of semantic understanding and logical reasoning to choose the best trajectory given the contextual information about the task. We evaluate our method in various outdoor scenes with wheeled robots and compare the performance with other global navigation algorithms. In practice, we observe an average improvement of 20.81% in satisfying traversability constraints and 28.51% in terms of human-like navigation in four different outdoor navigation scenarios.

Accurate geo-localization of Unmanned Aerial Vehicles (UAVs) is crucial for outdoor applications including search and rescue operations, power line inspections, and environmental monitoring. The vulnerability of Global Navigation Satellite Systems (GNSS) signals to interference and spoofing necessitates the development of additional robust localization methods for autonomous navigation. Visual Geo-localization (VG), leveraging onboard cameras and reference satellite maps, offers a promising solution for absolute localization. Specifically, Thermal Geo-localization (TG), which relies on image-based matching between thermal imagery with satellite databases, stands out by utilizing infrared cameras for effective nighttime localization. However, the efficiency and effectiveness of current TG approaches, are hindered by dense sampling on satellite maps and geometric noises in thermal query images. To overcome these challenges, we introduce STHN, a novel UAV thermal geo-localization approach that employs a coarse-to-fine deep homography estimation method. This method attains reliable thermal geo-localization within a 512-meter radius of the UAV's last known location even with a challenging 11\% size ratio between thermal and satellite images, despite the presence of indistinct textures and self-similar patterns. We further show how our research significantly enhances UAV thermal geo-localization performance and robustness against geometric noises under low-visibility conditions in the wild. The code is made publicly available.

Global visual geolocation predicts where an image was captured on Earth. Since images vary in how precisely they can be localized, this task inherently involves a significant degree of ambiguity. However, existing approaches are deterministic and overlook this aspect. In this paper, we aim to close the gap between traditional geolocalization and modern generative methods. We propose the first generative geolocation approach based on diffusion and Riemannian flow matching, where the denoising process operates directly on the Earth's surface. Our model achieves state-of-the-art performance on three visual geolocation benchmarks: OpenStreetView-5M, YFCC-100M, and iNat21. In addition, we introduce the task of probabilistic visual geolocation, where the model predicts a probability distribution over all possible locations instead of a single point. We introduce new metrics and baselines for this task, demonstrating the advantages of our diffusion-based approach. Codes and models will be made available.

Cross-view geo-localization is a promising solution for large-scale localization problems, requiring the sequential execution of retrieval and metric localization tasks to achieve fine-grained predictions. However, existing methods typically focus on designing standalone models for these two tasks, resulting in inefficient collaboration and increased training overhead. In this paper, we propose UnifyGeo, a novel unified hierarchical geo-localization framework that integrates retrieval and metric localization tasks into a single network. Specifically, we first employ a unified learning strategy with shared parameters to jointly learn multi-granularity representation, facilitating mutual reinforcement between these two tasks. Subsequently, we design a re-ranking mechanism guided by a dedicated loss function, which enhances geo-localization performance by improving both retrieval accuracy and metric localization references. Extensive experiments demonstrate that UnifyGeo significantly outperforms the state-of-the-arts in both task-isolated and task-associated settings. Remarkably, on the challenging VIGOR benchmark, which supports fine-grained localization evaluation, the 1-meter-level localization recall rate improves from 1.53\% to 39.64\% and from 0.43\% to 25.58\% under same-area and cross-area evaluations, respectively. Code will be made publicly available.

We introduce M2DGR: a novel large-scale dataset collected by a ground robot with a full sensor-suite including six fish-eye and one sky-pointing RGB cameras, an infrared camera, an event camera, a Visual-Inertial Sensor (VI-sensor), an inertial measurement unit (IMU), a LiDAR, a consumer-grade Global Navigation Satellite System (GNSS) receiver and a GNSS-IMU navigation system with real-time kinematic (RTK) signals. All those sensors were well-calibrated and synchronized, and their data were recorded simultaneously. The ground truth trajectories were obtained by the motion capture device, a laser 3D tracker, and an RTK receiver. The dataset comprises 36 sequences (about 1TB) captured in diverse scenarios including both indoor and outdoor environments. We evaluate state-of-the-art SLAM algorithms on M2DGR. Results show that existing solutions perform poorly in some scenarios. For the benefit of the research community, we make the dataset and tools public. The webpage of our project is https://github.com/SJTU-ViSYS/M2DGR.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

We propose a novel method for geolocalizing Unmanned Aerial Vehicles (UAVs) in environments lacking Global Navigation Satellite Systems (GNSS). Current state-of-the-art techniques employ an offline-trained encoder to generate a vector representation (embedding) of the UAV's current view, which is then compared with pre-computed embeddings of geo-referenced images to determine the UAV's position. Here, we demonstrate that the performance of these methods can be significantly enhanced by preprocessing the images to extract their edges, which exhibit robustness to seasonal and illumination variations. Furthermore, we establish that utilizing edges enhances resilience to orientation and altitude inaccuracies. Additionally, we introduce a confidence criterion for localization. Our findings are substantiated through synthetic experiments.

Accurate localization using visual information is a critical yet challenging task, especially in urban environments where nearby buildings and construction sites significantly degrade GNSS (Global Navigation Satellite System) signal quality. This issue underscores the importance of visual localization techniques in scenarios where GNSS signals are unreliable. This paper proposes U-ViLAR, a novel uncertainty-aware visual localization framework designed to address these challenges while enabling adaptive localization using high-definition (HD) maps or navigation maps. Specifically, our method first extracts features from the input visual data and maps them into Bird's-Eye-View (BEV) space to enhance spatial consistency with the map input. Subsequently, we introduce: a) Perceptual Uncertainty-guided Association, which mitigates errors caused by perception uncertainty, and b) Localization Uncertainty-guided Registration, which reduces errors introduced by localization uncertainty. By effectively balancing the coarse-grained large-scale localization capability of association with the fine-grained precise localization capability of registration, our approach achieves robust and accurate localization. Experimental results demonstrate that our method achieves state-of-the-art performance across multiple localization tasks. Furthermore, our model has undergone rigorous testing on large-scale autonomous driving fleets and has demonstrated stable performance in various challenging urban scenarios.

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.

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

Safety and robustness are crucial factors in developing trustworthy autonomous vehicles. One essential aspect of addressing these factors is to equip vehicles with the capability to predict future trajectories for all moving objects in the surroundings and quantify prediction uncertainties. In this paper, we propose the Sequential Neural Variational Agent (SeNeVA), a generative model that describes the distribution of future trajectories for a single moving object. Our approach can distinguish Out-of-Distribution data while quantifying uncertainty and achieving competitive performance compared to state-of-the-art methods on the Argoverse 2 and INTERACTION datasets. Specifically, a 0.446 meters minimum Final Displacement Error, a 0.203 meters minimum Average Displacement Error, and a 5.35% Miss Rate are achieved on the INTERACTION test set. Extensive qualitative and quantitative analysis is also provided to evaluate the proposed model. Our open-source code is available at https://github.com/PurdueDigitalTwin/seneva.

We propose 4DGT, a 4D Gaussian-based Transformer model for dynamic scene reconstruction, trained entirely on real-world monocular posed videos. Using 4D Gaussian as an inductive bias, 4DGT unifies static and dynamic components, enabling the modeling of complex, time-varying environments with varying object lifespans. We proposed a novel density control strategy in training, which enables our 4DGT to handle longer space-time input and remain efficient rendering at runtime. Our model processes 64 consecutive posed frames in a rolling-window fashion, predicting consistent 4D Gaussians in the scene. Unlike optimization-based methods, 4DGT performs purely feed-forward inference, reducing reconstruction time from hours to seconds and scaling effectively to long video sequences. Trained only on large-scale monocular posed video datasets, 4DGT can outperform prior Gaussian-based networks significantly in real-world videos and achieve on-par accuracy with optimization-based methods on cross-domain videos. Project page: https://4dgt.github.io

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data via the estimated epipolar geometries.We propose to better model the underlying noise distributions by directly propagating the uncertainty from the point correspondences into the rotation averaging. Such uncertainties are obtained for free by considering the Jacobians of two-view refinements. Moreover, we explore integrating a variant of the MAGSAC loss into the rotation averaging problem, instead of using classical robust losses employed in current frameworks. The proposed method leads to results superior to baselines, in terms of accuracy, on large-scale public benchmarks. The code is public. https://github.com/zhangganlin/GlobalSfMpy

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

The vision-based geo-localization technology for UAV, serving as a secondary source of GPS information in addition to the global navigation satellite systems (GNSS), can still operate independently in the GPS-denied environment. Recent deep learning based methods attribute this as the task of image matching and retrieval. By retrieving drone-view images in geo-tagged satellite image database, approximate localization information can be obtained. However, due to high costs and privacy concerns, it is usually difficult to obtain large quantities of drone-view images from a continuous area. Existing drone-view datasets are mostly composed of small-scale aerial photography with a strong assumption that there exists a perfect one-to-one aligned reference image for any query, leaving a significant gap from the practical localization scenario. In this work, we construct a large-range contiguous area UAV geo-localization dataset named GTA-UAV, featuring multiple flight altitudes, attitudes, scenes, and targets using modern computer games. Based on this dataset, we introduce a more practical UAV geo-localization task including partial matches of cross-view paired data, and expand the image-level retrieval to the actual localization in terms of distance (meters). For the construction of drone-view and satellite-view pairs, we adopt a weight-based contrastive learning approach, which allows for effective learning while avoiding additional post-processing matching steps. Experiments demonstrate the effectiveness of our data and training method for UAV geo-localization, as well as the generalization capabilities to real-world scenarios.

The prediction of ship trajectories is a growing field of study in artificial intelligence. Traditional methods rely on the use of LSTM, GRU networks, and even Transformer architectures for the prediction of spatio-temporal series. This study proposes a viable alternative for predicting these trajectories using only GNSS positions. It considers this spatio-temporal problem as a natural language processing problem. The latitude/longitude coordinates of AIS messages are transformed into cell identifiers using the H3 index. Thanks to the pseudo-octal representation, it becomes easier for language models to learn the spatial hierarchy of the H3 index. The method is compared with a classical Kalman filter, widely used in the maritime domain, and introduces the Fr\'echet distance as the main evaluation metric. We show that it is possible to predict ship trajectories quite precisely up to 8 hours with 30 minutes of context. We demonstrate that this alternative works well enough to predict trajectories worldwide.

Variational inequalities in general and saddle point problems in particular are increasingly relevant in machine learning applications, including adversarial learning, GANs, transport and robust optimization. With increasing data and problem sizes necessary to train high performing models across various applications, we need to rely on parallel and distributed computing. However, in distributed training, communication among the compute nodes is a key bottleneck during training, and this problem is exacerbated for high dimensional and over-parameterized models. Due to these considerations, it is important to equip existing methods with strategies that would allow to reduce the volume of transmitted information during training while obtaining a model of comparable quality. In this paper, we present the first theoretically grounded distributed methods for solving variational inequalities and saddle point problems using compressed communication: MASHA1 and MASHA2. Our theory and methods allow for the use of both unbiased (such as Randk; MASHA1) and contractive (such as Topk; MASHA2) compressors. New algorithms support bidirectional compressions, and also can be modified for stochastic setting with batches and for federated learning with partial participation of clients. We empirically validated our conclusions using two experimental setups: a standard bilinear min-max problem, and large-scale distributed adversarial training of transformers.

Cross-modal place recognition methods are flexible GPS-alternatives under varying environment conditions and sensor setups. However, this task is non-trivial since extracting consistent and robust global descriptors from different modalities is challenging. To tackle this issue, we propose Voxel-Cross-Pixel (VXP), a novel camera-to-LiDAR place recognition framework that enforces local similarities in a self-supervised manner and effectively brings global context from images and LiDAR scans into a shared feature space. Specifically, VXP is trained in three stages: first, we deploy a visual transformer to compactly represent input images. Secondly, we establish local correspondences between image-based and point cloud-based feature spaces using our novel geometric alignment module. We then aggregate local similarities into an expressive shared latent space. Extensive experiments on the three benchmarks (Oxford RobotCar, ViViD++ and KITTI) demonstrate that our method surpasses the state-of-the-art cross-modal retrieval by a large margin. Our evaluations show that the proposed method is accurate, efficient and light-weight. Our project page is available at: https://yunjinli.github.io/projects-vxp/

Considerable advancements have been achieved in SLAM methods tailored for structured environments, yet their robustness under challenging corner cases remains a critical limitation. Although multi-sensor fusion approaches integrating diverse sensors have shown promising performance improvements, the research community faces two key barriers: On one hand, the lack of standardized and configurable benchmarks that systematically evaluate SLAM algorithms under diverse degradation scenarios hinders comprehensive performance assessment. While on the other hand, existing SLAM frameworks primarily focus on fusing a limited set of sensor types, without effectively addressing adaptive sensor selection strategies for varying environmental conditions. To bridge these gaps, we make three key contributions: First, we introduce M3DGR dataset: a sensor-rich benchmark with systematically induced degradation patterns including visual challenge, LiDAR degeneracy, wheel slippage and GNSS denial. Second, we conduct a comprehensive evaluation of forty SLAM systems on M3DGR, providing critical insights into their robustness and limitations under challenging real-world conditions. Third, we develop a resilient modular multi-sensor fusion framework named Ground-Fusion++, which demonstrates robust performance by coupling GNSS, RGB-D, LiDAR, IMU (Inertial Measurement Unit) and wheel odometry. Codes and datasets are publicly available.

Worldwide Geo-localization aims to pinpoint the precise location of images taken anywhere on Earth. This task has considerable challenges due to immense variation in geographic landscapes. The image-to-image retrieval-based approaches fail to solve this problem on a global scale as it is not feasible to construct a large gallery of images covering the entire world. Instead, existing approaches divide the globe into discrete geographic cells, transforming the problem into a classification task. However, their performance is limited by the predefined classes and often results in inaccurate localizations when an image's location significantly deviates from its class center. To overcome these limitations, we propose GeoCLIP, a novel CLIP-inspired Image-to-GPS retrieval approach that enforces alignment between the image and its corresponding GPS locations. GeoCLIP's location encoder models the Earth as a continuous function by employing positional encoding through random Fourier features and constructing a hierarchical representation that captures information at varying resolutions to yield a semantically rich high-dimensional feature suitable to use even beyond geo-localization. To the best of our knowledge, this is the first work employing GPS encoding for geo-localization. We demonstrate the efficacy of our method via extensive experiments and ablations on benchmark datasets. We achieve competitive performance with just 20% of training data, highlighting its effectiveness even in limited-data settings. Furthermore, we qualitatively demonstrate geo-localization using a text query by leveraging CLIP backbone of our image encoder. The project webpage is available at: https://vicentevivan.github.io/GeoCLIP

We introduce Gaussian-Flow, a novel point-based approach for fast dynamic scene reconstruction and real-time rendering from both multi-view and monocular videos. In contrast to the prevalent NeRF-based approaches hampered by slow training and rendering speeds, our approach harnesses recent advancements in point-based 3D Gaussian Splatting (3DGS). Specifically, a novel Dual-Domain Deformation Model (DDDM) is proposed to explicitly model attribute deformations of each Gaussian point, where the time-dependent residual of each attribute is captured by a polynomial fitting in the time domain, and a Fourier series fitting in the frequency domain. The proposed DDDM is capable of modeling complex scene deformations across long video footage, eliminating the need for training separate 3DGS for each frame or introducing an additional implicit neural field to model 3D dynamics. Moreover, the explicit deformation modeling for discretized Gaussian points ensures ultra-fast training and rendering of a 4D scene, which is comparable to the original 3DGS designed for static 3D reconstruction. Our proposed approach showcases a substantial efficiency improvement, achieving a 5times faster training speed compared to the per-frame 3DGS modeling. In addition, quantitative results demonstrate that the proposed Gaussian-Flow significantly outperforms previous leading methods in novel view rendering quality. Project page: https://nju-3dv.github.io/projects/Gaussian-Flow

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Statistical channel models are instrumental to design and evaluate wireless communication systems. In the millimeter wave bands, such models become acutely challenging; they must capture the delay, directions, and path gains, for each link and with high resolution. This paper presents a general modeling methodology based on training generative neural networks from data. The proposed generative model consists of a two-stage structure that first predicts the state of each link (line-of-sight, non-line-of-sight, or outage), and subsequently feeds this state into a conditional variational autoencoder that generates the path losses, delays, and angles of arrival and departure for all its propagation paths. Importantly, minimal prior assumptions are made, enabling the model to capture complex relationships within the data. The methodology is demonstrated for 28GHz air-to-ground channels in an urban environment, with training datasets produced by means of ray tracing.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

SLAM plays a crucial role in automation tasks, such as warehouse logistics, healthcare robotics, and restaurant delivery. These scenes come with various challenges, including navigating around crowds of people, dealing with flying plastic bags that can temporarily blind sensors, and addressing reduced LiDAR density caused by cooking smoke. Such scenarios can result in over-degeneracy, causing the map to drift. To address this issue, this paper presents a multi-map LiDAR-inertial system (MM-LINS) for the first time. The front-end employs an iterated error state Kalman filter for state estimation and introduces a reliable evaluation strategy for degeneracy detection. If over-degeneracy is detected, the active map will be stored into sleeping maps. Subsequently, the system continuously attempts to construct new maps using a dynamic initialization method to ensure successful initialization upon leaving the over-degeneracy. Regarding the back-end, the Scan Context descriptor is utilized to detect inter-map similarity. Upon successful recognition of a sleeping map that shares a common region with the active map, the overlapping trajectory region is utilized to constrain the positional transformation near the edge of the prior map. In response to this, a constraint-enhanced map fusion strategy is proposed to achieve high-precision positional and mapping results. Experiments have been conducted separately on both public datasets that exhibited over-degenerate conditions and in real-world environments. These tests demonstrated the effectiveness of MM-LINS in over-degeneracy environment. Our codes are open-sourced on Github.

LiDAR-based localization is valuable for applications like mining surveys and underground facility maintenance. However, existing methods can struggle when dealing with uninformative geometric structures in challenging scenarios. This paper presents RELEAD, a LiDAR-centric solution designed to address scan-matching degradation. Our method enables degeneracy-free point cloud registration by solving constrained ESIKF updates in the front end and incorporates multisensor constraints, even when dealing with outlier measurements, through graph optimization based on Graduated Non-Convexity (GNC). Additionally, we propose a robust Incremental Fixed Lag Smoother (rIFL) for efficient GNC-based optimization. RELEAD has undergone extensive evaluation in degenerate scenarios and has outperformed existing state-of-the-art LiDAR-Inertial odometry and LiDAR-Visual-Inertial odometry methods.

Learning-based outlier (mismatched correspondence) rejection for robust 3D registration generally formulates the outlier removal as an inlier/outlier classification problem. The core for this to be successful is to learn the discriminative inlier/outlier feature representations. In this paper, we develop a novel variational non-local network-based outlier rejection framework for robust alignment. By reformulating the non-local feature learning with variational Bayesian inference, the Bayesian-driven long-range dependencies can be modeled to aggregate discriminative geometric context information for inlier/outlier distinction. Specifically, to achieve such Bayesian-driven contextual dependencies, each query/key/value component in our non-local network predicts a prior feature distribution and a posterior one. Embedded with the inlier/outlier label, the posterior feature distribution is label-dependent and discriminative. Thus, pushing the prior to be close to the discriminative posterior in the training step enables the features sampled from this prior at test time to model high-quality long-range dependencies. Notably, to achieve effective posterior feature guidance, a specific probabilistic graphical model is designed over our non-local model, which lets us derive a variational low bound as our optimization objective for model training. Finally, we propose a voting-based inlier searching strategy to cluster the high-quality hypothetical inliers for transformation estimation. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI datasets verify the effectiveness of our method.

Accurate ocean modeling and coastal hazard prediction depend on high-resolution bathymetric data; yet, current worldwide datasets are too coarse for exact numerical simulations. While recent deep learning advances have improved earth observation data resolution, existing methods struggle with the unique challenges of producing detailed ocean floor maps, especially in maintaining physical structure consistency and quantifying uncertainties. This work presents a novel uncertainty-aware mechanism using spatial blocks to efficiently capture local bathymetric complexity based on block-based conformal prediction. Using the Vector Quantized Variational Autoencoder (VQ-VAE) architecture, the integration of this uncertainty quantification framework yields spatially adaptive confidence estimates while preserving topographical features via discrete latent representations. With smaller uncertainty widths in well-characterized areas and appropriately larger bounds in areas of complex seafloor structures, the block-based design adapts uncertainty estimates to local bathymetric complexity. Compared to conventional techniques, experimental results over several ocean regions show notable increases in both reconstruction quality and uncertainty estimation reliability. This framework increases the reliability of bathymetric reconstructions by preserving structural integrity while offering spatially adaptive uncertainty estimates, so opening the path for more solid climate modeling and coastal hazard assessment.

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training data, learning under privacy constraints, or even heavy-tailed noise due to the dynamics of the algorithm itself. Here we study SGD with robust gradient estimators based on estimating the median. We first consider computing the median gradient across samples, and show that the resulting method can converge even under heavy-tailed, state-dependent noise. We then derive iterative methods based on the stochastic proximal point method for computing the geometric median and generalizations thereof. Finally we propose an algorithm estimating the median gradient across iterations, and find that several well known methods - in particular different forms of clipping - are particular cases of this framework.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Onboard sensors, such as cameras and thermal sensors, have emerged as effective alternatives to Global Positioning System (GPS) for geo-localization in Unmanned Aerial Vehicle (UAV) navigation. Since GPS can suffer from signal loss and spoofing problems, researchers have explored camera-based techniques such as Visual Geo-localization (VG) using satellite RGB imagery. Additionally, thermal geo-localization (TG) has become crucial for long-range UAV flights in low-illumination environments. This paper proposes a novel thermal geo-localization framework using satellite RGB imagery, which includes multiple domain adaptation methods to address the limited availability of paired thermal and satellite images. The experimental results demonstrate the effectiveness of the proposed approach in achieving reliable thermal geo-localization performance, even in thermal images with indistinct self-similar features. We evaluate our approach on real data collected onboard a UAV. We also release the code and Boson-nighttime, a dataset of paired satellite-thermal and unpaired satellite images for thermal geo-localization with satellite imagery. To the best of our knowledge, this work is the first to propose a thermal geo-localization method using satellite RGB imagery in long-range flights.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

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

In recent years, 3D Gaussian splatting (3D-GS) has emerged as a novel scene representation approach. However, existing vision-only 3D-GS methods often rely on hand-crafted heuristics for point-cloud densification and face challenges in handling occlusions and high GPU memory and computation consumption. LiDAR-Inertial-Visual (LIV) sensor configuration has demonstrated superior performance in localization and dense mapping by leveraging complementary sensing characteristics: rich texture information from cameras, precise geometric measurements from LiDAR, and high-frequency motion data from IMU. Inspired by this, we propose a novel real-time Gaussian-based simultaneous localization and mapping (SLAM) system. Our map system comprises a global Gaussian map and a sliding window of Gaussians, along with an IESKF-based odometry. The global Gaussian map consists of hash-indexed voxels organized in a recursive octree, effectively covering sparse spatial volumes while adapting to different levels of detail and scales. The Gaussian map is initialized through multi-sensor fusion and optimized with photometric gradients. Our system incrementally maintains a sliding window of Gaussians, significantly reducing GPU computation and memory consumption by only optimizing the map within the sliding window. Moreover, we implement a tightly coupled multi-sensor fusion odometry with an iterative error state Kalman filter (IESKF), leveraging real-time updating and rendering of the Gaussian map. Our system represents the first real-time Gaussian-based SLAM framework deployable on resource-constrained embedded systems, demonstrated on the NVIDIA Jetson Orin NX platform. The framework achieves real-time performance while maintaining robust multi-sensor fusion capabilities. All implementation algorithms, hardware designs, and CAD models will be publicly available.

Collaborative state estimation using different heterogeneous sensors is a fundamental prerequisite for robotic swarms operating in GPS-denied environments, posing a significant research challenge. In this paper, we introduce a centralized system to facilitate collaborative LiDAR-ranging-inertial state estimation, enabling robotic swarms to operate without the need for anchor deployment. The system efficiently distributes computationally intensive tasks to a central server, thereby reducing the computational burden on individual robots for local odometry calculations. The server back-end establishes a global reference by leveraging shared data and refining joint pose graph optimization through place recognition, global optimization techniques, and removal of outlier data to ensure precise and robust collaborative state estimation. Extensive evaluations of our system, utilizing both publicly available datasets and our custom datasets, demonstrate significant enhancements in the accuracy of collaborative SLAM estimates. Moreover, our system exhibits remarkable proficiency in large-scale missions, seamlessly enabling ten robots to collaborate effectively in performing SLAM tasks. In order to contribute to the research community, we will make our code open-source and accessible at https://github.com/PengYu-team/Co-LRIO.

Maintaining an up-to-date map that accurately reflects recent changes in the environment is crucial, especially for robots that repeatedly traverse the same space. Failing to promptly update the changed regions can degrade map quality, resulting in poor localization, inefficient operations, and even lost robots. 3D Gaussian Splatting (3DGS) has recently seen widespread adoption in online map reconstruction due to its dense, differentiable, and photorealistic properties, yet accurately and efficiently updating the regions of change remains a challenge. In this paper, we propose VG-Mapping, a novel online 3DGS-based mapping system tailored for such semi-static scenes. Our approach introduces a hybrid representation that augments 3DGS with a TSDF-based voxel map to efficiently identify changed regions in a scene, along with a variation-aware density control strategy that inserts or deletes Gaussian primitives in regions undergoing change. Furthermore, to address the absence of public benchmarks for this task, we construct a RGB-D dataset comprising both synthetic and real-world semi-static environments. Experimental results demonstrate that our method substantially improves the rendering quality and map update efficiency in semi-static scenes. The code and dataset are available at https://github.com/heyicheng-never/VG-Mapping.

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning probability measures to the spatial domain, which allows us to treat collocation grids probabilistically as random variables to be marginalised out. Adapting this spatial statistics view, we solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. The implementation of these random grids poses a unique set of challenges for inverse physics informed deep learning frameworks and we propose a new architecture called Grid Invariant Convolutional Networks (GICNets) to overcome these challenges. We further show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available but whose measurement location does not coincide with any fixed mesh or grid. The proposed method is tested on a nonlinear Poisson problem, Burgers equation, and Navier-Stokes equations, and we provide extensive numerical comparisons. We demonstrate significant computational advantages over current physics informed neural learning methods for parametric PDEs while improving the predictive capabilities and flexibility of these models.

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

This paper considers an integrated sensing and communication system, where some radar targets also serve as communication scatterers. A location domain channel modeling method is proposed based on the position of targets and scatterers in the scattering environment, and the resulting radar and communication channels exhibit a two-dimensional (2-D) joint burst sparsity. We propose a joint scattering environment sensing and channel estimation scheme to enhance the target/scatterer localization and channel estimation performance simultaneously, where a spatially non-stationary Markov random field (MRF) model is proposed to capture the 2-D joint burst sparsity. An expectation maximization (EM) based method is designed to solve the joint estimation problem, where the E-step obtains the Bayesian estimation of the radar and communication channels and the M-step automatically learns the dynamic position grid and prior parameters in the MRF. However, the existing sparse Bayesian inference methods used in the E-step involve a high-complexity matrix inverse per iteration. Moreover, due to the complicated non-stationary MRF prior, the complexity of M-step is exponentially large. To address these difficulties, we propose an inverse-free variational Bayesian inference algorithm for the E-step and a low-complexity method based on pseudo-likelihood approximation for the M-step. In the simulations, the proposed scheme can achieve a better performance than the state-of-the-art method while reducing the computational overhead significantly.

Geo-localization is an essential component of Unmanned Aerial Vehicle (UAV) navigation systems to ensure precise absolute self-localization in outdoor environments. To address the challenges of GPS signal interruptions or low illumination, Thermal Geo-localization (TG) employs aerial thermal imagery to align with reference satellite maps to accurately determine the UAV's location. However, existing TG methods lack uncertainty measurement in their outputs, compromising system robustness in the presence of textureless or corrupted thermal images, self-similar or outdated satellite maps, geometric noises, or thermal images exceeding satellite maps. To overcome these limitations, this paper presents UASTHN, a novel approach for Uncertainty Estimation (UE) in Deep Homography Estimation (DHE) tasks for TG applications. Specifically, we introduce a novel Crop-based Test-Time Augmentation (CropTTA) strategy, which leverages the homography consensus of cropped image views to effectively measure data uncertainty. This approach is complemented by Deep Ensembles (DE) employed for model uncertainty, offering comparable performance with improved efficiency and seamless integration with any DHE model. Extensive experiments across multiple DHE models demonstrate the effectiveness and efficiency of CropTTA in TG applications. Analysis of detected failure cases underscores the improved reliability of CropTTA under challenging conditions. Finally, we demonstrate the capability of combining CropTTA and DE for a comprehensive assessment of both data and model uncertainty. Our research provides profound insights into the broader intersection of localization and uncertainty estimation. The code and models are publicly available.

Robust and accurate localization for Unmanned Aerial Vehicles (UAVs) is an essential capability to achieve autonomous, long-range flights. Current methods either rely heavily on GNSS, face limitations in visual-based localization due to appearance variances and stylistic dissimilarities between camera and reference imagery, or operate under the assumption of a known initial pose. In this paper, we developed a GNSS-denied localization approach for UAVs that harnesses both Visual-Inertial Odometry (VIO) and Visual Place Recognition (VPR) using a foundation model. This paper presents a novel vision-based pipeline that works exclusively with a nadir-facing camera, an Inertial Measurement Unit (IMU), and pre-existing satellite imagery for robust, accurate localization in varied environments and conditions. Our system demonstrated average localization accuracy within a 20-meter range, with a minimum error below 1 meter, under real-world conditions marked by drastic changes in environmental appearance and with no assumption of the vehicle's initial pose. The method is proven to be effective and robust, addressing the crucial need for reliable UAV localization in GNSS-denied environments, while also being computationally efficient enough to be deployed on resource-constrained platforms.

Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical systems as factors of variation of the data generating process. By leveraging ideas from supervised disentanglement and causal factorization, we aim to separate the domain parameters from the dynamics in the latent space of generative models. In our experiments we model dynamics both in phase space and in video sequences and conduct rigorous OOD evaluations. Results indicate that disentangled VAEs adapt better to domain parameters spaces that were not present in the training data. At the same time, disentanglement can improve the long-term and out-of-distribution predictions of state-of-the-art models in video sequences.

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.

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.

Generative modeling of 3D LiDAR data is an emerging task with promising applications for autonomous mobile robots, such as scalable simulation, scene manipulation, and sparse-to-dense completion of LiDAR point clouds. While existing approaches have demonstrated the feasibility of image-based LiDAR data generation using deep generative models, they still struggle with fidelity and training stability. In this work, we present R2DM, a novel generative model for LiDAR data that can generate diverse and high-fidelity 3D scene point clouds based on the image representation of range and reflectance intensity. Our method is built upon denoising diffusion probabilistic models (DDPMs), which have shown impressive results among generative model frameworks in recent years. To effectively train DDPMs in the LiDAR domain, we first conduct an in-depth analysis of data representation, loss functions, and spatial inductive biases. Leveraging our R2DM model, we also introduce a flexible LiDAR completion pipeline based on the powerful capabilities of DDPMs. We demonstrate that our method surpasses existing methods in generating tasks on the KITTI-360 and KITTI-Raw datasets, as well as in the completion task on the KITTI-360 dataset. Our project page can be found at https://kazuto1011.github.io/r2dm.

As the development of cities, traffic congestion becomes an increasingly pressing issue, and traffic prediction is a classic method to relieve that issue. Traffic prediction is one specific application of spatio-temporal prediction learning, like taxi scheduling, weather prediction, and ship trajectory prediction. Against these problems, classical spatio-temporal prediction learning methods including deep learning, require large amounts of training data. In reality, some newly developed cities with insufficient sensors would not hold that assumption, and the data scarcity makes predictive performance worse. In such situation, the learning method on insufficient data is known as few-shot learning (FSL), and the FSL of traffic prediction remains challenges. On the one hand, graph structures' irregularity and dynamic nature of graphs cannot hold the performance of spatio-temporal learning method. On the other hand, conventional domain adaptation methods cannot work well on insufficient training data, when transferring knowledge from different domains to the intended target domain.To address these challenges, we propose a novel spatio-temporal domain adaptation (STDA) method that learns transferable spatio-temporal meta-knowledge from data-sufficient cities in an adversarial manner. This learned meta-knowledge can improve the prediction performance of data-scarce cities. Specifically, we train the STDA model using a Model-Agnostic Meta-Learning (MAML) based episode learning process, which is a model-agnostic meta-learning framework that enables the model to solve new learning tasks using only a small number of training samples. We conduct numerous experiments on four traffic prediction datasets, and our results show that the prediction performance of our model has improved by 7\% compared to baseline models on the two metrics of MAE and RMSE.

Generating 3D images of complex objects conditionally from a few 2D views is a difficult synthesis problem, compounded by issues such as domain gap and geometric misalignment. For instance, a unified framework such as Generative Adversarial Networks cannot achieve this unless they explicitly define both a domain-invariant and geometric-invariant joint latent distribution, whereas Neural Radiance Fields are generally unable to handle both issues as they optimize at the pixel level. By contrast, we propose a simple and novel 2D to 3D synthesis approach based on conditional diffusion with vector-quantized codes. Operating in an information-rich code space enables high-resolution 3D synthesis via full-coverage attention across the views. Specifically, we generate the 3D codes (e.g. for CT images) conditional on previously generated 3D codes and the entire codebook of two 2D views (e.g. 2D X-rays). Qualitative and quantitative results demonstrate state-of-the-art performance over specialized methods across varied evaluation criteria, including fidelity metrics such as density, coverage, and distortion metrics for two complex volumetric imagery datasets from in real-world scenarios.

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.

Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains. However, we argue that the domain variantions also contain useful information, ie, classification-aware information, for downstream tasks, which has been largely ignored. Different from learning domain invariant features from source domains, we decouple the input images into Domain Expert Features and noise. The proposed domain expert features lie in a learned latent space where the images in each domain can be classified independently, enabling the implicit use of classification-aware domain variations. Based on the analysis, we proposed a novel paradigm called Domain Disentanglement Network (DDN) to disentangle the domain expert features from the source domain images and aggregate the source domain expert features for representing the target test domain. We also propound a new contrastive learning method to guide the domain expert features to form a more balanced and separable feature space. Experiments on the widely-used benchmarks of PACS, VLCS, OfficeHome, DomainNet, and TerraIncognita demonstrate the competitive performance of our method compared to the recently proposed alternatives.

The global positioning system (GPS) has become an indispensable navigation method for field operations with unmanned surface vehicles (USVs) in marine environments. However, GPS may not always be available outdoors because it is vulnerable to natural interference and malicious jamming attacks. Thus, an alternative navigation system is required when the use of GPS is restricted or prohibited. To this end, we present a novel method that utilizes an Unmanned Aerial Vehicle (UAV) to assist in localizing USVs in GNSS-restricted marine environments. In our approach, the UAV flies along the shoreline at a consistent altitude, continuously tracking and detecting the USV using a deep learning-based approach on camera images. Subsequently, triangulation techniques are applied to estimate the USV's position relative to the UAV, utilizing geometric information and datalink range from the UAV. We propose adjusting the UAV's camera angle based on the pixel error between the USV and the image center throughout the localization process to enhance accuracy. Additionally, visual measurements are integrated into an Extended Kalman Filter (EKF) for robust state estimation. To validate our proposed method, we utilize a USV equipped with onboard sensors and a UAV equipped with a camera. A heterogeneous robotic interface is established to facilitate communication between the USV and UAV. We demonstrate the efficacy of our approach through a series of experiments conducted during the ``Muhammad Bin Zayed International Robotic Challenge (MBZIRC-2024)'' in real marine environments, incorporating noisy measurements and ocean disturbances. The successful outcomes indicate the potential of our method to complement GPS for USV navigation.

We give extensive empirical evidence against the common belief that variational learning is ineffective for large neural networks. We show that an optimizer called Improved Variational Online Newton (IVON) consistently matches or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of IVON where we improve finetuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence that variational learning is effective.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Visual object tracking is essential to intelligent robots. Most existing approaches have ignored the online latency that can cause severe performance degradation during real-world processing. Especially for unmanned aerial vehicles (UAVs), where robust tracking is more challenging and onboard computation is limited, the latency issue can be fatal. In this work, we present a simple framework for end-to-end latency-aware tracking, i.e., end-to-end predictive visual tracking (PVT++). Unlike existing solutions that naively append Kalman Filters after trackers, PVT++ can be jointly optimized, so that it takes not only motion information but can also leverage the rich visual knowledge in most pre-trained tracker models for robust prediction. Besides, to bridge the training-evaluation domain gap, we propose a relative motion factor, empowering PVT++ to generalize to the challenging and complex UAV tracking scenes. These careful designs have made the small-capacity lightweight PVT++ a widely effective solution. Additionally, this work presents an extended latency-aware evaluation benchmark for assessing an any-speed tracker in the online setting. Empirical results on a robotic platform from the aerial perspective show that PVT++ can achieve significant performance gain on various trackers and exhibit higher accuracy than prior solutions, largely mitigating the degradation brought by latency.

The objective of domain generalization (DG) is to enhance the transferability of the model learned from a source domain to unobserved domains. To prevent overfitting to a specific domain, Sharpness-Aware Minimization (SAM) reduces source domain's loss sharpness. Although SAM variants have delivered significant improvements in DG, we highlight that there's still potential for improvement in generalizing to unknown domains through the exploration on data space. This paper introduces an objective rooted in both parameter and data perturbed regions for domain generalization, coined Unknown Domain Inconsistency Minimization (UDIM). UDIM reduces the loss landscape inconsistency between source domain and unknown domains. As unknown domains are inaccessible, these domains are empirically crafted by perturbing instances from the source domain dataset. In particular, by aligning the loss landscape acquired in the source domain to the loss landscape of perturbed domains, we expect to achieve generalization grounded on these flat minima for the unknown domains. Theoretically, we validate that merging SAM optimization with the UDIM objective establishes an upper bound for the true objective of the DG task. In an empirical aspect, UDIM consistently outperforms SAM variants across multiple DG benchmark datasets. Notably, UDIM shows statistically significant improvements in scenarios with more restrictive domain information, underscoring UDIM's generalization capability in unseen domains. Our code is available at https://github.com/SJShin-AI/UDIM.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

This paper tackles the challenge of real-time 3D trajectory prediction for UAVs, which is critical for applications such as aerial surveillance and defense. Existing prediction models that rely primarily on position data struggle with accuracy, especially when UAV movements fall outside the position domain used in training. Our research identifies a gap in utilizing velocity estimates, first-order dynamics, to better capture the dynamics and enhance prediction accuracy and generalizability in any position domain. To bridge this gap, we propose a new trajectory prediction method using Gated Recurrent Units (GRUs) within sequence-based neural networks. Unlike traditional methods that rely on RNNs or transformers, this approach forecasts future velocities and positions based on historical velocity data instead of positions. This is designed to enhance prediction accuracy and scalability, overcoming challenges faced by conventional models in handling complex UAV dynamics. The methodology employs both synthetic and real-world 3D UAV trajectory data, capturing a wide range of flight patterns, speeds, and agility. Synthetic data is generated using the Gazebo simulator and PX4 Autopilot, while real-world data comes from the UZH-FPV and Mid-Air drone racing datasets. The GRU-based models significantly outperform state-of-the-art RNN approaches, with a mean square error (MSE) as low as 2 x 10^-8. Overall, our findings confirm the effectiveness of incorporating velocity data in improving the accuracy of UAV trajectory predictions across both synthetic and real-world scenarios, in and out of position data distributions. Finally, we open-source our 5000 trajectories dataset and a ROS 2 package to facilitate the integration with existing ROS-based UAV systems.

Multi-view graph clustering (MGC) methods are increasingly being studied due to the explosion of multi-view data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose Variational Graph Generator for Multi-View Graph Clustering (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then a simple yet effective graph encoder in conjunction with the multi-view clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck principle.Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs. The source code is publicly available at https://github.com/cjpcool/VGMGC.

We show that the GPS tags contained in photo metadata provide a useful control signal for image generation. We train GPS-to-image models and use them for tasks that require a fine-grained understanding of how images vary within a city. In particular, we train a diffusion model to generate images conditioned on both GPS and text. The learned model generates images that capture the distinctive appearance of different neighborhoods, parks, and landmarks. We also extract 3D models from 2D GPS-to-image models through score distillation sampling, using GPS conditioning to constrain the appearance of the reconstruction from each viewpoint. Our evaluations suggest that our GPS-conditioned models successfully learn to generate images that vary based on location, and that GPS conditioning improves estimated 3D structure.

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.

From crop mapping to flood detection, machine learning in remote sensing has a wide range of societally beneficial applications. The commonalities between remote sensing data in these applications present an opportunity for pretrained machine learning models tailored to remote sensing to reduce the labeled data and effort required to solve individual tasks. However, such models must be: (i) flexible enough to ingest input data of varying sensor modalities and shapes (i.e., of varying spatial and temporal dimensions), and (ii) able to model Earth surface phenomena of varying scales and types. To solve this gap, we present Galileo, a family of pretrained remote sensing models designed to flexibly process multimodal remote sensing data. We also introduce a novel and highly effective self-supervised learning approach to learn both large- and small-scale features, a challenge not addressed by previous models. Our Galileo models obtain state-of-the-art results across diverse remote sensing tasks.

In this paper, we introduce RaVAEn, a lightweight, unsupervised approach for change detection in satellite data based on Variational Auto-Encoders (VAEs) with the specific purpose of on-board deployment. Applications such as disaster management enormously benefit from the rapid availability of satellite observations. Traditionally, data analysis is performed on the ground after all data is transferred - downlinked - to a ground station. Constraint on the downlink capabilities therefore affects any downstream application. In contrast, RaVAEn pre-processes the sampled data directly on the satellite and flags changed areas to prioritise for downlink, shortening the response time. We verified the efficacy of our system on a dataset composed of time series of catastrophic events - which we plan to release alongside this publication - demonstrating that RaVAEn outperforms pixel-wise baselines. Finally we tested our approach on resource-limited hardware for assessing computational and memory limitations.

3D Gaussian Splatting (3DGS) has become a popular solution in SLAM due to its high-fidelity and real-time novel view synthesis performance. However, some previous 3DGS SLAM methods employ a differentiable rendering pipeline for tracking, lack geometric priors in outdoor scenes. Other approaches introduce separate tracking modules, but they accumulate errors with significant camera movement, leading to scale drift. To address these challenges, we propose a robust RGB-only outdoor 3DGS SLAM method: S3PO-GS. Technically, we establish a self-consistent tracking module anchored in the 3DGS pointmap, which avoids cumulative scale drift and achieves more precise and robust tracking with fewer iterations. Additionally, we design a patch-based pointmap dynamic mapping module, which introduces geometric priors while avoiding scale ambiguity. This significantly enhances tracking accuracy and the quality of scene reconstruction, making it particularly suitable for complex outdoor environments. Our experiments on the Waymo, KITTI, and DL3DV datasets demonstrate that S3PO-GS achieves state-of-the-art results in novel view synthesis and outperforms other 3DGS SLAM methods in tracking accuracy. Project page: https://3dagentworld.github.io/S3PO-GS/.

In this paper, we introduce a novel approach to fine-grained cross-view geo-localization. Our method aligns a warped ground image with a corresponding GPS-tagged satellite image covering the same area using homography estimation. We first employ a differentiable spherical transform, adhering to geometric principles, to accurately align the perspective of the ground image with the satellite map. This transformation effectively places ground and aerial images in the same view and on the same plane, reducing the task to an image alignment problem. To address challenges such as occlusion, small overlapping range, and seasonal variations, we propose a robust correlation-aware homography estimator to align similar parts of the transformed ground image with the satellite image. Our method achieves sub-pixel resolution and meter-level GPS accuracy by mapping the center point of the transformed ground image to the satellite image using a homography matrix and determining the orientation of the ground camera using a point above the central axis. Operating at a speed of 30 FPS, our method outperforms state-of-the-art techniques, reducing the mean metric localization error by 21.3% and 32.4% in same-area and cross-area generalization tasks on the VIGOR benchmark, respectively, and by 34.4% on the KITTI benchmark in same-area evaluation.

Existing deep learning-based cross-view geo-localization methods primarily focus on improving the accuracy of cross-domain image matching, rather than enabling models to comprehensively capture contextual information around the target and minimize the cost of localization errors. To support systematic research into this Distance-Aware Cross-View Geo-Localization (DACVGL) problem, we construct Distance-Aware Campus (DA-Campus), the first benchmark that pairs multi-view imagery with precise distance annotations across three spatial resolutions. Based on DA-Campus, we formulate DACVGL as a hierarchical retrieval problem across different domains. Our study further reveals that, due to the inherent complexity of spatial relationships among buildings, this problem can only be addressed via a contrastive learning paradigm, rather than conventional metric learning. To tackle this challenge, we propose Dynamic Contrastive Learning (DyCL), a novel framework that progressively aligns feature representations according to hierarchical spatial margins. Extensive experiments demonstrate that DyCL is highly complementary to existing multi-scale metric learning methods and yields substantial improvements in both hierarchical retrieval performance and overall cross-view geo-localization accuracy. Our code and benchmark are publicly available at https://github.com/anocodetest1/DyCL.

Detecting vehicles in aerial imagery is a critical task with applications in traffic monitoring, urban planning, and defense intelligence. Deep learning methods have provided state-of-the-art (SOTA) results for this application. However, a significant challenge arises when models trained on data from one geographic region fail to generalize effectively to other areas. Variability in factors such as environmental conditions, urban layouts, road networks, vehicle types, and image acquisition parameters (e.g., resolution, lighting, and angle) leads to domain shifts that degrade model performance. This paper proposes a novel method that uses generative AI to synthesize high-quality aerial images and their labels, improving detector training through data augmentation. Our key contribution is the development of a multi-stage, multi-modal knowledge transfer framework utilizing fine-tuned latent diffusion models (LDMs) to mitigate the distribution gap between the source and target environments. Extensive experiments across diverse aerial imagery domains show consistent performance improvements in AP50 over supervised learning on source domain data, weakly supervised adaptation methods, unsupervised domain adaptation methods, and open-set object detectors by 4-23%, 6-10%, 7-40%, and more than 50%, respectively. Furthermore, we introduce two newly annotated aerial datasets from New Zealand and Utah to support further research in this field. Project page is available at: https://humansensinglab.github.io/AGenDA

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we present Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast O(n^2) per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein W_1, W_2 distance of discretized densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

Score Distillation Sampling (SDS) has emerged as a prevalent technique for text-to-3D generation, enabling 3D content creation by distilling view-dependent information from text-to-2D guidance. However, they frequently exhibit shortcomings such as over-saturated color and excess smoothness. In this paper, we conduct a thorough analysis of SDS and refine its formulation, finding that the core design is to model the distribution of rendered images. Following this insight, we introduce a novel strategy called Variational Distribution Mapping (VDM), which expedites the distribution modeling process by regarding the rendered images as instances of degradation from diffusion-based generation. This special design enables the efficient training of variational distribution by skipping the calculations of the Jacobians in the diffusion U-Net. We also introduce timestep-dependent Distribution Coefficient Annealing (DCA) to further improve distilling precision. Leveraging VDM and DCA, we use Gaussian Splatting as the 3D representation and build a text-to-3D generation framework. Extensive experiments and evaluations demonstrate the capability of VDM and DCA to generate high-fidelity and realistic assets with optimization efficiency.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-t prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-t priors and primal-space guarantees for constrained generation, under varepsilon-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.