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Applications · Everything Else

Marius Miron, David Robinson, Milad Alizadeh, Ellen Gilsenan-McMahon, Gagan Narula, Emmanuel Chemla, Maddie Cusimano, Felix Effenberger, Masato Hagiwara, Benjamin Hoffman 等

Bioacoustics, the study of sounds produced by living organisms, plays a vital role in conservation, biodiversity monitoring, and behavioral studies. Many tasks in this field, such as species, individual, and behavior classification and detection, are well-suited to machine learning. However, they often suffer from limited annotated data, highlighting the need for a general-purpose bioacoustic encoder capable of extracting useful representations for diverse downstream tasks. Such encoders have been proposed before, but are often limited in scope due to a focus on a narrow range of species (typically birds), and a reliance on a single model architecture or training paradigm. Moreover, they are usually evaluated on a small set of tasks and datasets. In this work, we present a large-scale empirical study that covers aspects of bioacoustics that are relevant to research but have previously been scarcely considered: training data diversity and scale, model architectures and training recipes, and the breadth of evaluation tasks and datasets. We obtain encoders that are state-of-the-art on the existing and newly proposed benchmarks. We also identify *what matters* for training these encoders, such that this work can be extended when more data are available or better architectures are proposed. Specifically, across 26 datasets with tasks including species classification, detection, individual ID, and vocal repertoire discovery, we find that self-supervised pre-training followed by supervised post-training on a mixed bioacoustics + general-audio corpus yields the strongest in- and out-of-distribution performance. We show the importance of data diversity in both stages. To support ongoing research and applications, we release the model checkpoints as well as the Animal Vocalization Encoder library [AVEX](https://projects.earthspecies.org/avex/) (an API for model loading and inference, and a Python-based system for training and evaluating bioacoustics representation learning models)

Applications · Everything Else

Shufan Jiang, Sizhou Chen, Chi Zhang, Xiao-Lei Zhang, Xuelong Li

Creating an immersive and interactive theatrical experience is a long-term goal in the field of interactive narrative. The emergence of large language models (LLMs) provides a new path to achieve this goal. However, existing LLM-based drama generation methods often produce models that lack initiative and cannot interact with the physical scene, while typically requiring detailed user input that diminishes the immersion of live performance. To address these challenges, we propose HAMLET, a hierarchical adaptive multi-agent framework focused on drama creation and real-time online performance. Given a simple topic, the framework first generates a narrative blueprint to guide the subsequent improvisational performance. In the online performance phase, each actor is equipped with an adaptive reasoning module that enables decision-making based on their personas, memories, goals, and emotional states during complex group chat scenarios. Beyond dialogue, actor agents engage in embodied interactions by changing the state of scene props through actions such as opening a letter or picking up a weapon, which are broadcast to update the global environmental context. To objectively assess the quality of live embodied theatrics, we establish a comprehensive evaluation method and introduce HAMLETJudge, a specialized critic model for automated evaluation. Experimental results demonstrate that HAMLET excels in creating expressive, coherent, and physically interactive theatrical experiences in an autonomous manner.

Applications · Everything Else

Maria Ivanova, Pavel Zadorozhny, Rodion Levichev, Ivan Petrov, Adamenko Pavel, Ivan Lopatin, Alexey Kutalev, Dmitrii Babaev

LiveCodeBench (LCB) has recently become a widely adopted benchmark for evaluating large language models (LLMs) on code-generation tasks. By curating competitive programming problems, constantly adding fresh problems to the set, and filtering them by release dates, LCB provides contamination-aware evaluation and offers a holistic view of coding capability. However, LCB remains restricted to Python, leaving open the question of whether LLMs can generalize across the diverse programming languages required in real-world software engineering. We introduce Multi-LCB, a benchmark for evaluating LLMs across twelve programming languages, including Python. Multi-LCB transforms Python tasks from the LCB dataset into equivalent tasks in other languages while preserving LCB’s contamination controls and evaluation protocol. Because it is fully compatible with the original LCB format, Multi-LCB will automatically track future LCB updates, enabling systematic assessment of cross-language code generation competence and requiring models to sustain performance well beyond Python. We evaluated 24 LLMs for instruction and reasoning on Multi-LCB, uncovering evidence of Python overfitting, language-specific contamination, and substantial disparities in multilingual performance. Our results establish Multi-LCB as a rigorous new benchmark for multi-programming-language code evaluation, directly addressing LCB’s primary limitation and exposing critical gaps in current LLM capabilities.

General Machine Learning · Transfer, Multitask and Meta-learning

Zhihao Zeng, Ziquan Fang, Wei Shao, Lu Chen, Yunjun Gao

Trajectory data records the spatio-temporal movements of people and vehicles. However, raw trajectories are often noisy, incomplete, or inconsistent due to sensor errors and transmission failures. To ensure reliable downstream analytics, Trajectory Data Preparation (TDP) has emerged as a critical preprocessing stage, encompassing various tasks such as imputation, map matching, anomaly detection, trajectory recovery, compression, etc. However, existing TDP methods face two major limitations: (i) they assume centralized access to data, which is unrealistic under strict privacy regulations and data silo situations, and (ii) they train task-specific models that lack generalization across diverse or unseen TDP tasks. To this end, we propose FedTDP for Federated Trajectory Data Preparation (F-TDP), where trajectories are vertically partitioned across regions and cannot be directly shared. FedTDP introduces three innovations: (i) lightweight Trajectory Privacy AutoEncoder (TPA) with secret-sharing aggregation, providing formal privacy guarantees; (ii) Trajectory Knowledge Enhancer (TKE) that adapts LLMs to spatio-temporal patterns via trajectory-aware prompts, offsite-tuning, sparse-tuning, and bidirectional knowledge distillation; and (iii) Federated Parallel Optimization (FPO), which reduces communication overhead and accelerates federated training. We conduct experiments on 6 real-world datasets and 10 representative TDP tasks, showing that FedTDP surpasses 13 state-of-the-art baselines in accuracy, efficiency, and scalability, while also generalizing effectively across diverse TDP tasks.

Deep Learning · Generative Models and Autoencoders

Yinghua Yao, Yuangang Pan, Guoji Fu, Ivor Tsang

Recent advances in inference-time alignment of diffusion models have shown reduced susceptibility to reward over-optimization. However, when aligning with multiple black-box reward functions, the number of required queries grows exponentially with the number of reward functions, making the alignment process highly inefficient. To address the challenge, we propose the first inference-time soup strategy, named Sample Reward Soups (SRSoup), for Pareto-optimal sampling across the entire space of preferences. Specifically, at each denoising step, we independently steer multiple denoising distributions using reward-guided search gradients (one for each reward function) and then linearly interpolate their search gradients. This design is effective because sample rewards can be shared when two denoising distributions are close, particularly during the early stages of the denoising process. As a result, SRSoup significantly reduces the number of queries required in the early stages without sacrificing performance. Extensive experiments demonstrate the effectiveness of SRSoup in aligning T2I models with diverse reward functions, establishing a practical and scalable solution. The code is available at https://github.com/EvaFlower/Sample-Reward-Soups-ICLR26.

Applications · Robotics

Haisheng Su, Wei Wu, Feixiang Song, Junjie Zhang, Zhenjie Yang, Junchi Yan

Recent advances towards End-to-End Autonomous Driving (E2E-AD) focus on integrating modular designs into a unified framework for joint optimization. Most of these advances follow a sequential paradigm (i.e., perception-prediction-planning) based on separable Transformer decoders and rely on dense BEV features to encode scene representations. However, such manual ordering design can inevitably cause information loss and cumulative errors, lacking flexible and diverse relation modeling among different modules and sensors. Meanwhile, insufficient training of image backbone and quadratic-complexity of attention mechanism also hinder the scalability and efficiency of E2E-AD system to handle spatiotemporal input. To this end, we propose DriveMamba, a Task-Centric Scalable paradigm for efficient E2E-AD, which integrates dynamic task relation modeling, implicit view correspondence learning and long-term temporal fusion into a single-stage Unified Mamba decoder. Specifically, both extracted image features and expected task outputs are converted into token-level sparse representations in advance, which are then sorted by their instantiated positions in 3D space. The linear-complexity operator enables efficient long-context sequential token modeling to capture task-related inter-dependencies simultaneously. Additionally, a bidirectional trajectory-guided "local-to-global" scan method is designed to preserve spatial locality from ego-perspective, thus facilitating the ego-planning. Extensive experiments conducted on nuScenes and Bench2Drive datasets demonstrate the superiority, generalizability and great efficiency of DriveMamba.

Computer Vision · Vision Models & Multimodal

Bingjun Luo, Tony Wang, Hanqi Chen, Xinpeng Ding

Recent advances in Multimodal Large Language Models (MLLMs) have significantly advanced video understanding tasks, yet challenges remain in efficiently compressing visual tokens while preserving spatiotemporal interactions. Existing methods, such as LLaVA family, utilize simplistic pooling or interpolation techniques that overlook the intricate dynamics of visual tokens. To bridge this gap, we propose ST-GridPool, a novel training-free visual token enhancement method designed specifically for Video LLMs. Our approach integrates Pyramid Temporal Gridding (PTG), which captures multi-grained spatiotemporal interactions through hierarchical temporal gridding, and Norm-based Spatial Pooling (NSP), which preserves high-information visual regions by leveraging the correlation between token norms and semantic richness. Extensive experiments on various benchmarks demonstrate that ST-GridPool consistently enhances performance of Video LLMs without requiring costly retraining. Our method offers an efficient and plug-and-play solution for improving visual token representations. Our code is available in [https://github.com/bingjunluo/ST-GridPool](https://github.com/bingjunluo/ST-GridPool).

General Machine Learning · Transfer, Multitask and Meta-learning

Yongxian Wei, Runxi Cheng, Weike Jin, Enneng Yang, Li Shen, LU HOU, SiNan Du, Chun Yuan, Xiaochun Cao, Dacheng Tao

Foundation models update slowly due to resource-intensive training, whereas domain-specific models evolve rapidly between releases. Model merging seeks to combine multiple expert models into a single, more capable model, reducing storage and serving costs while supporting decentralized development. Despite its potential, previous studies have primarily focused on merging visual classification models or Large Language Models (LLMs) for code and math tasks. Recently, Multimodal LLMs (MLLMs) that extend LLMs through large-scale multimodal training have gained traction. However, no benchmark exists for model merging research that clearly divides the tasks of MLLM training and evaluation. In this paper, $(i)$ we introduce a model merging benchmark for MLLMs, which includes multiple tasks such as VQA, Geometry, Chart, OCR, and Grounding, studying both LoRA and full fine-tuning models. Moreover, we explore how model merging can combine different modalities (e.g., vision-language, audio-language, and video-language models), moving toward the Omni-language model. $(ii)$ We implement 10 model merging algorithms on the benchmark. Furthermore, we propose a novel method that removes noise from task vectors and robustly optimizes the merged vector based on a loss defined over task vector interactions, achieving an average performance gain of 2.48\%. $(iii)$ We find that model merging offers a promising way for building improved MLLMs without requiring training data. Our results also demonstrate that the complementarity among multiple modalities outperforms individual modalities.

Deep Learning · Attention Mechanisms

Haochen Shen, Davis Wertheimer, Zheng Wang, Garrett Goon, Derrick Liu, Naigang Wang, Mudhakar Srivatsa, Raghu Ganti, Minjia Zhang

Hybrid Mamba-Transformer models have emerged as promising alternatives to pure Transformers, offering efficiency and competitive performance. However, they struggle to generalize beyond their training context windows, collapsing on long-context tasks. We provide the first systematic analysis of this failure, showing that it arises from uncontrolled state growth and uneven receptive field contributions across the hybrid architecture. Guided by this understanding, we introduce Universal Position Interpolation (UPI), a closed-form, training-free scaling method that unifies Mamba's cumulative decay with Transformer rotary frequency scaling. UPI selectively stabilizes unstable Mamba dynamics while rescaling Transformer encodings, controlling state growth and enabling reliable long-context generalization, with only a few auxiliary forward passes. Evaluation shows that UPI extends multiple state-of-the-art hybrid and pure Mamba models from 4K to up to 64K tokens on PG-19 perplexity, LongBench and RULER benchmarks, without sacrificing short-context accuracy. These findings establish the first principled bridge between Transformers and state-space models and open a new direction for training-free context extension methods for emerging hybrid models.

General Machine Learning · Causality

Tommaso Mencattini, Riccardo Cadei, Francesco Locatello

Randomized Controlled Trials are one of the pillars of science; nevertheless, they rely on hand-crafted hypotheses and expensive analysis. Such constraints prevent causal effect estimation at scale, potentially anchoring on popular yet incomplete hypotheses. We propose to discover the unknown effects of a treatment directly from data. For this, we turn unstructured data from a trial into meaningful representations via pretrained foundation models and interpret them via a Sparse Auto Encoder. However, discovering significant causal effects at the neural level is not trivial due to multiple-testing issues and effects entanglement. To address these challenges, we introduce _Neural Effect Search_, a novel recursive procedure solving both issues by progressive stratification. After assessing the robustness of our algorithm on semi-synthetic experiments, we showcase, in the context of experimental ecology, the first successful unsupervised causal effect identification on a real-world scientific trial.

Applications · Neuroscience, Cognitive Science

Yifei Wang, Zhangyanxun, Changze Lv, Yiyang Lu, Jingwen Xu, Xiaohua Wang, Di Yu, Xin Du, Xuanjing Huang, Xiaoqing Zheng

Developing biologically plausible learning algorithms that can achieve performance comparable to error backpropagation remains a longstanding challenge. Existing approaches often compromise biological plausibility by entirely avoiding the use of spikes for error propagation or relying on both positive and negative learning signals, while the question of how spikes can represent negative values remains unresolved. To address these limitations, we introduce Bidirectional Spike-based Distillation (BSD), a novel learning algorithm that jointly trains a feedforward and a backward spiking network. We formulate learning as a transformation between two spiking representations (i.e., stimulus encoding and concept encoding) so that the feedforward network implements perception and decision-making by mapping stimuli to actions, while the backward network supports memory recall by reconstructing stimuli from concept representations. Extensive experiments on diverse benchmarks, including image recognition, image generation, and sequential regression, show that BSD achieves performance comparable to networks trained with classical error backpropagation. These findings represent a significant step toward biologically grounded, spike-driven learning in neural networks.

Applications · Language, Speech and Dialog

Zijian Li, Xin Guan, Bo Zhang, Shen Huang, Houquan Zhou, Shaopeng Lai, Ming Yan, Yong Jiang, Pengjun Xie, Fei Huang 等

This paper tackles \textbf{open-ended deep research (OEDR)}, a complex challenge where AI agents must synthesize vast web-scale information into insightful reports. Current approaches are plagued by dual-fold limitations: static research pipelines that decouple planning from evidence acquisition and monolithic generation paradigms that include redundant, irrelevant evidence, suffering from hallucination issues and low citation accuracy. To address these challenges, we introduce \textbf{WebWeaver}, a novel dual-agent framework that emulates the human research process. The planner operates in a dynamic cycle, iteratively interleaving evidence acquisition with outline optimization to produce a comprehensive, citation-grounded outline linking to a memory bank of evidence. The writer then executes a hierarchical retrieval and writing process, composing the report section by section. By performing targeted retrieval of only the necessary evidence from the memory bank via citations for each part, it effectively mitigates long-context issues and citation hallucinations. Our framework establishes a new state-of-the-art across major OEDR benchmarks, including DeepResearch Bench, DeepConsult, and DeepResearchGym. These results validate our human-centric, iterative methodology, demonstrating that adaptive planning and focused synthesis are crucial for producing comprehensive, trusted, and well-structured reports.

Reinforcement Learning · Multi-agent

Ido Levy, Ben wiesel, Sami Marreed, Alon Oved, Avi Yaeli, Segev Shlomov

Autonomous web agents solve complex browsing tasks, yet existing benchmarks measure only whether an agent finishes a task, ignoring whether it does so safely or in a way enterprises can trust. To integrate these agents into critical workflows, safety and trustworthiness (ST) are prerequisite conditions for adoption. We introduce ST-WebAgentBench, a configurable and extensible framework designed as a first step toward enterprise-grade evaluation. Each of its 375 tasks carries one or more ST policies (3,057 in total), concise rules encoding constraints, and is scored along six orthogonal dimensions (e.g., user consent, robustness). Tasks span three difficulty tiers for fine-grained capability profiling, and a “Modality Challenge” disentangles vision-only from DOM-only information retrieval, isolating the contribution of each perceptual modality to agent failures. Beyond raw task success, we propose the Completion Under Policy (CuP) metric, which credits only completions that respect all applicable policies, and the Risk Ratio, which quantifies ST breaches across dimensions. Evaluating three open state-of-the-art agents shows their average CuP is less than two-thirds of their nominal completion rate, revealing substantial safety gaps. To support growth and adaptation to new domains, ST-WebAgentBench provides modular code and extensible templates that enable new workflows to be incorporated with minimal effort, offering a practical foundation for advancing trustworthy web agents at scale.

Theory · Optimization

Ravindran Kannan, Kijun Shin, David Woodruff

We study the Nearest Neighbor Search (NNS) problem in a high-dimensional setting where data originates from a low-dimensional subspace and is corrupted by Gaussian noise. Specifically, we consider a semi-random model where $n$ points from an unknown $k$-dimensional subspace of $\mathbb{R}^d$ ($k \ll d$) are perturbed by zero-mean $d$-dimensional Gaussian noise with variance $\sigma^2$ on each coordinate. Without loss of generality, we may assume the nearest neighbor is at distance $1$ from the query, and that all other points are at distance at least $1+\varepsilon$. We assume we are given only the noisy data and are required to find NN of the uncorrupted data. We prove the following results: 1. For $\sigma \in O(1/k^{1/4})$, we show that simply performing SVD denoises the data; namely, we provably recover accurate NN of uncorrupted data (Theorem 1.1). 2. For $\sigma \gg 1/k^{1/4}$, NN in uncorrupted data is not even {\bf identifiable} from the noisy data in general. This is a matching lower bound on $\sigma$ with the above result, demonstrating the necessity of this threshold for NNS (Lemma 3.1). 3. For $\sigma \gg 1/\sqrt k$, the noise magnitude ($\sigma \sqrt{d}$) is significantly exceeds the inter-point distances in the unperturbed data. Moreover, NN in noisy data is different from NN in the uncorrupted data in general. \end{enumerate} Note that (1) and (3) together imply SVD identifies correct NN in uncorrupted data even in a regime where it is different from NN in noisy data. This was not the case in existing literature (see e.g. (Abdullah et al., 2014)). Another comparison with (Abdullah et al., 2014) is that it requires $\sigma$ to be at least an inverse polynomial in the ambient dimension $d$. The proof of (1) above uses upper bounds on perturbations of singular spaces of matrices as well as concentration and spherical symmetry of Gaussians. We thus give theoretical justification for the performance of spectral methods in practice. We also provide empirical results on real datasets to corroborate our findings.

Computer Vision · 3D Rendering & Reconstruction

Hao Qin, Yukai Sun, Meng Wang, Ming Kong, Mengxu Lu, Qiang Zhu

Indirect editing methods for 3D Gaussian Splatting (3DGS) have recently witnessed significant advancements. These approaches operate by first applying edits in the rendered 2D space and subsequently projecting the modifications back into 3D. *However, this paradigm inevitably introduces cross-view inconsistencies and constrains both the flexibility and efficiency of the editing process*. To address these challenges, we present **VF-Editor**, which enables native editing of Gaussian primitives by predicting attribute variations in a feedforward manner. To accurately and efficiently estimate these variations, we design a novel variation predictor distilled from 2D editing knowledge. The predictor encodes the input to generate a variation field and employs two learnable, parallel decoding functions to iteratively infer attribute changes for each 3D Gaussian. Thanks to its unified design, VF-Editor can seamlessly distill editing knowledge from diverse 2D editors and strategies into a single predictor, allowing for flexible and effective knowledge transfer into the 3D domain. Extensive experiments on both public and private datasets reveal the inherent limitations of indirect editing pipelines and validate the effectiveness and flexibility of our approach.

Applications · Time Series

Dongbin Kim, Youngjoo Park, Woojin Jeong, Jaewook Lee

Transformers have demonstrated strong performance in time series forecasting, yet they often fail to capture the intrinsic structure of temporal data, making them susceptible to real-world noise and anomalies. Unlike in vision or language, the local geometry of temporal patterns is a critical feature in time series forecasting, but it is frequently disrupted by corruptions. In this work, we address this gap with two key contributions. First, we propose Local Geometry Attention (LGA), a novel attention mechanism theoretically grounded in local Gaussian process theory. LGA adapts to the intrinsic data geometry by learning query-specific distance metrics, enabling it to model complex temporal dependencies and enhance resilience to noise. Second, we introduce TSRBench, the first comprehensive benchmark for evaluating forecasting robustness under realistic, statistically-grounded corruptions. Experiments on TSRBench show that LGA significantly reduces performance degradation, consistently outperforming both Transformer and linear model. These results establish a foundation for developing robust time series models that can be deployed in real-world applications where data quality is not guaranteed. Our code is available at: https://github.com/dongbeank/LGA.

Deep Learning · Robustness

Miaoyun Zhao, Qiang Zhang

Achieving group-robust generalization in the presence of spurious correlations remains a significant challenge, particularly when bias annotations are unavailable. Recent studies on Class-Conditional Distribution Balancing (CCDB) reveal that spurious correlations often stem from mismatches between the class-conditional and marginal distributions of bias attributes. They achieve promising results by addressing this issue through simple distribution matching in a bias-agnostic manner. However, CCDB approximates each distribution using a single Gaussian, which is overly simplistic and rarely holds in real-world applications. To address this limitation, we propose a novel Multi-stage data-Selective reTraining strategy (MST), which describes each distribution in greater detail using the hard confusion matrix. Building on these finer descriptions, we propose a fine-grained variant of CCDB, termed FG-CCDB, which enhances distribution matching through more precise confusion-cell-wise reweighting. FG-CCDB learns sample weights from a global perspective, effectively mitigating spurious correlations without incurring substantial storage or computational overhead. Extensive experiments demonstrate that MST serves as a reliable proxy for ground-truth bias annotations and can be seamlessly integrated with bias-supervised methods. Moreover, when combined with FG-CCDB, our method performs on par with bias-supervised approaches on binary classification tasks and significantly outperforms them in highly biased multi-class and multi-shortcut scenarios.

Reinforcement Learning · Planning

Alessio Russo, Ryan Welch, Aldo Pacchiano

We study the _active sequential hypothesis testing_ problem, also known as _pure exploration_: given a new task, the learner _adaptively collects data_ from the environment to efficiently determine an underlying correct hypothesis. A classical instance of this problem is the task of identifying the best arm in a multi-armed bandit problem (a.k.a. BAI, Best-Arm Identification), where actions index hypotheses. Another important case is generalized search, a problem of determining the correct label through a sequence of strategically selected queries that indirectly reveal information about the label. In this work, we introduce _In-Context Pure Explorer_ (ICPE), which meta-trains Transformers to map _observation histories_ to _query actions_ and a _predicted hypothesis_, yielding a model that transfers in-context. At inference time, ICPE actively gathers evidence on new tasks and infers the true hypothesis without parameter updates. Across deterministic, stochastic, and structured benchmarks, including BAI and generalized search, ICPE is competitive with adaptive baselines while requiring no explicit modeling of information structure. Our results support Transformers as practical architectures for _general sequential testing_.

Social Aspects · Accountability, Transparency and Interpretability

Bharat Chandra Yalavarthi, Nalini Ratha, Venu Govindaraju

Vision-Language Models (VLMs) have demonstrated impressive zero-shot capabilities across a wide range of tasks and domains. However, their performance is often compromised by learned spurious correlations, which can adversely affect downstream applications. Existing mitigation strategies typically depend on additional data, model retraining, labeled features or classes, domain-specific expertise, or external language models posing scalability and generalization challenges. In contrast, we introduce a fully interpretable, zero-shot method that requires no auxiliary data or external supervision named DIAL (Disentangle, Identify, And Label-free removal). Our approach begins by filtering the representations that might be disproportionately influenced by spurious features, using distributional analysis. We then apply a sparse autoencoder to disentangle the representations and identify the feature directions associated with spurious features. To mitigate their impact, we remove the subspace spanned by these spurious directions from the affected representations. Additionally, for cases where prior knowledge of spurious features in a dataset is unknown, we introduce DIAL+ which can detect and mitigate the spurious features. We validate our method through extensive experiments on widely used spurious correlation benchmarks. Results show that our approach consistently outperforms or matches existing baselines in terms of overall accuracy and worst-group performance, offering a scalable and interpretable solution to a persistent challenge in VLMs.

Computer Vision · 3D Rendering & Reconstruction

Feng Wu, Tsai Hor Chan, Yihang Chen, Lingting Zhu, Guosheng Yin, Lequan Yu

We introduce Horseshoe Splatting, a Bayesian extension of 3D Gaussian Splatting (3DGS) that jointly addresses structured sparsity in per-splat covariances and delivers calibrated uncertainty. While neural radiance fields achieve high-fidelity view synthesis and 3DGS attains real-time rendering with explicit anisotropic Gaussians, existing pipelines do not explicitly encode structural sparsity in the covariance—e.g., axis-wise variances or pairwise correlations—leaving noise-dominated components insufficiently regularized. Uncertainty is likewise essential for trustworthy and robust novel-view prediction, yet most 3DGS variants remain deterministic. We place a global-local Horseshoe prior on the covariance scales, whose spike-at-zero and heavy-tails adaptively shrink irrelevant directions while preserving the salient structure. We fit the model with a factorized variational inference scheme that mirrors the Horseshoe's inverse-Gamma augmentation, enabling Monte Carlo rendering and pixel-wise posterior uncertainty with minimal overhead. Theoretically, we establish posterior contraction rates for the scale parameters and transfer them to the rendered image via a local Lipschitz mapping, providing guarantees that estimation error and predictive uncertainty diminish with data. Empirically, Horseshoe Splatting produces high-quality uncertainty maps while matching state-of-the-art 3DGS visual fidelity and runtime, yielding a practical, uncertainty-aware renderer that is robust to structured sparsity in the radiance field. The code is available at https://github.com/HKU-MedAI/Horseshoe-Splatting.