论文检索

Probabilistic Methods · Bayesian Models and Methods

Gyeonghun Kang, Changwoo Lee, Xiang Cheng

Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance and ability to go beyond point predictions, theoretical understandings of the algorithmic capability of transformers to learn distributions in context are still lacking. Focusing on Gaussian process regression problems, we show by construction that transformers can implement a gradient descent algorithm targeting the posterior predictive mean and variance, followed by nonlinear mappings that yield binned probabilities of PPD. We study the error bounds of the approximated PPD in terms of attention depth and bin resolution. Based on these results, we further demonstrate the key role of normalization and the choice of attention depth in enabling the extrapolation abilities of transformers beyond the pretraining sample size range. We conduct simulations that corroborate our findings, providing insight into the expressivity of PFNs targeting PPDs and how architectural choices may influence generalization capabilities.

Probabilistic Methods · Bayesian Models and Methods

Weifeng Zhang, Wenyuan Zhao, Amir Hossein Rahmati, Yucheng Wang, Zhiyuan Wang, Chao Tian, Xiaoning Qian

Principled uncertainty quantification (UQ) is increasingly recognized as essential for trustworthy artificial general intelligence (AGI). Bayesian Low-Rank Adaptation (LoRA) provides a principled mechanism for uncertainty-aware fine-tuning of large language models (LLMs). However, existing techniques either face scalability constraints, e.g. Laplace-LoRA, or rely on approximate inference schemes that lead to poorly calibrated posterior uncertainty, often manifesting as overconfident predictions under distribution shift. To address this challenge, we propose GPan-LoRA, the first scalable Gaussian Process (GP)-based framework for Bayesian LoRA, which integrates neural network-based sparse GP approximations with amortized variational inference. By preserving the Bayesian function prior and posterior semantics intrinsic to GPs, GPan-LoRA achieves a faithful balance between computational scalability and principled UQ. Empirically, GPan-LoRA produces well-calibrated uncertainty that remains reliable under distribution shift, mitigating overconfident failures while preserving competitive task performance.

Deep Learning · Generative Models and Autoencoders

Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spectral formulation enables significant dimensionality reduction compared to grid-based diffusion models and ensures that the induced process in function space remains within a class of functions for which the PDE operators are well defined. Building on diffusion posterior sampling, we enforce physics-informed constraints and measurement conditions during inference, applying Adam-based updates at each diffusion step. We evaluate the proposed approach on Poisson, Helmholtz, and incompressible Navier--Stokes equations, demonstrating improved accuracy and computational efficiency compared with existing diffusion-based PDE solvers, which are state of the art for sparse observations. Code is available at https://anonymous.4open.science/r/PISD-32A0/.

Applications · Computer Vision

Zhiyang Lu, Ming Cheng

Cross-modal 2D–3D gait recognition is impeded by inherent domain discrepancies between 2D silhouette and 3D point cloud distributions. While prior methods align only final embeddings, we propose DiffCrossGait, which enforces trajectory-level alignment by driving both modalities with shared noise in a unified latent diffusion process. By driving both modalities with shared Gaussian noise within a latent space, we enable continuous alignment throughout the generative evolution. We introduce a Tri-Phase Alignment Strategy that exploits varying noise intensities to enforce identity anchoring, dynamics consistency, and cross-modal structural recoverability, thereby constraining both modalities to share denoising dynamics and bottleneck structure, which promotes modality-invariant gait features. Crucially, our framework decouples generative alignment from the discriminative backbone; the diffusion mechanism serves exclusively as a training objective, ensuring high inference efficiency by eliminating the computational overhead of iterative denoising. Extensive experiments on the SUSTech1K and FreeGait benchmarks demonstrate that DiffCrossGait achieves state-of-the-art performance.

General Machine Learning · Representation Learning

Nathan Kessler, Robin Magnet, Jean Feydy

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers a principled approach to smoothing via heat diffusion, with strong theoretical guarantees. However, constructing such Laplacians requires a carefully defined domain structure, which is not always available. Most practitioners thus rely on simple convolution kernels and message-passing layers, which are biased against the boundaries of the domain. We bridge this gap by introducing a broad class of smoothing operators, derived from general similarity or adjacency matrices, and demonstrate that they can be normalized into diffusion-like operators that inherit desirable properties from Laplacians. Our approach relies on a symmetric variant of the Sinkhorn algorithm, which rescales positive smoothing operators to match the structural behavior of heat diffusion. This construction enables Laplacian-like smoothing and processing of irregular data such as point clouds, sparse voxel grids or mixture of Gaussians. We show that the resulting operators not only approximate heat diffusion but also retain spectral information from the Laplacian itself, with applications to shape analysis and matching.

Applications · Computer Vision

Roger Hsiao, Yuchen Fang, Xiangru Huang, Ruilong Li, Hesam Rabeti, Zan Gojcic, Javad Lavaei, James Demmel, Sophia Shao

We propose 3DGS$^2$-TR, a second-order optimizer for accelerating the scene training problem in 3D Gaussian Splatting (3DGS). Unlike existing second-order approaches that rely on explicit or dense curvature representations, such as 3DGS-LM (Höllein et al., 2025) or 3DGS2 (Lan et al., 2025), our method approximates curvature using only the diagonal of the Hessian matrix, estimated efficiently via Hutchinson’s method. Our approach is fully matrix-free and has the same complexity as ADAM (Kingma, 2024), $O(n)$ in both computation and memory costs. To ensure stable optimization in the presence of strong nonlinearity in the 3DGS rasterization process, we introduce a parameter-wise trust-region technique based on the squared Hellinger distance, regularizing updates to Gaussian parameters. Under identical parameter initialization and without densification, 3DGS$^2$-TR is able to achieve better reconstruction quality on standard datasets, using 50\% fewer training iterations compared to ADAM, while incurring less than 1GB of peak GPU memory overhead (17\% more than ADAM and 85\% less than 3DGS-LM), enabling scalability to very large scenes and potentially to distributed training settings.

Reinforcement Learning · Deep RL

Hai Zhong, Zhuoran Li, Xun Wang, Longbo Huang

Reparameterization Policy Gradient (RPG) has emerged as a powerful paradigm for model-based reinforcement learning, enabling high sample efficiency by backpropagating gradients through differentiable dynamics. However, prior RPG approaches have been predominantly restricted to Gaussian policies, limiting their performance and failing to leverage recent advances in generative models. In this work, we identify that flow policies, which generate actions via differentiable ODE integration, naturally align with the RPG framework, a connection not established in prior work. Yet, naively realizing this synergy is non-trivial: it often suffers from training instability and a lack of exploration. We propose Reparameterization Flow Policy Optimization (RFO). RFO computes policy gradients by backpropagating jointly through the flow generation process and system dynamics, unlocking high sample efficiency without requiring intractable log-likelihood calculations. RFO includes two tailored regularization terms for stability and exploration. We also propose a variant of RFO with action chunking. Extensive experiments on diverse locomotion and manipulation tasks—involving both rigid and soft bodies with state or visual inputs—demonstrate the effectiveness of RFO. Notably, on a challenging locomotion task controlling a soft-body quadruped, RFO achieves almost $2\times$ the reward of the state-of-the-art baseline.

Liang Feng, Shikang Zheng, Jiacheng Liu, Yuqi Lin, Qinming Zhou, Peiliang Cai, Xinyu Wang, Junjie Chen, Chang Zou, Yue Ma 等

Diffusion models have achieved remarkable success in content generation but suffer from prohibitive computational costs due to iterative sampling. While recent feature caching methods tend to accelerate inference through temporal extrapolation, these methods still suffer from severe quality loss due to the failure in modeling the complex dynamics of feature evolution. To solve this problem, this paper presents HiCache (Hermite Polynomial-based Feature Cache), a training-free acceleration framework that fundamentally improves feature prediction by aligning mathematical tools with empirical properties. Our key insight is that feature derivative approximations in Diffusion Transformers exhibit multivariate Gaussian characteristics, motivating the use of Hermite polynomials, the potentially theoretically optimal basis for Gaussian-correlated processes. Besides, we introduce a dual-scaling mechanism that ensures numerical stability while preserving predictive accuracy, which is also effective when applied standalone to TaylorSeer. Extensive experiments demonstrate HiCache's superiority: achieving \$5.55\times\$ speedup on FLUX.1-dev while exceeding baseline quality, maintaining strong performance across text-to-image, video generation, and super-resolution tasks. Moreover, HiCache can be naturally added to the previous caching methods to enhance their performance, e.g., improving ClusCa from \$0.9480\$ to \$0.9840\$ in terms of image rewards. Our code is included in the supplementary material, and will be released on GitHub.

Deep Learning · Generative Models and Autoencoders

Nuria Chandra, Yucen Li, Alan Amin, Alex Ali, Joshua Rollins, Sebastian W. Ober, Aniruddh Raghu, Andrew Gordon Wilson

To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite their shared goal, these models have disparate algorithms, theoretical structures, and tradeoffs: discrete diffusion has the most natural domain, Gaussian diffusion has more mature algorithms, and diffusion on the simplex in principle combines the strengths of the other two but in practice suffers from a numerically unstable stochastic processes. Ideally we could see each of these models as instances of the same underlying framework, and enable practitioners to switch between models for downstream applications. However previous theories have only considered connections in special cases. Here we build a theory unifying all three methods of discrete diffusion as different parameterizations of the same underlying process: the Wright-Fisher population genetics model. In particular, we find simplicial and Gaussian diffusion as two large-population limits. Our theory formally connects the likelihoods and hyperparameters of these models and leverages decades of mathematical genetics literature to unlock stable simplicial diffusion. Finally, we relieve the practitioner of balancing model trade-offs by demonstrating it is possible to train a single model that can perform diffusion in any of these three domains at test time. Our experiments show that Wright-Fisher simplicial diffusion is more stable and outperforms previous simplicial diffusion models on conditional DNA generation. We also show that we can train models on multiple domains at once that are competitive with models trained on any individual domain.

Computer Vision · 3D Rendering & Reconstruction

Zheng Zhou, Yu-Jie Xiong, Jia-Chen Zhang, Chun-Ming Xia, Xihe Qiu, Hongjian Zhan

The emergence of 3D Gaussian Splatting (3DGS) has significantly advanced Novel View Synthesis (NVS) through explicit scene representation, enabling real-time photorealistic rendering. However, existing approaches manifest two critical limitations in complex scenarios: (1) Over-reconstruction occurs when persistent large Gaussians cannot meet adaptive splitting thresholds during density control. This is exacerbated by conflicting gradient directions that prevent effective splitting of these Gaussians; (2) Over-densification of Gaussians occurs in regions with aligned gradient aggregation, leading to redundant component proliferation. This redundancy significantly increases memory overhead due to unnecessary data retention. We present Gradient-Direction-Aware Gaussian Splatting (GDAGS) to address these challenges. Our key innovations: the Gradient Coherence Ratio (GCR), computed through normalized gradient vector norms, which explicitly discriminates Gaussians with concordant versus conflicting gradient directions; and a nonlinear dynamic weighting mechanism leverages the GCR to enable gradient-direction-aware density control. Specifically, GDAGS prioritizes conflicting-gradient Gaussians during splitting operations to enhance geometric details while suppressing redundant concordant-direction Gaussians. Conversely, in cloning processes, GDAGS promotes concordant-direction Gaussian densification for structural completion while preventing conflicting-direction Gaussian overpopulation. Comprehensive evaluations across diverse real-world benchmarks demonstrate that GDAGS achieves superior rendering quality while effectively mitigating over-reconstruction, suppressing over-densification, and constructing compact scene representations.

Computer Vision · Everything Else

Jinhui Hou, Zhiyu Zhu, Junhui Hou

Diffusion bridge models have shown great promise in image restoration by explicitly connecting clean and degraded image distributions. However, they often rely on complex and high-cost trajectories, which limit both sampling efficiency and final restoration quality. To address this, we propose an Energy-oriented diffusion Bridge (E-Bridge) framework to approximate a set of low-cost manifold geodesic trajectories to boost the performance of the proposed method. We achieve this by designing a novel bridge process that evolves over a shorter time horizon and makes the reverse process start from an entropy-regularized point that mixes the degraded image and Gaussian noise, which theoretically reduces the required trajectory energy. To solve this process efficiently, we draw inspiration from consistency models to learn a single-step mapping function, optimized via a continuous-time consistency objective tailored for our trajectory, so as to analytically map any state on the trajectory to the target image. Notably, the trajectory length in our framework becomes a tunable task-adaptive knob, allowing the model to adaptively balance information preservation against generative power for tasks of varying degradation, such as denoising versus super-resolution. Extensive experiments demonstrate that our E-Bridge achieves state-of-the-art performance across various image restoration tasks while enabling high-quality recovery with a single or fewer sampling steps. Our project page is https://jinnh.github.io/E-Bridge/.

General Machine Learning · Causality

Erdun Gao, Dino Sejdinovic

Estimating causal quantities (CQs) typically requires large datasets, which can be expensive to obtain, especially when measuring individual outcomes is costly. This challenge highlights the importance of sample-efficient active learning strategies. To address the narrow focus of prior work on the conditional average treatment effect, we formalize the broader task of Active Estimation of Causal Quantities (ActiveCQ) and propose a unified framework for this general problem. Built upon the insight that many CQs are integrals of regression functions, our framework models the regression function with a Gaussian process. For the distribution component, we explore both a baseline using explicit density estimators and a more integrated method using conditional mean embeddings in a reproducing kernel Hilbert space. This latter approach offers key advantages: it bypasses explicit density estimation, operates within the same function space as the GP, and adaptively refines the distributional model after each update. Our framework enables the principled derivation of acquisition strategies from the CQ's posterior uncertainty; we instantiate this principle with two utility functions based on information gain and total variance reduction. A range of simulated and semi-synthetic experiments demonstrate that our proposed framework significantly outperforms relevant baselines, achieving substantial gains in sample efficiency across a variety of CQs.

Computer Vision · 3D Rendering & Reconstruction

Weiyi Xue, Fan Lu, Chi Zhang, Tianhang Wang, Sanqing Qu, Zehan Zheng, Boyuan Zheng, Junqiao Zhao, Guang Chen

3D Gaussian Splatting has demonstrated remarkable potential in novel view synthesis. In contrast to small-scale scenes, large-scale scenes inevitably contain sparsely observed regions with excessively sparse initial points. In this case, supervising Gaussians initialized from low-frequency sparse points with high-frequency images often induces uncontrolled densification and redundant primitives, degrading both efficiency and quality. Intuitively, this issue can be mitigated with scheduling strategies, which can be categorized into two paradigms: modulating target signal frequency via densification and modulating sampling frequency via image resolution. However, previous scheduling strategies are primarily hardcoded, failing to perceive the convergence behavior of the scene frequency. To address this, we reframe scene reconstruction problem from the perspective of signal structure recovery, and propose SIG, a novel scheduler that Synchronizes Image supervision with Gaussian frequencies. Specifically, we derive the average sampling frequency and bandwidth of 3D representations, and then regulate the training image resolution and the Gaussian densification process based on scene frequency convergence. Furthermore, we introduce Sphere-Constrained Gaussians, which leverage the spatial prior of initialized point clouds to control Gaussian optimization. Our framework enables frequency-consistent, geometry-aware, and floater-free training, achieving state-of-the-art performance with a substantial margin in both efficiency and rendering quality in large-scale scenes.

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.

Soham Bonnerjee, Zhipeng Lou, Wei Biao Wu

Despite the sustained popularity of Q-learning as a practical tool for policy determination, a majority of relevant theoretical literature deals with either constant ($\eta_t\equiv \eta$) or polynomially decaying ($\eta_t = \eta t^{-\alpha}$) learning schedules. However, it is well known the these choices suffer from either persistent bias or prohibitively slow convergence. In contrast, the recently proposed linear decay to zero (\texttt{LD2Z}: $\eta_t=\eta(1-t/n)$) schedule has shown appreciable empirical performance, but its theoretical and statistical properties remain largely unexplored, especially in the Q-learning setting. We address this gap in the literature by first considering a general class of power-law decay to zero (\texttt{PD2Z}-$\nu$: $\eta_t=\eta(1-t/n)^{\nu}$). Proceeding step-by-step, we present a sharp non-asymptotic error bound for Q-learning with \texttt{PD2Z}-$\nu$ schedule, which then is used to derive a central limit theory for a new \textit{tail} Polyak-Ruppert averaging estimator. Finally, we also provide a novel time-uniform Gaussian approximation (also known as \textit{strong invariance principle}) for the partial sum process of Q-learning iterates, which facilitates bootstrap-based inference. All our theoretical results are complemented by extensive numerical experiments. Beyond being new theoretical and statistical contributions to the Q-learning literature, our results definitively establish that \texttt{LD2Z} and in general \texttt{PD2Z}-$\nu$ achieve a best-of-both-worlds property: they inherit the rapid decay from initialization (characteristic of constant step-sizes) while retaining the asymptotic convergence guarantees (characteristic of polynomially decaying schedules). This dual advantage explains the empirical success of \texttt{LD2Z} while providing practical guidelines for inference through our results.

Optimization · Sampling and Optimization

Nishant Jain, Tong Zhang

Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through reverse SDEs or probability flow ODEs. The best known guarantees, without any smoothness assumptions, for the KL divergence so far achieve a linear dependence on the data dimension $d$ and an inverse quadratic dependence on accuracy level $\varepsilon$. In this work, we present a refined analysis for the standard Exponential Integrator discretization that improves the dependence on $\varepsilon$, at the same time maintaining the linear dependence on $d$. Following recent works on higher order/randomized midpoint discretizations, we model the generation process as a composition of two steps: a reverse ODE step followed by a smaller noising step, which leads to better dependence on step size. We then provide a novel analysis which achieves linear dependence on $d$ for the ODE discretization error without any smoothness assumptions. Specifically, we introduce a general ODE-based counterpart of the stochastic localization argument from Benton et al and develop new proof techniques to bound second-order spatial derivatives of the score function -- terms that do not arise in previous diffusion analyses and cannot be handled by existing techniques. Leveraging this framework, we prove that $\tilde{O}\left(\tfrac{d \log^{3/2}(1/\delta)}{\varepsilon}\right)$ steps suffice to approximate the target distribution—corrupted by Gaussian noise of variance $\delta$—to within $O(\varepsilon^2)$ in KL divergence, improving upon the previous best result requiring $\tilde{O}\left(\tfrac{d \log^2(1/\delta)}{\varepsilon^2}\right)$ steps.

Social Aspects · Accountability, Transparency and Interpretability

Anjali Parashar, Yingke Li, Eric Yu, Fei Chen, James Neidhoefer, devesh upadhyay, Chuchu Fan

As autonomous systems such as drones, become increasingly deployed in high-stakes, human-centric domains, it is critical to evaluate the ethical alignment since failure to do so imposes imminent danger to human lives, and long term bias in decision-making. Automated ethical benchmarking of these systems is understudied due to the lack of ubiquitous, well-defined metrics for evaluation, and stakeholder-specific subjectivity, which cannot be modeled analytically. To address these challenges, we propose SEED-SET, a Bayesian experimental design framework that incorporates domain-specific objective evaluations, and subjective value judgments from stakeholders. SEED-SET models both evaluation types separately with hierarchical Gaussian Processes, and uses a novel acquisition strategy to propose interesting test candidates based on learnt qualitative preferences and objectives that align with the stakeholder preferences. We validate our approach for ethical benchmarking of autonomous agents on two applications and find our method to perform the best. Our method provides an interpretable and efficient trade-off between exploration and exploitation, by generating up to $2\times$ optimal test candidates compared to baselines, with $1.25\times$ improvement in coverage of high dimensional search spaces.

Theory · Probabilistic Methods

Qiaochu Xu, Zi Yang, Ying Li, Michael Minyi Zhang, Pablo Olmos

Multi-output Gaussian processes (MOGPs) provide a Bayesian framework for modeling non-linear functions with multiple outputs, in which nonstationary kernels are essential for capturing input-dependent variations in observations. However, from a spectral (dual) perspective, existing nonstationary kernels inherit the inflexibility and over-parameterization of their spectral densities due to the restrictive spectral–kernel duality. To overcome this, we establish a generalized spectral–kernel duality that enables fully flexible matrix-valued spectral densities — albeit at the cost of quadratic parameter growth in the number of outputs. To achieve linear scaling while retaining sufficient expressiveness, we propose the multi-output low-rank nonstationary (MO-LRN) kernel: by modeling the spectral density through a low-rank matrix whose rows are independently parameterized by bivariate Gaussian mixtures. Experiments on synthetic and real-world datasets demonstrate that MO-LRN consistently outperforms existing MOGP kernels in regression, missing-data interpolation, and imputation tasks.

Xiaobiao Du, Yida Wang, Kun Zhan, Xin Yu

3D Gaussian Splatting (3DGS) has emerged as a powerful representation for high-quality rendering across a wide range of applications. However, its high computational demands and large storage costs pose significant challenges for deployment on mobile devices. In this work, we propose a mobile-tailored real-time Gaussian Splatting method, dubbed Mobile-GS, enabling efficient inference of Gaussian Splatting on edge devices. Specifically, we first identify alpha blending as the primary computational bottleneck, since it relies on the time-consuming Gaussian depth sorting process. To solve this issue, we propose a depth-aware order-independent rendering scheme that eliminates the need for sorting, thereby substantially accelerating rendering. Although this order-independent rendering improves rendering speed, it may introduce transparency artifacts in regions with overlapping geometry due to the scarcity of rendering order. To address this problem, we propose a neural view-dependent enhancement strategy, enabling more accurate modeling of view-dependent effects conditioned on viewing direction, 3D Gaussian geometry, and appearance attributes. In this way, Mobile-GS can achieve both high-quality and real-time rendering. Furthermore, to facilitate deployment on memory-constrained mobile platforms, we propose first-degree spherical harmonics distillation, a neural vector quantization technique, and a contribution-based pruning strategy to reduce the number of Gaussian primitives and compress the 3D Gaussian representation with the assistance of neural networks. Extensive experiments demonstrate that our proposed Mobile-GS achieves real-time rendering and compact model size while preserving high visual quality, making it well-suited for mobile applications.