DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting

• URL: http://arxiv.org/abs/2607.10912v1
• Date: Sun, 12 Jul 2026 20:31:15 GMT
• Title: DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting
• Abstract summary: 3D Splatting represents finite mixtures of anisotropic Gaussians whose number of components $K$ is set by density control or user caps.<n>We replace the symmetric symmetric Dirichlet over mixture weights with a truncated stick-breaking Dirichlet-process prior.<n>We give an exact monotonicity guarantee, a rigorous truncation-error bound correcting an anti-conservative large-error approximation in common use.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components $K$ is set by heuristic density control or user caps. Variational Bayes Gaussian Splatting (VBGS) recast splat fitting as conjugate variational inference, but $K$ remains fixed. We replace the finite symmetric Dirichlet over mixture weights with a truncated stick-breaking Dirichlet-process prior -- and, as a theory-backed alternative, a sparse overfitted finite Dirichlet -- so that the number of occupied components adapts to the data while every update remains a closed-form coordinate-ascent step; a natural-gradient stochastic variant makes the per-step cost independent of the number of points. We give an exact monotonicity guarantee, a rigorous truncation-error bound correcting an anti-conservative large-$α$ approximation in common use, and an honest account of what the fitted number of components estimates. Empirically: (i) the effective complexity $\hat{K}$ adapts to scene complexity and recovers the true $K$ within $\pm 1$ on well-separated synthetic data with regime-appropriate concentration; (ii) a deconfounded comparison shows the DP prior's contribution is complexity selection, not per-component efficiency -- converged DP fits exceed single-pass fixed-$K$ VBGS by +2.7 dB at matched budgets yet tie an equally converged fixed-$K$ baseline, and on 3D scenes DP-Splat matches or exceeds VBGS's held-out color prediction with 5.9-7.6x fewer components; (iii) the posterior-predictive color variance is well calibrated on model-matched synthetic data; and (iv) the ordering suggested by exact-posterior asymptotics reverses under mean-field coordinate ascent: the DP prior resists over-splitting while the sparse finite mixture saturates its truncation, a gap between variational practice and posterior asymptotics documented across three orders of magnitude in $N$.

Related papers

• Saturation Makes Quantization Error Additive: A Coverage Model with a Certificate [0.0]
  Mixed-precision quantization must decide which parts of a model to keep at higher precision.<n>We show that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation.<n>We propose the coverage model $f(S)=cbigl (1-prod_iin S (1-a_i)bigr)$, which reproduces the measured variance profile of $f$ to within a few percent from its $L$ fitted break-rates.
  arXiv  Detail & Related papers  (2026-07-14T02:08:33Z)
• ITSPACE: Monotone Gaussian Optimal Transport Updates [0.04687712818521871]
  Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings.<n>We propose ITSPACE, a majorization-minimization method that directly optimize this exact BW objective through closed-form updates in a square-root factorization.<n>In exact arithmetic, each satisfies a sufficient-decrease inequality for the BW objective; under inexact polar computations, we provide an explicit certificate-gap bound controlling deviations from exact descent.
  arXiv  Detail & Related papers  (2026-06-29T16:29:19Z)
• $Ω$: Operator-based Mixture Ensemble for Generative Assimilation [7.915816961228985]
  $$ is a scalable framework that integrates conditional Gaussian surrogate modeling, unsupervised score learning, and generative sampling.<n>$$ exploits closed-form conditional posterior distributions to analytically recover the high-dimensional unobserved component.<n>$$ is validated on several turbulent models with intermittency and extreme events, consistently improving posterior accuracy.
  arXiv  Detail & Related papers  (2026-06-18T20:19:44Z)
• Beyond Heuristics: Learnable Density Control for 3D Gaussian Splatting [78.96382179408054]
  We introduce bfLeGS, a framework that reformulates density control as a parameterized policy network optimized via Reinforcement Learning (RL)<n>To maintain computational tractability, we derive a closed-form solution that reduces the complexity of reward calculation from $O(N2)$ to $O(N)$.<n>Experiments on the Mip-NeRF 360, Tanks & Temples, and Deep Blending datasets demonstrate that bfLeGS significantly outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2026-05-01T05:04:49Z)
• High-Probability Convergence in Decentralized Stochastic Optimization with Gradient Tracking [69.90407799170687]
  We study high-probability (HP) convergence guarantees in decentralized optimization.<n>Our results establish the same conditions on the horizon as in achieving comparable times.
  arXiv  Detail & Related papers  (2026-04-30T22:45:21Z)
• Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions [3.6997773420183866]
  We develop new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method.<n>Unlike unbiased estimators such as mini-batching, developing biased variants faces a fundamental technical challenge.<n>We show that the best oracle complexities for the $n$-finite-sum and expectation settings are $mathcalO(n2/3-2)$ and $mathcalO(-10/3)$, respectively, when employing loopless-SVRG or SAGA.
  arXiv  Detail & Related papers  (2026-03-16T17:39:25Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning [61.07540493350384]
  Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth and the teacher's own predictions.<n>We show that for any prediction risk, the optimally mixed student improves upon the ridge teacher for every regularization level.<n>We propose a consistent one-shot tuning method to estimate $star$ without grid search, sample splitting, or refitting.
  arXiv  Detail & Related papers  (2026-02-19T17:21:15Z)
• Robust inverse material design with physical guarantees using the Voigt-Reuss Net [0.0]
  We propose a spectrally normalized surrogate for forward and inverse mechanical homogenization with hard physical guarantees.<n>In 3D linear elasticity on an open dataset of biphasic microstructures, a fully connected Voigt-Reuss net trained on $>!7.5times 105$ FFT-based labels with 236 isotropy-in descriptors.<n>Overall, the Voigt-Reuss net unifies accurate, physically admissible forward prediction with large-batch, constraint-consistent inverse design.
  arXiv  Detail & Related papers  (2025-11-14T15:17:37Z)
• FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA [68.44043212834204]
  Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in learning (FL)<n>Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in learning (FL)
  arXiv  Detail & Related papers  (2025-05-19T07:32:56Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate.<n>We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Demystifying SGD with Doubly Stochastic Gradients [13.033133586372612]
  We establish the convergence properties of doubly SGD with independent minibatching and random reshuffling under general conditions.<n>We prove that random reshuffling improves the complexity dependence on the subsampling noise.
  arXiv  Detail & Related papers  (2024-06-03T01:13:19Z)
• A New Framework for Variance-Reduced Hamiltonian Monte Carlo [88.84622104944503]
  We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution. We show that the unbiased gradient estimators, including SAGA and SVRG, based HMC methods achieve highest gradient efficiency with small batch size. Experimental results on both synthetic and real-world benchmark data show that our new framework significantly outperforms the full gradient and gradient HMC approaches.
  arXiv  Detail & Related papers  (2021-02-09T02:44:24Z)
• Robustly Learning any Clusterable Mixture of Gaussians [55.41573600814391]
  We study the efficient learnability of high-dimensional Gaussian mixtures in the adversarial-robust setting. We provide an algorithm that learns the components of an $epsilon$-corrupted $k$-mixture within information theoretically near-optimal error proofs of $tildeO(epsilon)$. Our main technical contribution is a new robust identifiability proof clusters from a Gaussian mixture, which can be captured by the constant-degree Sum of Squares proof system.
  arXiv  Detail & Related papers  (2020-05-13T16:44:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.