NeurIPS 2026 Papers

We consider the active learning problem where the goal is to learn an unknown function with low error under a Boltzmann distribution induced by the function itself. This self-induced weighting arises naturally in problems such as molecular energy modeling and free energy estimation, yet poses unique challenges as the target distribution is unknown and its partition function is intractable. We propose an acquisition function, AB-SID-iVAR, based on Gaussian Process surrogates that approximates the intractable Bayesian target distribution in closed form while avoiding partition function estimation, applicable to both discrete and continuous input domains. We also analyze a Thompson sampling alternative (TS-SID-iVAR) as a higher variance Monte Carlo variant. Despite the unknown target, under mild conditions, we establish that the terminal prediction error vanishes with high probability, and provide a tighter average-case guarantee. We demonstrate superior performance over existing active learning approaches on synthetic benchmarks and real-world modeling tasks.

3D Gaussian Splatting (3DGS) has emerged as a powerful paradigm for real-time photorealistic novel view synthesis. However, its training-time densification remains largely heuristic, often resulting in redundant Gaussian proliferation and inaccurate geometric reconstruction. Existing methods predominantly rely on first-order screen-space gradients to trigger cloning and splitting, which fail to distinguish true geometric discontinuities from high-frequency textures or noisy residuals. To address this limitation, we propose ACD-GS, an Asymmetric Curvature-aware Densification framework for compact and geometry-aware 3D Gaussian optimization. Our key insight is that second-order depth responses provide a more reliable structural prior for density control, enabling asymmetric regulation of cloning and splitting to better capture geometric discontinuities. Building on this, we introduce a multi-view photometric consistency constraint to suppress transient single-view errors, together with a capacity-aware adaptive regulation strategy that balances densification and pruning during training. Unlike post-hoc compression or quantization-based approaches, ACD-GS directly prevents redundant Gaussian generation during training, yielding inherently compact representations. Extensive experiments demonstrate that our method reduces nearly 60\% of Gaussian count and storage while maintaining competitive rendering fidelity, consistently outperforming existing methods across multiple datasets. Our code is available in https://anonymous.4open.science/r/ACD_GS-0E2C

Kernel methods, and Gaussian Processes (GPs) in particular, require a conditionally negative-definite (CND) distance measure to guarantee positive semi-definiteness (PSD) of the kernel matrix — a condition that fails for many natural input spaces, including smooth manifolds and spaces of probability distributions. We propose the Sparse Landmark Embedding (SLE) kernel, which eliminates this requirement entirely. Each input is embedded into a sparse feature vector via compactly supported bump functions centered at all training points $|\mathcal{D}|$; applying any standard PSD kernel in this embedding space yields a kernel that is provably PSD for arbitrary distance measures. The compact support automatically controls embedding sparsity, keeping kernel matrices well-conditioned and computationally tractable despite the high ambient dimension. We provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and demonstrate, using geodesic and Wasserstein distances, that the SLE kernel matches or substantially exceeds domain-specific baselines in both predictive accuracy and uncertainty quantification.

3D Gaussian Splatting (3DGS) has become a vital tool in novel view synthesis. 3D Gaussian functions with attributes like color, opacity, and scale are stacked together to explicitly model a radiance field. However, discrete 3D Gaussians usually produce poor depth with few geometry details but lots of floaters, which makes modeling smooth radiance fields remain a challenge. To address this issue, we propose to learn a radiance field within a continuous view-dependent color field parameterized by neural networks. With the continuous constraints in color, the bias on low-frequency signals of neural networks highly encourages the geometry to contribute to high-frequency color variations on images, but not solely relying on the color attribute itself. Moreover, we impose a constraint to improve the Lipschitz continuity of the neural color field, making large changes of each Gaussian's color also match with large changes of its position in terms of a ratio. To this end, we additionally introduce novel self-learning strategies to learn neural view-dependent color fields without any external knowledge or priors, aiming for better generalization. Our numerical and visual comparisons on widely used benchmarks justify our idea and show better ability of high fidelity geometry recovery in 3DGS.

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This dependency becomes a significant bottleneck for long-context and streaming reconstruction, as it forces the network to maintain an arbitrary temporal origin and handle translation magnitudes that grow unbounded over time. Our solution, which we call $R^3$, employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference. $R^3$ supports both full-context offline reconstruction and causal, bounded-memory streaming. Our evaluation in both offline and streaming settings validates the effectiveness of our relative mechanism.