We propose symmetric power transformation to enhance the capacity of Implicit Neural Representation (INR) from the perspective of data transformation. Unlike prior work utilizing random permutation or index rearrangement, our method features a reversible operation that does not require additional storage consumption. Specifically, we first investigate the characteristics of data that can benefit the training of INR, proposing the Range-Defined Symmetric Hypothesis, which posits that specific range and symmetry can improve the expressive ability of INR. Based on this hypothesis, we propose a nonlinear symmetric power transformation to achieve both range-defined and symmetric properties simultaneously. We use the power coefficient to redistribute data to approximate symmetry within the target range. To improve the robustness of the transformation, we further design deviation-aware calibration and adaptive soft boundary to address issues of extreme deviation boosting and continuity breaking. Extensive experiments are conducted to verify the performance of the proposed method, demonstrating that our transformation can reliably improve INR compared with other data transformations. We also conduct 1D audio, 2D image and 3D video fitting tasks to demonstrate the effectiveness and applicability of our method.

We propose EVOlutionary Selector (EVOS), an efficient training paradigm for accelerating Implicit Neural Representation (INR). Unlike conventional INR training that feeds all samples through the neural network in each iteration, our approach restricts training to strategically selected points, reducing computational overhead by eliminating redundant forward passes. Specifically, we treat each sample as an individual in an evolutionary process, where only those fittest ones survive and merit inclusion in training, adaptively evolving with the neural network dynamics. While this is conceptually similar to Evolutionary Algorithms, their distinct objectives (selection for acceleration vs. iterative solution optimization) require a fundamental redefinition of evolutionary mechanisms for our context. In response, we design sparse fitness evaluation, frequency-guided crossover, and augmented unbiased mutation to comprise EVOS. These components respectively guide sample selection with reduced computational cost, enhance performance through frequency-domain balance, and mitigate selection bias from cached evaluation. Extensive experiments demonstrate that our method achieves approximately 48%-66% reduction in training time while ensuring superior convergence without additional cost, establishing state-of-the-art acceleration among recent sampling-based strategies. Our code is available at this link.

3D Gaussian Splatting (3DGS) is a prevailing technique to reconstruct large-scale 3D scenes from multiview images for novel view synthesis, like a room, a block, and even a city. Such large-scale scenes are not static with changes constantly happening in these scenes, like a new building being built or a new decoration being set up. To keep the reconstructed 3D Gaussian fields up-to-date, a naive way is to reconstruct the whole scene after changing, which is extremely costly and inefficient. In this paper, we propose a new method called GauUpdate that allows partially updating an old 3D Gaussian field with new objects from a new 3D Gaussian field. However, simply inserting the new objects leads to inconsistent appearances because the old and new Gaussian fields may have different lighting environments from each other. GauUpdate addresses this problem by applying inverse rendering techniques in the 3DGS to recover both the materials and environmental lights. Based on the materials and lighting, we relight the new objects in the old 3D Gaussian field for consistent global illumination. For an accurate estimation of the materials and lighting, we put additional constraints on the materials and lighting conditions, that these two fields share the same materials but different environment lights, to improve their qualities. We conduct experiments on both synthetic scenes and real-world scenes to evaluate GauUpdate, which demonstrate that GauUpdate achieves realistic object insertion in 3D Gaussian fields with consistent appearances.

In this paper, we examine the impact and significance of bias terms in Implicit Neural Representations (INRs). While bias terms are known to enhance nonlinear capacity by shifting activations in typical neural networks, we discover their functionality differs markedly in neural representation networks. Our analysis reveals that INR performance neither scales with increased number of bias terms nor shows substantial improvement through bias term gradient propagation. We demonstrate that bias terms in INRs primarily serve to eliminate \textit{spatial aliasing} caused by symmetry from both coordinates and activation functions, with input-layer bias terms yielding the most significant benefits. These findings challenge the conventional practice of implementing full-bias INR architecture. We propose using freezing bias terms exclusively in input layers, which consistently outperforms fully biased networks in signal fitting tasks. Furthermore, we introduce Feature-Biased INRs~(Feat-Bias), which initialize input-layer bias with high-level features extracted from pre-trained models. This feature-biasing approach effectively addresses the limited performance in INR post-processing tasks due to neural parameter uninterpretability, achieving superior accuracy while reducing parameter count and improving reconstruction quality.

We study the problem of retrieving accurate correspondence through multi-scale consistency (MSC) for robust point cloud registration. Existing works in a coarse-to-fine manner either suffer from severe noisy correspondences caused by unreliable coarse matching or struggle to form outlier-free coarse-level correspondence sets. To tackle this, we present Hierarchical Sinkhorn Tree (HST), a pruned tree structure designed to hierarchically measure the local consistency of each coarse correspondence across multiple feature scales, thereby filtering out the local dissimilar ones. In this way, we convert the modeling of MSC for each correspondence into a BFS traversal with pruning of a K-ary tree rooted at the superpoint, with its K nearest neighbors in the feature pyramid serving as child nodes. To achieve efficient pruning and accurate vicinity characterization, we further propose a novel overlap-aware Sinkhorn Distance, which retains only the most likely overlapping points for local measurement and next level exploration. The modeling process essentially involves traversing a pair of HSTs synchronously and aggregating the consistency measures of corresponding tree nodes. Extensive experiments demonstrate HST consistently outperforms the state-of-the-art methods on both indoor and outdoor benchmarks.