Across humans and all 76 networks, we were able to obtain good fits (with low standard error) for all 3 parameters.

Across humans and all 76 networks, we were able to obtain good fits (with low standard error) for all 3 parameters.

Pairwise distance-based costs are crucial for self-supervised and contrastive feature learning. Mixture Density Networks (MDNs) are a widely used approach for generative models and density approximation, using neural networks to produce multiple centers that define a Gaussian mixture. By combining MDNs with contrastive costs, this paper proposes data density approximation using four types of kernelized matrix costs: the scalar cost, the vector-matrix cost, the matrix-matrix cost (the trace of Schur complement), and the SVD cost (the nuclear norm), for learning multiple centers required to define a mixture density.

We would like to thank all reviewers for their time and effort writing these valuable reviews. Reviewer 3 mentioned that a performance measure with other recent methods would be beneficial. The code for this paper will be released with the camera-ready version. In the following, we focus on the questions given by Reviewer 2. The presented network does not contain fewer parameters compared to the classical B-spline method for optimization. Furthermore, it is straightforward to extend for the 3D case.

Network compression techniques have become increasingly important in recent years because the loads of Deep Neural Networks (DNNs) are heavy for edge devices in real-world applications. While many methods compress neural network parameters, deploying these models on edge devices remains challenging. To address this, we propose the fractional Gaussian filter and pruning (FGFP) framework, which integrates fractional-order differential calculus and Gaussian function to construct fractional Gaussian filters (FGFs). To reduce the computational complexity of fractional-order differential operations, we introduce Grünwald-Letnikov fractional derivatives to approximate the fractional-order differential equation. The number of parameters for each kernel in FGF is minimized to only seven. Beyond the architecture of Fractional Gaussian Filters, our FGFP framework also incorporates Adaptive Unstructured Pruning (AUP) to achieve higher compression ratios. Experiments on various architectures and benchmarks show that our FGFP framework outperforms recent methods in accuracy and compression. On CIFAR-10, ResNet-20 achieves only a 1.52% drop in accuracy while reducing the model size by 85.2%. On ImageNet2012, ResNet-50 achieves only a 1.63% drop in accuracy while reducing the model size by 69.1%.

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.

Splatting-based 3D reconstruction methods have gained popularity with the advent of 3D Gaussian Splatting, efficiently synthesizing high-quality novel views. These methods commonly resort to using exponential family functions, such as the Gaussian function, as reconstruction kernels due to their anisotropic nature, ease of projection, and differentiability in rasterization. However, the field remains restricted to variations within the exponential family, leaving generalized reconstruction kernels largely underexplored, partly due to the lack of easy integrability in 3D to 2D projections. In this light, we show that a class of decaying anisotropic radial basis functions (DARBFs), which are non-negative functions of the Mahalanobis distance, supports splatting by approximating the Gaussian function's closed-form integration advantage. With this fresh perspective, we demonstrate up to 34% faster convergence during training and a 15% reduction in memory consumption across various DARB reconstruction kernels, while maintaining comparable PSNR, SSIM, and LPIPS results. We will make the code available.

Service robots that work alongside humans in a shared environment need a navigation system that takes into account not only physical safety but also social norms for mutual cooperation. In this paper, we introduce a motion planning system that includes human states such as positions and velocities and their personal space for social-aware navigation. The system first extracts human positions from the LiDAR and the RGB-D camera. It then uses the Kalman filter to fuse that information for human state estimation. An asymmetric Gaussian function is then employed to model human personal space based on their states. This model is used as the input to the dynamic window approach algorithm to generate trajectories for the robot. Experiments show that the robot is able to navigate alongside humans in a dynamic environment while respecting their physical and psychological comfort.