CEC-MMR: Cross-Entropy Clustering Approach to Multi-Modal Regression

In practical applications of regression analysis, it is not uncommon to encounter a multitude of values for each attribute. In such a situation, the univariate distribution, which is typically Gaussian, is suboptimal because the mean may be situated between modes, resulting in a predicted value that differs significantly from the actual data. Consequently, to address this issue, a mixture distribution with parameters learned by a neural network, known as a Mixture Density Network (MDN), is typically employed. However, this approach has an important inherent limitation, in that it is not feasible to ascertain the precise number of components with a reasonable degree of accuracy. In this paper, we introduce CEC-MMR, a novel approach based on Cross-Entropy Clustering (CEC), which allows for the automatic detection of the number of components in a regression problem. Furthermore, given an attribute and its value, our method is capable of uniquely identifying it with the underlying component. The experimental results demonstrate that CEC-MMR yields superior outcomes compared to classical MDNs.

HyConEx: Hypernetwork classifier with counterfactual explanations

In recent years, there has been a growing interest in explainable AI methods. We want not only to make accurate predictions using sophisticated neural networks but also to understand what the model's decision is based on. One of the fundamental levels of interpretability is to provide counterfactual examples explaining the rationale behind the decision and identifying which features, and to what extent, must be modified to alter the model's outcome. To address these requirements, we introduce HyConEx, a classification model based on deep hypernetworks specifically designed for tabular data. Owing to its unique architecture, HyConEx not only provides class predictions but also delivers local interpretations for individual data samples in the form of counterfactual examples that steer a given sample toward an alternative class. While many explainable methods generated counterfactuals for external models, there have been no interpretable classifiers simultaneously producing counterfactual samples so far. HyConEx achieves competitive performance on several metrics assessing classification accuracy and fulfilling the criteria of a proper counterfactual attack. This makes HyConEx a distinctive deep learning model, which combines predictions and explainers as an all-in-one neural network. The code is available at https://github.com/gmum/HyConEx.

REdiSplats: Ray Tracing for Editable Gaussian Splatting

Gaussian Splatting (GS) has become one of the most important neural rendering algorithms. GS represents 3D scenes using Gaussian components with trainable color and opacity. This representation achieves high-quality renderings with fast inference. Regrettably, it is challenging to integrate such a solution with varying light conditions, including shadows and light reflections, manual adjustments, and a physical engine. Recently, a few approaches have appeared that incorporate ray-tracing or mesh primitives into GS to address some of these caveats. However, no such solution can simultaneously solve all the existing limitations of the classical GS. Consequently, we introduce REdiSplats, which employs ray tracing and a mesh-based representation of flat 3D Gaussians. In practice, we model the scene using flat Gaussian distributions parameterized by the mesh. We can leverage fast ray tracing and control Gaussian modification by adjusting the mesh vertices. Moreover, REdiSplats allows modeling of light conditions, manual adjustments, and physical simulation. Furthermore, we can render our models using 3D tools such as Blender or Nvdiffrast, which opens the possibility of integrating them with all existing 3D graphics techniques dedicated to mesh representations.

MeshSplats: Mesh-Based Rendering with Gaussian Splatting Initialization

Gaussian Splatting (GS) is a recent and pivotal technique in 3D computer graphics. GS-based algorithms almost always bypass classical methods such as ray tracing, which offers numerous inherent advantages for rendering. For example, ray tracing is able to handle incoherent rays for advanced lighting effects, including shadows and reflections. To address this limitation, we introduce MeshSplats, a method which converts GS to a mesh-like format. Following the completion of training, MeshSplats transforms Gaussian elements into mesh faces, enabling rendering using ray tracing methods with all their associated benefits. Our model can be utilized immediately following transformation, yielding a mesh of slightly reduced quality without additional training. Furthermore, we can enhance the reconstruction quality through the application of a dedicated optimization algorithm that operates on mesh faces rather than Gaussian components. The efficacy of our method is substantiated by experimental results, underscoring its extensive applications in computer graphics and image processing.

RaySplats: Ray Tracing based Gaussian Splatting

3D Gaussian Splatting (3DGS) is a process that enables the direct creation of 3D objects from 2D images. This representation offers numerous advantages, including rapid training and rendering. However, a significant limitation of 3DGS is the challenge of incorporating light and shadow reflections, primarily due to the utilization of rasterization rather than ray tracing for rendering. This paper introduces RaySplats, a model that employs ray-tracing based Gaussian Splatting. Rather than utilizing the projection of Gaussians, our method employs a ray-tracing mechanism, operating directly on Gaussian primitives represented by confidence ellipses with RGB colors. In practice, we compute the intersection between ellipses and rays to construct ray-tracing algorithms, facilitating the incorporation of meshes with Gaussian Splatting models and the addition of lights, shadows, and other related effects.

Neural Surface Priors for Editable Gaussian Splatting

In computer graphics, there is a need to recover easily modifiable representations of 3D geometry and appearance from image data. We introduce a novel method for this task using 3D Gaussian Splatting, which enables intuitive scene editing through mesh adjustments. Starting with input images and camera poses, we reconstruct the underlying geometry using a neural Signed Distance Field and extract a high-quality mesh. Our model then estimates a set of Gaussians, where each component is flat, and the opacity is conditioned on the recovered neural surface. To facilitate editing, we produce a proxy representation that encodes information about the Gaussians' shape and position. Unlike other methods, our pipeline allows modifications applied to the extracted mesh to be propagated to the proxy representation, from which we recover the updated parameters of the Gaussians. This effectively transfers the mesh edits back to the recovered appearance representation. By leveraging mesh-guided transformations, our approach simplifies 3D scene editing and offers improvements over existing methods in terms of usability and visual fidelity of edits. The complete source code for this project can be accessed at \url{https://github.com/WJakubowska/NeuralSurfacePriors}

PR-ENDO: Physically Based Relightable Gaussian Splatting for Endoscopy

Endoscopic procedures are crucial for colorectal cancer diagnosis, and three-dimensional reconstruction of the environment for real-time novel-view synthesis can significantly enhance diagnosis. We present PR-ENDO, a framework that leverages 3D Gaussian Splatting within a physically based, relightable model tailored for the complex acquisition conditions in endoscopy, such as restricted camera rotations and strong view-dependent illumination. By exploiting the connection between the camera and light source, our approach introduces a relighting model to capture the intricate interactions between light and tissue using physically based rendering and MLP. Existing methods often produce artifacts and inconsistencies under these conditions, which PR-ENDO overcomes by incorporating a specialized diffuse MLP that utilizes light angles and normal vectors, achieving stable reconstructions even with limited training camera rotations. We benchmarked our framework using a publicly available dataset and a newly introduced dataset with wider camera rotations. Our methods demonstrated superior image quality compared to baseline approaches.

VeGaS: Video Gaussian Splatting

Implicit Neural Representations (INRs) employ neural networks to approximate discrete data as continuous functions. In the context of video data, such models can be utilized to transform the coordinates of pixel locations along with frame occurrence times (or indices) into RGB color values. Although INRs facilitate effective compression, they are unsuitable for editing purposes. One potential solution is to use a 3D Gaussian Splatting (3DGS) based model, such as the Video Gaussian Representation (VGR), which is capable of encoding video as a multitude of 3D Gaussians and is applicable for numerous video processing operations, including editing. Nevertheless, in this case, the capacity for modification is constrained to a limited set of basic transformations. To address this issue, we introduce the Video Gaussian Splatting (VeGaS) model, which enables realistic modifications of video data. To construct VeGaS, we propose a novel family of Folded-Gaussian distributions designed to capture nonlinear dynamics in a video stream and model consecutive frames by 2D Gaussians obtained as respective conditional distributions. Our experiments demonstrate that VeGaS outperforms state-of-the-art solutions in frame reconstruction tasks and allows realistic modifications of video data. The code is available at: https://github.com/gmum/VeGaS.

FreSh: Frequency Shifting for Accelerated Neural Representation Learning

Implicit Neural Representations (INRs) have recently gained attention as a powerful approach for continuously representing signals such as images, videos, and 3D shapes using multilayer perceptrons (MLPs). However, MLPs are known to exhibit a low-frequency bias, limiting their ability to capture high-frequency details accurately. This limitation is typically addressed by incorporating high-frequency input embeddings or specialized activation layers. In this work, we demonstrate that these embeddings and activations are often configured with hyperparameters that perform well on average but are suboptimal for specific input signals under consideration, necessitating a costly grid search to identify optimal settings. Our key observation is that the initial frequency spectrum of an untrained model's output correlates strongly with the model's eventual performance on a given target signal. Leveraging this insight, we propose frequency shifting (or FreSh), a method that selects embedding hyperparameters to align the frequency spectrum of the model's initial output with that of the target signal. We show that this simple initialization technique improves performance across various neural representation methods and tasks, achieving results comparable to extensive hyperparameter sweeps but with only marginal computational overhead compared to training a single model with default hyperparameters.

Make Interval Bound Propagation great again

In various scenarios motivated by real life, such as medical data analysis, autonomous driving, and adversarial training, we are interested in robust deep networks. A network is robust when a relatively small perturbation of the input cannot lead to drastic changes in output (like change of class, etc.). This falls under the broader scope field of Neural Network Certification (NNC). Two crucial problems in NNC are of profound interest to the scientific community: how to calculate the robustness of a given pre-trained network and how to construct robust networks. The common approach to constructing robust networks is Interval Bound Propagation (IBP). This paper demonstrates that IBP is sub-optimal in the first case due to its susceptibility to the wrapping effect. Even for linear activation, IBP gives strongly sub-optimal bounds. Consequently, one should use strategies immune to the wrapping effect to obtain bounds close to optimal ones. We adapt two classical approaches dedicated to strict computations -- Dubleton Arithmetic and Affine Arithmetic -- to mitigate the wrapping effect in neural networks. These techniques yield precise results for networks with linear activation functions, thus resisting the wrapping effect. As a result, we achieve bounds significantly closer to the optimal level than IBPs.