This paper presents Planar Gaussian Splatting (PGS), a novel neural rendering approach to learn the 3D geometry and parse the 3D planes of a scene, directly from multiple RGB images. The PGS leverages Gaussian primitives to model the scene and employ a hierarchical Gaussian mixture approach to group them. Similar Gaussians are progressively merged probabilistically in the tree-structured Gaussian mixtures to identify distinct 3D plane instances and form the overall 3D scene geometry. In order to enable the grouping, the Gaussian primitives contain additional parameters, such as plane descriptors derived by lifting 2D masks from a general 2D segmentation model and surface normals. Experiments show that the proposed PGS achieves state-of-the-art performance in 3D planar reconstruction without requiring either 3D plane labels or depth supervision. In contrast to existing supervised methods that have limited generalizability and struggle under domain shift, PGS maintains its performance across datasets thanks to its neural rendering and scene-specific optimization mechanism, while also being significantly faster than existing optimization-based approaches.

This paper presents Neural Mesh Fusion (NMF), an efficient approach for joint optimization of polygon mesh from multi-view image observations and unsupervised 3D planar-surface parsing of the scene. In contrast to implicit neural representations, NMF directly learns to deform surface triangle mesh and generate an embedding for unsupervised 3D planar segmentation through gradient-based optimization directly on the surface mesh. The conducted experiments show that NMF obtains competitive results compared to state-of-the-art multi-view planar reconstruction, while not requiring any ground-truth 3D or planar supervision. Moreover, NMF is significantly more computationally efficient compared to implicit neural rendering-based scene reconstruction approaches.

In recent years, self-attentive sequential learning models have surpassed conventional collaborative filtering techniques in next-item recommendation tasks. However, Euclidean geometry utilized in these models may not be optimal for capturing a complex structure of behavioral data. Building on recent advances in the application of hyperbolic geometry to collaborative filtering tasks, we propose a novel approach that leverages hyperbolic geometry in the sequential learning setting. Our approach replaces final output of the Euclidean models with a linear predictor in the non-linear hyperbolic space, which increases the representational capacity and improves recommendation quality.

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations - usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

Recent advances in high-fidelity semantic image editing heavily rely on the presumably disentangled latent spaces of the state-of-the-art generative models, such as Style-GAN. Specifically, recent works show that it is possible to achieve decent controllability of attributes in face images via linear shifts along with latent directions. Several recent methods address the discovery of such directions, implicitly assuming that the state-of-the-art GANs learn the latent spaces with inherently linearly separable attribute distributions and semantic vector arithmetic properties.In our work, we show that nonlinear latent code manipulations realized as flows of a trainable Neural ODE are beneficial for many practical non-face image domains with more complex non-textured factors of variation. In particular, we investigate a large number of datasets with known attributes and demonstrate that certain attribute manipulations are challenging to obtain with linear shifts only.

Computer vision tasks such as image classification, image retrieval, and few-shot learning are currently dominated by Euclidean and spherical embeddings so that the final decisions about class belongings or the degree of similarity are made using linear hyperplanes, Euclidean distances, or spherical geodesic distances (cosine similarity). In this work, we demonstrate that in many practical scenarios, hyperbolic embeddings provide a better alternative.

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably, even with such a minimalistic approach, we not only outperform the Euclidean counterpart but also achieve a competitive performance with respect to the current state-of-the-art. We additionally explore the effects of space curvature on the quality of hyperbolic models and propose an efficient data-driven method for estimating its optimal value.