Related papers: Geometrically Enriched Latent Spaces
We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…
In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…
Interpolations in the latent space of deep generative models is one of the standard tools to synthesize semantically meaningful mixtures of generated samples. As the generator function is non-linear, commonly used linear interpolations in…
Deep generative models can automatically create content of diverse types. However, there are no guarantees that such content will satisfy the criteria necessary to present it to end-users and be functional, e.g. the generated levels could…
Functional brain graphs are often characterized with separate graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across brains and conditions. We anticipate that dense, weighted functional…
Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…
In this work, we introduce a two-step framework for generative modeling of temporal data. Specifically, the generative adversarial networks (GANs) setting is employed to generate synthetic scenes of moving objects. To do so, we propose a…
This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) to facilitate controllable image synthesis. Such interpretable directions correspond to…
Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…
With the rapidly growing model complexity and data volume, training deep generative models (DGMs) for better performance has becoming an increasingly more important challenge. Previous research on this problem has mainly focused on…
Generative artificial intelligence revolutionized society. Current models are trained by minimizing the distance between the produced data and the training set. Consequently, development is plateauing as they are intrinsically data-hungry…
Generative adversarial nets (GANs) have been successfully applied in many fields like image generation, inpainting, super-resolution and drug discovery, etc., by now, the inner process of GANs is far from been understood. To get deeper…
Variational Autoencoder is typically understood from the perspective of probabilistic inference. In this work, we propose a new geometric reinterpretation which complements the probabilistic view and enhances its intuitiveness. We…
We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called \textit{graphon autoencoder} to build an interpretable…
We study the problem of 3D object generation. We propose a novel framework, namely 3D Generative Adversarial Network (3D-GAN), which generates 3D objects from a probabilistic space by leveraging recent advances in volumetric convolutional…
Recent empirical evidence shows that LLM representations encode human-interpretable concepts. Nevertheless, the mechanisms by which these representations emerge remain largely unexplored. To shed further light on this, we introduce a novel…
Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…
Training intelligent agents that can drive autonomously in various urban and highway scenarios has been a hot topic in the robotics society within the last decades. However, the diversity of driving environments in terms of road topology…