Related papers: Autoencoding Dynamics: Topological Limitations and…
Euclidean geometry has historically been the typical "workhorse" for machine learning applications due to its power and simplicity. However, it has recently been shown that geometric spaces with constant non-zero curvature improve…
In spite of the remarkable potential of Latent Diffusion Models (LDMs) in image generation, the desired properties and optimal design of the autoencoders have been underexplored. In this work, we analyze the role of autoencoders in LDMs and…
Autoencoders are a powerful and versatile tool often used for various problems such as anomaly detection, image processing and machine translation. However, their reconstructions are not always trivial to explain. Therefore, we propose a…
We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…
In this work, we study the representation space of contextualized embeddings and gain insight into the hidden topology of large language models. We show there exists a network of latent states that summarize linguistic properties of…
Motion planning with constraints is an important part of many real-world robotic systems. In this work, we study manifold learning methods to learn such constraints from data. We explore two methods for learning implicit constraint…
Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the…
In multiple access channels (MAC), multiple users share a transmission medium to communicate with a common receiver. Traditional constellations like quadrature amplitude modulation are optimized for point-to-point systems and lack…
Local causal states are latent representations that capture organized pattern and structure in complex spatiotemporal systems. We expand their functionality, framing them as spacetime autoencoders. Previously, they were only considered as…
Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or…
In this paper, we study the space of translational limits T(M) of a surface M properly embedded in R^3 with nonzero constant mean curvature and bounded second fundamental form. There is a natural map T which assigns to any surface M' in…
Recently, generative adversarial networks and adversarial autoencoders have gained a lot of attention in machine learning community due to their exceptional performance in tasks such as digit classification and face recognition. They map…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
The benefit of pretrained autoencoders for reinforcement learning in comparison to training on raw observations is already known [1]. In this paper, we address the generation of a compact and information-rich state representation. In…
Understanding terrain topology at long-range is crucial for the success of off-road robotic missions, especially when navigating at high-speeds. LiDAR sensors, which are currently heavily relied upon for geometric mapping, provide sparse…
We study why continuous diffusion language models (DLMs) have lagged behind discrete diffusion approaches despite their appealing continuous generative dynamics. Under a controlled token--recovery study, we identify token rounding, the…
In the last years, deep learning has shown to be a game-changing technology in artificial intelligence thanks to the numerous successes it reached in diverse application fields. Among others, the use of deep learning for the recommendation…
Self-supervised learning has become a central strategy for representation learning, but the majority of architectures used for encoding data have only been validated on regularly-sampled inputs such as images, audios. and videos. In many…
This paper proposes an autoencoder (AE) that is used for improving the performance of once-class classifiers for the purpose of detecting anomalies. Traditional one-class classifiers (OCCs) perform poorly under certain conditions such as…
Compact models often lose the structure of their embedding space. The issue shows up when the capacity is tight or the data spans several languages. Such collapse makes it difficult for downstream tasks to build on the resulting…