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Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
This work investigates three methods for calculating loss for autoencoder-based pretraining of image encoders: The commonly used reconstruction loss, the more recently introduced deep perceptual similarity loss, and a feature prediction…
Autoencoders are unsupervised deep learning models used for learning representations. In literature, autoencoders have shown to perform well on a variety of tasks spread across multiple domains, thereby establishing widespread…
We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…
In this paper, we investigate the usage of autoencoders in modeling textual data. Traditional autoencoders suffer from at least two aspects: scalability with the high dimensionality of vocabulary size and dealing with task-irrelevant words.…
Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based…
Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…
Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…
Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…
This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert…
We focus on a specific use case in anomaly detection where the distribution of normal samples is supported by a lower-dimensional manifold. Here, regularized autoencoders provide a popular approach by learning the identity mapping on the…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
Deep learning is playing an instrumental role in the design of the next generation of communication systems. In this letter, we address the massive MIMO interconnect's bandwidth constraint relaxation using autoencoders. The autoencoder is…
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the…
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…
We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…
Variational Autoencoders are one of the most commonly used generative models, particularly for image data. A prominent difficulty in training VAEs is data that is supported on a lower-dimensional manifold. Recent work by Dai and Wipf (2020)…
Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
A new trend uses LLMs as dense text encoders via contrastive learning. However, since LLM embeddings predict the probability distribution of the next token, they are inherently generative and distributive, conflicting with contrastive…