Related papers: Topological Autoencoders

In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…

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…

Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…

Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…

The organization of latent token representations plays a crucial role in determining the stability, generalization, and contextual consistency of language models, yet conventional approaches to embedding refinement often rely on parameter…

Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…

This paper addresses the dual challenge of improving anomaly detection and signal integrity in high-speed dynamic random access memory signals. To achieve this, we propose a joint training framework that integrates an autoencoder with a…

As an increasing amount of image and video content will be analyzed by machines, there is demand for a new codec paradigm that is capable of compressing visual input primarily for the purpose of computer vision inference, while secondarily…

While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…

Efficient lossless compression is essential for minimizing storage costs and transmission overhead while preserving data integrity. Traditional compression techniques, such as dictionary-based and statistical methods, often struggle to…

The traditional SegNet architecture commonly encounters significant information loss during the sampling process, which detrimentally affects its accuracy in image semantic segmentation tasks. To counter this challenge, we introduce an…

We explore the topology of representation manifolds arising in autoregressive neural language models trained on raw text data. In order to study their properties, we introduce tools from computational algebraic topology, which we use as a…

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…

Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…

Semantic communication enables intelligent agents to extract meaning (or semantics) of information via interaction, to carry out collaborative tasks. In this paper, we study semantic communication from a topological space perspective, in…

Sentence and word embeddings encode structural and semantic information in a distributed manner. Part of the information encoded -- particularly lexical information -- can be seen as continuous, whereas other -- like structural information…

An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this…

This paper develops a feedback-based method to preserve the topology privacy of consensus protocols in network systems. The key idea is to intentionally violate topology identifiability conditions, thereby preventing unique or accurate…

We propose Deep Autoencoding Predictive Components (DAPC) -- a self-supervised representation learning method for sequence data, based on the intuition that useful representations of sequence data should exhibit a simple structure in the…

Recent advances in deep generative modeling have enabled efficient modeling of high dimensional data distributions and opened up a new horizon for solving data compression problems. Specifically, autoencoder based learned image or video…