Related papers: BERTops: Studying BERT Representations under a Top…
We describe the topology of superlevel sets of ($\alpha$-stable) L\'evy processes X by introducing so-called stochastic $\zeta$-functions, which are defined in terms of the widely used $\text{Pers}_p$-functional in the theory of persistence…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…
Echoing recent calls to counter reliability and robustness concerns in machine learning via multiverse analysis, we present PRESTO, a principled framework for mapping the multiverse of machine-learning models that rely on latent…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
The effects of seeing on Sersic r^{1/n} profile parameters are extensively studied using a Moffat function. This analytical approximation to the point spread function (PSF) is shown to provide the best fit to the PSF predicted from…
\emph{Topological data analysis} (TDA) has recently emerged as a new technique to extract meaningful discriminitve features from high dimensional data. In this paper, we investigate the possibility of applying TDA to improve the…
Attention-based models have shown significant improvement over traditional algorithms in several NLP tasks. The Transformer, for instance, is an illustrative example that generates abstract representations of tokens inputted to an encoder…
BERT-based architectures currently give state-of-the-art performance on many NLP tasks, but little is known about the exact mechanisms that contribute to its success. In the current work, we focus on the interpretation of self-attention,…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
A second-order-based latent factor (SLF) analysis model demonstrates superior performance in graph representation learning, particularly for high-dimensional and incomplete (HDI) interaction data, by incorporating the curvature information…
Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By…
Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature…
This paper proposes inverse feature learning as a novel supervised feature learning technique that learns a set of high-level features for classification based on an error representation approach. The key contribution of this method is to…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
Although BERT and its variants have reshaped the NLP landscape, it still remains unclear how best to derive sentence embeddings from such pre-trained Transformers. In this work, we propose a contrastive learning method that utilizes…
In this paper, we use topological data analysis techniques to construct a suitable neural network classifier for the task of learning sensor signals of entire power plants according to their reference designation system. We use…