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This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…
Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…
The long acquisition time has limited the accessibility of magnetic resonance imaging (MRI) because it leads to patient discomfort and motion artifacts. Although several MRI techniques have been proposed to reduce the acquisition time,…
In the paper we introduce a novel bipolar morphological neuron and bipolar morphological layer models. The models use only such operations as addition, subtraction and maximum inside the neuron and exponent and logarithm as activation…
To understand the black-box characteristics of deep networks, counterfactual explanation that deduces not only the important features of an input space but also how those features should be modified to classify input as a target class has…
Intrinsic graph convolution operators with differentiable kernel functions play a crucial role in analyzing 3D shape meshes. In this paper, we present a fast and efficient intrinsic mesh convolution operator that does not rely on the…
Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
We report an interpretation method for deep learning models that allows us to handle high-dimensional spectral data in materials science. The proposed method uses feature extraction and clustering analysis to categorize materials into…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
We demonstrate the use of machine learning through convolutional neural networks to solve inverse design problems of optical resonator engineering. The neural network finds a harmonic modulation of a spherical mirror to generate a resonator…
Contrastive learning has recently established itself as a powerful self-supervised learning framework for extracting rich and versatile data representations. Broadly speaking, contrastive learning relies on a data augmentation scheme to…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the…
Contemporary deep learning models effectively handle languages with diverse morphology despite not being directly integrated into them. Morphology and word order are closely linked, with the latter incorporated into transformer-based models…