Related papers: Topological Learning for Brain Networks

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…

We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure…

Although image denoising algorithms have attracted significant research attention, surprisingly few have been proposed for, or evaluated on, noise from imagery acquired under real low-light conditions. Moreover, noise characteristics are…

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered…

This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data.…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…

We explore encoding brain symmetry into a neural network for a brain tumor segmentation task. A healthy human brain is symmetric at a high level of abstraction, and the high-level asymmetric parts are more likely to be tumor regions. Paying…

Our interest is in multiplex network data with multiple network samples observed across the same set of nodes. Examples originate from a variety of fields, including brain connectivity, international trade networks, and social networks,…

This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…

Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously…

We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving…

This work introduces a novel framework for testing topological variability in weighted networks by combining Hodge decomposition with Wasserstein variance minimization. Traditional approaches that analyze raw edge weights are susceptible to…

Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork,…