Related papers: Topological Learning for Brain Networks

Existing convolution techniques in artificial neural networks suffer from huge computation complexity, while the biological neural network works in a much more powerful yet efficient way. Inspired by the biological plasticity of dendritic…

Parts of the brain that carry sensory tasks are organized topographically: nearby neurons are responsive to the same properties of input signals. Thus, in this work, inspired by the neuroscience literature, we proposed a new topographic…

We prove that for a broad class of permutation-equivariant learning rules (including SGD, Adam, and others), the training process induces a bi-Lipschitz mapping between neurons and strongly constrains the topology of the neuron distribution…

In many human brain network studies, we do not have sufficient number (n) of images relative to the number (p) of voxels due to the prohibitively expensive cost of scanning enough subjects. Thus, brain network models usually suffer the…

Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks.…

Network inference is a rapidly advancing field, with new methods being proposed on a regular basis. Understanding the advantages and limitations of different network inference methods is key to their effective application in different…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

Structural information of phylogenetic tree topologies plays an important role in phylogenetic inference. However, finding appropriate topological structures for specific phylogenetic inference tasks often requires significant design effort…

Automatic segmentation of neuronal topology is critical for handling large scale neuroimaging data, as it can greatly accelerate neuron annotation and analysis. However, the intricate morphology of neuronal branches and the occlusions among…

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…

We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…

Continual learning in neural networks suffers from a phenomenon called catastrophic forgetting, in which a network quickly forgets what was learned in a previous task. The human brain, however, is able to continually learn new tasks and…

Persistent homology (PH) characterizes the shape of brain networks through persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space…

Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…

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…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…