Related papers: Topology-Aware Activation Functions in Neural Netw…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

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…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Neurons in the brain are organized such that nearby cells tend to share similar functions. AI models lack this organization, and past efforts to introduce topography have often led to trade-offs between topography and task performance. In…

Despite the increasing prevalence of deep neural networks, their applicability in resource-constrained devices is limited due to their computational load. While modern devices exhibit a high level of parallelism, real-time latency is still…

At the heart of neural network force fields (NNFFs) is the architecture of neural networks, where the capacity to model complex interactions is typically enhanced through widening or deepening multilayer perceptrons (MLPs) or by increasing…

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…

In this study, we explore the impact of network topology on the approximation capabilities of artificial neural networks (ANNs), with a particular focus on complex topologies. We propose a novel methodology for constructing complex ANNs…

Several current bounds on the maximal number of affine regions of a ReLU feed-forward neural network are special cases of the framework [1] which relies on layer-wise activation histogram bounds. We analyze and partially solve a problem in…

The mathematical complexity and high dimensionality of neural networks slow both training and deployment, demanding heavy computational resources. This has driven the search for alternative architectures built from novel components,…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Addressing the imperative need for efficient artificial intelligence in IoT and edge computing, this study presents RepAct, a re-parameterizable adaptive activation function tailored for optimizing lightweight neural networks within the…

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…

In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

Recent findings suggest that consecutive layers of neural networks with the ReLU activation function \emph{fold} the input space during the learning process. While many works hint at this phenomenon, an approach to quantify the folding was…

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows…

Dense prediction tasks such as depth perception and semantic segmentation are important applications in computer vision that have a concrete topological description in terms of partitioning an image into connected components or estimating a…

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…

Activity recognition has become a popular research branch in the field of pervasive computing in recent years. A large number of experiments can be obtained that activity sensor-based data's characteristic in activity recognition is…