English
Related papers

Related papers: Partition of Unity Neural Networks for Interpretab…

200 papers

When neural networks are trained to classify a dataset, one finds a set of weights from which the network produces a label for each data point. We study the algorithmic complexity of finding a collision in a single-layer neural net, where a…

Deep neural networks (NNs) are known to lack uncertainty estimates and struggle to incorporate new data. We present a method that mitigates these issues by converting NNs from weight space to function space, via a dual parameterization.…

Machine Learning · Statistics 2023-09-06 Aidan Scannell , Riccardo Mereu , Paul Chang , Ella Tamir , Joni Pajarinen , Arno Solin

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Analysis of PDEs · Mathematics 2019-09-04 Dongkun Zhang , Lu Lu , Ling Guo , George Em Karniadakis

For a broad variety of critical applications, it is essential to know how confident a classification prediction is. In this paper, we discuss the drawbacks of softmax to calculate class probabilities and to handle uncertainty in Bayesian…

Machine Learning · Computer Science 2019-06-11 Christian Herta , Benjamin Voigt

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Numerical Analysis · Mathematics 2023-05-08 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino

It is often useful to perform integration over learned functions represented by neural networks. However, this integration is usually performed numerically, as analytical integration over learned functions (especially neural networks) is…

Machine Learning · Computer Science 2023-12-27 Ryan Kortvelesy

A sum-product network (SPN) is a graphical model that allows several types of inferences to be drawn efficiently. There are two types of learning for SPNs: Learning the architecture of the model, and learning the parameters. In this paper,…

Machine Learning · Computer Science 2021-10-18 Ernst Althaus , Mohammad Sadeq Dousti , Stefan Kramer , Nick Johannes Peter Rassau

Precise boundary segmentation of volumetric images is a critical task for image-guided diagnosis and computer-assisted intervention, especially for boundary confusion in clinical practice. However, U-shape networks cannot effectively…

Computer Vision and Pattern Recognition · Computer Science 2023-12-14 Xin You , Ming Ding , Minghui Zhang , Hanxiao Zhang , Yi Yu , Jie Yang , Yun Gu

The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by…

Machine Learning · Statistics 2025-12-30 Georgios Arampatzis , Stylianos Katsarakis , Charalambos Makridakis

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

Machine Learning · Computer Science 2021-08-16 Khashayar Filom , Konrad Paul Kording , Roozbeh Farhoodi

Binary neural networks leverage $\mathrm{Sign}$ function to binarize weights and activations, which require gradient estimators to overcome its non-differentiability and will inevitably bring gradient errors during backpropagation. Although…

Computer Vision and Pattern Recognition · Computer Science 2023-07-18 Yefei He , Luoming Zhang , Weijia Wu , Hong Zhou

Neural networks are powerful function approximators, yet their ``black-box" nature often renders them opaque and difficult to interpret. While many post-hoc explanation methods exist, they typically fail to capture the underlying reasoning…

Machine Learning · Computer Science 2024-08-29 Nisal Ranasinghe , Yu Xia , Sachith Seneviratne , Saman Halgamuge

Graph neural networks (GNNs) have become a popular approach to integrating structural inductive biases into NLP models. However, there has been little work on interpreting them, and specifically on understanding which parts of the graphs…

Computation and Language · Computer Science 2022-10-04 Michael Sejr Schlichtkrull , Nicola De Cao , Ivan Titov

This work makes a substantial step in the field of split computing, i.e., how to split a deep neural network to host its early part on an embedded device and the rest on a server. So far, potential split locations have been identified…

Computer Vision and Pattern Recognition · Computer Science 2022-12-20 Federico Cunico , Luigi Capogrosso , Francesco Setti , Damiano Carra , Franco Fummi , Marco Cristani

Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when…

Machine Learning · Computer Science 2026-05-28 Ze Tao , Hanxuan Wang , Fujun Liu

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based…

Machine Learning · Computer Science 2025-07-21 Jon Vadillo , Roberto Santana , Jose A. Lozano , Marta Kwiatkowska

A robust theoretical framework that can describe and predict the generalization ability of deep neural networks (DNNs) in general circumstances remains elusive. Classical attempts have produced complexity metrics that rely heavily on global…

Machine Learning · Computer Science 2020-01-20 Marelie H. Davel , Marthinus W. Theunissen , Arnold M. Pretorius , Etienne Barnard

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the…

Machine Learning · Computer Science 2017-11-20 Volodymyr Kuleshov , Stefano Ermon

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Machine Learning · Computer Science 2025-10-29 Diego Doimo

We report on a gate-based variational quantum classifier implemented with single photons and probabilistic gates, to emulate the standard quantum circuit model framework. We evaluate the expressive power of two deployable quantum neural…

Quantum Physics · Physics 2026-05-27 Solomon McKiernan , Luca Sapienza