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Interpretability of deep neural networks (DNNs) is essential since it enables users to understand the overall strengths and weaknesses of the models, conveys an understanding of how the models will behave in the future, and how to diagnose…

Computer Vision and Pattern Recognition · Computer Science 2017-03-31 Yinpeng Dong , Hang Su , Jun Zhu , Bo Zhang

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

Computational Physics · Physics 2026-03-03 Wei Wang , Tang Paai Wong , Haihui Ruan , Somdatta Goswami

Deep neural networks (DNNs) with high expressiveness have achieved state-of-the-art performance in many tasks. However, their distributed feature representations are difficult to interpret semantically. In this work, human-interpretable…

Computer Vision and Pattern Recognition · Computer Science 2019-10-22 Jindong Gu , Volker Tresp

Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are…

Neural and Evolutionary Computing · Computer Science 2022-08-05 Beren Millidge , Yuhang Song , Tommaso Salvatori , Thomas Lukasiewicz , Rafal Bogacz

Biological networks such as gene regulatory networks possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated…

Molecular Networks · Quantitative Biology 2024-02-16 Claus Kadelka , David Murrugarra

Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…

Discrete Mathematics · Computer Science 2024-03-29 Elisa Tonello , Loïc Paulevé

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Machine Learning · Statistics 2019-05-28 Aliaksandr Hubin , Geir Storvik

Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…

Computational Engineering, Finance, and Science · Computer Science 2021-01-14 Xiaoxuan Zhang , Krishna Garikipati

The prevalence of employing attention mechanisms has brought along concerns on the interpretability of attention distributions. Although it provides insights about how a model is operating, utilizing attention as the explanation of model…

Computer Vision and Pattern Recognition · Computer Science 2022-09-16 Tristan Gomez , Suiyi Ling , Thomas Fréour , Harold Mouchère

Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…

Quantitative Methods · Quantitative Biology 2013-07-04 Yi Ming Zou

To advance the transparency of learning machines such as Deep Neural Networks (DNNs), the field of Explainable AI (XAI) was established to provide interpretations of DNNs' predictions. While different explanation techniques exist, a popular…

In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a…

Discrete Mathematics · Computer Science 2025-07-29 Kévin Perrot , Sylvain Sené , Léah Tapin

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

Computation · Statistics 2018-10-16 Lampros Bouranis , Nial Friel , Florian Maire

Compact neural networks are essential for affordable and power efficient deep learning solutions. Binary Neural Networks (BNNs) take compactification to the extreme by constraining both weights and activations to two levels, $\{+1, -1\}$.…

Machine Learning · Computer Science 2020-06-16 Vishnu Raj , Nancy Nayak , Sheetal Kalyani

We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical…

Cellular Automata and Lattice Gases · Physics 2012-06-12 Xinwei Gong , Joshua E. S. Socolar

The question of how and why the phenomenon of mode connectivity occurs in training deep neural networks has gained remarkable attention in the research community. From a theoretical perspective, two possible explanations have been proposed:…

Machine Learning · Computer Science 2021-10-22 Quynh Nguyen , Pierre Brechet , Marco Mondelli

We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…

Artificial Intelligence · Computer Science 2017-05-16 Paul Beaumont , Michael Huth

Formal verification is only as good as the specification of a system, which is also true for neural network verification. Existing specifications follow the paradigm of data as specification, where the local neighborhood around a reference…

Machine Learning · Computer Science 2025-03-17 Chuqin Geng , Zhaoyue Wang , Haolin Ye , Xujie Si

In this contribution, we provide a comprehensive evaluation of graph neural networks applied to Boolean satisfiability problems, accompanied by an intuitive explanation of the mechanisms enabling the model to generalize to different…

Machine Learning · Computer Science 2025-04-03 David Mojžíšek , Jan Hůla , Ziwei Li , Ziyu Zhou , Mikoláš Janota

In linear models, visualizing a weight vector naturally reveals the model's preferred input direction, but extending this intuition to deep networks via gradients or gradient ascent often yields brittle or adversarial-looking features. We…

Machine Learning · Computer Science 2026-05-08 Maciej Satkiewicz , Roberto Corizzo , Marcin Pietroń
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