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A key property of neural networks driving their success is their ability to learn features from data. Understanding feature learning from a theoretical viewpoint is an emerging field with many open questions. In this work we capture…

This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis and adopting a generative modelling…

The study of phonon dynamics is pivotal for understanding material properties, yet it faces challenges due to the irreversible information loss inherent in powder inelastic neutron scattering spectra and the limitations of traditional…

We present TabPFN, a trained Transformer that can do supervised classification for small tabular datasets in less than a second, needs no hyperparameter tuning and is competitive with state-of-the-art classification methods. TabPFN performs…

Recent work has shown that feed-forward networks (FFNs) in pre-trained Transformers are a key component, storing various linguistic and factual knowledge. However, the computational patterns of FFNs are still unclear. In this work, we study…

Convolutional Neural Networks (CNNs) are widely used in fault diagnosis of mechanical systems due to their powerful feature extraction and classification capabilities. However, the CNN is a typical black-box model, and the mechanism of…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

We present a novel graphical framework for modeling non-negative sequential data with hierarchical structure. Our model corresponds to a network of coupled non-negative matrix factorization (NMF) modules, which we refer to as a positive…

Despite the enormous success of artificial neural networks (ANNs) in many disciplines, the characterization of their computations and the origin of key properties such as generalization and robustness remain open questions. Recent…

Assessing the compliance of a white-box turbulence model with known turbulent knowledge is straightforward. It enables users to screen conventional turbulence models and identify apparent inadequacies, thereby allowing for a more focused…

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In…

To develop a preliminary understanding towards Graph Foundation Models, we study the extent to which pretrained Graph Neural Networks can be applied across datasets, an effort requiring to be agnostic to dataset-specific features and their…

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…

Predictive models are being increasingly used across a wide range of domains, including safety-critical applications such as medical diagnosis and criminal justice. Reliable uncertainty estimation is a crucial task in such settings. Tabular…

Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a…

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…

This paper proposed a novel radial basis function neural network (RBFNN) to solve various partial differential equations (PDEs). In the proposed RBF neural networks, the physics-informed kernel functions (PIKFs), which are derived according…

The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…