Related papers: The neural network approach to parton fitting

We construct a parametrization of deep-inelastic structure functions which retains information on experimental errors and correlations, and which does not introduce any theoretical bias while interpolating between existing data points. We…

This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and…

In social networks, neighborhood is crucial for understanding individual behavior in response to environments, and thus it is essential to analyze an individual's local perspective within the global network. This paper studies how to…

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…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…

The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each…

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…

This thesis presents a local-to-global perspective on graph neural networks (GNN), the leading architecture to process graph-structured data. After categorizing GNN into local Message Passing Neural Networks (MPNN) and global Graph…

A novel approach to parton distributions parameterization in terms of quantum statistical functions is here outlined. The description, already proposed in previous publications, is here improved by adding to the statistical distributions an…

The Hessian method is widely applied in the global analysis of parton distribution functions (PDFs), which uses a set of orthogonal eigenvectors to give predictions of a physical observable. Its uncertainty is estimated based on the…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

We study the uncertainties in parton distributions, determined in global fits to deep inelastic and related hard scattering data, due to so-called theoretical errors. Amongst these, we include potential errors due to the change of…

The global inducing point variational approximation for BNNs is based on using a set of inducing inputs to construct a series of conditional distributions that accurately approximate the conditionals of the true posterior distribution. Our…

We investigate the problem of weight uncertainty originally proposed by [Blundell et al. (2015). Weight uncertainty in neural networks. In International conference on machine learning, 1613-1622, PMLR.] in the context of neural networks…

As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…