Related papers: Differential Bayesian Neural Nets

Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work,…

We observe that the standard log likelihood training objective for a Recurrent Neural Network (RNN) model of time series data is equivalent to a variational Bayesian training objective, given the proper choice of generative and inference…

The unprecedented availability of large-scale datasets in neuroscience has spurred the exploration of artificial deep neural networks (DNNs) both as empirical tools and as models of natural neural systems. Their appeal lies in their ability…

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address…

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Neural Ordinary Differential Equations (Neural ODEs) are the continuous analog of Residual Neural Networks (ResNets). We investigate whether the discrete dynamics defined by a ResNet are close to the continuous one of a Neural ODE. We first…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Despite the huge success of deep neural networks (NNs), finding good mechanisms for quantifying their prediction uncertainty is still an open problem. Bayesian neural networks are one of the most popular approaches to uncertainty…

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…

End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions,…

Training networks consisting of biophysically accurate neuron models could allow for new insights into how brain circuits can organize and solve tasks. We begin by analyzing the extent to which the central algorithm for neural network…

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

Bayesian Networks (BNs) are of interest from an explainable AI viewpoint, offering transparent probabilistic models for decision support. Baymex is a recently introduced multi-objective evolutionary algorithm for learning discretized BNs,…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of…

We present an algorithm for model-based reinforcement learning that combines Bayesian neural networks (BNNs) with random roll-outs and stochastic optimization for policy learning. The BNNs are trained by minimizing $\alpha$-divergences,…

Despite the dominant role of deep models in machine learning, limitations persist, including overconfident predictions, susceptibility to adversarial attacks, and underestimation of variability in predictions. The Bayesian paradigm provides…

Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural…

The manifold hypothesis suggests that high-dimensional neural time series lie on a low-dimensional manifold shaped by simpler underlying dynamics. To uncover this structure, latent dynamical variable models such as state-space models,…