Related papers: An Infinite-Feature Extension for Bayesian ReLU Ne…
The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a…
While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…
Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we…
In many research fields in artificial intelligence, it has been shown that deep neural networks are useful to estimate unknown functions on high dimensional input spaces. However, their generalization performance is not yet completely…
We conduct a thorough analysis of the relationship between the out-of-sample performance and the Bayesian evidence (marginal likelihood) of Bayesian neural networks (BNNs), as well as looking at the performance of ensembles of BNNs, both…
Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this…
Recent works have suggested that finite Bayesian neural networks may sometimes outperform their infinite cousins because finite networks can flexibly adapt their internal representations. However, our theoretical understanding of how the…
Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…
Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…
Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…
Graph neural networks (GNNs) have shown superiority in many prediction tasks over graphs due to their impressive capability of capturing nonlinear relations in graph-structured data. However, for node classification tasks, often, only…
Bayesian neural networks (BNNs) offer a natural probabilistic formulation for inference in deep learning models. Despite their popularity, their optimality has received limited attention through the lens of statistical decision theory. In…
The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior…
Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability…
Bayesian Neural Networks (BNNs) often result uncalibrated after training, usually tending towards overconfidence. Devising effective calibration methods with low impact in terms of computational complexity is thus of central interest. In…
We study the least-square regression problem with a two-layer fully-connected neural network, with ReLU activation function, trained by gradient flow. Our first result is a generalization result, that requires no assumptions on the…
Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…
Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as \textit{benign overfitting}. Recently, a few studies have attempted to…
Understanding how overparameterized neural networks generalize despite perfect interpolation of noisy training data is a fundamental question. Mallinar et. al. 2022 noted that neural networks seem to often exhibit ``tempered overfitting'',…
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…