Utilizing mutual learning can effectively enhance the performance of peer BNNs.

Ensembles of geophysical models improve prediction accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotem-porally varying model weights and bias, while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware predictions without sacrificing interpretability.

However, they often underperform compared to deterministic neural networks. Utilizing mutual learning can effectively enhance the performance of peer BNNs. In this paper, we propose a novel approach to improve BNNs performance through deep mutual learning. The proposed approaches aim to increase diversity in both network parameter distributions and feature distributions, promoting peer networks to acquire distinct features that capture different characteristics of the input, which enhances the effectiveness of mutual learning. Experimental results demonstrate significant improvements in the classification accuracy, negative log-likelihood, and expected calibration error when compared to traditional mutual learning for BNNs.

Tuning scientific and probabilistic machine learning models - for example, partial differential equations, Gaussian processes, or Bayesian neural networks - often relies on evaluating functions of matrices whose size grows with the data set or the number of parameters.While the state-of-the-art for these quantities is almost always based on Lanczos and Arnoldi iterations, the present work is the first to explain how to these workhorses of numerical linear algebra efficiently.To get there, we derive previously unknown adjoint systems for Lanczos and Arnoldi iterations, implement them in JAX, and show that the resulting code can compete with Diffrax when it comes to differentiating PDEs, GPyTorch for selecting Gaussian process models and beats standard factorisation methods for calibrating Bayesian neural networks.All this is achieved without any problem-specific code optimisation.Find the code at [link redacted] and install the library with .

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 posterior distribution can be used for providing ensemble predictions and quantifying prediction uncertainty. It is well-known that deep learning models with lower sharpness have better generalization ability. However, existing posterior inferences are not aware of sharpness/flatness in terms of formulation, possibly leading to high sharpness for the models sampled from them. In this paper, we develop theories, the Bayesian setting, and the variational inference approach for the sharpness-aware posterior. Specifically, the models sampled from our sharpness-aware posterior, and the optimal approximate posterior estimating this sharpness-aware posterior, have better flatness, hence possibly possessing higher generalization ability. We conduct experiments by leveraging the sharpness-aware posterior with state-of-the-art Bayesian Neural Networks, showing that the flat-seeking counterparts outperform their baselines in all metrics of interest.

Human intelligence has shown remarkably lower latency and higher precision than most AI systems when processing non-stationary streaming data in real-time. Numerous neuroscience studies suggest that such abilities may be driven by internal predictive modeling. In this paper, we explore the possibility of introducing such a mechanism in unsupervised domain adaptation (UDA) for handling non-stationary streaming data for real-time streaming applications. We propose to formulate internal predictive modeling as a continuous-time Bayesian filtering problem within a stochastic dynamical system context. Such a dynamical system describes the dynamics of model parameters of a UDA model evolving with non-stationary streaming data. Building on such a dynamical system, we then develop extrapolative continuous-time Bayesian neural networks (ECBNN), which generalize existing Bayesian neural networks to represent temporal dynamics and allow us to extrapolate the distribution of model parameters before observing the incoming data, therefore effectively reducing the latency. Remarkably, our empirical results show that ECBNN is capable of continuously generating better distributions of model parameters along the time axis given historical data only, thereby achieving (1) training-free test-time adaptation with low latency, (2) gradually improved alignment between the source and target features and (3) gradually improved model performance over time during the real-time testing stage.

Distributional robustness is a promising framework for training deep learning models that are less vulnerable to adversarial examples and data distribution shifts. Previous works have mainly focused on exploiting distributional robustness in the data space. In this work, we explore an optimal transport-based distributional robustness framework in model spaces. Specifically, we examine a model distribution within a Wasserstein ball centered on a given model distribution that maximizes the loss. We have developed theories that enable us to learn the optimal robust center model distribution. Interestingly, our developed theories allow us to flexibly incorporate the concept of sharpness awareness into training, whether it's a single model, ensemble models, or Bayesian Neural Networks, by considering specific forms of the center model distribution. These forms include a Dirac delta distribution over a single model, a uniform distribution over several models, and a general Bayesian Neural Network. Furthermore, we demonstrate that Sharpness-Aware Minimization (SAM) is a specific case of our framework when using a Dirac delta distribution over a single model, while our framework can be seen as a probabilistic extension of SAM. To validate the effectiveness of our framework in the aforementioned settings, we conducted extensive experiments, and the results reveal remarkable improvements compared to the baselines.

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 learned hidden layer representations of finite networks differ from the fixed representations of infinite networks remains incomplete. Perturbative finite-width corrections to the network prior and posterior have been studied, but the asymptotics of learned features have not been fully characterized. Here, we argue that the leading finite-width corrections to the average feature kernels for any Bayesian network with linear readout and Gaussian likelihood have a largely universal form. We illustrate this explicitly for three tractable network architectures: deep linear fully-connected and convolutional networks, and networks with a single nonlinear hidden layer. Our results begin to elucidate how task-relevant learning signals shape the hidden layer representations of wide Bayesian neural networks.

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open.