Without loss of generality, we illustrate OTO on a model with only vanilla convolutional layers, and for simplicity we only show Layeri with m 3D filters and their biases.

Despite their promising performance, the learned knowledge remains implicit in these black-box neural structures, which hinders understanding the importance of input features and how they influencedecisions.

Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In this work, we present a Bayesian autoencoder for unsupervised representation learning, which is trained using a novel variational lower bound of the autoencoder evidence. This is maximized using Monte Carlo EM with a variational distribution that takes the shape of a Laplace approximation. We develop a new Hessian approximation that scales linearly with data size allowing us to model high-dimensional data. Empirically, we show that our Laplacian autoencoder estimates well-calibrated uncertainties in both latent and output space. We demonstrate that this results in improved performance across a multitude of downstream tasks.

A plant's phenome is defined by its physical and biochemical characteristics, and is the result of the interaction of its genome and its environment.