# Probabilistic Numeric Convolutional Neural Networks Source: [Probabilistic Numeric Convolutional Neural Networks]() Collection index: [llms.txt]() Data updated: 2025-12-14T17:37:16.039Z Authors: Marc Finzi, Roberto Bondesan, Max Welling Published: 2020-10-21T10:08:21.000Z ## Abstract Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved regions of the input. Drawing from the work in probabilistic numerics, we propose Probabilistic Numeric Convolutional Neural Networks which represent features as Gaussian processes (GPs), providing a probabilistic description of discretization error. We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity. This approach also naturally admits steerable equivariant convolutions under e.g. the rotation group. In experiments we show that our approach yields a $3\\times$ reduction of error from the previous state of the art on the SuperPixel-MNIST dataset and competitive performance on the medical time series dataset PhysioNet2012. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Handwritten Digit Classification on Superpixel MNIST 75 vertices (test)](): Handwritten digit classification; Superpixel MNIST 75 vertices (test); Accuracy: 0.9876. ## Original sources and implementation [Original paper]() [PDF]()