Sketched Lanczos uncertainty score: a low-memory summary of the Fisher information

Marco Miani, Lorenzo Beretta, Søren Hauberg

Keywords: Sketching, Uncertainty, Lanczos, Laplace

TL;DR: We propose a memory-efficient and provably-good approximation of an enstablished uncertainty score

Abstract: Current uncertainty quantification is memory and compute expensive, which hinders practical uptake. To counter, we develop Sketched Lanczos Uncertainty (SLU): an architecture-agnostic uncertainty score that can be applied to pre-trained neural networks with minimal overhead. Importantly, the memory use of SLU only grows logarithmically with the number of model parameters. We combine Lanczos' algorithm with dimensionality reduction techniques to compute a sketch of the leading eigenvectors of a matrix. Applying this novel algorithm to the Fisher information matrix yields a cheap and reliable uncertainty score. Empirically, SLU yields well-calibrated uncertainties, reliably detects out-of-distribution examples, and consistently outperforms existing methods in the low-memory regime.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 17623