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

TL;DR

The paper introduces Sketched Lanczos Uncertainty (SLU), a memory-efficient method for uncertainty quantification in neural networks that is scalable and reliable, especially in low-memory settings.

Contribution

SLU combines Lanczos' algorithm with dimensionality reduction to efficiently approximate Fisher information eigenvectors, enabling low-memory uncertainty scoring.

Findings

SLU provides well-calibrated uncertainties.

SLU reliably detects out-of-distribution examples.

SLU outperforms existing low-memory uncertainty methods.

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.