Accelerated Linearized Laplace Approximation for Bayesian Deep Learning
This work addresses computational bottlenecks in Bayesian deep learning for researchers and practitioners, offering a more efficient method that is incremental but enhances practical usability.
The paper tackles the inefficiency of linearized Laplace approximation (LLA) for Bayesian deep learning by developing a Nyström approximation to neural tangent kernels (NTKs) to accelerate LLA, achieving scalability to architectures like vision transformers with improved performance.
Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve their tractability. However, LA and LLA are still confronted with non-trivial inefficiency issues and should rely on Kronecker-factored, diagonal, or even last-layer approximate GGN matrices in practical use. These approximations are likely to harm the fidelity of learning outcomes. To tackle this issue, inspired by the connections between LLA and neural tangent kernels (NTKs), we develop a Nystrom approximation to NTKs to accelerate LLA. Our method benefits from the capability of popular deep learning libraries for forward mode automatic differentiation, and enjoys reassuring theoretical guarantees. Extensive studies reflect the merits of the proposed method in aspects of both scalability and performance. Our method can even scale up to architectures like vision transformers. We also offer valuable ablation studies to diagnose our method. Code is available at \url{https://github.com/thudzj/ELLA}.