Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficient

Vu C. Dinh; Lam Si Tung Ho; Cuong V. Nguyen

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arXiv · 2410.22065

Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficient

Vu C. Dinh·Lam Si Tung Ho·Cuong V. Nguyen

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Abstract

We analyze the error rates of the Hamiltonian Monte Carlo algorithm with leapfrog integrator for Bayesian neural network inference. We show that due to the non-differentiability of activation functions in the ReLU family, leapfrog HMC for networks with these activation functions has a large local error rate of $\Omega(\epsilon)$ rather than the classical error rate of $O(\epsilon^3)$. This leads to a higher rejection rate of the proposals, making the method inefficient. We then verify our theoretical findings through empirical simulations as well as experiments on a real-world dataset that highlight the inefficiency of HMC inference on ReLU-based neural networks compared to analytical networks.

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BibTeX RIS

Vu C. Dinh, Lam Si Tung Ho, Cuong V. Nguyen. 2024-10-29. Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficient. https://arxiv.org/abs/2410.22065

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