Inverse-Free Sparse Variational Gaussian Processes

• URL: http://arxiv.org/abs/2604.00697v1
• Date: Wed, 01 Apr 2026 09:53:04 GMT
• Title: Inverse-Free Sparse Variational Gaussian Processes
• Abstract summary: We propose a drop-in replacement for sparse variational GP approximations.<n>We show that our method recovers similar performance to traditional methods, and can be faster than baselines when well tuned.
• Score: 24.916660624139638
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision, massively parallel hardware. While one can construct valid variational bounds that rely only on matrix multiplications (matmuls) via an auxiliary matrix parameter, optimising them with off-the-shelf first-order methods is challenging. We make the inverse-free approach practical by proposing a better-conditioned bound and deriving a matmul-only natural-gradient update for the auxiliary parameter, markedly improving stability and convergence. We further provide simple heuristics, such as step-size schedules and stopping criteria, that make the overall optimisation routine fit seamlessly into existing workflows. Across regression and classification benchmarks, we demonstrate that our method 1) serves as a drop-in replacement in SVGP-based models (e.g., deep GPs), 2) recovers similar performance to traditional methods, and 3) can be faster than baselines when well tuned.

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