Conditioning Gaussian Processes on Almost Anything
Authors: Henry Moss, Lachlan Astfalck, Thomas Cowperthwaite et al.
Summary
arXiv:2605. 21041v1 Announce Type: new Abstract: Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime.
Relevance
Read next because Conditioning Gaussian Processes on Almost Anything overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Only continuous soft prefixes hit both EM axes at once on Qwen-2.5-7B-Instruct: discrete prompt searches split between the alignment objective and the distributional objective, and both discretizations of the soft prefix collapse (MODERATE confidence)". Matching terms: class, eval, line, full, language, model. Source: arxiv stat.ML (Machine Learning).
Threat model
Potential threat/caveat for clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)": this item discusses evaluation.
Abstract
arXiv:2605.21041v1 Announce Type: new Abstract: Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models, recasting predictive sampling as an ODE with closed-form Gaussian dynamics and a likelihood-dependent guidance term that admits a simple Monte Carlo approximation. In the linear-Gaussian setting, we recover standard GP conditioning exactly; beyond conjugacy, the same machinery handles any conditioning statement admitting point-wise likelihood evaluation -- including non-linear physics, and, for the first time, natural language via large language models. Whitening isolates the irreducible non-Gaussian dynamics, minimising Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations. Together, these results provide a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, opening a new frontier for the probabilistic modelling of real-world problems.