How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs
Compositional priors describe the generic properties of layered functions in deep Bayesian models, where deep neural networks with random weights are a canonical example.In the wide-network limit, the prior is a Gaussian process with a depth-dependent kernel, and its behaviour as depth grows has been extensively studied through this kernel. Here, we study another case, where each layer itself is a vector valued Gaussian process, and our aim is similarly to understand the limiting behaviour of the prior as depth grows. Previous GP work has established that for the RBF kernel and a certain range of bandwidths $r$, the prior degenerates in the limit, converging to the set of constant functio...
| Authors | Mark Kozdoba, Shie Mannor |
|---|---|
| Primary category | cs.LG |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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