Clockwise from top left: Rachel Johnson, Polly Toynbee, Jeanette Winterson, Cathy Newman, Ann Widdecombe, Fiona Marr. Clockwise from top left: Rachel Johnson, Polly Toynbee, Jeanette Winterson, Cathy Newman, Ann Widdecombe, Fiona Marr. I asked AI to name my wife. Authors, a newsreader, a lawyer and an esteemed colleague: they're all great - but I'm not married to any of them. Can we really depend on this technology?

We further design an effective mechanism to inject PH information into GP at both feature and topology levels, with a novel topology-preserving loss function.

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting an appropriate kernel can be challenging. Deep GPs avoid manual kernel engineering by successively parameterizing kernels with GP layers, allowing them to learn low-dimensional embeddings of the inputs that explain the output data. Following the architecture of deep neural networks, the most common deep GPs warp the input space layer-by-layer but lose all the interpretability of shallow GPs. An alternative construction is to successively parameterize the lengthscale of a kernel, improving the interpretability but ultimately giving away the notion of learning lower-dimensional embeddings.