# Three Costs of Amortizing Gaussian Process Inference with Neural Processes

arXiv: https://arxiv.org/abs/2605.21798 · HTML: https://mlsanity.com/paper/2605.21798/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 9 of 9)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [On the Conditioning Consistency Gap in Conditional Neural Processes](https://mlsanity.com/paper/2604.19312/) (2026)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2408.09583/) (2024)

## Built on by (most cited first, 1 of 1)

- [Characterizing the Representational Capacity of Neural Processes](https://mlsanity.com/paper/2605.24210/) (2026)

## Abstract (arXiv)

Neural processes amortize Gaussian process inference, replacing the exact O(n3) posterior with a learned O(n) map from context sets to predictive distributions. For a class of latent neural processes, we bound the Kullback--Leibler (KL) divergence between the GP and LNP predictives, decomposing it into three interpretable sources, namely label contamination as the neural process uses label values to estimate a quantity that is label-independent in the exact GP, an information bottleneck because the finite-dimensional representation cannot resolve the full context geometry, and amortization error from a single encoder network shared across all contexts. The bottleneck truncation term decays in the representation dimension d as O(e^-cd2/dx) for squared-exponential kernels on ℝdx where c > 0 is a kernel-dependent constant and as O(d-2nu/dx) for Mat'ern-nu kernels, directly linking architecture sizing to kernel smoothness and input dimension. The label contamination term is O(1) in general, with only the observation-noise component decaying as O(1/n), identifying a persistent cost of routing uncertainty estimation through a label-dependent representation. These results characterize the costs of amortization within the analyzed class and yield architectural recommendations to predict variance from context locations alone in the GP-amortization regime, and replace mean aggregation with second-order pooling to close the dominant amortization gap.