# Bayesian Convolutional Deep Sets with Task-Dependent Stationary Prior

arXiv: https://arxiv.org/abs/2210.12363 · HTML: https://mlsanity.com/paper/2210.12363/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 22 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Sequential Neural Processes](https://mlsanity.com/paper/1906.10264/) (2019)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [Non-Stationary Spectral Kernels](https://mlsanity.com/paper/1705.08736/) (2017)
- [The Gaussian Neural Process](https://mlsanity.com/paper/2101.03606/) (2021)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes](https://mlsanity.com/paper/2011.12916/) (2020)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)
- [Robustifying Sequential Neural Processes](https://mlsanity.com/paper/2006.15987/) (2020)
- [GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Data](https://mlsanity.com/paper/2106.04967/) (2021)
- [Approximate Inference for Spectral Mixture Kernel](https://mlsanity.com/paper/2006.07036/) (2020)

## Built on by (most cited first, 2 of 2)

- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

Convolutional deep sets are the architecture of a deep neural network (DNN) that can model stationary stochastic process. This architecture uses the kernel smoother and the DNN to construct the translation equivariant functional representations, and thus reflects the inductive bias of the stationarity into DNN. However, since this architecture employs the kernel smoother known as the non-parametric model, it may produce ambiguous representations when the number of data points is not given sufficiently. To remedy this issue, we introduce Bayesian convolutional deep sets that construct the random translation equivariant functional representations with stationary prior. Furthermore, we present how to impose the task-dependent prior for each dataset because a wrongly imposed prior forms an even worse representation than that of the kernel smoother. We validate the proposed architecture and its training on various experiments with time-series and image datasets.