# Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?

arXiv: https://arxiv.org/abs/2408.07588 · HTML: https://mlsanity.com/paper/2408.07588/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 30 of 30)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Towards Robust Evaluations of Continual Learning](https://mlsanity.com/paper/1805.09733/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [Sparse Gaussian Processes with Spherical Harmonic Features](https://mlsanity.com/paper/2006.16649/) (2020)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Continual Learning via Sequential Function-Space Variational Inference](https://mlsanity.com/paper/2312.17210/) (2023)
- [Modeling and interpolation of the ambient magnetic field by Gaussian processes](https://mlsanity.com/paper/1509.04634/) (2015)
- [Deep Neural Networks as Point Estimates for Deep Gaussian Processes](https://mlsanity.com/paper/2105.04504/) (2021)
- [Variational Auto-Regressive Gaussian Processes for Continual Learning](https://mlsanity.com/paper/2006.05468/) (2020)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)
- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [When, where, and how to add new neurons to ANNs](https://mlsanity.com/paper/2202.08539/) (2022)
- [Self-Expanding Neural Networks](https://mlsanity.com/paper/2307.04526/) (2023)
- [Hierarchical Indian Buffet Neural Networks for Bayesian Continual Learning](https://mlsanity.com/paper/1912.02290/) (2019)
- [Memory-Based Dual Gaussian Processes for Sequential Learning](https://mlsanity.com/paper/2306.03566/) (2023)
- [Adaptive Inducing Points Selection For Gaussian Processes](https://mlsanity.com/paper/2107.10066/) (2021)
- [Fully Scalable Gaussian Processes using Subspace Inducing Inputs](https://mlsanity.com/paper/1807.02537/) (2018)

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

- [Dynamic Learning Rate for Deep Reinforcement Learning: A Bandit Approach](https://mlsanity.com/paper/2410.12598/) (2024)

## Abstract (arXiv)

Many machine learning models require setting a parameter that controls their size before training, e.g. number of neurons in DNNs, or inducing points in GPs. Increasing capacity typically improves performance until all the information from the dataset is captured. After this point, computational cost keeps increasing, without improved performance. This leads to the question "How big is big enough?" We investigate this problem for Gaussian processes (single-layer neural networks) in continual learning. Here, data becomes available incrementally, and the final dataset size will therefore not be known before training, preventing the use of heuristics for setting a fixed model size. We develop a method to automatically adjust model size while maintaining near-optimal performance. Our experimental procedure follows the constraint that any hyperparameters must be set without seeing dataset properties, and we show that our method performs well across diverse datasets without the need to adjust its hyperparameter, showing it requires less tuning than others.