# Mixture-of-Variational-Experts for Continual Learning

arXiv: https://arxiv.org/abs/2110.12667 · HTML: https://mlsanity.com/paper/2110.12667/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 96 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 30 of 63)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [PathNet: Evolution Channels Gradient Descent in Super Neural Networks](https://mlsanity.com/paper/1701.08734/) (2017)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Learning to Remember: A Synaptic Plasticity Driven Framework for Continual Learning](https://mlsanity.com/paper/1904.03137/) (2019)
- [Using Hindsight to Anchor Past Knowledge in Continual Learning](https://mlsanity.com/paper/2002.08165/) (2020)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Continual Unsupervised Representation Learning](https://mlsanity.com/paper/1910.14481/) (2019)
- [Uncertainty-based Continual Learning with Adaptive Regularization](https://mlsanity.com/paper/1905.11614/) (2019)
- [A Neural Dirichlet Process Mixture Model for Task-Free Continual Learning](https://mlsanity.com/paper/2001.00689/) (2020)

## Built on by (most cited first, 8 of 8)

- [A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2503.07137/) (2025)
- [Theory on Mixture-of-Experts in Continual Learning](https://mlsanity.com/paper/2406.16437/) (2024)
- [Improving Expert Specialization in Mixture of Experts](https://mlsanity.com/paper/2302.14703/) (2023)
- [Mixture of Experts in Image Classification: What's the Sweet Spot?](https://mlsanity.com/paper/2411.18322/) (2024)
- [Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers](https://mlsanity.com/paper/2603.09453/) (2026)
- [MECAD: A multi-expert architecture for continual anomaly detection](https://mlsanity.com/paper/2512.15323/) (2025)
- [How to Find and Reuse Policies for Continuous Adaptation in Lifelong Reinforcement Learning](https://mlsanity.com/paper/2610.03119/) (2026)
- [Cost-Aware Mixture-of-Experts Coordination for Model Markets](https://mlsanity.com/paper/2610.11908/) (2026)

## Abstract (arXiv)

One weakness of machine learning algorithms is the poor ability of models to solve new problems without forgetting previously acquired knowledge. The Continual Learning (CL) paradigm has emerged as a protocol to systematically investigate settings where the model sequentially observes samples generated by a series of tasks. In this work, we take a task-agnostic view of continual learning and develop a hierarchical information-theoretic optimality principle that facilitates a trade-off between learning and forgetting. We discuss this principle from a Bayesian perspective and show its connections to previous approaches to CL. Based on this principle, we propose a neural network layer, called the Mixture-of-Variational-Experts layer, that alleviates forgetting by creating a set of information processing paths through the network which is governed by a gating policy. Due to the general formulation based on generic utility functions, we can apply this optimality principle to a large variety of learning problems, including supervised learning, reinforcement learning, and generative modeling. We demonstrate the competitive performance of our method in continual supervised learning and in continual reinforcement learning.