# Separating the what and how of compositional computation to enable reuse and continual learning

arXiv: https://arxiv.org/abs/2510.20709 · HTML: https://mlsanity.com/paper/2510.20709/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Continual learning with hypernetworks](https://mlsanity.com/paper/1906.00695/) (2019)
- [Continual Learning of Context-dependent Processing in Neural Networks](https://mlsanity.com/paper/1810.01256/) (2018)
- [Alleviating catastrophic forgetting using context-dependent gating and synaptic stabilization](https://mlsanity.com/paper/1802.01569/) (2018)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [Continual Learning via Local Module Composition](https://mlsanity.com/paper/2111.07736/) (2021)
- [Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer](https://mlsanity.com/paper/2211.00789/) (2022)
- [Task Agnostic Continual Learning via Meta Learning](https://mlsanity.com/paper/1906.05201/) (2019)
- [Continual Learning for Recurrent Neural Networks: an Empirical Evaluation](https://mlsanity.com/paper/2103.07492/) (2021)
- [Modelling continual learning in humans with Hebbian context gating and exponentially decaying task signals](https://mlsanity.com/paper/2203.11560/) (2022)
- [Continual task learning in natural and artificial agents](https://mlsanity.com/paper/2210.04520/) (2022)
- [Restricted Orthogonal Gradient Projection for Continual Learning](https://mlsanity.com/paper/2301.12131/) (2023)
- [Flexible task abstractions emerge in linear networks with fast and bounded units](https://mlsanity.com/paper/2411.03840/) (2024)

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

- [Learning Options for Compositional Motor Control with Adapter Banks](https://mlsanity.com/paper/2609.17042/) (2026)

## Abstract (arXiv)

The ability to continually learn, retain and deploy skills to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of skills remain elusive. Here, we study continual learning and the compositional reuse of learned computations in recurrent neural network (RNN) models using a novel two-system approach: one system that infers what computation to perform, and one that implements how to perform it. We focus on a set of compositional cognitive tasks commonly studied in neuroscience. To construct the what system, we first show that a large family of tasks can be systematically described by a probabilistic generative model, where compositionality stems from a shared underlying vocabulary of discrete task epochs. The shared epoch structure makes these tasks inherently compositional. We first show that this compositionality can be systematically described by a probabilistic generative model. Furthermore, We develop an unsupervised online learning approach that can learn this model on a single-trial basis, building its vocabulary incrementally as it is exposed to new tasks, and inferring the latent epoch structure as a time-varying computational context within a trial. We implement the how system as an RNN whose low-rank components are composed according to the context inferred by the what system. Contextual inference facilitates the creation, learning, and reuse of low-rank RNN components as new tasks are introduced sequentially, enabling continual learning without catastrophic forgetting. Using an example task set, we demonstrate the efficacy and competitive performance of this two-system learning framework, its potential for forward and backward transfer, as well as fast compositional generalization to unseen tasks.