# Training neural networks to encode symbols enables combinatorial generalization

## TL;DR

This paper introduces VARS, a novel vector-based method for neural networks to explicitly encode symbolic structures, enabling them to achieve combinatorial generalization in both symbolic and non-symbolic outputs.

## Contribution

The paper presents VARS, a new approach allowing standard neural networks to explicitly represent symbolic knowledge and generalize combinatorially without specialized mechanisms.

## Key findings

- Neural networks can learn to produce VARS representations.
- VARS enables combinatorial generalization in neural outputs.
- The approach works across different neural architectures.

## Abstract

Combinatorial generalization - the ability to understand and produce novel combinations of already familiar elements - is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body of research suggests that conventional neural networks can't solve this problem unless they are endowed with mechanisms specifically engineered for the purpose of representing symbols. In this paper we introduce a novel way of representing symbolic structures in connectionist terms - the vectors approach to representing symbols (VARS), which allows training standard neural architectures to encode symbolic knowledge explicitly at their output layers. In two simulations, we show that neural networks not only can learn to produce VARS representations, but in doing so they achieve combinatorial generalization in their symbolic and non-symbolic output. This adds to other recent work that has shown improved combinatorial generalization under specific training conditions, and raises the question of whether specific mechanisms or training routines are needed to support symbolic processing.