Emergent latent symbol systems in recurrent neural networks

Fodor and Pylyshyn [1988. Connectionism and cognitive architecture: A critical analysis. Cognition, 281–2, 3–71] famously argued that neural networks cannot behave systematically short of implementing a combinatorial symbol system. A recent response from Frank et al. [2009. Connectionist semantic systematicity. Cognition, 1103, 358–379] claimed to have trained a neural network to behave systematically without implementing a symbol system and without any in-built predisposition towards combinatorial representations. We believe systems like theirs may in fact implement a symbol system on a deeper and more interesting level: one where the symbols are latent – not visible at the level of network structure. In order to illustrate this possibility, we demonstrate our own recurrent neural network that learns to understand sentence-level language in terms of a scene. We demonstrate our model's learned understanding by testing it on novel sentences and scenes. By paring down our model into an architecturally minimal version, we demonstrate how it supports combinatorial computation over distributed representations by using the associative memory operations of Vector Symbolic Architectures. Knowledge of the model's memory scheme gives us tools to explain its errors and construct superior future models. We show how the model designs and manipulates a latent symbol system in which the combinatorial symbols are patterns of activation distributed across the layers of a neural network, instantiating a hybrid of classical symbolic and connectionist representations that combines advantages of both.