The Importance of Positional Encoding Initialization in Transformers for Relational Reasoning

Relational reasoning refers to the ability to infer and understand the relations between multiple entities. In humans, this ability underpins many higher cognitive functions, such as problem solving and decision-making, and has been reliably linked to fluid intelligence. Despite machine learning models making impressive advances across various domains, such as natural language processing and vision, the extent to which such models can perform relational reasoning tasks remains unclear. Here we study the importance of positional encoding (PE) for relational reasoning in the Transformer, and find that a learnable PE outperforms all other commonly-used PEs (e.g., absolute, relative, rotary, etc.). Moreover, we find that when using a PE with a learnable parameter, the choice of initialization greatly influences the learned representations and its downstream generalization performance. Specifically, we find that a learned PE initialized from a small-norm distribution can 1) uncover ground-truth position information, 2) generalize in the presence of noisy inputs, and 3) produce behavioral patterns that are consistent with human performance. Our results shed light on the importance of learning high-performing and robust PEs during relational reasoning tasks, which will prove useful for tasks in which ground truth positions are not provided or not known.