The Simplicity Bias in Multi-Task RNNs: Shared Attractors, Reuse of Dynamics, and Geometric Representation

How does a single interconnected neural population perform multiple tasks, each with its own dynamical requirements? The relation between task requirements and neural dynamics in Recurrent Neural Networks (RNNs) has been investigated for single tasks. The forces shaping joint dynamics of multiple tasks, however, are largely unexplored. In this work, we first construct a systematic framework to study multiple tasks in RNNs, minimizing interference from input and output correlations with the hidden representation. This allows us to reveal how RNNs tend to share attractors and reuse dynamics, a tendency we define as the "simplicity bias". We find that RNNs develop attractors sequentially during training, preferentially reusing existing dynamics and opting for simple solutions when possible. This sequenced emergence and preferential reuse encapsulate the simplicity bias. Through concrete examples, we demonstrate that new attractors primarily emerge due to task demands or architectural constraints, illustrating a balance between simplicity bias and external factors. We examine the geometry of joint representations within a single attractor, by constructing a family of tasks from a set of functions. We show that the steepness of the associated functions controls their alignment within the attractor. This arrangement again highlights the simplicity bias, as points with similar input spacings undergo comparable transformations to reach the shared attractor. Our findings propose compelling applications. The geometry of shared attractors might allow us to infer the nature of unknown tasks. Furthermore, the simplicity bias implies that without specific incentives, modularity in RNNs may not spontaneously emerge, providing insights into the conditions required for network specialization.