Navigation is crucial for animal behavior and is assumed to require an internal representation of the external environment, termed a cognitive map. The precise form of this representation is often considered to be a metric representation of space. An internal representation, however, is judged by its contribution to performance on a given task, and may thus vary between different types of navigation tasks. Here we train a recurrent neural network that controls an agent performing several navigation tasks in a simple environment. To focus on internal representations, we split learning into a task-agnostic pre-training stage that modifies internal connectivity and a task-specific Q learning stage that controls the network's output. We show that pre-training shapes the attractor landscape of the networks, leading to either a continuous attractor, discrete attractors or a disordered state. These structures induce bias onto the Q-Learning phase, leading to a performance pattern across the tasks corresponding to metric and topological regularities. Our results show that, in recurrent networks, inductive bias takes the form of attractor landscapes -- which can be shaped by pre-training and analyzed using dynamical systems methods. Furthermore, we demonstrate that non-metric representations are useful for navigation tasks.  
Task agnostic pre-training can shape RNN's attractor landscape, and form diverse inductive bias for different navigation tasks    This paper studies the internal representations of recurrent neural networks trained on navigation tasks, and finds that RNNs pre-trained to use path integration contain 2D continuous attractors while RNNs pre-trained for landmark memory contain discrete attractors. This paper explores how pre-training recurrent networks on different navigational objectives confers different benefits for solving downstream tasks, and shows how different pretraining manifests as different dynamical structures in the networks after pre-training.