  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.
By combining two types of networks in a modular structure, we could get better
performance for both 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, and their combination with metric representation leads to
flexibile multiple-task learning.
