Abstract
How does the brain generate sequences of discrete elements, such as actions or words, that follow an abstract rule (a grammar)? Motivated by an experiment in which monkeys learned to draw multi-object images according to grammatical rules, we trained a recurrent neural network to generate sequences A
m
B
n
: producing shape A m times, then B n times, or vice versa. Our findings are threefold. First, the network plans the sequence by moving to an initial state encoding m and n along orthogonal directions for upcoming execution. Second, the network repeats each shape by progressing along a shape-specific manifold. Third, transitions from A
m
to B
n
follow parallel trajectories between manifolds across values of n, thus preserving n. Each of these is an experimentally testable prediction. The network generalizes to longer novel sequences by starting further along the same orthogonal directions. These results reveal a neural circuit implementation of a symbolic algorithm for generating rule-based action sequences.