  Grid cells enable the brain to model the physical space of the world and
navigate effectively via path integration, updating self-position using
information from self-movement. Recent proposals suggest that the brain might
use similar mechanisms to understand the structure of objects in diverse
sensory modalities, including vision. In machine vision, object recognition
given a sequence of sensory samples of an image, such as saccades, is a
challenging problem when the sequence does not follow a consistent, fixed
pattern - yet this is something humans do naturally and effortlessly. We
explore how grid cell-based path integration in a cortical network can support
reliable recognition of objects given an arbitrary sequence of inputs. Our
network (GridCellNet) uses grid cell computations to integrate visual
information and make predictions based on movements. We use local Hebbian
plasticity rules to learn rapidly from a handful of examples (few-shot
learning), and consider the task of recognizing MNIST digits given only a
sequence of image feature patches. We compare GridCellNet to k-Nearest
Neighbour (k-NN) classifiers as well as recurrent neural networks (RNNs), both
of which lack explicit mechanisms for handling arbitrary sequences of input
samples. We show that GridCellNet can reliably perform classification,
generalizing to both unseen examples and completely novel sequence
trajectories. We further show that inference is often successful after sampling
a fraction of the input space, enabling the predictive GridCellNet to
reconstruct the rest of the image given just a few movements. We propose that
dynamically moving agents with active sensors can use grid cell representations
not only for navigation, but also for efficient recognition and feature
prediction of seen objects.
