III - 14 . Time - warped PCA : simultaneous alignment and dimensionality reduc - tion of neural data

firing patterns, e.g. by producing stochastic drift in grid attractor networks. Recently, Hardcastle et al. (Neuron, 2015) proposed that border cells may provide one mechanism for correcting such drift. We construct a model in which experience-dependent Hebbian plasticity during exploration allows border cells to self-organize their responses, while also learning connectivity to grid cells which maintain their activity through an attractor network. We show that border cells in this learned network effectively correct for grid drift despite stochasticity of border cell firing. This error-correction is robust with respect to environmental shape including squares and circles. Furthermore, it survives insertion of barriers within an enclosure (consistent with Solstad et al., 2008) even though a given border cell can fire ambiguously at multiple boundaries with the same allocentric orientation (Solstad et al, 2008; Lever et al, 2009). In our mechanism, the learned border-grid connectivity pattern compensates for such ambiguities. Upon deformation of an environment, e.g., by shrinking or changing shape, the error correction initially fails and grid drift resumes. However, in our model the border-grid connectivity adapts to boundaries of the deformed environment, restoring error correction after a characteristic timescale. Our results demonstrate a class of self-organized mechanisms that achieve robust path integration. These mechanisms predict that: (a) disrupting synaptic plasticity between grid cells and border cells will cause grid patterns to drift in a random walk, and (b) deforming an environment will initially lead to grid drift, which is subsequently stabilized.