Similar Navigation, Different Spatial Codes: Temporal Credit in a Path-Integrating RNN

Recurrent neural networks (RNNs) trained to track position from self-motion can develop grid-like units. These models are usually trained with backpropagation through time (BPTT), although models using local plasticity or predictive coding can also produce grid-like activity. We ask how navigation and spatial representations change when the architecture and task stay fixed but temporal credit is assigned differently. We compare BPTT with a one-step gradient control and with random feedback local online (RFLO) learning, a biologically motivated local rule that maintains a fading record of recent activity at each synapse. The one-step control leaves the forward dynamics intact but limits gradients to one recurrent step, producing substantially worse navigation than BPTT. The longest RFLO trace yields a mean position-decoding error of 5.1 cm, compared with 4.5 cm under BPTT. Because longer traces also give past activity more total weight, we compare the shortest and longest traces after rescaling the trace-dependent parts of their updates to match average trace weight. The resulting networks navigate similarly but develop different spatial codes, both in individual units and across the population. These population-level differences reappear in five additional pairs of independently trained networks. Navigation accuracy alone does not reveal which spatial code the network has learned.