Extended Data Fig. 9: Low-dimensional spatial modes of mouse RSC activity.

(a) Top left: the speed at which the neural activity evolves (avg. speed of largest 5 principal components, filtered at 1 Hz, CIs via bootstrap) correlates with running speed. Top right: When landmarks appear/disappear, they perturb neural activity (effect of mouse speed is regressed out). Bottom: Analysis of the time course of the prediction of LM0,1,2 state from RSC firing rates around the time when the landmarks appeared. Plots show 95% CIs for the mean of the state prediction, aligned to the mean, corresponding to a de-biased state estimation probability over time. Decoding was performed using the same method as in Fig. 1. (b) For some analyses of the low-dimensional dynamics in RSC (Fig. 4, this figure panel h), rate fluctuations related to non-spatial covariates such as speed, heading, etc. were removed: a single-layer LSTM with 20 hidden units was trained to predict the mouse position in a 10×10 grid from the RSC rates. The network learned 20 spatially relevant mixtures of input firing rates, with appropriate temporal smoothing to represent the mouse location. These activations were then embedded into 3-D space via isomap⁵³. (c) To find trials across which mouse trajectories as they approached the 2^nd landmark were similar, mouse trajectories were clustered (see Methods) leading to a subset of trials with similar locomotion and visual inputs. (d) The activity of RSC, in the low-dimensional representation, and in raw spike counts was then analyzed further. The example plot shows low-dimensional neural trajectories from LM0,1,2 states during matched mouse trajectories. (e) Alternative hypotheses for smoothness / predictability of neural dynamics across trials (corresponding to Fig. 4c). Dynamics across trials could behave like a laminar flow, so that trials with similar neural state remain so (top), or they could shuffle, leading to a loss of the pairwise distance relationships across trials (bottom). (f) We measured this maintenance vs. loss of correlation in a sliding 750 ms window beginning at the 2^nd landmark onset, versus a window just before. CIs were computed across sessions (See Methods). (g) Hypotheses for whether stable neural dynamics (Fig. 3b,c, Extended Data Fig. 8) can determine how RSC activity encodes disambiguated landmark identity (‘a’ or ‘b’). Top: trials in which the correct identity is ‘a’ but that are neurally close to other trials where the answer is ‘b’ might get dragged along in the wrong direction at least transiently. This would indicate relevance of recurrent dynamics on this computation. Bottom: alternatively, neural activity could be determined by the correct answer, even in trials that (in neural rate space) are close to trials from the opposing class. (h) We tested this by finding the closest trial from the opposing class (for example the closest LM1_a for a LM1_b trial) in the 3-D embedded (via Isomap) RSC rate space. To evaluate co-evolution regardless of this selection confound, we then analyzed the direction of flow of the neural state over time (red). As a control, we also analyzed neurally far trials (grey). The flow direction of the neural activity was significantly aligned for ~100 ms. Median and CI via bootstrap. (i) Left: Schematic for the analysis of representation of LM1_a vs. LM1_b states. Trial-to-trial distances were compared within group vs. across group. Right: Both before and after the 2^nd landmark becomes visible, the classes are distinct in neural state space. (Same data as in Fig. 4b, 5 sessions, 101 matched trials). (j) Whether a trial comes from LM1_a or _b can also be decoded from low-pass filtered (2 Hz) firing rates before the 2^nd landmark onset (via regression tree, cross-validated across trials, balanced N across conditions, 5 sessions).