Using SI to evaluate neural representations.

a, In the neural manifold framework, firing rates from N-neurons at a given time (ts) are represented in an N-dimensional Euclidean space. Activity is constrained in a subspace which can be retrieved using dimensionality reduction approaches (d-dimension). b, Neural manifold computed from the head-direction system by Chaudhuri et al.[5], with the head-direction angle projected over the data cloud. c, SI of the head-direction angle in the original (og) and embedded representations (emb). Dashed lines indicate results from shuffled distribution values (99th percentile). d, Example of the weighted directed graphs from the same mouse in the original and in the low-dimensional embedding. Note similar organization. e, Relationship between the SI and the mean square error (MSE) of the decoder trained by Chaudhuri et al.[5] in the reduced space. Fitting curve parameters: α = -0.12; β = 4.47; γ = -4.7 and Δ = 0.9; tested significant at pf, Head-direction data plotted over the 3D embedding for awake, REM, and SWS states separately. g, SI for states and angles separately, and for both features together as expressed in vector form. Results are shown for both the original (og) and the reduced space (emb). ANOVA effects for space (F(2,1) = 8.2, p = 0.007) but not for feature nor interaction. Post-hoc tests: **, ph, SI of the head direction angle for each state separately both in the original (og) and the reduced space (emb). ANOVA effects for state (F(2,1) = 83.5, p<0.0001), space (F(2,1) = 25.7, p<0.0001) and interaction. Post-hoc tests: **, p<0.001; ***, p<0.0001.