Effects of network interactions on spatial encoding. A, A schematic of the circuit model with variable excess correlations and fixed population firing rate (see Materials and Methods). Two connectivity patterns are compared: “structured” (mimicking the inferred excess correlation vs tuning similarity relationship) versus “random.” B, Estimated spatial information (MI; error bar, 99th percentile CI for the mean) using structured and random interactions, in the novel-like and familiar-like scenario (see text). Structured interactions significantly increase the spatial information (***p < 0.001 or **p < 0.01 under a nonparametric Mann–Whitney U test). C, Effective single-cell tuning for random versus structured models in the novel-like (orange; left) and familiar-like (blue; right) scenarios. D, Average single place cell spatial information (I_spike) for random versus structured interactions (dashed bars) and data (solid bar) in the novel-like (orange; left) and familiar-like (blue; right) scenarios E, The performance of a simple population vector (PV) decoder is compared with the performance of a decoder which takes into account the co-variability of neurons (COV). F, Improvement in decoding performance, measured as error of PV decoder minus error of COV decoder, evaluated on <mml:math display="inline"><mml:mrow><mml:mn>4</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math>4·104 samples for random (left), data-like structure (center), and data (right). Random 50% of data were used for train/test. Decoding error measured in spatial bins. Error bars and significance tests as in B. G, Fraction of variance explained by the first principal component for responses to random pairs of stimuli, used to measure the effect of structured interactions on population responses to different stimuli. H, Fraction of variance explained by the first principal component of population vectors for 10³ random pairs of locations in the maze for random (left) versus data-like structure (center) versus data (right). The fraction is unchanged between the novel and familiar environments on structured network and on real data but differs significantly on the random network (error bars and significance tests as in B). I, Linear separability of responses to pairs of stimuli. The schematic depicts the 2D PCA projection of the responses to a random pair of stimuli (light gray vs dark gray) when using random (left) and structured (right) excess correlations. J, Linear SVM classification accuracy of the responses to random pairs of stimuli trained on 1000 pairs of same versus different positions for random (left) versus data-like structure (center) versus data (right). See Extended Data Figures 3-1, 3-2, 3-3 for more information.