(A–F) Covariance-based analysis of synaptic currents for the same example cell as in Figure 1. Covariance analysis follows the intuition of spike-triggered covariance (STC), but uses continuous current input rather than spikes (see Materials and methods). (A) Left: Cross-correlation between the stimulus and current response (the equivalent of a spike-triggered average) for high contrast (HC, blue) and low contrast (LC, red) stimuli. Filters are scaled to have the same standard deviation, for comparisons of shape. Middle: The eigenvalue spectrum for the response-triggered covariance matrix in HC, revealing two significant eigenvalues (color-coded). Right: The corresponding eigenvectors. (B) The locations of the cross-correlations in HC (blue, left) and LC (red, right) within the 2-D subspace spanned by the two significant eigenvectors for all neurons (n = 13). Because they are all close to the unit circle, both HC and LC cross-correlations were largely contained in the covariance (COV) subspace, consistent with previously reported results for spikes (Liu and Gollisch, 2015). (C) Model performance for the LN, DivS, and COV models (n = 13), reproduced from Figure 2E. This demonstrates that the COV filters coupled to a 2-D nonlinearity (described below) can nearly match the performance of the DivS model. (D) Left: The excitatory (green) and suppressive (cyan) filters of the DivS model, plotted in comparison to the filters identified by covariance analysis (dashed lines). Middle: The DivS model filters shared the same 2-D subspace as the covariance filters, as shown by comparing the filters to optimal linear combinations of the COV filters (black dashed), following previous work based on spikes (Butts et al., 2011). Right: The DivS filters projected into the COV filters subspace across neurons, using the same analysis as in (B). Their proximity to the unit circle shows they are almost completely in the covariance subspace for all neurons, again consistent with previous work with spikes (Butts et al., 2011). (E) Left: The 2-D nonlinearity associated with the COV filters, for the example neuron considered. Right: The best 2-D nonlinearity reconstructed from 1-D nonlinearities operating on the COV filters. Unlike the 2-D nonlinearity associated with the DivS filters (Figure 2F), this nonlinearity could not be represented as the product of two 1-D nonlinearities. (F) The separability of 2-D nonlinearities for the COV and DivS models, measured as the ability of the 1-D nonlinearities to reproduce the measured 2-D nonlinearity (R2) across neurons (**p<0.0005, n = 13). (G–H) STC analysis applied to an example neuron for which there was enough spiking data. (G) The spike-triggered average (left), eigenvalue spectrum (middle), and significant STC filters (right). (H) As with the analyses of current responses above, the DivS filters (green, cyan) did not match those identified by STC (left, dashed), but were largely contained in the subspace spanned by the STC filters (right), as shown by comparing to their projections into the STC subspace (dashed black). Note that there was not enough data to estimate 2-D nonlinearities for the spiking data, and so no comparison of STC model performances could be made.