Measurements of neural responses to different stimulus feature values (such as orientation, (A), or spatial position, (B)) often reveal selectivity for particular feature values (such as orientation TFs or spatial RFs). Such selectivity can be observed with single-unit firing rates, calcium transients, fMRI BOLD responses, or even scalp EEG. When encoding models are measured for many neurons/voxels/electrodes, it is possible to combine all encoding models to compute an inverted encoding model (IEM, C). This IEM allows a new pattern of activation measured using a separate dataset to be transformed into a stimulus reconstruction (D), reflecting the population-level representation of a stimulus along the features spanned by the encoding model (here, visual spatial position). This reconstruction (right) reflects data from a single trial, which is inherently noisy. However, when many similar trials are combined (Fig. 2E), high-fidelity stimulus representations can be recovered.