Inverted Encoding Models Reconstruct an Arbitrary Model Response, Not the Stimulus

Probing how large populations of neurons represent stimuli is key to understanding sensory representations as many stimulus characteristics can only be discerned from population activity and not from individual single-units. Recently, inverted encoding models have been used to produce channel response functions from large spatial-scale measurements of human brain activity that are reminiscent of single-unit tuning functions and have been proposed to assay "population-level stimulus representations" (Sprague et al., 2018a). However, these channel response functions do not assay population tuning. We show by derivation that the channel response function is only determined up to an invertible linear transform. Thus, these channel response functions are arbitrary, one of an infinite family and therefore not a unique description of population representation. Indeed, simulations demonstrate that bimodal, even random, channel basis functions can account perfectly well for population responses without any underlying neural response units that are so tuned. However, the approach can be salvaged by extending it to reconstruct the stimulus, not the assumed model. We show that when this is done, even using bimodal and random channel basis functions, a unimodal function peaking at the appropriate value of the stimulus is recovered which can be interpreted as a measure of population selectivity. More precisely, the recovered function signifies how likely any value of the stimulus is, given the observed population response. Whether an analysis is recovering the hypothetical responses of an arbitrary model rather than assessing the selectivity of population representations is not an issue unique to the inverted encoding model and human neuroscience, but a general problem that must be confronted as more complex analyses intervene between measurement of population activity and presentation of data.