Characterizing the function of a neuron in a sensory neural network is fundamental in sensory systems neuroscience. Systems theory offers an unbiased approach to characterize the function of neural systems by their response to unstructured white noise stimuli (WN)[1,2]. Although effective in early sensory stages[3,4], it yields limited insights into neurons that perform nonlinear computations such as motion detection. Determining where the WN approach fails in the processing hierarchy constitutes an experimental question. We recorded spiking activity from mouse retinal ganglion cells (RGCs) in response to various stimuli, including WN (Fig. A,B,C). Compared to other stimuli, WN elicited the lowest firing rates despite the highest overall contrast changes, highlighting nonlinear computations already in the retina (Fig. D,E). In contrast, a stimulus featuring moving white squares elicited the highest firing rates despite low overall contrast changes. This stimulus, termed Random Moving Objects (RMO), consisted of objects with random, uncorrelated parameters, such as initial position and movement direction (Fig. G). To analyze structured stimuli like the RMO, we developed Reverse Correlation Against Stimulus Elements (RCASE). Instead of reverse correlating against the highly correlated pixel space, we reparametrized the stimulus by encoding the presence of objects in terms of their parameters (Fig. F,H). Our approach identified high-quality, nonlinear receptive fields (RFs) in nearly all recorded RGCs (99.3%), with 90% identified within 3 minutes (Fig. J,K,L,M). In contrast, only half of the RGCs showed a WN RF (49.9%), with 90% identified within 14 minutes, highlighting that nonlinear computations in the mouse retina challenge the WN approach. In the primate retina RCASE and WN analysis showed comparable results, indicating that primate RGCs compute more linearly (Fig. O,P,Q,R). To investigate whether nonlinearities compound across processing stages, we performed neuropixel[5] recordings in the mouse nucleus of the optic tract, a subcortical structure receiving direct retinal input[6,7]. WN RF estimation efficacy reduced drastically (28%) compared to the retina, while nonlinear RFs were estimated in nearly all recorded neurons (94.7%) (Fig. T,U,V,W). These findings highlight stark differences in the functions performed by visual neurons across processing stages and species and demonstrate our methodology’s efficacy in their functional characterization.